INDEX CLASS - X (VISTAAR-NTSE PLUS) S. NO. SUBJECT NAME
PAGE NO.
SPECIMEN COPY 1.
PHYSICS
1-11
2.
CHEMISTRY
12-25
3.
MATHEMATICS
26-40
4.
BIOLOGY
41-45
5.
SOCIAL SCIENCE
46-63
6.
MENTAL ABILITY
64-71
7.
ANSWER KEY
72-74
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FORCE EFFECTS OF FORCE To define force first of all one has to see the effects of force. By ‘effects of force’ we mean what force can do or what changes a force can bring about.
ILLUSTRATIONS 1.
Effects of Force : A force can produce the following effects : (i) A force can move a stationary body. (ii) A force can stop a moving body. (iii) A force can change the speed of a moving body. (iv) A force can change the direction of a moving body.
A force produces an acceleration of 5.0 cm/s2 in a body of mass 20g. Then find out the force acting on the body in Newton.
Sol. Acceleration of the body, a = 5 cm/s = 0.05 m/s Mass of the body, m = 20 g = 0.02 kg F = ma F = 0.05 × 0.02 = 10–3 N 2.
A force of 15 N acts on a body of mass 5 kg for 2s. What is the change in velocity of body ?
(v) A force can change the shape (and size) of a body. Sol. Given : F = 15 N , t = 2s , m = 5 kg F = ma Based on the effects of force, it may be defined as : a= Force is a pull or push, which changes or tends to change the state of rest or of uniform motion of a body or changes its direction or shape. (a) Mathematical Representation of Force : Mathematically, force F is equal to the product of mass, m of a body and acceleration a, produced in the body due to that force. i.e. F = ma Where a = final velocity – initial velocity/time (b) Units of Force : (i) In C.G.S. system :
a =
F 15 = = 3 m/s2 m 5
v u v – u = at = 3 × 2 = 6m/s t
RESULTANT FORCE Many forces may be simultaneously applied on a body, for example- several persons may jointly make an effort to move a heavy body, each person pushes it i.e. each person applies a force on it. t is also possible that a stronger man pushes that body hard enough and produces same acceleration in it. f a single force acting on a body produces the same acceleration as produced by a number of forces, then that single force is called the resultant force of these individual forces .
F = ma gram × cm/s2 = dyne If m = 1 gram, a = 1 cm/s2, then F = 1 dyne When a force is applied on a 1 gram body and the acceleration produced in the body is 1 cm/s2 then the force acting on the body will be one dyne. (ii) In S.I. system : F = ma kg × m/s2 = Newton If m = 1 kg and a = 1 m/s2 then by F = ma, F = 1 × 1 = 1 kg × m/s2 = 1 Newton. If a force is applied on a body of mass 1 kg and acceleration produced in the body is 1 m/s2 then the force acting on the body will be one Newton.
Relationship between the newton and dyne 1 N = 1 kg × 1 m s–2 = 1000 g × 100 cm s–2 = 100000 g cm s–2 = 105 dyne
BALANCED AND UNBALANCED FORCES Suppose a toy car can move on its wheels along eastwest direction. If we push the car with our left hand, it moves towards east. If we push the car with our right hand, it will move towards west. If we push the car with our left hand towards east and with right hand towards west simultaneously, it is possible that the car will remain at rest.n this case the forces balance each other and there is no acceleration. So if a set of forces acting on a body produces no acceleration in it, the forces are said to be balanced forces.f it produces a non-zero acceleration, the forces are said to be unbalanced. If two forces balance each other, they must be in opposite direction and have equal magnitudes.
Thus 1 N = 105 dyne
PAGE # 1
as force of friction. If we increase the applied force and the body is still at rest, it means force of friction also increases till it is balanced by the applied force. The force of friction is self adjusting force. On increasing the applied force the force of friction will increase upto a limit. t is known as limiting friction after it on increasing the applied force, the body starts to move.
(a) Definition of Balanced Forces : When two forces of equal magnitude are acting in opposite directions on an object simultaneously, then the object continues in its state of rest or of uniform motion in a straight line. Such forces acting on the object are known as balanced forces. (b) Definition of Unbalanced Forces :
Force of friction is of two types.
When two forces of unequal magnitudes are acting in opposite directions on an object simultaneously, then the object moves in the direction of a large force. These forces acting on the object are known as unbalanced forces.
(i) Static Friction : The magnitude of static friction is equal and opposite to the external force exerted, till the object at which force is exerted, is at rest. This means it is a variable and self adjusting force. However it has a maximum value called limiting friction. fs(max) = s N
SOME COMMON FORCES
The actual force of static friction may be smaller than sN and its value depends on other forces acting on the body. the magnitude of frictional force is equal to that required to keep the body at relative rest. 0 fs fs(max)
(a) Contact Force : When a body A is in contact with body B, A can exert force on B and B can exert force on A, these forces are called contact forces. Push or pull by a person, force by wind, force by a weight on the head of a porter etc, are the examples of contact forces.
(ii) Kinetic Friction : The magnitude of the kinetic friction is proportional to the normal force acting between the two bodies. We can write fk N fk = k N
(b) Normal Force: If the contact forces between the bodies are perpendicular to the surfaces in contact, then the forces are known as normal forces. Eg. : Consider a book on a table. The table pushes the book upwards and book pushes the table downwards, these forces are perpendicular to the surfaces of book and table. Thus the table applies a normal force on book in the upward direction and book applies a normal force on table in downward direction.
Where N is normal force. The proportionality constant k is called the coefficient of kinetic friction and its value depends of the nature of the two surfaces in contact. If the surfaces are smooth k will be small, if the surfaces are rough k will be large. It also depends on the materials of the two bodies in contact.
Here s and k are proportionality constants. s is called coefficient of static friction and k is called coefficient of kinetic friction. They are dimensionless quantities and independent of shape and area of contact. It is a property of the two contact surfaces.
(c) Force of Friction : Two bodies placed in contact can also exert forces parallel to the surfaces in contact, such a force is called force of friction or simply friction.
normal force by table applied force force of friction table force by earth Suppose a body is placed on the table following three forces act on it :
Force by earth in downward direction.
Normal force due to table in upward direction.
Applied force towards right.
NOTE :
s is always greater then k for a given pair of surfaces. If it is not mentioned, then s = k can be taken. The value of can be from 0 to1. Following graph shows the variation of frictional force with applied force.The actual value of depends on the degree of smoothness and other environmental factors. Eg. : Wood may be prepared at various degress of smoothness and the coefficient of friction will vary.
Body is not moving, so all the forces must be balanced. Normal force by table and force by earth are balanced with each other.To balance the applied force there must be an equal and opposite force. This force in known
PAGE # 2
(d) Force Exerted by Spring :
(f) Tension :
A spring is made of a coiled metallic wire having a definite length. When it is neither pushed nor pulled then its length is called natural length. At natural length the spring does not exert any force on the objects attached to its ends.f the spring is pulled at the ends, its length becomes larger than its natural length, it is known as stretched or extended spring. Extended spring pulls objects attached to its ends.
Tension is the magnitude of pulling force exerted by a string, cable, chain, rope etc. W hen a string is connected to a body and pulled out, the string said to be under tension. It pulls the body with a force T, whose direction is away from the body and along the length of the string. Usually strings are regarded to be massless and unstretchable, known as ideal string.
A
B Normal spring
Force on B
Force on A
B
A
Note : (i) Tension in a string is an electromagnetic force and it arises only when string is pulled. If a massless string is not pulled, tension in it is zero. (ii) String can not push a body in direct contact.
Stretched spring CONSERVATIVE AND NON-CONSERVATIVE FORCE
Force on B
Force on A
(a) Conservative Force :
B
A
Compressed spring If the spring is pushed at the ends, its length becomes less than natural length. It is known as compressed spring. A compressed spring pushes the objects attached to its ends.
A force is said to be conservative if the amount of work done in moving an object against that force is independent of how the object moves from the initial position to the final position. One important example of conservative force is the gravitational force. It means that amount of work done in moving a body against gravity from location A to location B is the same whichever path we may follow in going from A to B. This is illustrated in figure.
B m
F = 0 spring in natural length does not exerts any force on its ends
A m
x F
F
Fext
F = – kx ;k = spring constant or stiffness constant (unit = N/m) x = extension in spring
A force is conservative if the total work done by the force on an object in one complete round is zero, i.e. when the object moves around any closed path (returning to its initial position).
x F
h
F Fext
F = – kx x = compression in spring
(e) Weight : The earth attracts all the bodies towards its centre.The force exerted by the earth on the body is known as the weight of the body .It acts in vertically downward direction. These forces are not contact forces. If mass of the body is m and gravitational acceleration is g, then the weight of the body will be mg, here g = 9.8 m/s2.
This definition illuminates an important aspect of a conservative force viz. Work done by a conservative force is recoverable. Thus in figure, we shall have to do mgh amount of work in taking the body from A to B. However, when body is released from B, we recover mgh of work. Other examples of conservative forces are spring force, electrostatic force etc. (b) Non-Conservative Force : A force is non-conservative if the work done by that force on a particle moving between two points depends on the path taken between the points. PAGE # 3
The force of friction is an example of non-conservative force. Let us illustrate this with an instructive example. Suppose we were to displace a book between two points on a rough horizontal surface (such as a table). If the book is displaced in a straight line between the two points, the work done by friction is simply FS where :
v
v
(c)
F = force of friction ; If the other side is made horizontal, the ball will never stop because it will never be able to reach the same height, it means its speed will not decrease. It will have uniform velocity on the horizontal surface. Thus, if unbalanced forces do not act on a body, the body will either remain at rest or will move with a uniform velocity. It will remain unaccelerated.
S = distance between the points. However, if the book is moved along any other path between the two points (such as a semicircular path), the work done by friction would be greater than FS. Finally, if the book is moved through any closed path, the work done by friction is never zero, it is always negative. Thus the work done by a non-conservative force is not recoverable, as it is for a conservative force.
GALILEO’S EXPERIMENTS
Newton concluded the idea suggested by Galileo and was formulated in the laws by Newton.
NEWTON’S FIRST LAW OF MOTION
Experiment 1 : It was observed by Galileo that when a ball is rolled down on an inclined frictionless plane its speed increases, whereas if it is rolled up an inclined frictionless plane its speed decreases .If it is rolled on a horizontal frictionless plane the result must be between the cases describe above i.e. the speed
Every body remain in its state of rest or uniform motion in a straight line unless it is compelled by some external force. It means a body remain unaccelerated if and only if, the resultant force on it is zero. In such a case the body is said to be in equilibrium.
should remain constant. It can be explain as :
INERTIA (a) Definition of Inertia : The tendency of the body to oppose the change its states of rest or uniform motion in a straight line is called inertia. Newton’s first law of motion is also called law of inertia. (b) Description : v’
v v’ = v
moving down : speed increases moving up : speed decreases moving horizontal : speed remains constant
It follows from first law of motion that in absence of any external force, a body continues to be in its state of rest or in uniform motion along a straight line. In other words, the body cannot change by itself its position of rest or of uniform motion.
Experiments 2 :
(c) Inertia Depends upon Mass :
When a ball is released on the inner surface of a smooth hemisphere, it will move to the other side and reach the same height before coming to rest momentarily. f the hemisphere is replaced by a surface shown in figure(b) in order to reach the same height the ball will have to move a larger distance.
We know that it is difficult to move a heavier body than the lighter one. Similarly it is difficult to stop a moving heavier body than a lighter body moving with the same velocity. Thus, we conclude that mass of the body is the measure of inertia, more the mass, more the inertia.
TYPES OF INERTIA There are three types of Inertia which are :
h
h (a)
(b)
(a) Inertia of Rest : The tendency of the body to oppose the change in its state of rest when some external unbalance force is applied on it, is called the inertia of rest. PAGE # 4
Example based on Inertia of rest : A person sitting in a bus falls backwards when the bus suddenly starts. The reason is that lower part of his body begins to move along with the bus but the upper part of his body tends to remain at rest due to inertia of rest.
(b) Inertia of Motion : The tendency of the body to oppose its state of motion when some unbalance forces are applied on it, is called the inertia of motion. Example based on Inertia of motion : A man carelessly getting down a moving bus falls forward, the reason being that his feet come to rest suddenly, whereas the upper part of his body retains the forward motion. Definition of force from first law of motion : According to first law of motion, if there is no force, there is no change in state of rest or of uniform motion. In other words, if a force is applied, it may change the state of rest or of uniform motion. If the force is not sufficient, it may not produce a change but only try to do so. Hence force is that which changes or tries to change the state of rest or of uniform motion of a body in straight line.
MOMENTUM Definition : Momentum of a particle may be defined as the quantity of motion possessed by it and it is measured by the product of mass of the particle and its velocity.
Momentum is a vector quantity and it is represented (c) Inertia of Direction :
by p
The tendency of a body to oppose any change in its direction of motion is known as inertia of direction.
Example based on Inertia of direction :
p mv
Unit of momentum : Tie a stone to one end of a string and holding other end of the string in hand, rotate the stone in a horizontal circle. If during rotation, the string breaks at certain stage, the stone is found to fly off tangentially at that point of the circle.
(In C.G.S. system) p = mv gram × cm/s = dyne × s (In M.K.S. system) p = mv kg × m/s = Newton × s 3.
A ball of mass 100 gm. is moving with a velocity of 15 m/s. Calculate the momentum associated with the ball.
Sol . String Breaks
String breaks, stone goes away tangentially
Mass of the ball
Velocity of the ball So, momentum
= 100 gm. =
100 kg. 1000
= 0.1 kg. = 15 m/s = mass of the ball × velocity of the ball = 0.1 kg. × 15 m/s = 1.5 kg. m/s
PAGE # 5
(c) Kilogram Force (kgf) :
NEWTON’S SECOND LAW OF MOTION
Kilogram force (kgf) or Kilogram weight (kg. wt.) is force with which a mass of 1 kg is attracted by the earth towards its centre. 1kgwt = 1kgf = 9.8 N
The rate of change of momentum of a body is directly proportional to the applied unbalanced forces i.e. Rate of change of momentum Force applied
(d) Gram Force (gf) : Gram force or gram weight is the force with which a mass of 1 gram is attracted by the earth towards its centre. 1gwt = 1gf = 981 dyne
Let a body is moving with initial velocity u and after applying a force F on it, its velocity becomes v in time t. Initial momentum of the body p1 = mu Final momentum of the body p2 = mv Change in momentum in time t is mv – mu So rate of change of momentum =
F
m( v – u) t
Here,
Relation between Newton and dyne.
mv – mu t
But according to Newton’s second law,
or
Abou both the units are called gravitational unit of force.
We know : 1 N = 1kg × 1ms-2 or 1 N = 1000 g × 100 cms-2 or 1 N = 105 g cms-2 = 105 dyne 1 N = 105 dyne
mv – mu F t
v–u = a (acceleration) t
So Fma or F = kma (Here k is proportionality constant. If 1N force is applied on a body of mass 1 kg and the acceleration produced in the body is 1 m/s 2, then 1 = k × 1 × 1 or k = 1 Hence, F = ma So the magnitude of the resultant force acting on a body is equal to the product of mass of the body and the acceleration produced. Direction of the force is same as that of the acceleration.
4.
A force of 20N acting on a mass m1 produces an acceleration of 4 ms–2. The same force is applied on mass m2 then the acceleration produced is 0.5 ms–2. What acceleration would the same force produce, when both masses are tied together ?
Sol. For mass m1: F = 20N, a = 4 ms–2 then
m1 =
20 F = = 5 kg a 4
For mass m2 : F = 20N, a = 0.5 ms–2 then
m2 =
F 20 = = 40 kg a 0 .5
When m1 and m2 are tied together : Total mass = m1 + m2 = 45 kg, F = 20N
UNITS OF FORCE
then
a=
20 F = = 0.44 ms–2 45 (m1 m 2 )
(a) In C.G.S. System :
F = ma gm × cm/s2 = Dyne IMPULSE OF FORCE Definition of one dyne : If m = 1 gm, a = 1 cm/s2, then F = 1 dyne. When a force is applied on a body of mass 1 gram and the acceleration produced in the body is 1 cm/s2, then the force acting on the body will be one dyne. (b) In S.I. System :
A large force acting for a short time to produce a finite change in momentum is called impulsive force. The product of force and time is called impulse of force. i.e., Impulse = Force × Time or
I = Ft
F = ma kg × m/s = Newton
The S.I. unit of impulse is Newton-second (N-s) and the C.G.S unit is dyne- second (dyne-s)
Definition of one Newton :
Impulse and Momentum :
2
If m = 1 kg and a = 1 m/s2 then by, F = ma F = 1 × 1 = 1 kg × m/s2 = 1 N. If a force is applied on a body of mass 1 kg and acceleration produced in the body is 1 m/s2, then the force acting on the body will be one Newton.
From Newton’s second law of motion Force, F =
p 2 p1 t
or Ft = p2 – p1
i.e., Impulse = Change in momentum This relation is called impulse equation or momentumimpulse theorem. It has an important application in our everyday life. PAGE # 6
IMPULSE DURING AN IMPACT OR COLLISION
ANY PAIR OF EQUAL AND OPPOSITE FORCES IS NOT AN ACTION–REACTION PAIR
The impulsive force acting on the body produces a change in momentum of the body on which it acts. We know, Ft = mv – mu, therefore the maximum force needed to produce a given impulse depends upon time. If time is short, the force required in a given impulse or the change in momentum is large and viceversa.
Consider a book kept on a table. We have seen that the table pushes the book in the upward direction. Then why does not the book fly up? It does not fly up because there is another force on the book pulling it down. This is the force exerted by the earth on the book, which we call the weight of the book. So, there are two forces on the book– the normal force, N acting upwards, applied by the table and the force, W acting downwards, applied by the earth. As the book does not accelerate, we conclude that these two forces are balanced. In other words, they have equal magnitudes but opposite directions.
NEWTON’S THIRD LAW (a) Statement : The law states that “ To every action there is an equal and opposite reaction“. Moreover, action and reaction act on different bodies. (b) Demonstration :
N
Two similar spring balances A and B joined by hook as shown in the figure. The other end of the spring balance B is attached to a hook rigidly fixed in a rigid wall.
N=W V
V
V
Can we call N the action and W the reaction ? We cannot. This is because, although they are equal and opposite, they are not forces applied by two bodies on each other. The force N is applied by the table on the book, its reaction will be the force applied by the book on the table. Weight W is the force applied by the earth on the book, its reaction will be the force applied by the book on the earth. So, although N and W are equal and opposite, they do not form an action–reaction pair.
Demonstration- Newton’s third law of motion The other end of the spring balance A is pulled out to the left. Both balances show the same reading (20 N) for the force. The pulled balance A exerts a force of 20N on the balance B. It acts as action, B pulls the balance A in opposite direction with a force of 20 N. This force is known as reaction. We conclude that action-reaction forces are equal and opposite and act on two different bodies.
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
NO ACTION IS POSSIBLE WITHOUT REACTION
By Newton’s second law, the rate of change of momentum is equal to the applied force.
Examples :
Change in momentum = Force time
(i) A nail cannot be fixed on a suspended wooden ball.
Change in momentum = F × t If F = 0 then,
(ii) A paper cannot be cut by scissors of single blade. (iii) A hanging piece of paper cannot be cut by blade.
Change in momentum = 0
(iv) Writing on a hanging page is impossible.
If the force applied on the body is zero then its momentum will be conserved, this law is also applicable on the system. If in a system the momentum of the objects present in the system are P1, P2, P3........... and external force on the system is zero, then– P1 + P2 + P3 +................. = Constant
(v) Hitting on a piece of sponge does not produce reaction. You do not enjoy hitting.
ACTION AND REACTION ARE NOT BALANCED Action and reaction, though equal and opposite are not balanced because they act on two different bodies. In case when they act on two different bodies forming a single system, they become balanced.
NOTE : If only internal forces are acting on the system then its linear momentum will be conserved.
PAGE # 7
(a) The Law of Conservation of Momentum by Third Law of Motion :
Linear
Suppose A and B are two objects of masses m1 and m2 are moving in the same direction with velocity u1 and u2 respectively (u1 > u2). Object A collides with object B and after time t both move in their original direction with velocity v1 and v2 respectively. The change in momentum of object A = m1v1 – m1u1
m1
m2 u1 u2 before collision (u1 > u2)
mv M mv M
Hence the recoil velocity of gun =
and the velocity of the gun is = –
m v – m1u1 F1 = 1 1 t
.............(1)
mv M
(b) The Working of a Rocket :
The change in momentum of object B = m2v2 – m2u2
The force on A by B is F2 =
Change in momentum time
m 2 v 2 – m 2u 2 t
m1
0 = MV + mv or V = –
Change in momentum The force on B by A is F1 = time
=
Let the bullet and the gun have masses m and M respectively. Let the bullet move forward with velocity v and the gun recoils with velocity V. Then final momentum of the gun and bullet is MV + mv By the law of conservation of momentum– Initial momentum of the system = Final momentum of the system.
.............(2)
m2 v1 v2 after collision
By Newtons third law, F1 = –F2
the momentum of a rocket before it is fired is zero. When the rocket is fired, gases are produced. These gases come out of the rear of the rocket with high speed. The direction of the momentum of the gases coming out of the rocket is in the downward direction. Thus, to conserve the momentum of the system i.e., (rocket + gases), the rocket moves upward with a momentum equal to the momentum of the gases. So, the rocket continues to move upward as long as the gases are ejected out of the rocket. Thus a rocket works on the basis of the law of conservation of momentum.
TRANSLATORY EQUILIBRIUM
m1v 1 – m1u1 m v – m 2u 2 = – 2 2 m1v1 – m1u1 t t
When several forces acts on a body simultaneously in such a way that resultant force on the body is zero, i.e.,
= –m2v2 + m2u2
F = 0 with F =
or
m1u1 + m2u2 = m1v1 + m2v2
or
Initial momentum = Final momentum
i
equilibrium. Here it is worthy to note that : (i)
SOME ILLUSTRATION ON CONSERVATION OF MOMENTUM
As if a vector is zero all its components must vanish i.e. in equilibrium as -
F = 0 with F =
(a) Recoil of Gun : A loaded gun (rifle) having bullet inside it forming one system is initially at rest. The system has zero initial momentum. V
F the body is said to be in translatory
v
F
x
=0;
F = 0
F
i
y
=0;
F
z
=0
So in equilibrium forces along x axis must balance each other and the same is true for other directions. If a body is in translatory equilibrium it will be either at rest or in uniform motion. If it is at rest, equilibrium is called static, otherwise dynamic. Static equilibrium can be divided into following three types :
When the trigger (T) is pressed, the bullet is fired due to internal force of explosion of powder in cartidge inside. The bullet moves forward with a high velocity and the gun move behind (recoils) with a lesser velocity.
(a) Stable equilibrium : If on slight displacement from equilibrium position a body has a tendency to regain its original position it is said to be in stable equilibrium. In case of stable equilibrium potential energy is minimum and so center of gravity is lowest. PAGE # 8
Torque of force F about the axis passing through the point O is Torque = force × perpendicular distance
O
F
(b) Unstable equilibrium : If on slight displacement from equilibrium position a body moves in the direction of displacement, the equilibrium is said to be unstable. In this situation potential energy of body is maximum and so center of gravity is highest.
r O
P M
O
(c) Neutral equilibrium : If on slight displacement from equilibrium position a body has no tendency to come back to its original position or to move in the direction of displacement, it is said to be in neutral equilibrium. In this situation potential energy of body is constant and so center of gravity remains at constant height.
= F(OM) From OMP sin =
OM , OM = rsin r
Hence,
= Fr sin
.....(i)
Case-I If = 0º From equation (i)= Fr sin 0º= 0 Case-II If = 90º From equation (i)= Fr sin 90ºFr max.
CENTRE OF MASS (C.M.) It is the point inside or outside the body at which the whole mass of the body is supposed to be concentrated. If an external force applied on the centre of mass, it will produce the same motion in the body as if the body is a point mass.
CENTRE OF GRAVITY (C.G.) It is a point inside or outside the body at which the whole weight of the body is supposed to be acting. If an external force is applied on the centre of gravity, it will make the body move in the direction of the force just as a particle moves.
Case-III If = 180º From equation (i)= Fr sin 180º = 0
EXERCISE 1.
A force of 10 N is applied on a body of 2 kg mass at rest . The distance travelled by the body in 2 sec. is: (A) 10 m (B) 20 m (C) 30 m (D) 40 m
2.
A body of 10 N weight is resting on a plane surface . If external force of 5 N is exerted on the body as shown in the figure , then friction force acting on the body by surface is :
IMPORTANT NOTE : For bodies of regular shape having uniform density the C.M and the C.G. lie at the geometrical centre of the body. Example :
For Ring : The centre of the ring (it lies out side the body)
For Rectangle or Square : At the point of intersection of its diagonals.
For cylinder : At the centre of the axis.
TORQUE If a body is free to move about an axis and a force is applied on the body then it rotates about that axis. The capability of the force to rotate the body or to change the rotational motion of the body is known as torque.
(A) 0 (C) 10 N 3.
(B) 5 N (D) 15 N
When a body is stationary : (A)there may be no force acting on it (B)there may be one force acting on it (C)there may be couple of forces acting on it (D)the body is in vacuum
4. A body of mass 'm' and velocity ‘u’ strikes a wall and rebounds with a velocity ‘v’. The change in momentum is (A) m (v – u) (B) m (u – v) (C) – m(v + u) (D) none of these
PAGE # 9
5. A constant force acts on a body of mass m at rest for t seconds and then ceases to act. In next t seconds the body travels a distance x, magnitude of force is. (A)
mx t
(B)
2
mx t
(D) mxt2
(C) mxt
6. A truck and a car are moving with same kinetic energy. They are brought to rest by the application of brakes which provide equal force. (A) both will cover equal distance (B) the truck will cover a greater distance (C) the car will cover a greater distance (D) none of the above. 7. Newton's third law of motion can be used to explain: (A) Why the passengers in a bus tend to fall backward when its starts suddenly (B) Swimming of a man (C) Motion of a rocket (D) Both (B) and (C). 8. Two blocks are kept in contact with each other on a smooth surface. The force on the lighter block and its acceleration is : -
10N
(A) 6 N, 1 m/s2 (C) 10 N, 1 m/s2 9.
6Kg
12. External forces are : (A) always balanced (B) never balanced (C) may or may not be balanced (D) none of these 13. If a force is conservative : (A) Work is path independent (B) Work is path dependent (C) Potential energy remains constant (D) none of these 14. A body is in translatory equilibrium if : (A) Resultant force on it is zero (B) It is at rest (C) It is in uniform motion (D) All options are correct 15. When a body is stationary : (A) There is no force acting on it (B) The forces acting on it are not in contact with it (C) The combination of forces acting on it balance each other (D) The body is in vacuum 16. A particle is in straight line motion with uniform velocity. A force is not required : (A) To increase the speed (B) To decrease the speed (C) To keep the speed constant (D) To change the direction 17. When a constant force is applied to a body, it moves with uniform : (A) Acceleration (B) Velocity (C) Speed (D) Momentum
4Kg
(B) 4 N, 1 m/s2 (D) 0 N, 0 m/s2
When the momentum of a body increases by 100% its kinetic energy increases by : (A) 20% (B) 40% (C) 200% (D) 300%
10. A stationary ball weighing 0.25 kg acquires a speed of 10 m/s when hit by a hockey stick. The impulse imparted to the ball is : (B) 2.5 N × s (A) 0.25 N × s (C) 2 N × s (D) 0.5 N × s
18. An object will continue accelerating until : (A) Resultant force on it begins to decrease (B) Its velocity changes direction (C) The resultant force on it is zero (D) The resultant force is at right angles to its direction of motion 19. When a force of constant magnitude always act perpendicular to the motion of a particle then : (A) Velocity is constant (B) Acceleration is constant (C) K.E. is constant (D) None of these 20. A block of mass 2 kg is placed on the floor. The coefficient
11. Which of the following class of forces is different from others ? (A) Pulling of a cart (B) Stretching of a coiled spring (C) Kicking of a football (D) Weight of the body
of static friction is 0.4. If a force of 2.8 N is applied on the block parallel to floor the force of friction between the block and floor (taking g = 10 m/s2) is : (A) 2.8 N (B) 8 N (C) 2 N
(D) Zero
PAGE # 10
25. When a bicycle is in motion the force of friction exerted
21. Torque is the cause of :
by the ground on the two wheels is such that it acts : (A) In the backward direction on the front wheel and in
(A) Translatory motion (B) Rotatory motion (C) Oscillatory motion (D) Combined translatory and rotatory motion 22. It becomes easier to open or close a door turning about
the forward direction on the rear wheel (B) In the forward direction on the front wheel and in the backward direction on the rear wheel (C) In the backward direction on both front and the rear
(A) Two third of the door
wheels (D) In the forward direction on both the front and rear
(B) Free edge of the door
wheels
its hinges if the force is applied at the :
(C) Middle of the door
26. A body of mass 20 kg is kept initially at rest. A force of
(D) Point near the hinges
80 N is applied on the body then the acceleration produced in the body is 3 m/s2, force of friction acting
23. Which of the following is non-conservative force ? (A) Electrostatic force
(B) Gravitational force
on the body is : (A) 80 N
(B) 12 N
(C) Viscous force
(D) Spring force
(C) 20 N
(D) zero
27. It is required to increase the velocity of a scooter of 24. A box weighing 20 kg is pushed along the floor at a constant speed by applying a horizontal force. If the coefficient of friction is 0.25, then force applied is : (g = 10 m/s2) (A) 5N
(B) 10 N
(C) 50 N
(D) 200 N
mass 80 kg from 5 ms–1 to 25 ms–1 in 2 s. The force required will be : (A) 200 N
(B) 600 N
(C) 800 N
(D) 100 N
28. A car of mass 1000 kg is moving with a velocity of 10 m/s and is acted upon by a forward force of 1000 N due to engine and retarding force of 500 N. The velocity after 10 seconds will be : (A) 10 m/s
(B) 15 m/s
(C) 20 m/s
(D) zero
PAGE # 11
STRUCTURE OF ATOM DALTON’S ATOMIC THEORY
ELECTRON Electrons are the fundamental particles of all substances.
In 1808 John Dalton proposed atomic theory of matter, assuming atoms are ultimate indivisible particles of matter based on the law of conservation
(a) Cathode Rays - Discovery of Electron :
of mass and law of definite proportion.
The nature and existence of electron was established by experiments on conduction of electricity through gases.
The important points of Dalton’s theory are (i) Elements consist of small indivisible particles called atoms and atoms take part in chemical reactions. (ii) Atoms of same element are alike in all respect. (iii) Atoms of different elements are different in all respect. (iv) Atoms cannot be created or destroyed. (v) Atoms combine in a fixed, small, whole number to form compound atoms called molecules.
Note : The term “ Element “ was coined by Lavoisier. (a) Merits : (i) Dalton’s theory explains the law of conservation of mass (point iv) and law of constant proportion (point v).
Note : In 1859, Julius Plucker started the study of conduction of electricity through gases at low pressure in a discharge tube. A number of interesting things happen when a high voltage (say, 10,000 V) is applied across the electrodes of the discharge tube, and the pressure of the gas inside the tube is lowered. (i) When the pressure of the gas in the discharge tube is at atmospheric pressure and a high voltage is applied across the electrodes, nothing noticeable happens. But as we lower the pressure and increase the voltage, sparking or irregular streaks of light are seen in the tube. This is called positive column. (ii) As the pressure of gas is reduced further, the length of the positive column reduces, a fine glow can be seen at the cathode. The dark space or gap left between the cathode and the positive column is called the Faraday’s dark space.
(ii) Atoms of elements take part in chemical reaction this is true till today. (b) Demerits : (i) The atom is no longer supposed to be indivisible. The atom is not a simple particle but a complex one. (ii) He could not explain that why do atoms of same element combined with each other. (iii) Atoms of the same element may not necessarily be identical in all aspects. There are a number of elements whose atoms possess different masses. All these atoms of the same element with same atomic number but different mass number are called isotopes. e.g. 1H1, 1H2, 1H3 are the three isotopes of hydrogen. (iv) Atoms of different elements may not necessarily be different in all aspects. There are a number of elements whose atoms possess same mass number. All these elements with different atomic number but same mass number are called isobars. e.g. 20Ca40 and 18Ar40 are isobars of each other.
12 12
PAGE # 12
(iii) They consist of negatively charged particles. When the cathode rays pass through an electric field, they bent towards the positive plate of the electric field. This indicates that cathode rays are negatively charged.
(iii) When the pressure of gas is reduced to about 1 mm of Hg, the cathode glow moves away from the cathode, creating a dark space between cathode and the cathode glow. This dark space is called Crookes dark space. (iv) The Crookes dark space expands with further fall in pressure at 0.1 mm of Hg. The positive column gets split into a number of bands called striations. (v) At pressure 0.01 mm of Hg or less, the striations move towards the anode and vanish finally. At this stage the glass tubes begins to glow at the end opposite to the cathode. This phenomenon is called fluorescence.
(iv) Cathode rays can affect the photographic plate.
Thus, some sort of invisible rays travel from the negative electrode to the positive electrode. Since the negative electrode is called cathode, these rays were called cathode rays. The colour of glow depends upon the nature of the glass used. For soda glass the
(v) The nature of cathode rays is independent of the nature of gas used in discharge tube or material of cathode. (vi) Cathode rays are deflected in the magnetic field also.
fluorescence is of yellowish green colour.
S
(b) Properties of cathode rays : (i) Cathode rays travel in a straight line at a high velocity and generate normally from the surface of the cathode. If an opaque object is placed in the path of cathode rays its shadow falls on opposite side of the cathode. It shows that cathode rays travel in straight lines. To vacuum pump
N High voltage
Shadow
(viii) When cathode rays fall on materials having high atomic mass, new type of penetrating rays of very small wavelength are emitted which are called X rays.
–
+
Thus, investigations on cathode rays showed that these consisted of negatively charged particles.
Anode
Deflection of cathode rays in magnetic field
(vii) If cathode rays are focused on a thin metal foil, the metal foil gets heated up to incandescence.
Cathode
Object High voltage
+
–
Note : Cathode rays travel with very high velocities ranging from 109 to 1011 cm per second.
Note : The negatively charged particles of cathode rays were called ‘negatrons‘ by Thomson. The name negatron was changed to ‘electron‘ by Stoney.
(ii) They are a beam of minute material particles having definite mass and velocity. When a light paddle wheel is placed in the path of the cathode rays, the blades of the paddle wheel begin to rotate. This also proves that cathode rays have mechanical energy.
(c) Characteristics of electron : (i) Electrons are sub - atomic particles which constitute cathode rays. (ii) In 1897, J.J.Thomson determined the charge to mass (e/m) ratio of electron by studying the deflections of cathode rays in electric and magnetic fields. The value of e/m has been found to be 1.7588 × 108 coulombs/g. The e/m for electrons from different gases was found to be the same. This indicates that atoms of all kinds have the same kind of negatively charged particles. Thus electrons are the common constituents of all atoms.
Note : A cathode ray tube is used to measure the charge to mass ratio of the electrons.
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(iii) Charge on the electron : The charge (e) on an electron was determined by Robert Millikan in 1909. Millikan found the charge on oil drops to be -1.6 × 10-19 C or its multiples. So, the charge on an electron is to be -1.6 × 10-19 coulombs / unit.
(iv) Mass of an electron :
named positive rays by J.J.Thomson.
By Thomson’s experiment e/m = 1.76 × 1011 C/kg By Millikan’s experiment e = – 1.6 × 10-19 C
(b) Characteristics of Anode Rays :
19
So mass of electron (m) =
Mass of an electron in amu
1.6 10 1.76 1011
(i) Anode rays travel in straight lines. (ii) These rays rotate the light paddle wheel placed in their path. This shows that anode rays are made up of material particles.
= 9.1096 × 10-31 kg = 0.000549
(v) Mass of electron in comparison to that of hydrogen : Mass of hydrogen = 1.008 amu = 1.008 × 1.66 × 10-24 g ( since 1 amu = 1.66 × 10-24 g ) = 1.673 × 10-24 g
(iii) Anode rays are deflected by magnetic or electric field. In the electric field they get deflected towards negatively charged plate. This indicates that these rays are positively charged. (iv) The anode rays affect photographic plate.
24
Note : Anode rays are called canal rays because they pass through the canals or holes of the cathode. These rays are also called anode rays since they originate from the anode side. Anode rays are produced from a positively charged electrode, therefore these were
1.6 73 10 Mass of hydrogen atom = = 1837 Mass of electron 9.1096 10 – 28
(v) The nature of anode rays depend upon the type of gas used.
Note :
(c) Discovery of Proton :
1 Thus, the mass of an electron is times the 1837
J.J.Thomson in 1906, found that particles obtained in the discharge tube containing hydrogen have e/m value as 9.579 × 10 4 coulomb/g. This was the maximum value of e/m observed for any positive particle. It was thus assumed that the positive particles given by hydrogen represent fundamental particle of positive charge. This particle was named proton.
mass of a hydrogen atom.
PROTON (a) Anode Rays (Canal rays) : It has been established that electron is a negatively charged particle and present in all the atoms. As an atom is electrically neutral, there must be some positively charged particles present in the atom to neutralize the negative charges of the electrons. It has been confirmed by experiments. Scientist Goldstein in 1886 discovered the existence of a new type of rays in the discharge tube. He carried out the experiment in discharge tube containing perforated cathode. It was observed that when high potential difference was applied between the electrodes, not only cathode rays were produced but also a new type of rays were produced simultaneously from anode, moving from anode towards cathode and passed through the holes of cathode.
Anode rays
+ H e H (Proton)
Note : The name ‘proton’ was given by Rutherford in 1911. (d) Characteristics of Proton : (i) A proton is a sub - atomic particle which constitute anode rays produced when hydrogen is taken in the discharge tube. (ii) Charge of a proton : Proton is a positively charged particle. The charge on a proton is equal but opposite to that on an electron. Thus, the charge on a proton is +1.602 × 10 –19 coulombs/ unit.
Fluorescence
(iii) Mass of a proton : Anode
High voltage source
The mass of a proton is equal to the mass of a Perforated cathode
hydrogen atom. m p = 1.0073 amu = 1.673 × 10-24 g = 1.673 × 10-27 kg
14 14
PAGE # 14
(ii) About 99.0% of the -particles passed undeflected through the gold foil and caused illumination of zinc sulphide screen.
(iv) Mass of proton relative to mass of electron :
1.673 10 24 g Mass of a proton = = 1837 Mass of an electron 9.110 28 g
(iii) Very few -particles underwent small and large deflections after passing through the gold foil. (iv) A very few (about 1 in 20,000) were deflected backward on their path at an angle of 180º.
Thus, the mass of a proton is 1837 times larger than the mass of an electron. (v) Charge to mass ratio for a proton : The e/m of particles constituting the anode rays is different for different gases.
1.602 10 19 e of proton = = 9.579 × 104 C/g 1.673 10 24 m THOMSON MODEL OF AN ATOM J.J. Thomson (1898) tried to explain the structure of atom. He proposed that an atom consists of a sphere of positive electricity in which electrons are embedded like plum in pudding or seeds evenly distributed in red spongy mass in case of a watermelon. The radius of the sphere is of the order 10–8 cm.
Rutherford was able to explain these observations as follows: (i) Since a large number of -particles pass through the atom undeflected, hence, there must be large empty space within the atom. (ii) As some of the -particles got deflected, therefore, there must be something massive and positively charged structure present in the atom. (iii) The number of -particles which get deflected is very small, therefore, the whole positive charge in the atom is concentrated in a very small space.
(a) Merits : (i) Thomson’s model could explain the electrical neutrality of an atom.
(iv) Some of the -particles retracted their path i.e. came almost straight back towards the sources as a result of their direct collisions with the heavy mass.
(ii) Thomson’s model could explain why only negatively charged particles are emitted when a metal is heated as he considered the positive charge to be immovable by assuming it to be spread over the total volume of the atom. (iii) He could explain the formation of ions and ionic compounds. (b) Demerits : This model could not satisfy the facts proposed by Rutherford through his alpha particle scattering experiment and hence was discarded.
RUTHERFORD MODEL OF AN ATOM (a) Rutherford’s Alpha Particle Scattering Experiment (1909) : Ernest Rutherford and his coworkers performed numerous experiments in which - particles emitted from a radioactive element such as polonium were allowed to strike thin sheets of metals such as gold or platinum. (i) A beam of -particles (He2+) was obtained by placing polonium in a lead box and letting the alpha particles come out of a pinhole in the lead box. This beam of rays was directed against a thin gold foil (0.0004 cm). A circular screen coated with zinc sulphide was placed on the other side of the foil.
Note : - particles are made up of two protons and two neutrons and are Helium (He) nuclei. (b) Rutherford Nuclear Model of Atom (1911) : Rutherford proposed a new picture of the structure of atom. Main features of this model are as follows(i) The atom of an element consists of a small positively charged “Nucleus” which is situated at the centre of the atom and which carries almost the entire mass of the atom. (ii) The electrons are distributed in the empty space of the atom around the nucleus in different concentric circular paths (orbits).
15 15
PAGE # 15
(iii) The number of electrons in the orbits is equal to the number of positive charges (protons) in the nucleus.
When the electron moves from inner to outer orbit by absorbing definite amount of energy, the new state of the electron is said to be excited state.
(iv) Volume of nucleus is very small as compared to the volume of atom.
(v) Negatively charged electrons revolves around the nucleus in circular path. The force of attraction between the nucleus and the electron is equal to centrifugal force of the moving electron. Force of attraction towards nucleus = Centrifugal force
(v) Most of the space in the atom is empty.
Note : Rutherford’s model is also called “Planetary model’.
(vi) Out of infinite number of possible circular orbits around the nucleus, the electron can revolve only in those orbits whose angular momentum is an integral
(c) Defects in Rutherford’s Model : (i) Rutherford did not specify the number of electrons in each orbit.
multiple of
(ii) According to electromagnetic theory, if a charged particle (like electron) is accelerated around another charged particle (like protons in nucleus) then there would be continuous loss of energy due to continuous emission of radiations. This loss of energy would slow down the speed of electron and eventually the electron would fall into the nucleus. But such a collapse does not occur. Rutherford’s model could not explain this theory. (iii) If the electron loses energy continuously, the observed spectrum should be continuous but the actual observed spectrum consists of well defined lines of definite frequencies. Hence the loss of energy is not continuous in an atom.
h h , i.e. mvr = n 2 2
where : m = mass of the electron v = velocity of electron r = radius of the orbit, and n =1,2,3 ---- number of the orbit. The angular momentum can have values such as
h 2h 3h , , , but it cannot have a fractional value. 2 2 2 Thus, the angular momentum is quantized. The specified circular orbits (quantized) are called stationary orbits.
RADII OF VARIOUS ORBITS Radii of various orbits can be given by formula.
BOHR MODEL OF AN ATOM (1913) To overcome the objections to Rutherford’s model and to explain the hydrogen spectrum, Bohr proposed a quantum mechanical model of the atom. The important postulates on which Bohr’s model is based are the following (i) The atom has a nucleus where all the protons are present. The size of the nucleus is very small. It is present at the centre of the atom. (ii) Each stationary orbit is associated with a definite amount of energy. The greater is distance of the orbit from the nucleus, more shall be the energy associated with it. These orbits are also called energy levels and are numbered as 1, 2, 3, 4 ------or K, L, M, N ---- from nucleus to outwards. (iii) By the time, the electron remains in any one of the allowed stationary orbits, it does not lose energy. Such a state is called ground or normal state. (iv) The emission or absorption of energy in the form of radiation can only occur when an electron jumps from one stationary orbit to another. E = Efinal - Einitial = h Where h is Planck’s constant (h = 6.625 × 10–34 Js) Energy is absorbed when the electron jumps from lower to higher orbit and is emitted when it moves from higher to lower orbit.
r=
n 2h 2 2
4 mkZe 2
Note : Greater is the value of ‘n’ larger is the size of atom. On the other hand, greater is the value of ‘Z’ smaller is the size of the atom. For hydrogen atom, Z = 1; so r =
n 2h 2 4 2mke 2
Now putting the values of h, , m, e and k. r=
n 2 (6.625 10 –34 ) 2 2
4 (3.14 ) (9.1 10 – 31 ) (9 10 9 ) (1.6 10 –19 )2
= 0.529 ×n2 × 10–10 m = 0.529 × n2 Å = 0.529 × 10–8 × n2 cm Thus, radius of 1st orbit = 0.529 × 10–8 × 12 = 0.529 × 10–8 cm = 0.529 × 10–10 m = 0.529 Å Radius of 2nd orbit = 0.529 × 10–8 × 22 = 2.11 × 10–8 cm = 2.11 × 10–10 m = 2.11 Å Radius of 3rd orbit = 0.529 × 10–8 × 32 = 4.76 × 10–8 cm = 4.76 × 10–10 m = 4.76 Å
16 16
PAGE # 16
NEUTRONS
Energy of an electron in Bohr’s orbit can be given by the formula : 2 2 Z 2 K 2 me n 2h 2
E=–
4
For hydrogen atom, Z = 1 So,
E–
In 1932, James Chadwick bombarded the element beryllium with - particles. He observed the emission of a radiation with the following properties (i) The radiation was highly penetrating. (ii) The radiation remained unaffected in the electric or magnetic field i.e. the radiation was neutral. (iii) The particle constituting the radiation had the same mass as that of the proton. These neutral particles were called neutrons.
2 2k 2me 4 n 2h 2
Putting the values of , k, m, e and h. 2 (3.14)2 (9 10 9 )2 (9.1 10 –31 ) (1.6 10 –19 )4
E=–
=– = –
n 2 (6.625 10 – 34 )2
21.79 10 –19 n 13.6 n2
2
J per atom
eV per atom (1 J = 6.2419 × 1018 eV)
9 4 Be
4 2 He
+
12 6C
(Beryllium) (á particle)
1 0n
+
(Carbon)
(Neutron)
COMPARATIVE STUDY OF ELECTRON, PROTON AND NEUTRON Property
Electron
Proton
Neutron
Symbol
e
p
n
Note :
The negative sign indicates that the electron is under attraction towards nucleus, i.e. it is bound to the nucleus. The electron has minimum energy in the first orbit and its energy increases as n increases, i.e., it becomes less negative. The electron can have a maximum energy value of zero when n = . The zero energy means that the electron is no longer bound to the nucleus , i.e. , it is not under the force of attraction towards nucleus.
Nature
Negatively charged Positively charged
Neutral
Relative charge
-1
+1
0
Absolute charge
–1.602 × 10-19 C
+1.602 × 10-19 C
0
Relative mass
1 18 37
1
1
1.6725 × 10-24 g
1.6748 × 10-24 g
Absolute mass
9.109 × 10-28 g
ATOMIC STRUCTURE VELOCITY OF AN ELECTRON IN BOHR'S ORBIT Velocity of an electron in Bohr’s orbit can be given by the formula :
Z v= n
2e 2 h
Substituting the values of h, , e. v=
2 3.14 ( 4.8 10 10 )2 Z × 6.625 10 27 n
v=
Z × 2.188 × 108 cm/sec ----------- (iii) n
An atom consists of two parts (a) Nucleus (b) Extra - nuclear region (a) Nucleus : Nucleus is situated at the centre of an atom. All the protons & neutrons are situated in the nucleus, therefore, the entire mass of an atom is almost concentrated in the nucleus. The overall charge of nucleus is positive due to the presence of positively charged protons (neutrons have no charge). The protons & neutrons are collectively called nucleons. Note :
2.188 10 8 v= cm/sec (For hydrogen , Z = 1) n
The radius of the nucleus of an atom is of the order of 10–13 cm and its density is of the order of 1014 g/cm3.
v1 = 2.188 × 108 cm/sec
(b) Extra Nuclear Region :
v2 =
1 × 2.188 × 108 cm/sec = 1.094 × 108 cm/sec 2
v3 =
1 × 2.188 × 108 cm/sec = 0.7293 × 108 cm/sec 3
Here v1, v2 and v3 are the velocities of electron in first, second and third Bohr orbit in hydrogen.
In extra nuclear part or in the region outside the nucleus, electrons are present which revolve around the nucleus in orbits of fixed energies. These orbits are called energy levels. These energy levels are designated as K, L, M, N & so on. (i) The maximum number of electrons that can be accommodated in a shell is given by the formula 2n2.(n = number of shells i.e. 1,2,3 -------)
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PAGE # 17
n 1 2 3 4
Y
max. no.of electrons 2 8 18 32
u cl e
us
First energy level Second energy level Third energy level Fourth energy level
2n2 2 2(1) 2 2(2) 2 2(3) 2 2(4)
N
Shell K L M N
+
K L M N
Electron shells
2
Maximum number of electrons which can be accommodated in the various shells
8 18 32
X s- orbital (2) p - orbitals : The p-subshell contains three orbitals which have dumb-bell shape and a directional character. The three p-orbitals are designated as px, py & pz which are oriented in the perpendicular axis (x,y,z). The maximum number of electrons which can be accommodated in the p subshell is 6 (2 electrons in each of three orbitals). z
(ii) Each energy level is further divided into subshells designated as s,p,d,f . 1st shell (K) contains 1 subshell (s) 2nd shell (L) contains 2 subshells (s,p) 3rd shell (M) contains 3 subshells (s,p,d) 4th shell (N) contains 4 subshells (s,p,d,f).
z
x
x
y
y
y
y
px
pz
py
(3) d - orbitals : The d-subshells contains 5 orbitals which are double dumb-bell in shape. These orbitals are designated as dxz, dxy, dyz, d x 2 y 2 , d 2 . The d-subshell z
can accommodate a maximum of 10 electrons. z
(A) An orbital may be defined as
z
y
x
z
y
x
x
y
dxz
dxy
(B)The maximum capacity of each orbital is that of two electrons.
z
x
(iii) Shells are divided into sub-shells, sub shells further contain orbitals.
“A region in the three - dimensional space around the nucleus where the probability of finding the electron is maximum.”
Z
dyz
z
z
Note : The maximum number of orbitals that can be present in a shell is given by the formula n2.
x
y dx – y 2
(C) Types of orbitals : (1) s-orbitals : The s-subshell contains just one orbital which is non-directional & spherically symmetrical in shape. The maximum number of electrons which can be accommodated in s-orbital is 2. (iv) Differences between orbit and orbital : S.No.
Orbit
y
x
2
dz2
(4) f-orbitals : The f-subshell contains 7 orbitals which are complex in structure.The f-subshell can accommodate a maximum of 14 electrons.
Note : Letters s, p, d & f have originated from the words sharp, principle, diffused & fundamental respectively. Orbital
It is a region in three dimensional space around the nucleus where the probability of finding electron is maximum. s,p and d-orbitals are spherical, dumb-bell and double dumb-bell in shape respectively. It represents that an electron can move around nucleus along three dimensional space (x,y and z axis).
1
It is well defined circular path around the nucleus in which the electron revolves.
2
It is circular in shape.
3
It represents that an electron moves around the nucleus in one plane.
4
It represents that position as well as momentum of an electron can be known simultaneously with certainty. It is against Heisenberg's uncertainty principle.
It represents that position as well as momentum of an electron cannot be known simultaneously with certainty. It is in accordance with Heisenberg's uncertainty principle.
5
The maximum number of electrons in an 2 orbit is 2n where 'n' is the number of the orbit.
The maximum number of electrons in an orbital is two.
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PAGE # 18
(iii) It represents the sub-shell present in shell. = 0 represents s sub shell. = 1 represents p sub shell. = 2 represents d sub shell. = 3 represents f sub shell.
Note : Heisenberg’s uncertainty principle - “It is impossible to determine exactly both the position and momentum (or velocity) of an electron or of any other moving particle at the same time.”
QUANTUM NUMBERS To describe the position and energy of electron in an atom, four numbers are required, which are known as quantum numbers. Four quantum numbers are : (a) Principal quantum number (b) Azimuthal quantum number (c) Magnetic quantum number (d) Spin quantum number
(iv) Number of sub-shell in a shell = Principal quantum number of shell. (v) Maximum value of is always less than the value of n. So 1p, 1f, 2d, 2f, 3f subshells are not possible. s will start from 1s p will start from 2p d will start from 3d f will start from 4f
(a) Principal Quantum Number : (i) It is denoted by ‘n’.
(vi) Relative energy of various sub-shell in a shell are as follows s
(ii) It represents the name, size and energy of the orbit or shell to which the electron belongs. (iii) Higher is the value of ‘n’ , greater is the distance of the shell from the nucleus. r1 < r2 < r3 < r4 < r5 < ----
(vii) Subshells having equal values but with different n values have similar shapes but their sizes increases as the value of ‘n’ increases. 2s-subshell is greater in size than 1s- subshell. Similarly 2p, 3p, 4p subshells have similar shapes but their sizes increase in order 2p < 3p < 4p.
(iv) Higher is the value of ‘n’, greater is the magnitude of energy. E1 < E2 < E3 < E4 < E5 ---(v) Maximum number of electrons in a shell is given by 2n2. Shell Max. number of electrons First (n =1) 2 × 12 = 2 Second (n = 2) 2 × 22 = 8 Third ( n = 3) 2 × 32 = 18 Fourth ( n = 4) 2 × 42 = 32 (vi) Angular momentum can also be calculated using principal quantum number.
mvr
nh 2ð
(viii) Maximum no. of electrons present in a subshell = 2 (2 +1) Subshell Max. electrons s ( = 0) 2 (2 × 0 +1) = 2 p ( = 1) 2 (2 × 1 +1) = 6 d ( = 2) 2 (2 × 2 +1) = 10 f ( = 3) 2 (2 × 3 +1) = 14
Note : Azimuthal quantum number was given by Sommerfeld.
(vii) Value of n is from 1 to
(c) Magnetic quantum number :
(viii) Every shell is given a specific alphabetic name. First shell (n = 1) is known as K shell. Second shell (n = 2) is known as L shell. Third shell (n = 3) is known as M shell and so on.
(i) It is denoted by ‘m’.
Note : Principal quantum number was given by Bohr. (b) Azimuthal Quantum Number : (i) It is represented by ‘’.
Note : s,p,d and f signify sharp, principal, diffused and fundamental respectively.
Note : Azimuthal quantum number is also called angular quantum number, subsidiary quantum number or secondary quantum number. (ii) For a given value of n values of is 0 to n – 1 Value of n Values of 1 (1st shell) 0 2 (2nd shell) 0,1 3 (3rd shell) 0,1,2 4 (4th shell) 0,1,2,3
(ii) It represents the orbitals present in sub-shell. An orbital can be defined as : “Region in the three - dimensional space around the nucleus where the probability of finding an electron is maximum”. (iii) For a given value of , values of m are from – through 0 to +. m 0 0 1 –1, 0, +1 2 –2, –1, 0, +1, +2 3 –3, –2, –1, 0, +1, +2, +3 (iv) Maximum number of orbitals in a sub-shell = (2+1) Sub shell Orbitals s ( = 0) (2 × 0 +1) = 1 p ( = 1) (2 × 1 +1) = 3 d ( = 2) (2 × 2 +1) = 5 f ( = 3) (2 × 3 +1) = 7
19 19
PAGE # 19
(vii) Characteristics of orbitals :
(v) Maximum number of orbitals in a shell = n2 Shell Max. orbitals First (n = 1) 12 = 1 Second (n = 2) 22 = 4 Third (n = 3) 32 = 9 Fourth (n = 4) 42 = 16
(A) All orbitals of a subshell possess same energy i.e., they are degenerate. (B) All orbitals of the same shell differ in the direction of their space orientation. (C) Total number of orbitals in a shell is equal to n2.
(vi) It represents the orientation of orbital in three dimensional space. When l = 0, m = 0, i.e. one value implies that ‘s’ subshell has only one space orientation and hence, it can be arranged in space only in one way along x,y or z axis. Thus, ‘s’ orbital has a symmetrical spherical shape. Y Z
(d) Spin Quantum Number : (i) It is denoted by ‘s’. (ii) It represents the direction of spin of electron around its own axis. (iii) Clockwise spin is represented by +1/2 or and anticlockwise by –1/2 or .
X
(iv) Maximum two electrons with opposite spin can be placed in an orbital.
s- orbital When = 1,’m’ has three values –1, 0, +1 . It implies that ‘p’ subshell of any energy shell has three space orientations, i.e. three orbitals. Each p-orbital has dumb-bell shape. Each one is disposed symmetrically along one of the three axis. p orbitals have directional character. orbital m z
Pz 0
Px ±1
Py ±1
z
(ii) Each of the orbits can accommodate a fixed number of electrons. Maximum number of electrons in an orbit is equal to 2n2, where ‘n’ is the number of the orbit.
pz
py
(iii) Electrons are filled in the increasing order of energy, i.e. K < L < M < N ......
When = 2 ‘m’ has five values –2, –1, 0, +1, +2. It implies that d-subshell of any energy shell has five orientations, i.e. five orbitals. All the five orbitals are not identical in shape. Four of the d-orbitals dxy, dyz, dzx, d
x 2 – y2
contain four lobes while fifth orbital
dz2 consists of only two lobes. z
z
y
x
z
y
x
z
(iv) In the outermost shell of any atom, the maximum possible number of electrons is 8, except in the first shell which can have at the most 2 electrons.
Note : If the outermost shell has its full quota of 8 electrons it is said to be an octet. If the first shell has its full quota of 2 electrons, it is said to be duplet. The pictorial representation of Bohr’s model of hydrogen, helium, carbon, sodium and calcium atoms having 1, 2, 6, 11 and 20 electrons respectively are shown in the figure where the centre of the circle represents the nucleus.
y
x dyz
dxz
dxy
Note : Spin quantum number was given by Gold Schmidt.
(i) The arrangement of the electrons in different shells is known as the electronic configuration of the element.
y
y
px
x
x
y
y
(v) Electrons with same spin are called spin parallel and those with opposite spin are called spin paired.
ELECTRONIC CONFIGURATION OF AN ATOM
z
x
Note : Magnetic quantum number was given by Zeeman.
z
x
y 2
dx – y
y
x
2
dz2
There are seven f-orbitals designated as
f
, fx ( x2 – y2 ), fy ( x2 – y2 ), fz( x2 –y2 ), and fxyz . Their shapes are complicated ones.
f f yz2 , xz2 , z3
20 20
PAGE # 20
(a) Significance of Electronic Configuration :
(c) Hund’s Rule of Maximum Multiplicity : According to this rule : “no electron pairing takes place in the orbitals with equivalent energy until each orbital in the given subshell contains one electron & the spins of all unpaired electrons are parallel i.e. in the same direction”.
The electronic configuration of an atom plays an important role in determining the chemical behaviour of an element. (i) When the atoms of an element have completely filled outermost shell, the element will be chemically unreactive. For example the noble gases (He, Ne, Ar, Kr, Xe and Rn) have completely filled outermost shell i.e. contains 8 electrons (except helium which has two valence electrons) in outermost shell. (ii) When the atom of an element has less than 8 electrons in its outermost shell, the element will be reactive.
ORDER OF FILLING OF ELECTRONS IN SUBSHELLS
Electronic configuration of some elements Atom ic Sym bol of Nam e of num ber the elem ent the elem ent
Electronic configuration
1
H
Hydrogen
1s 1
2
He
Helium
1s
3
Li
Lithium
1s , 2s
4
Be
Beryllium
5
B
Boron
2 2
1
2
2
2
2
2
2
1s , 2s
1s , 2s , 2p
1
6
C
Carbon
1s , 2s , 2p 2
There are different rules governing the filling of subshells. They are described briefly as follows -
7
N
Nitrogen
1s 2, 2s 2 , 2p 3
8
O
Oxygen
1s 2, 2s 2 , 2p 4
9
F
Fluorine
1s 2, 2s 2 , 2p 5
(a) Aufbau Principle : The filling of subshells in atoms is based on their energies. Electrons first occupy the subshell with lowest energy and progressively fill the other subshells in increasing order of energy. Note :
10
Ne
Neon
1s 2, 2s 2 , 2p 6
11
Na
Sodium
1s , 2s , 2p ,3s
12
Mg
Magnes ium
1s , 2s , 2p ,3s
The subshell with lowest energy is filled first. The order of energy of different subshells of an atom is 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p. The number present before the subshells like 1,2,3 ------ represents the number of the shell i.e. n. The order of filling of different sub-shells is represented diagrammatically as follows :
1s 2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
2
2
6
1
2
2
6
2
2
2
6
2
1
2
2
6
2
2
2
2
6
2
13
Al
Alum inium
1s , 2s , 2p ,3s ,3p
14
Si
Silicon
1s , 2s , 2p ,3s ,3p
Phos phorus 1s , 2s , 2p ,3s ,3p 3
15
P
16
S
Sulphur
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 4
17
Cl
Chlorine
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 5
18
Ar
Argon
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6
19
K
Potas s ium
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6, , 4s 1
20
Ca
Calcium
1s , 2s , 2p ,3s ,3p , 4s
21
Sc
Scandium
2
2
6
2
6,
2
2
6
2
6,
1
2 2
2
2
6
2
6,
2
2
2
2
6
2
6,
3
2
2
2
6
2
6,
5
1s , 2s , 2p ,3s ,3p 3d , 4s
22
Ti
Titanium
1s , 2s , 2p ,3s ,3p 3d , 4s
23
V
Vanadium
1s , 2s , 2p ,3s ,3p 3d , 4s
1s , 2s , 2p ,3s ,3p 3d , 4s 1
24
Cr
C hrom ium
25
Mn
Manganes e 1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6, 3d 5, 4s 2
26
Fe
Iron
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6, 3d 6, 4s 2
27
Co
Cobalt
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6, 3d 7, 4s 2
28
Ni
Nickel
1s 2, 2s 2 , 2p 6 ,3s 2 ,3p 6, 3d 8, 4s 2
29
Cu
Copper
1s , 2s , 2p ,3s ,3p 3d , 4s
30
Zn
Zinc
1s , 2s , 2p ,3s ,3p 3d , 4s
2
2
6
2
6,
10
1
2
2
6
2
6,
10
2
VALENCE SHELL AND VALENCE ELECTRONS The outermost shell of an atom is known as the valence shell. The electrons present in the valence shell of an atom are known as valence electrons. The remainder of the atom i.e. the nucleus and other electrons is called the core of the atom. Electrons present in the core of an atom are known as core electrons. e.g. The electronic configuration of the sodium (Na) atom is :Na (11) K L M 2 8 1 Thus, valence electron in Na atom = 1 and core electrons in Na atom = 2 + 8 = 10
(b) Pauli’s Exclusion Principle : According to Pauli’s exclusion principle “an orbital cannot accommodate more than two electrons. If there are two electrons in an orbital they must have opposite spins.”
(a) Significance of Valence Electrons : (i) The valence electrons of an atom are responsible for, and take part in, chemical changes. (ii) The valence electrons in an atom determine the mode of chemical combination.
21 21
PAGE # 21
(iii) The valence electrons determine the combining capacity or the valency of the atom. The number of electrons in an atom that actually take part in bond formation is known as the valency of the element. e.g. In the carbon atom, there are four valence electrons. C(6) K L 2 4 The carbon atom is capable of forming four bonds. Hence, the valency of carbon is four.
VALENCY Valency of an element is the combining capacity of the atoms of the element with atoms of the same or different elements. The combining capacity of the atoms was explained in terms of their tendency to attain a fully filled outermost shell (stable octet or duplet)
(iv) If the outermost shell of an atom is completely filled, its valency is zero. The outermost shells of helium, neon, argon, krypton etc. are completely filled. Hence the valency of these elements is zero.
Valency of an element is determined by the number of valence electrons in an atom of the element. The valency of an element = number of valence electrons (if the number of valence electrons is1 to 4) The valency of an element = 8– number of valence electrons. (if the number of valence electrons is 4 to 8)
(v) Elements having the same number of valence electrons in their atoms possess similar chemical properties. e.g. All alkali metals have one valence electron in their atoms. Hence, their chemical properties are similar.
ISOTOPES
(vi) Elements having different number of valence electrons in their atoms show different chemical properties.
The isotopes of an element have the same atomic number but different atomic masses.
e.g. Let us consider the electronic configuration of alkali metals and halogens. Alkali metal atoms have single valence electron whereas halogen atoms have seven valence electrons. It is observed that the chemical properties of the alkali metals are entirely different from those of halogens. (vii) The number of the valence shell in the atom of an element determines the period number of the element in the periodic table. e.g. Sodium (Na) : Valence shell number = 3. period number = 3 Calcium (Ca) Valence shell number = 4 period number = 4 (viii) Elements with 1, 2 or 3 valence electrons in their atoms are metals.
Note : The number of electrons gained, lost or contributed for sharing by an atom of the element gives us directly the combining capacity or valency of the element.
Note : The term isotope was given by Margaret Todd. The difference in their masses is due to the presence of different number of neutrons. e.g. Isotopes of hydrogen : Hydrogen isotopes
Pr ot iu m 1 1H
De u t e r iu m 2 1H
T r itium 3 1H
1. Atomic number
1
1
1
2. No. of protons
1
1
1
3. No. of electrons
1
1
1
4. Mass number
1
2
3
5. No. of neutrons
0
1
2
Isotopes of oxygen :
Note : Hydrogen and helium are exceptions to this rule. Hydrogen and helium atoms have 1 and 2 valence electrons respectively, but they are non-metals.
Oxygen isotopes
16 8O
17 8O
18 8O
(ix) Elements with 4, 5, 6, 7 or 8 valence electrons in their atoms are non metals. e.g. carbon (C), nitrogen (N) and oxygen (O) are non metals. C = 2,4 6 N = 2,5 7 O = 2,6 8
1. Atomic number
8
8
8
2. No. of protons
8
8
8
3. No. of electrons
8
8
8
4. Mass number
16
17
18
5. No. of neutrons
8
9
10
Note : Whether the atom while combining with other atoms can form ionic or covalent bonds is determined by the number of valence electrons present in the atom.
Note : All the isotopes of an element have identical chemical properties.
22 22
PAGE # 22
(a) Characteristics of Isotopes :
ISOBARS (i) The physical properties of the isotopes of an element are different. This is due to the fact that isotopes have different numbers of neutrons in their nuclei. Hence mass, density and other physical properties of the isotopes of an element are different.
The atoms of different elements with different atomic numbers, which have same mass number are called isobars. e.g.
(ii) All the isotopes of an element contain the same number of electrons. So, they have the same electronic configuration with the same number of valence electrons. Since the chemical properties of an element are determined by the number of valence electrons in its atom, all the isotopes of an element have identical chemical properties.
35 17 Cl
and
37 17 Cl
with abundance of 75%
40
3. No. of electrons
18
20
4. No. of protons
18
20
5. No. of neutrons
22
20
2, 8, 8
2, 8, 8, 2
6. Electronic configuration
Note Isobars contain different number of electrons, protons and neutrons.
ISOTONES Isotones may be defined as the atoms of different elements containing same number of neutrons. e.g.
13 6C
and
30 31 14 Si , 15 P
and
(Both contain 7 neutrons)
32 16 S
(All three contain 16 neutrons)
Ion or atom or molecule which have the same number of electrons are called as isoelectronic species. 17Cl
(i) In agriculture : Certain elements such as boron, cobalt, copper, manganese, zinc and molybdenum are necessary in very minute quantities for plant nutrition. By radioactive isotopes we can identify the presence and requirement of these element in the nutrition of plants.
No. of electrons
18
18 Ar
19 K
18
18
20 Ca
2
18
EXERCISE 1.
Cathode rays : (A) travel in straight line (B) can do mechanical work (C) are negatively charged (D) all of these
2.
Which of the following has the greatest mass ? (A) electron (B) proton (C) neutron (D) hydrogen cation
3.
Chlorine has atomic mass 35.5 . This mass is fractional due to : (A) existence of electrons (B) existence of isotopes having different masses (C) rapid conversion of proton into neutron and vice versa in nucleus (D) fractional atomic masses are meaningless
24 32 the help of radioactive isotope 11 Na, 131 53 É, 15P etc.
Note : Isotopes (Like Uranium-238) are used in Nuclear reactor to produce energy and power.
14 7N
ISOELECTRONIC
(ii) In industry : Isotopes are used for coating on the arm of clock to see in dark. To identify the cracks in metal casting.
Ca
20
e.g.
(v) In carbon dating : Will and Libby (1960) developed the technique of radiocarbon to determine the age of plant, fossil and archeological sample.
40 20
Ar
40
(c) Applications of Radioactive Isotopes :
(iv) Determination of the mechanism of chemical reaction by replacing an atom or molecule by its isotopes.
40 18
18
= 26.25 + 9.25 = 35.5 u. Thus, the average atomic mass of chlorine is 35.5 u.
(iii) In medicine :Thyroid, bone diseases, brain tumors and cancer are controlled or destroyed with
are isobars.
2. Mass number
75 25 = 35 × + 37 × 100 100 2625 925 + 100 100
40 20 Ca
1. Atomic number
and 25% respectively. Thus the average mass of a chlorine atom will be 75% of 35 and 25% of 37, which is 35.5 u. So, Average atomic mass of chlorine
=
and
are isobars.
Isobars
of Elements :
two isotopes
14 7N
and
40 18 Ar
(b) Reason for the Fractional Atomic Masses
The atomic masses of many elements are in fraction and not whole number. The fractional atomic masses of elements are due to the existence of their isotopes having different masses. e.g. The atomic mass of chlorine is 35.5 u. Chlorine has
14 6C
23 23
PAGE # 23
4.
5.
6.
7.
8.
9.
Which of the following ray does not have mass? (A) cathode rays (B) -rays (C) x-rays (D) anode rays Hund’s rule states that (A) matter and radiation have a dual nature. (B) in the orbitals of equivalent energy, pairing begins only after all the orbitals have been singly occupied. (C) the position and velocity of an electron cannot be exactly measured at the same time. (D) no two electrons in an atom can have the same set of four quantum numbers. The electrons, identified by quantum numbers n and (i) n = 4, = 1 (ii) n = 4, = 0 (iii) n = 3, = 2, (iv) n = 3 , = 1 can be placed in order of increasing energy from the lowest to highest as (A) (iv) < (ii) < (iii) < (i) (B) (ii) < (iv) < (i) < (iii) (C) (i) < (iii) < (ii) < (iv) (D) (iii) < (i) < (iv) < (ii) If the nitrogen atom had electronic configuration 1s7, it would have energy lower than that of the normal ground state configuration 1s2, 2s2 2p3, because the electrons would be closer to the nucleus. Yet 1s7 is not observed because it violates (A) Heisenberg uncertainty principle (B) Hund Rule (C) Pauli exclusion principle (D) Bohr postulate of stationary orbits The ratio of the difference in energy of electron between the first and second Bohr’s orbits to that between second and third Bohr’s orbits is (A) 1/3 (B) 27/5 (C) 9/4 (D) 4/9 The velocity of electron in the fourth Bohr’s orbit of hydrogen is u. The velocity of the electron in the first orbit would be (A) 4u (B) 16u (C) u/4 (D) u/16
10. In any subshell, the maximum number of electroons having same value of spin quantum number is: (A)
( 1)
(C) 2 +1
(B) +2 (D) 4 +2
11. In ‘aufbau principle’, the term aufbau represents : (A) The name of scientist. (B) German term meaning for building up. (C) The energy of electron. (D) The angular momentum of electron. 12. For azimuthal quantum number= 3, the maximum number of electrons will be : (A) 2 (B) 6 (C) Zero (D) 14.
13. The n + value for the 3p-energy level is : (A) 4 (B) 7 (C) 3 (D) 1 14. Which one represents an impossible arrangement ? n m s (A) 3 2 –2 1/2 (B) 4 0 0 1/2 (C) 3 2 –3 1/2 (D) 5 3 0 1/2 15. The number of vacant orbitals in the valence shell of an element with atomic number 14 is : (A) 2 (B) 4 (C) 8 (D) 6 16. n and values of an orbital “A” are 3 and 2 and of another orbital “B” are 5 and 0. The energy of : (A) B is more than A (B) A is more than B (C) A and B are of same energy (D) None of the above 17. The energy of electron in – 871.6 × 10–20 J. The energy orbit of H is : (A) –871.6 × 10–20 J (C) –217.9 × 10–20 J 18.
first orbit of He + is of electron in the first (B) –435.8 ×10–20 J (D) –108.9 × 10–20 J
Which of the following set of quantum numbers correctly represents Beryllium’s fourth electron ? n m s (A) 1
0
0
–
1 2
(B) 1
1
1
+
1 2
(C) 2
0
0
–
(D) 2
1
0
1 2 1 + 2
19. The number of subshells in the second energy level is (A) 4 (B) 11 (C) 9 (D) 2 20. The number of orbitals in the fourth energy level is (A) 4 (B) 16 (C) 32 (D) 9 21. Azimuthal quantum number value for a dumb-bell shaped orbital is : (A) – 1 (B) 1 (C) 0 (D) 2 22. The total number of orbitals in 3rd orbit is : (A) 3 (B) 5 (C) 4 (D) 9 23. Which of the quantum numbers describe shape of electron cloud ? (A) Principal quantum number (B) Azimuthal quantum number (C) Magnetic quantum number (D) Spin quantum number.
24 24
PAGE # 24
24. Correct set of all four quantum number for an unpaired electron for 3d9 is : (A) 3, 2, – 3, + 1/2 (B) 3, 2, –2, – 1/2 (C) 3, 3, + 2 + 1/2 (D) 3, 3, + 2, – 1/2 25. The number of electrons with the azimuthal quantum number = 1 and 2 for 24Cr in ground state are : (A) 16 and 5 (B) 12 and 5 (C) 16 and 4 (D) 12 and 4 26. The energy of second Bohr’s orbit in H-atom is –328 kJ mol–1, hence the energy of fourth Bohr orbit would be : (A) – 82 kJ mol–1 (B) –41 kJ mol–1 (C) –1312 kJ mol–1 (D) –164 kJ mol–1 27. Which of the following is not the basic postulate of Dalton’s atomic theory ? (A) Atoms are neither created nor destroyed in a chemical reaction. (B) In a given cmpound, the relative number and kinds of atoms are constant. (C) Atoms of all elements are alike, including their masses. (D) Each element is composed of extermely small particles called atoms. 28. Two electrons A and B in an atom have the following set of quantum numbers : A : 3, 2, –2, + 1/2. B : 3, 0, 0, +1/2. Which statement is correct for A and B. (A) A and B have same energy. (B) A has more energy than B. (C) B has more energy than A. (D) A and B represents same electron.
29. Which of the following has more number of unpaired electron ? (A) Zn+ (B) Fe2+ 2+ (C) Ni (D) Cu+ 30. From the discharge tube experiment, it is concluded that : (A) mass of proton is in fraction. (B) matter contains electrons. (C) nucleus contains positive charge. (D) positive rays are heavier than protons. 31. According to classical theory, the proposed circular path of an electron in Rutherford atomic model will be : (A) Circular (B) Straight line (C) Parabolic (D) Spiral. 32. Alpha-particles that come closer to nuclei in Rutherford’s alpha particle scattering experiment. (A) are deflected more (B) are deflected less (C) make more collisions. (D) none of these. 33. Consider the ground state of Cr atom (Z=24). The number of electrons with the azimuthal quantum numbers, = 1 and 2 are, respectively: (A) 16 and 5 (C) 16 and4
(B) 12 and 5 (D) 12 and4
34. Number of electrons having + m value equal to zero in 26Fe may be (A) 13 (B) 15 (C) 7 (D) 12 35. The Bohr radius for the hydrogen atom(n = 1)is approx 0.53 Å. The radius for the first excited state (n = 2 orbit) is (in Å) (A) 0.13 (B) 1.06 (C) 4.77 (D) 2.12
25 25
PAGE # 25
P E R C E N TA G E To calculate what percentage of a is b, use the The word 'percentage' literally means 'per hundred' or 'for every hundred.' Therefore, whenever we calculate something as a part of 100, that part is numerically termed as percentage. In other words, percentage is a ratio whose second term is equal to 100. i.e. 1 : 4 can be written as 25 : 100 or 25%, 3 : 8 can be written as 37.5 : 100 or 37.5%, 3 :2 can be written as 150 : 100 or 150%, and so on.
formula : Percentage =
Ex.4 What percentage of 240 is 90 ? Sol. Percentage =
90 × 100 = 37.5%. 240
Ex.5 What percentage of 75 is 125 ? Sol. Percentage
To express a% as a fraction divide it by 100. i.e. a% = a/100
b ×100. a
125 ×100 = 166.66%. 75
REMARK : In short, if you ask yourself, “of what are we calculating
To express a fraction (x/y) as a percent multiply it by
percentage ?” you will get the answer of a. Therefore, a
100. i.e. x/y = (x/y x 100)%
will form the whole and b will form the part of the whole.
Basic Formula of Percentage :
Percentage increase/decrease when a quantity
p p% of a number N is = N × 100
‘a’ is increased/decreased to become another quantity ‘b’. Percentage Increase/Decrease
Ex.1 What is 37.5% of 648 ?
=
37.5 Sol. 37.5% of 648 = × 648 100
=
b – a a 100, when b a ;(increase ) = a – b a 100, when b a ;(decrease )
375 × 648 = 3 × 81 = 243. 1000
Ex.2 What is 20% of 50% of 60% of 200 ? 60 50 20 Sol. Required percentage 200 100 100 × 100
Therefore new quantity b = 12.
Ex.3 In a market survey, 20% opted for product B & the remaining individuals were uncertain. If the difference between those who opted for product B and those who were uncertain was 720. How many individuals were covered in the survey ? Sol. Clearly, 80% were uncertain. 80% of x – 20% of x = 720 60% of x = 720 or
So, x =
Increase / Decrease × 100 Initial Value
60 x = 720 100
720 100 = 1200. 60
To increase or decrease a number by x% , multiply [100 x] 100 Where, (+) Increase, (–) Decrease.
the number by
REMARK : To solve these type of problems calculate x% of given number & add or subtract the value from given number for increase or decrease respectively.
percentage increase a 1 100 = percentage decrease a 1 – 100 Ex.6 A dealer buys products for Rs.80 and hikes up the price to Rs.125. He sells it to the customer after giving a discount of Rs.5. Find his profit percentage. Sol. Profit percentage = Percentage Increase/Decrease in his income. Pr ofit 120 – 80 = Cost Pr ice ×100 = ×100 = 50%. 80 Ex.7 A dealer sells goods priced at Rs.180 after giving a discount of 25%. Find his selling price. 25 = 135. Sol. Selling price after discount = 180 1 – 100
If the price of a commodity increase/decrease by r%, then the decrease/increase in consumption so as r 100 % not to change the expenditure is : (100 r)
PAGE # 2626
Ex.8 The price of wheat falls by 16%. By what percentage a
Given below are the fractions converted into percentage.
person can increase the consumption of wheat so that his overall budget does not change ?
r
Sol. Increase in consumption =
(100 r)
Fraction
100 %
16 100 % = 400 % = 19.04% 19%. = 84 21
If one quantity A is x% more or less than another quantity B, than B is less or more than A by : x 100 100 x
Ex.9 The salary of Ramesh is 25% more than that of Anil’s salary. By what percentage is Anil’s salary less than that of Ramesh’s ? Sol. Anil’s salary is less than that of Ramesh’s by x 25 = × 100 = × 100 = 20%. 100 x 125
Percentage
Fraction
Percentage
Fraction
Percentage
50%
1 10
10%
1 18
1 3
33.33%
1 11
9.09%
1 19
5.26%
1 4
25%
1 12
8.33%
1 20
5%
1 5
20%
1 13
7.69%
1 21
4.76%
1 6
16.66%
1 14
7.14%
1 22
4.54%
1 7
14.28%
1 15
6.66%
1 23
4.34%
1 8
12.50%
1 16
6.25%
1 24
4.16%
1 9
11.11%
1 17
5.88%
1 25
4%
1 2
5.55%
Ex.12 The salary of Sachin Tendulkar is 20% more than that of Ricky Ponting. By what percentage is Ricky’s salary less than that of Sachin’s ? Sol. 20% =
1 , so if Ricky’s salary is divided into 5 parts, 5
Ex.10 Vijay’s salary was reduced by 50%. Again the reduced
Sachin’s salary will one more part added to Rickey’s
salary was increased by 50%. Then, what will be the %
salary. i.e. Therefore, if Ricky’s salary is 5 parts,
loss in salary ?
Sachin’s salary is 6 parts. Now if Sachin’s salary is
Sol. Say, salary was Rs.100
6 parts, Ricky’s salary is one part less. Therefore, for
Reduction 50% Now salary = Rs. 50
Sachin, Ricky’s salary is
Increase = 50%
than its previous height. What height will the ball reach on its 4th bounce ?
Ex.11 Entry fee in an exhibition was Rs.1. Later, this was reduced by 25% which increased the sale by 20%. Then find the percentage of slump in business. Sol. Let the total original sale be Rs. 100. Then, original number of visitors = 100.
Sol. I wonder how many of you will notice that 14.28% =
1 7 th
1 7 less than the previous height. Or, the ball is rising up to Therefore, the ball is rising up to a height which is
6 of the previous height. 7 Therefore, on its 4th bounce the ball will reach a height of
a height which is 120 = 160. 0.75
Increase% = 60%. 4802 ×
Conversion of Fractions into Percentages : Knowing conversion of common fractions into percentages helps your convert many fractions into percentage immediately, For example, knowing that 1 3 = 12.5% will help you convert fractions like 8 8
or
less or 16.66% less.
bounces every time to a height which is 14.28% less
100 75 Loss % = = 25 100 Hence, loss is 25%.
th
Ex.13 A ball drops from a height of 4802 m. Thereafter, it
50 150 = Rs.75 100
New number of visitors =
1 6
5 into percentages immediately.. 8
6 6 6 6 × × × = 2592 m. 7 7 7 7
Ex.14 A man spends 75% of his income. If his income is increased by 20% and he increased his expenditure by 10%. By what % will saving increased ? Sol. Let his income be Rs 100, Expenditure = Rs. 75. Now, Income is increased by 20%. New income = 120, expenditure is increased by 10% 75 110 = Rs. 82.50 100 Saving = 120 – 82.50 = 37.50 Earlier saving = 100 – 75 = 25
=
Increase in saving =
37.50 25 × 100 = 50%. 25
PAGE # 2727
Ex.15 A students scores 40 marks in an examination and fails by 26 marks. If the passing percentage is 33 then find the maximum marks in the examination. Sol. Let, the maximum marks in the examination is 100. Then he needs 33 marks to pass. But, passing marks required are 40 + 26 = 66 marks. 33 marks are required to pass if maximum marks are 100 Here, 66 marks are required to pass, then maximum marks are
Ex.18 Arvind spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. By what percent his savings are increased ? Sol. Let the income be 100. Expenditure = 75 & Savings = 25. New income = 120,
100 66 = 200 marks. 33
110 75 = 165 100 2
New expenditure =
165 75 = 2 2 75 25 = 25 Increase in savings = 2 2 25 1 100 = 50% %age increase in savings = 2 25
If a quantity x is increased or decreased successively by A%, B%, C% then the final value of x will be
New savings = 120
A B C 1 1 . = x 1 100 100 100
Let the present population of town be P and let there be an increase or decrease of R% per annum.
R Then Population after n years = P 1 100
n
Ex.19 A cricket team won 40% of the total number of matches it played during a year. If it lost 50% of the
If length & breadth of a rectangle is changed by a % &
matches played and 20 matches were drawn. Find the
b% respectively, than % change in area will be
total number of matches played by the team during the ( a b) = a b 100 %
year.
(use +ve for increase & –ve for decrease) Ex.16 The population of a variety of tiny bush in an experimental field increased by 10% in the first year, increased by 8% in the second year but decreased by 10% in the third year. If the present number of bushes in the experimental field is 26730, then find the number of bushes in the beginning. Sol. Let the number of bushes in the beginning is P so,
Sol. 40% of x + 50% of x + 20 = x where x = Total number of matches
Short cut : 10% of the matches were drawn. So by unitary method
10 8 10 1 1 = 26730 P × 1 100 100 100
P=
26730 10 8 10 1 1 1 100 100 100
10 25 10 P = 26730 11 27 9
P = 25000.
20%
100%
? 200
Ex.20 5% of income of A is equal to 15% of income of B and
Sol. Applying percentage change = a + b +
10 x 11x = 10 100 10
100 1 =9 % 11 11
10% of income of B is equal to 20% of income of C. If the income of C is Rs. 2,000, then find the total income of A, B and C.
ab 100
Let decrease in breadth be x%.
x=
10%
10 10
Ex.17 The length of a rectangle is increased by 10%. What will be the percentage decrease in its breadth so as to have a constant area ?
Then 0 = 10 – x –
40 50 x x + 20 = x or x = 200 100 100
Sol.
5 15 10 20 A= B& B= C 100 100 100 100 A = 3B and B = 2C = 2 × 2000 = 4000 A = 3 × 4000 = 12000 A + B + C = 12000 + 4000 + 2000 = 18000. PAGE # 2828
1.
If 37% of a number is 990.86, what will be approximately 19% of that number ? (A) 600 (B) 500 (C) 700 (D) 550
2.
Passing percentage marks in an exam is 40. A obtained 72 out of 200. By what per cent did he fail? (A) 8 (B) 5 (C) 4 (D) 6
3.
The price of rice increased from Rs.15 by 15% and then reduced by 30 paise. What was the net increase? (A) 10% (B) 12% (C) 13% (D) 23%
4.
In order to increase sales, price of a product was decreased by 20%. The net sales increased by 28%. What is the increase in unit sales ? (A) 48% (B) 50% (C) 60% (D) 83%
5.
If 1L of water is added to 5 L of a 20% solution of sugar in water, what is the strength of the solution now? (A) 12.66 (B) 8.33% (C) 16.66% (D) 16%
6.
Al Pacino invested 40% of his money in shares, 20% of the rest in property and lost 25% of the remaining in a casino. What per cent does he have now? (A) 15 (B) 42 (C) 30 (D) 36
Directions for questions 7 to 9 : Answer the questions based on the given information. In an election, there were only 2 candidates. The losing candidate received 66
2 % of the votes the winner 3
got. If the votes polled in loser were 60 less than that of
11. In an examination, a student needs to get 45% to secure passing marks. A student got 138 marks and failed by 15%. What were the maximum marks? (A) 400 (B) 450 (C) 460 (D) 500 12. Avinash spends 30% of his income on conveyance.
1 of the remaining on house rent and the balance on 4 food. If he spends Rs. 300 on conveyance, what is the expenditure on house rent ? (A) Rs. 525
(B) Rs. 675
(C) Rs. 175
(D) Rs. 200
13. If x% of a is the same as y% of b, then z% of b is :
xy % of a z z (C) xy % of a (A)
x zy % of a xz (D) y % of a (B)
14. In an examination, A got 10% marks less than B; B got 25% marks more than C and C got 20% less than D. If A got 360 marks out of 500, then the percentage of marks obtained by D was : (A) 70 (B) 75 (C) 80 (D) 90 15. In an election involving two candidates, 68 votes were found invalid. The winning candidate scores 52% and wins by 98 votes. The total number of votes casted is : (A) 2450 (B) 2382 (C) 2158 (D) 2518 16. The price of sugar is increased by 20%. As a result, a family decreases its consumption by 25%. The expenditure of the family on sugar will be decreased by : (A) 10% (B) 5% (C) 14% (D) 15%
winner, then : 7.
How many votes did the loser get ? (A) 200 (B) 150 (C) 120 (D) 160
8.
How many total votes were cast ? (A) 225 (B) 300 (C) 180 (D) 240
9.
What per cent of the total votes did the winner get? (A) 60 (B) 80 (C) 66.66 (D) 65
10. If the numerator of a fraction is increased by 25% and the denominator decreased by 20%, the new value is
5 . What was the original fraction ? 4 3 4 (A) (B) 5 5 7 3 (C) (D) 8 7
17. A man’s basic pay for a 40-hour week is Rs. 20. Overtime is paid for at 25% above the basic rate. In a certain week, he worked overtime and his total wage was Rs. 25. He therefore, worked for : (A) 45 hr (B) 48 hr (C) 47 hr (D) 50 hr 18. When any number is divided by 12, then dividend 1 th of the other number. By how much 4 first number is greater than the second ? (B) 200 (D) Date inadequate
becomes percent number (A) 150 (C) 300
4 of its original 5 value. If the premium on it at the rate of 1.3 percent amounts to Rs.910, the original value of the tempo is : (A) Rs.78500 (B) Rs.80000 (C) Rs.82500 (D) Rs.87500
19. A tempo is insured to the extent of
PAGE # 2929
20. Gauri went to the stationers and bought things worth Rs.25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items ? (A) Rs. 15 (B) Rs. 15.70 (C) Rs. 19.70 (D) Rs. 20 21. In a recent survey, 40% houses contained two or more people. Of those houses containing only one person, 25% were having only a male. What is the percentage of all houses, which contain exactly one female and no males ? (A) 15 (B) 45 (C) 75 (D) Can’t be determined
28. 8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote ? (A) 4.2 (B) 6.4 (C) 6.8 (D) 8.0 29. A bag contains 600 coins of 25 p denomination and 1200 coins of 50 p denomination. If 12% of 25 p coins and 24% of 50 p coins are removed, the percentage of money removed from the bag is nearly : (A) 15.6% (B) 17.8% (C) 21.6% (D) 30%
22. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ? (A) 32 kg (B) 40 kg (C) 52 kg (D) 80 kg
30. Due to an increase of 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the increased price per dozen ? (A) Rs. 8.64 (B) Rs. 8.88 (C) Rs. 9.36 (D) Rs. 10.40
23. One bacteria splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, what is the number in first generation ? (A) 1 million (B) 2 million (C) 4 million (D) 8 million
31.
24. A man earns x% on the first Rs.2,000 and y% on the rest of his income. If he earns Rs.700 from Rs.4,000 and Rs.900 from Rs.5,000 of income, find x%. (A) 20% (B) 15% (C) 25% (D) None of these 25. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens? (A) 37·5% (B) 62·5% (C) 50% (D) None of these 26. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then, the number of papers in which he got more than 50% marks is : (A) 1 (B) 3 (C) 4 (D) 5 27. A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited ? . (A) 300 (B) 250 (C) 400 (D) 500
2 of the voters promise to vote for P and the rest 5 promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then, the total number of voters is : (A) 100 (B) 110 (C) 90 (D) 95
32. In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10 kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was : (A) 10 kg (B) 15 kg (C) 20 kg (D) 25 kg 33. In expressing a length of 81.472 km as nearly as possible with three significant digits, find the percentage error. (A) 0.014% (B) 0.018% (C) 0.024% (D) 0.034% 34. If 50% of (x – y) = 30% of (x + y). then what percent of x is y ? (A) 10% (B) 15% (C) 25% (D) 50% 35. Mr. Jones gave 40% percent of the money he had, to his wife. He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of Rs. 12,000 was deposited in the bank. How much money did Mr. Jones have initially ? (A) Rs. 1,00,000 (B) Rs. 1,10,000 (C) Rs. 1,15,000 (D) Rs. 1,20,000 36. The value of machine depreciates at the rate 10% per annum. If its present value is Rs. 1,62,000. What was the value of the machine 2 years ago ? (A) Rs. 100000 (B) Rs. 150000 (C) Rs. 200000 (D) Rs. 250000 PAGE # 3030
37. During one year, the population of a town increased by 5% and during the next year, the population decreased by 5%. If the total population is 9975 at the end of the second year, then what was the population size in the beginning of the first year ? (A) 10000 (B) 15000 (C) 20000 (D) 25000 38. In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, find the total number of students. (A) 350 (B) 400 (C) 450 (D) 500 39. Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week ? (A) Rs. 200 (B) Rs. 250 (C) Rs. 300 (D) None of these 40. 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is : 2 (A) 58% (B) 62 % 3 (C) 64% (D) 78% 41. In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination ? (A) 30,000 (B) 35,000 (C) 37,000 (D) None of these 42. If A = x% of y and B = y% of x, then which of the following is true ? (A) A is smaller than B. (B) A is greater than B. (C) Relationship between A and B cannot be determined (D) None of these.
45. Peter could save 10% of his income. But two years later when his income is increased by 20%, he could save the same amount only as before. By how much percent has his expenditure increased ? 2 (A) 22% (B) 22 % 9 1 (C) 23 % (D) 24% 3 46. Mr. X, a businessman had the income in the year 2000, such that he earned a profit of 20% on his investment in the business. In the year 2001, his investment was less by Rs. 5000 but still had the same income (Income = Investment + Profit) as that in 2000. Thus, the percent profit earned in 2001 increased by 6%. What was his investment in 2000 ? (A) Rs. 1,02,000
(B) Rs. 1,05,000
(C) Rs. 1,50,500
(D) None of these
47. Prices register an increase of 10% on foodgrains and 15% on other items of expenditure. If the ratio of an employee’s expenditure on foodgrains and other items be 2 : 5, by how much should his salary be increased in order that he may maintain the same level of consumption as before, his present salary being Rs. 2590. (A) Rs. 323.75
(B) Rs. 350
(C) Rs. 360.50
(D) None of these
48. In the month of January, the Railway Police caught 4000 ticketless travellers. In February, the number rose by 5%. However, due to constant vigilance by the Police and the Railway staff, the number reduced by 5% and in April it further reduced by 10%. The total number of ticketless travellers caught in the month of April was : (A) 3125
(B) 3255
(C) 3575
(D) 3591
43. From the salary of an officer, 10% is deducted as house rent, 20% of the rest he spends on conveyance, 20% of the rest he pays as income tax and 10% of the balance he spends on clothes. Then, he left with Rs. 15,552. Find his total salary. (A) Rs. 25,000 (B) Rs. 30,000 (C) Rs. 35,000 (D) Rs. 40,000
49. In an examination in which full marks were 800, A gets
44. The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was Rs. 1, then the original price was :
50. One type of liquid contains 20% water and the second
2
1 r (B) Rs. 100
(A) Rs. 1 (C) Rs.
1 r2 100
10000 (D) Rs. 2 10000 r
20% more than B, B gets 20% more than C, and C gets 15% less than D. If A got 576, what percentage of full marks did D get (approximately) ? (A) 45.7%
(B) 51.2%
(C) 58.8%
(D) 61.7%
type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The percentage of water in the new mixture in the glass is :
2 % 7
(A) 20%
(B) 24
(C) 37%
(D) 40%
PAGE # 3131
RATIO-PROPORTION, PARTNERSHIP, MIXTURE & ALLIGATION RATIO
Ratio : If a and b (b 0) are two quantities of the same kind, then the fraction
a is called the ratio of a to b, we b
write it as a : b. or
a anticedent a = b consequent b
In the ratio a : b, the first term is ‘a’ and the second term is ‘b’. A ratio is said to be in the simplest form if its two
Comparison of ratios In order to compare two given ratios, we follow the following steps : Step-I : Obtain the given ratios Step-II : Express each one of them in the form of a fraction in the simplest form. Step-III : Find the L.C.M. of the denominators of the fractions obtained in step II.
terms have no common factor other than 1.
Step-IV : Obtain first fraction and its denominator. Divide
NOTE :
the L.C.M. obtained in step III by the denominator to get a number x (say).
(i) The ratio of two numbers is usually expressed in its simplest form.
Now, multiply the numerator and denominator of the fraction by x. Apply the same procedure to the other
(ii) In a ratio, we compare two quantities. The
fraction. Now, the denominators of both the fractions will be
comparison becomes meaningless if the quantities being compared are not of the same kind i.e. they are not measured in the same units. (iii) It is just meaningless to compare 20 bags with
same. Step-V : Compare the numerators of the fractions obtained in step IV. The fraction having larger numerator will be larger than the other.
200 crows. Therefore, to find the ratio of two quantities, they must be expressed in the same units.
Ex.3 Compare the ratios, 7 : 6 and 4 : 9. Sol. Writing the given ratios as fractions, we have
(iv) Since the ratio of two quantities of the same kind determines how many times one quantity is contained by the other. So the ratio of any two quantities of the same kind is an abstract quantity. In other words, ratio has no unit or it is independent of the units used in the quantities compared. (v) The order of the terms in a ratio a : b is very important. The ratio 3 : 2 is different from the ratio 2 : 3. Ex.1 Express the ratio 45 : 108 in its simplest form. Sol. In order to express the given ratio in its simplest form we divide its first and second terms by their HCF. We have, 45 = 3 × 3 × 5 and 108 = 2 × 2 × 3 × 3 × 3 So, HCF of 45 and 108 is 3 × 3 = 9 45 45 9 5 = = = 5 : 12 108 108 9 12 Hence, 45 : 108 in its simplest form is 5 : 12
45 : 108 =
7 4 and 4 : 9 = 6 9 Now, L.C.M. of 6 and 9 is 18
7:6=
Making the denominator of each fraction equal to 18, we have 7 73 21 4 42 8 = = and = = 6 63 18 9 92 18 Clearly, 21 > 8.
21 8 7 4 > > 18 18 6 9
Ex.4 5 kg of wheat flour is mixed with 500 gm of sugar extract. What is the ratio of sugar extract to the rest of the mixture, after adding 1.5 kg of water ? Sol. We first need to convert all figures into one single unit. Wheat flour = 5 kg Water = 1.5 kg Sugar extract = 500 gm = 0.5 kg Total weight of the mixture = 7 kg
Ex.2 If a : b = 5 : 9 and b : c = 4 : 7, find a : b : c. Sol. a : b = 5 : 9 and b : c = 4 : 7 9 9 63 or, b : c = 4 : 7 = 9 : 4 4 4 63 a:b:c=5:9: = 20 : 36 : 63. 4
Ratio of sugar extract to the total mixture =
0 .5 7
= 1 : 14 Ratio of sugar extract to the rest of the mixture =
0.5 = 1 : 13 6.5
PAGE # 32
Variation : PROPORTION
Proportion : Four (non-zero) quantities of the same kind a, b, c & d are said to be in proportion if the ratio of a to b is equal to the ratio of c to d. a c i.e., if = , we write it as a : b : : c : d. b d
Here a, b, c & d are called first, second, third & fourth proportions respectively.
a, b, c & d are in proportion if ad = bc. Continued Proportion : The (non-zero) quantities of the same kind a, b, c, d, e, f,... are said to be in continued proportion if
a b c d e = = = = ... b c d e f
Mean Proportional : If a, b & c are in continued proportion, then a & c are called first & third proportional respectively and b is called mean proportional of a and c. So, a : b : : b : c.
a b = b c b2 = ac
b=
Then,
ac .
Comparison of Ratios : We say that : a b
>
c d
.
Sub-duplicate Ratio : The sub-duplicate ratio of a : b is
Ex.6 If 3 : x : : 12 : 20, find the value of x. Sol. We have 3 : x : : 12 : 20 3, x, 12, 20 are in proportion Product of extremes = Product of means 3 × 20 = x × 12 60 = 12x
12x 60 = 12 12 x=5
[Dividing both sides by 12]
Ex.7 Find out : (i) the fourth proportional to 4, 9, 12; (ii) the third proportional to 16 and 36; (iii) the mean proportional between 0.08 and 0.18. Sol. (i) Let the fourth proportional of 4, 9, 12 be x. Then, 4 : 9 : : 12 : x 4 × x = 9 × 12 x=
9 12 = 27. 4
Fourth proportional to 4, 9, 12 is 27. (ii) Let the third proportional to 16 and 36 is x. Then, 16 : 36 : : 36 : x
b. 16 × x = 36 × 36 x =
36 36 = 81. 16
Triplicate Ratio : The triplicate ratio of a : b is a3 : b3.
Sub-triplicate Ratio : The sub-triplicate ratio of a : b is
Third proportional to 16 and 36 is 81.
1 a3
(iii) Mean proportional between 0.08 and 0.18
:
1 b3
.
a c b d = then = . b d a c a c a b Alternendo : If = then = . b d c d
Invertendo : If
Componendo : If Dividendo : If
a c ab cd = then = . b d b d
a c ab cd = then = . b d b d
Componendo and Dividendo : If
a c = b d
ab cd then, a b = c d .
1 . y
Ex.5 Are 36, 49, 6, 7 in proportion ? Sol. We have, Product of extremes = 36 × 7 = 252 Product of means= 49 × 6 = 294 Clearly, Product of extremes Product of means Hence, 36, 49, 6, 7 are not in proportion
Duplicate Ratio : The duplicate ratio of a : b is a2 : b2.
a :
for some constant k and we write, x
Compound Ratio : The compound ratio of the ratios a : b, c : d & e : f is ace : bdf.
(a : b) > (c : d)
(i) We say that x is directly proportional to y, if x = ky for some constant k and we write, x y. (ii) We say that x is inversely proportional to y, if xy = k
If
a c e ace = = then each ratio is equal to . b d f bd f
= 0.08 0.18 =
8 18 = 100 100
144 100 100
=
12 = 0.12 100
Ex.8 What must be added to the numbers 6, 10, 14 and 22 so that they are in proportion? Sol. Let the required number be x. Then, 6 + x, 10 + x, 14 + x, 22 + x are in proportion. Product of extremes = Product of means (6 + x) (22 + x) = (10 + x)(14 + x) 132 + 6x + 22x + x2 = 140 + 10x + 14x + x2 132 + 28x = 140 + 24x 28x – 24x = 140 – 132 4x = 8 8 x= = 2. 4
PAGE # 33
Ex.9 If three loaves of bread are consumed by 9 people, how many people will consume 9 loaves of bread? Sol. Suppose x people will consume 9 loaves of bread. More the people, more will be the number of loaves of bread required. We have, Number of People Number of Loaves of bread
9 x
3 9
9:x=3:9 9×9=x×3 81 = 3x
[direct proportion]
81 = 27 3 Hence, 27 people will consume 9 loaves of bread.
x=
PARTNERSHIP Partnership : When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership. Ratio of Division of Gains : (i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs.x and Rs.y respectively for a year in a business, then at the end of the year : (A’s share of profit) : (B’s share of profit) = x : y. (ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital × number of units of time). Now, gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs.x for t1 months and B invests Rs.y for t2 months, then A ' s share in profit B' s share in profit = A' s amount A' s time of investing of money B' s amount B' s time of investing of money
x t1 A ' s share in profit = y t2 B' s share in profit
Working and Sleeping Partners : A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner. Ex.10 A and B invested Rs. 3600 and Rs. 4800 respectively to open a shop. At the end of the year B’s profit was Rs.1208. Find A’s profit. Sol. Profit sharing ratio = 3600 : 4800 = 3 : 4 Profit of A 3 Profit of B 4
Ex.11 A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital? Sol. Let B’s capital be Rs. x. Then,
3500 12 2 = 7x 3
14x = 126000
Ex.12 Ramesh started a business by investing Rs. 25000. 3 months later Mahesh joined the business by investing Rs. 25000. At the end of the year Ramesh got Rs. 1000 more than Mahesh out of the profit. Find the total profit. Sol. Ramesh invested for 12 month, Mahesh invested for 9 month. Profit sharing ratio = 12x : 9x = 12 : 9 = 4 : 3. Let Capital be Rs P. 4 P 7
Profit of Ramesh = Profit of Mahesh =
3 P 7
4 3 P = P + 1000 7 7 4 3 P – P = 1000 7 7 P = 1000 P = Rs.7000. 7
Ex.13 Nitesh & Jitesh invested Rs.15000 and Rs.18000 respectively in a business. If the total profit at the end of the year is Rs. 8800 and Nitesh, being an active partner, gets an additional 12.5% of the profit, find the total profit of Nitesh. Sol. Profit sharing ratio = 15000 : 18000 = 5 : 6 Total profit = 8800 Nitesh gets 12.5% of the profit =
3 Profit of B 4
Profit of A =
3 × 1208 = Rs. 906 4
12.5 × 8800 100
= Rs. 1100 Net profit = 8800 – 1100 = Rs. 7700 Nitesh share in profit =
5 × 7700 = 3500 56
Total profit of Nitesh = 3500 + 1100 = Rs. 4600. Ex.14 Tanoj & Manoj started a business by investing Rs. 75000 and Rs. 90000 respectively. It was decided to pay Tanoj a monthly salary of Rs. 1875 as he was the active partner. At the end of the year if the total profit is Rs. 39000, find the profit of each. Sol. Profit sharing ratio = 75000 : 90000 = 5 : 6 Total profit = Rs. 39000 Salary of Tanoj = 12 × 1875 = Rs. 22500 Profit left = Rs.39000 – Rs. 22500 = Rs.16500. Tanoj’s profit =
Profit of A =
x = 9000.
5 × 16500 = 7500. 11
Total profit of Tanoj = 22500 + 7,500 = Rs. 30,000 Manoj’s profit =
6 × 16500 = Rs. 9,000 11
PAGE # 34
Alligation : It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price. Mean Price : The cost price of a unit quantity of mixture is called the mean price.
Quantity of cheaper C.P. of dearer – Mean price Mean price – C.P. of cheaper Quantity of dearer
We can also represent this thing as under
Milk in 1 litre mixture in 2nd can =
(d) Mean price (m) (m – c)
Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid
Milk in 1 litre of final mixture = Mean price = Rs.
is Rs.20 per kg. If both type-1 and type-2 are mixed in ratio of 2 : 3 , then find the price per kg of the mixed variety of rice. Sol. Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have : Cost of 1 kg of Type 2 rice
Rs. 20 Mean price Rs. x
(20 – x ) 2 = ( x – 15) 3
60 – 3x = 2x – 30
5x = 90
x = 18.
5 . 8
x 1/ 8 1 y = 1/ 8 = 1 . C.P. of 1 litre mixture in 1st can
3/4
(x – 15)
Mean price 5/8
1/2
1/8
We will mix 6 from each can. Ex.17 Tea worth Rs.126 per kg and Rs.135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, then find the price of the third variety per kg. Sol. Since first and second varieties are mixed in equal 126 135 proportions, so their average price = Rs. 2
= Rs.130.50 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have : Cost of 1 kg tea of 1st kind
130.50
So, price of the mixture is Rs.18 per kg.
C.P. of 1 litre mixture in 2nd can
1/8
Ex.15 The cost of Type 1 rice is Rs.15 per kg and Type 2 rice
5 litre, 8
x 3/4 5 / 8 y = 5 / 8 1/ 2 ;
n y = x 1 – x units.
(20 – x)
1 . 2
By the rule of alligation, we have :
(d – m)
Rs. 15
1 litre, 2
C.P. of 1 litre mixture in 2nd can = Rs.
C.P. of a unit quantity of dearer
(c)
Cost of 1 kg of Type 1 rice
3 . 4
C.P. of 1 litre mixture in 1st can = Rs.
Rule of Alligation : If two ingredients are mixed, then,
C.P. of a unit quantity of cheaper
Ex.16 A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5 ? Sol. Let cost of 1 litre milk be Rs.1. 3 Milk in 1 litre mixture in 1st can = litre, 4
(x – 153) 1=
Cost of 1 kg tea of 2nd kind
Rs. x Mean price Rs. 153 22.50
x 153 22.5
153 + 22.5 = x x = Rs.175.50 PAGE # 35
Ex.18 A jar full of whisky contains 40% alcohol . A part of this
5.
12 labours can construct a road in 20 days. Then 30
whisky is replaced by another containing 19% alcohol
labours can construct the same road in x days. The
and now the percentage of alcohol was found to be
value of x will be found from the proportion.
26%. Find the quantity of whisky replaced. Sol. By the rule of alligation, we have : Strength of first jar
40%
Strength of 2nd jar
19%
Mean strength 26%
6.
(A) 12 : 30 :: 20 : x
(B) 30 : 12 :: 20 : x
(C) 30 : 12 :: x : 20
(D) 20 : 8 :: x : 20
The third proportional to (x2 – y2) and (x – y) is : (A) (x + y)
14
7
(C)
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2.
Required quantity replaced =
2 . 3
7.
and 5 parts syrup. How much of the mixture must be 8.
may be half water and half syrup ?
5x 3x x = 5 – 3 – 8 8
If the ratio of the areas of two circles is 100 : 1, then the (A) 4 : 1
(B) 1 : 8
(C)10 : 1
(D) 1 : 10
The ratio of the boys to girls in a class is 2 : 3. If 20% of is :
Let x litres of this liquid be replaced with water.
5x litres. Quantity of syrup in new mixture = 5 – 8
(D) x2 – y2
boys leave this class, then the new ratio of boys to girls
Sol. Suppose the vessel initially contains 8 litres of liquid.
3x x litres. Quantity of water in new mixture = 3 – 8
x–y xy
xy x–y
ratio of their radii is :
Ex.19 A vessel is filled with liquid, 3 parts of which are water drown off and replaced with water so that the mixture
(B)
9.
(A) 8 : 15
(B) 8 : 3
(C) 3 : 7
(D) 4 : 7
In a 60 liter mixture of milk and water, the ratio of milk to water is 2 : 1. How many liters of water is to be added to this, to make this ratio 1 : 2 in the new mixture ? (A) 56
(B) 50
(C) 70
(D) 60
10. An amount of Rs.735 was divided between A, B and C. If each of them had received Rs.25 less, their shares
5x + 24 = 40 – 5x 10x = 16 x =
would have been in the ratio of 1 : 3 : 2, The money
8 . 5
received by C was :
8 1 1 So, part of the mixture replaced = = . 5 8 5
(A) Rs. 195
(B) Rs. 200
(C) Rs. 225
(D) Rs. 245
11. A, B and C enter into a partnership. They invest Rs.40,000, Rs. 80,000 and Rs.1,20,000 respectively. At the end of the first year, B withdraws Rs.40,000, 1.
2.
3.
4.
If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is : (A) 22 : 29
(B) 26 : 61
(C) 29 : 22
(D) 25 : 27
while at the end of the second year, C withdraws Rs.80,000. In what ratio will the profit be shared at the end of 3 years ?
If x : 6 : : 32 : 24 then, what is the value of x ?
(A) 2 : 3 : 5
(B) 3 : 4 : 7
(A) 7
(B) 8
(C) 4 : 5 : 9
(D) None of these
(C) 6
(D) 5
The ratio of 43.5 : 25 is same as : (A) 2 : 1
(B) 4 : 1
(C) 7 : 5
(D) 5 : 2
The mean proportional between 234 and 104 is : (A) 39
(B) 54
(C) 27
(D) None of these
12. If a, b, c are in continued proportion, the expression
a 2 ab b 2 b 2 bc c 2 ac (A) ab c (C) a
can be simplified to :
a c ac (D) b (B)
PAGE # 36
13. Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is : (A) 4 : 1 (B) 151 : 48 (C) 157 : 53 (D) 5 : 2 14. A bag contains Rs. 600 in the from of 1 rupee, 50 paise and 25 paise coins in the ratio 3 : 4 : 12. The number of 25 paise coins is : (A) 600 (B) 800 (C) 1200 (D) 900 15. The ages of a man and his son is in the ratio of 7 : 2. After 15 years, they would be in the ratio of 2 : 1, what was father’s age when son was born ? (A) 25 years (B) 30 years (C) 35 years (D) 42 years 16. Two alloys containing copper and iron in the ratios 5 : 8 and 5 : 3 are melted in equal qualities. The ratio of iron to copper in the resulting alloy is (A) 103 : 105 (B) 15 : 24 (C) 105 : 103 (D) 19 : 21 17. The cost of manufacturing a product including labor, material and overhead are in the ratio 5 : 7 : 3. If the profits are calculated as 20% on costs, what is the ratio of material costs to profit ? (A) 5 : 2 (B) 10 : 3 (C) 11 : 9 (D) 7 : 3 18. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B, Rs.8400 for 5 months and C, Rs.10,000 for 3 months. A wants to be the working member for which he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. (A) Rs.1900 (B) Rs.2660 (C) Rs.2800 (D) Rs.2840 19. A and B started a business jointly. A’s investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs.4000 as profit, then their total profit is : (A) Rs.16,000 (B) Rs.20,000 (C) Rs.24,000 (D) Rs.28,000 20. A and B started a business with initial investments in the ratio 14 : 15 and their annual profits were in the ratio 7 : 6. If A invested the money for 10 months, for how many months did B invest his money ? (A) 6 (B) 7 (C) 8 (D) 9
21. A man wants to reach a certain destination. One sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of traveling in mud, in water and on tar road is in the ratio 3 : 4 : 5. The ratio of the durations he requires to cross the patch of mud, stream and tar road is : (A)
1 4 5 : : 2 5 2
(C) 10 : 15 : 18
(B) 3 : 8 : 15 (D) 1 : 2 : 3
22. If Rs.510 be divided among A, B, C in such a way that A gets
2 1 of what B gets and B gets of what C gets, 3 4
then, their shares are respectively : (A) Rs. 120, Rs. 240, Rs. 150 (B) Rs. 60, Rs. 90, Rs. 360 (C) Rs. 150, Rs. 300, Rs. 60 (D) None of these. 23. A fraction which bears the same ratio to does to
1 3 that 27 11
5 , is equal to : 9
1 55 3 (C) 11 (A)
(B)
1 11
(D) 55
24. 60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, then the amount of tin in the new alloy is : (A) 36 kg (B) 44 kg (C) 53 kg (D) 80 kg 25. 15 litres of mixtures contains 20% alcohol and the rest water. If 3 litres of water be mixed with it, the percentage of alcohol in the new mixture would be : (A) 15% (C) 17%
2 % 3 1 (D) 18 % 2 (B) 16
26. The side of a triangle are in the ratio
2 : 3 : 4 and
its perimeter is 104 cm. The length of the longest side is : (A) 52 cm (B) 48 cm (C) 32 cm (D) 26 cm 27. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the students does not get scholarship ? (A) 56%
(B) 70%
(C) 78%
(D) 80%
PAGE # 37
28. The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of elctricity consumed. When in a certain month 540 units are consumed, the bill is Rs. 1800. In another month 620 units are consumed and the bill is Rs. 2040. In yet another month 500 units are consumed. The bill for that month would be : (A) Rs. 1560
(B) Rs. 1680
(C) Rs. 1840
(D) Rs. 1950
29. Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it ? (A) 58 kg
(B) 60 kg
(C) 64 kg
(D) 70 kg
30. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be : (A) 5 : 7
(B) 5 : 9
(C) 7 : 5
(D) 9 : 5
35. A, B and C enter into a partnership in the ratio
7 4 6 : : . 2 3 5
After four months, A increase his share by 50%. If the total profit at the end of one year be Rs. 21,600, then B’s share in the profit is : (A) Rs. 2100 (B) Rs. 2400 (C) Rs. 3600 (D) Rs. 4000
1 1 of the capital for of the 6 6 1 1 time, B invests of the capital for of the time and 3 3
36. In a partnership, A invests
C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, B’s share is : (A) Rs. 650 (B) Rs. 800 (C) Rs. 960 (D) Rs. 1000 37. Manick received Rs.6000 as his share out of the total profit of Rs. 9000 which he and Raunak earned at the end of one year. If Manick invested Rs. 20,000 for 6 months, whereas Raunak invested his amount for the whole year, what was the amount invested by Raunak ? (A) Rs. 4000 (B) Rs. 5000 (C) Rs. 6000 (D) Rs. 10,000
31. Four milkmen rented a pasture. A grazed 24 cows for 3 months, B 10 cows for 5 months, C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is Rs. 720, find the total rent of the field. (A) Rs. 3100
(B) Rs. 3150
(C) Rs. 3200
(D) Rs. 3250
32. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B’s share in the total profit of Rs. 25,000. earned at the end of 2 years from the starting of the business ? (A) Rs. 7,500
(B) Rs. 9,000
(C) Rs. 9,500
(D) Rs. 10,000
33. Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was gain of Rs. 4005, then what will be the share of Kamal ? (A) Rs. 890
(B) Rs. 1335
(C) Rs. 1602
(D) Rs. 1780
34. A and B start a business with investment of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of year they earn a profit of Rs. 5080. Find the share of each member in the profit. (A) A – Rs. 1400, B – Rs. 1900, C – Rs. 1780 (B) A – Rs. 1600, B – Rs. 1800, C – Rs. 1680 (C) A – Rs. 1800, B – Rs. 1500, C – Rs. 1780 (D) None of these
38. A and B start a business jointly. A invests Rs. 16,000 for 8 months and B remains in the business for 4 months. Out of total profit, B claims
2 of the profit. How much 7
money was contributed by B ? (A) Rs. 10,500 (B) Rs. 11,900 (C) Rs. 12,800 (D) Rs. 13,600 39. Two friends P and Q started a business investing in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s. At the end of the year, 20% profit was earned which was equal to Rs. 98,000. What was the amount invested by R ? (A) Rs. 1,05,000 (B) Rs. 1,75,000 (C) Rs. 2,10,000 (D) None of these 40. A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another Rs. 2,70,000 and C at the end of 2 years, also invests Rs. 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of C. (A) Rs. 2,70,000 (B) Rs. 1,80,000 (C) Rs. 3,60,000 (D) None of these 41. In a mixture of 100 L, the ratio of milk and water is 3 : 1. If 200 L of water is added to the mixture, what is the new ratio of milk and water ? (A) 1 : 3 (B) 3 : 1 (C) 2 : 5 (D) 5 : 2 42. 80 L of mixture of milk and water is in the ratio 5 : 3. If 16 L of this mixture is replaced by 16 L of milk, ratio of milk and water becomes : (A) 2 : 1 (B) 6 : 3 (C) 7 : 3 (D) 8 : 3 PAGE # 38
43. In a mixture of 28 L, the ratio of milk and water is 2 : 5. If 2 L of milk is added and 5 L of water is removed from the mixtures, find the new ratio. (A) 9 : 20
(B) 1 : 4
(C) 2 : 3
(D) 3 : 2
44. How many kg. of wheat costing Rs.8 per kg must be mixed with 36 kg of rice costing Rs.5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs.7.20 per kg ? (A) 10.08 kg
(B) 8.6 kg
(C) 9.2 kg
(D) 10.8 kg
45. In what ratio must water be mixed with milk costing Rs.12 per litre to obtain a mixture worth of Rs.8 per litre ? (A) 1 : 2
(B) 2 : 1
(C) 2 : 3
(D) 3 : 2
4 46. A tin of oil was full. When six bottles of oil were taken 5
3 full. 4 How many bottles of oil did the tin contain initially ?
out and four bottles of oil were poured in, it was
(A) 16
(B) 40
(C) 32
(D) None of these
47. In what ratio must rice at Rs. 9.30 per kg mixed with
51. Two varieties of soda water with different prices is mixed in the ratio of 2 : 3. The price of first soda water is Rs. 10 per litre while the price of second soda water is Rs. 15 per litre, respectively. The average price of the mixture (per litre) is : (A) Rs. 12 (B) Rs. 13 (C) Rs. 14 (D) Rs. 15 52. 5 kg of superior quality of sugar is mixed with 25 kg of inferior quality sugar. The price of superior quality and inferior quality sugar is Rs. 18 and Rs. 12 respectively. The average price per kg of the mixture is : (A) Rs. 13 (B) Rs. 15 (C) Rs. 18 (D) Rs. 21 53. 16 litres of kerosine is mixed with 5 litres of petrol. The price of kerosine is Rs. 12 per litre and the price of petrol is Rs. 33 per litre. The average price of the mixture per litre is : (A) Rs. 15 (B) Rs. 17 (C) Rs. 23 (D) Rs. 27 54. Avinash covered 150 km distance in 10 hours. The first part of his journey he covered by car, then he hired a rickshaw. The speed of car and rickshaw is 20 km/hr and 12 km/hr respectively. The ratio of distances covered by car and the rickshaw respectively are : (A) 2 : 3 (B) 4 : 5 (C) 1 : 1 (D) None of these
rice at Rs.10.80 per kg so that the mixture be worth Rs.10 per kg ? (A) 7 : 8
(B) 6 : 7
(C) 7 : 6
(D) 8 : 7
48. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? (A) 26.34 litres
(B) 27.36 litres
(C) 28 litres
(D) 29.16 litres
49. A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and
55. A mixture of rice is sold at Rs. 3.00 per kg. This mixture is formed by mixing the rice of Rs. 2.10 and Rs. 2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned. (A) 5 : 2 (B) 2 : 7 (C) 2 : 5 (D) 15 : 8 56. The ratio of expenditure and savings is 3 : 2. If the income increase by 15% and the savings increases by 6%, then by how much percent should his expenditure increases ? (A) 25 (B) 21 (C) 12 (D) 24
the can is filled with B, the ratio A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially? (A) 10
(B) 20
(C) 21
(D) 25
50. You have a measuring cup with capacity 25 ml and another with capacity 110 ml, the cups have no markings showing intermediate volumes. Using large container an as much tap water as you wish. W hat is the smallest amount of water you can measure accurately ? (A) 1 ml
(B) 5 ml
(C) 10 ml
(D) 25 ml
57. 450 litres of a mixture of milk and water contain the milk and water in the ratio 9 : 1. How much water should be added to get a new mixture containing milk and water in the ratio 3 : 1 ? (A) 54 (B) 90 (C) 45 (D) 63 58. The ratio of petrol and kerosine in the container is 3 : 2 when 10 litres of the mixture is taken out and is replaced by the kerosine, the ratio becomes 2 : 3. The total quantity of the mixture in the container is : (A) 25 (B) 30 (C) 45 (D) Cannot be determined
PAGE # 39
59. From a container, 6 litres milk was drawn out and was
60. The average weight of boys in a class is 30 kg and the
replaced by water. Again 6 litres of mixture was drawn
average weight of girls in the same class is 20 kg. If
out and was replaced by the water. Thus the quantity of
the average weight of the whole class is 23.25 kg,
milk and water in the container after these two
what could be the possible strength of boys and girls
operations is 9 : 16. The quantity of mixture is :
respectively in the same class ?
(A) 15
(B) 16
(A) 14 and 26
(B) 13 and 27
(C) 25
(D) 31
(C) 17 and 27
(D) None of these
PAGE # 40
CONTROL AND COORDINATION PLANT HORMONES/PHYTOHORMONES Living organisms respond and react to their external environment. Plants do not have any special structure for perception of stimuli. In plants control and coordination is performed by chemical substances known as plant hormones or phytohormone. Phytohormones are of five types namely Auxins, Gibberellins, Cytokinins, Abscisic Acid (ABA) and Ethylene. (a) Auxin :
• • • • •
Indole acetic acid is the principal naturally occurring auxin found in all plants including fungi. Auxin initiate as well as promote cell division, cell elongation, root formation. Causes apical dominance and prevents abscission layer. Initiation of flowering. Synthetic auxins are resistant to oxidation by enzymes some are widely used to regulate various aspects of plant development. They are more effective & have greater stability than indole acetic acid (I.A.A). e.g. 2, 4 - D (b) Gibberellins :
• • • •
Significant elongation of internodes. Leaf expansion • Reversal of dwarfism Breaking dormancy • Parthenocarpy Flowering (c) Cytokinin :
• • • •
Promote cell division Counteraction of apical dominance Delay of senescence Delay of senescence - Disappearance of chlorophyll and degradation of proteins are two important symptoms of senescence. Cytokinins delay these processes & thus the senescence is also delayed. This effect of cytokinins is known as Richmond - lang effect.
(d) Ethylene :
• • •
Promotes fruit growth and ripening Promotes seed germination Promotes abscission of leaves, flowers and fruits. (e) Abscissic Acid :
• • •
Promotes abscission, senescence, bud dormancy Growth inhibition ABA suppresses the growth promoting effects of gibberellins and hence is also known as antigibberellins.
PLANT MOVEMENTS Movement of plant towards the direction of stimulus is called tropism. Bending of plant towards light is called phototropism. Shoot of plants show positive phototropism. Downward movement is in response to gravitational force is called geotropism. Roots of plants shows positive geotropisms, stems show negative geotropism. Such movements in plants which are caused by external stimuli but are not directional are called nastic movements (such as in touch-me-not plant). - Mimosa pudica
PHOTOPERIODISM Flowering and germination of seeds in plants is controlled by duration of day light (photoperiod). This phenomenon is called photoperiodism. On the basis of length of photoperiod requirements of plants, they have been classified into. (i) Short day plants — Xanthium (ii) Long day plants — Spinach, Radish (iii) Day neutral plants — Cotton, sunflower Response of plants to photoperiodic stimulus is due to a specialized pigment phytochrome.
Fig : Requirement of light and dark periods during 24 hours for flowering in short day, long day and day neutral plants.
PAGE # 41
CONTROL AND COORDINATION IN ANIMALS Animals receive external information through specialized structure called sense organs (receptors). These are photoreceptors for light, phonoreceptor for sound and olfactoreceptors for smell. Control and coordination is achieved by two systems (a) endocrine system (b)) nervous system Table : Differences Between Exocrine and Endocrine Glands. Exocrine glands 1 Exocrine glands have ducts .
Endocrine glands Endocrine glands are ductles s .
2 Thes e glands dis charge their s ecretions into the Thes e glands dis charge their s ecretions directly ducts . into the blood. Thes e glands are pres ent far away from the s ite 3 Thes e glands are pres ent near the s ite of action. Exam ples : Sweat and oil glands of s kin, s alivary of action. glands , etc. Exam ples : Pituitary, thyroid, hypothalam us , etc.
Table : Differences Between Hormones and Enzymes.
Hormones
Enzymes
1 Hormones are peptides, proteins, derivatives and steroids in nature.
amino
acid All enzymes, are complex proteins.
2 They have low molecular weight.
They have very high molecular weight.
3 They are secreted by cells at one site and pass into They are secreted by cells and may act in the cells blood to another site to act. themselves or pass via ducts to act in some cavity in the body. 4 They are used up in their action. 5 Hormone-controlled reactions are not reversible.
They are not used up in their action. Enzymes-controlled reactions are reversible.
6 Hormones are effective in low concentration. Their Enzymes also act in low concentration. However, excess or deficiency may cause physiological the rate of enzymes-catalysed reactions steadily increase disorders. with an increase in their concentration. 7 They may act slowly or quickly. 8 Hormones may accelerate or physiological processes. •
They act slowly. inhibit
specific Enzymes speed up the biochemical reactions.
Similarities between hormones and enzymes : 1. Both are synthesized in body. 2. Both are not stored in body.
3. Both are required in minute quantities.
Table : Summary of the Effect of Hypersecretion and Hyposecretion of Some Important Endocrine Glands. Glands and Hormones
Hypersecretion
Hyposecretion
1. Pituitary GH ADH
Gigantism In child; Acromegaly in adulthood
2. Thyroid Thyroxine
Exophthalm ic Goitre
Cretinism in young, Myxoedema in adults .
3. Parathyroid PTH
Decalcification of bones ; increas e calcium level.
Tetany; low calcium and high phos phate levels .
Hypertens ion
Conn's disease.
Cushings' disease
Addison's disease.
4. Adrenal (i) Mineralocorticoid (aldos terone) (ii) Glucocorticoid (cortis one) (iii) Adrenaline (iv) Noradrenaline 5. Pancreas Ins ulin
Dw arfism in child. Diabetes insipidus
Hypertens ion Increas es blood pres s ure. Decreas e in blood glucos e level.
Increas e in blood glucos e level hyperglycemia; diabetes mellitus.
PAGE # 42
Nervous system in vertebrates is highly evolved and comprises of (1) Central Nervous System (2) Peripheral Nervous system (3) Autonomic nervous system
•
•
The central nervous system comprises of : (i) Brain (ii) Spinal cord
•
•
Peripheral nervous system consists of two sets of nerves : 1. Cranial nerves — 12 pairs 2. Spinal nerves — 31 pairs
Spinal Nerves Cervical Thoraic Lumbar Sacral Coccygeal
– 8 Pairs – 12 Pairs – 5 Pairs – 5 Pairs — 1 Pairs
The Autonomic nervous system comprises of : 1. Sympathetic nervous system — Thoracico-lumbar outflow 2. Parasympathetic nervous system — Cranio sacral outflow The action of sympathetic and parasympathetic nervous system is antagonistic to each other. Both interact and maintain homeostasis inside the body.
Table : Functions of Autonomic Nervous System. S.No. Organs
Sympathetic system
Parasympathetic system
Heart
accelerates heart beat
retards heart beat
Blood vessels
constricts all blood vessels except coronary vessels which are dilated
dilates all blood vessels except coronary vessels which are constricted
3.
Lungs
dilates bronchi and bronchioles
constricts bronchi and bronchioles
4.
Intestines
peristalsis decreased
peristalsis increased
Urinary bladder
sphincter contraction, muscle relaxed
Pupil of eye
dilation
sphincter relaxation, muscle contraction (feeling to urinate) constriction
Salivary glands
inhibits secretion of saliva (dryness of mouth) stimulates secretion
1. 2.
5. 6. 7.
stimulates secretion of saliva
8. 9.
Lacrimal (tear) glands
Arrector (or erector) pili stimulates contraction (hairs raised) (hair) muscles of skin
relaxes (hairs flattened)
10.
Body (as a whole)
prepares body for relaxation
prepares body for action
inhibits secretion
REFLEX ACTION AND REFLEX ARC You must have experienced a sudden withdrawl of a body part which comes in contact with objects that are extremely hot, cold, pointed or animals that are scary or poisonous. The entire process of response to a peripheral nervous stimulation, that occurs involuntarily, i.e., without conscious effort or thought and requires the involvement of a part of the central nervous system is called a reflex action.
Diagrammatic Presentation of Reflex Action (Showing Jerk Reflex)
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Mammals show a wide range of reflexes which can be broadly classified into two types : unconditioned and conditioned reflexes. (a) Unconditioned reflexes : Even when the body has no past experience of a stimulus it still responds spontaneously and such responses or actions are called unconditioned reflexes. These are responses to a natural unconditioned stimulus. The examples of unconditioned reflexes are the blinking of an eye when a particle of dust touches the eyelids, excitement of the salivary glands after seeing the food, etc. Other reflex actions are shown in the Table. These reflexes are said to be unconditioned or inborn because they are a natural part of an animal’s make up. Another class of reflex produced by the previous experience of an animals is considered below. (b) Conditioned reflexes : When a reflex which does not naturally exist had becomes a part of the animal behaviour. Such a reflex is said to be conditioned. Conditioned reflex were first demonstrated by the Russian physiologist, Pavlov. The cerebrum controls the conditioned reflexes.
Reflex
Pavlov’s experiment on dog to show conditional reflex.
Table Showing Different Unconditioned Reflex Actions.
Stimulus
Blinking Swallowing Sneezing and coughing
Knee-jerk
Response
Foreign in body on surface of eye. Food touches sensitive spot at back of pharynx. Foreign particle irritating lining of nose or larynx.
Eyelids close and eye "waters". Peristaltic waves pass down oesophagus. Chest muscles and diaphragm contract and relax violently to produce a gust of air. Sharp tap of tendon below knee-cap of Leg 'kicks' up. crossed leg.
Differences between Unconditioned and Conditioned Reflexes
Unconditioned reflexes 1. Unconditioned reflexes are inborn (hereditary). 2. Learning does not form the basis of unconditioned reflexes. 3. These are mainly protective in function. Examples : Breast feeding and swallowing in newly born babies, blinking of eyes, sneezing and coughing and knee-jerk, etc.
Conditioned reflexes 1. Conditioned reflexes are acquired after birth. 2. Learning forms the basis of conditioned reflexes. Examples : Withdrawal of limb when it is touched by hot things, typing, riding a bicycle, knitting, etc.
KNOWLEDGE BOOSTERS
• • • • • • • • •
The smallest cranial nerve is trochlear in human. The largest cranial nerve is trigeminal in human. Protein hormones are secreted by : Parathyroid • Pituitary Hypothalamus • Pancreas Steroid hormones are secreted by : Adrenal cortex Gonads Amino acids derived hormones are secreted by : Thyroid gland Adrenal medulla Pineal gland
EXERCISE 1.
Photoperiodic stimulus is picked up by : (A) Phytochrome (B) Phytohormones (C) Stomata (D) Enzymes
2.
Posterior lobe of pituitary gland secretes following hormones : (A) ADH (B) MSH (C) Oxytocin (D) Both (A) and (C)
3.
Smallest cranial nerve is : (A) Trochlear (B) Trigeminal (C) Facial (D) Hypoglossal
PAGE # 44
4.
Hormones of pituitary gland are : (A) All steroids (B) All proteins (C) Some steroids and some proteins (D) Complex substances formed from proteins, steroids, carbohydrates
5.
Parasympathetic nervous system is not involved in : (A) Peristalsis (B) Secretion of Saliva (C) Dilation of pupil (D) Excitation of reproductive organs
6.
Which is not a reflex action ? (A) Swallowing of food (B) Shivering in cold (C) Both A and B (D) None of these
7.
What is common in following substances ? (i) acetylcholine (ii) noradrenaline (iii) serotonin (A) All are chemical transmitters (B) All are antidiuretic drugs (C) All are blood pressure-lowering drugs (D) None of the above
8.
Conn’s disease is caused due to : (A) ADH (B) ACTH (C) Aldosterone (D) None of these
9.
Which one of the following four glands is correctly matched with the accompanying description ? (A) Thyroid - hyperactivity in young children causes cretinism (B) Thymus- starts undergoing atrophy after puberty (C) Parathyroid - secretes parathormone which promotes movement of calcium ions from blood into bones during calcification. (D) Pancreas - Delta cells of the islets of Langerhans secrete a hormone which stimulates glycolysis in liver.
10. Which of the following diseases is not related to thyroid gland ? (A) Myxoedema (B) Cretinism (C) Acromegaly (D) Goitre 11. The thyroid gland secretes thyroxine hormone. Function of thyroxine is : (A) It increases metabolic rate and maintains BMR. (B) It promotes growth of the body tissues and brain (C) It stimulates differentiation of tissue (D) All of the above 12. Glucagon is secreted from which cells of islet of Langerhans ? (A) – cells (B) – cells (C) – cells (D) Both and – cells 13. Outer part of cerebrum that is called as cerebral cortex is made up of : (A) Grey matter (B) White matter (C) Both A & B (D) None of the above
14. Watering of mouth to see good food is : (A) Unconditioned reflex action (B) Conditioned reflex action (C) Spinal reflex (D) None of the above 15. On surgical removal of pituitary gland there is fall in Na+ level & rise in K+ in serum, this is due to : (A) Oxytocin is no longer available from pituitary (B) Atrophy of adrenal medulla (C) Atrophy of adrenal cortex (D) LTH from pituitary is no longer available 16. Prevention of senescence is not a function of : (A) Auxins (B) Gibberelins (C) Ethylene (D) Abscissic acid 17. Gibberelic acid takes part in : (A) Bolting of rosette plants (B) Replacing long day requirement (C) Overcome genetic dwarfism (D) All the above 18. Which of the mammalian cells usually do not divide in adult life ? (A) Epithelial cells in lung (B) Nerve cell in brain (C) Liver cells (D) Osteoblast cells 19. Receptors for Neurotransmitter are located on the : (A) Cell surface (B) Nucleus (C) Endosome (D) Golgi apparatus 20. IAA was first isolated from : (A) Corn germ oil (B) Gibberella (C) Human urine (D) Rhizopus 21. Which of the following graphs accurately represents the insulin levels (Y-axis) in the body as a function of time (X-axis) after eating sugar and bread/roti ? [KVPY 2010]
(A)
(B)
(C)
(D)
22. The cell that transfers information about pain to the brain is called a [KVPY 2011] (A) neuron (B) blastocyst (C) histoblast (D) vitamins
PAGE # 45
PRINT CULTURE AND THE MODERN WORLD THE FIRST PRINTED BOOKS The imperial state in China was, for a very long time, the major producer of printed material. China possessed a huge bureaucratic system which recruited its personnel through civil service examinations. Textbooks for this examination were printed in vast numbers under the sponsorship of the imperial state. From the sixteenth century, the number of examination candidates went up and that increased the volume of print. This new reading culture was accompanied by a new technology. W estern printing techniques and mechanical presses were imported in the late nineteenth century as Western powers established their outposts in China. Shanghai became the hub of the new print culture, catering to the Western-style schools. From hand printing there was now a gradual shift to mechanical printing.
the system. The first book he printed was the Bible. About 180 copies were printed and it took three years to produce them. By the standards of the time this was fast production. In the hundred years between 1450 and 1550, printing presses were set-up in most countries of Europe. Printers from Germany travelled to other countries, seeking work and helping start new presses. As the number of printing presses grew, book production boomed. The second half of the fifteenth century saw 20 million copies of printed books flooding the markets in Europe. The number went up in the sixteenth century to about 200 million copies.
THE PRINTING REVOLUTION AND ITS IMPACT (i)
Print in Japan: Printing of visual material led to interesting publishing practices. In the late eighteenth century, in the flourishing urban circles at Edo (later to be known as Tokyo), illustrated collections of paintings depicted an elegant urban culture, involving artists, courtesans, and teahouse gatherings. Libraries and bookstores were packed with hand-printed material of various types-books on women, musical instruments, calculations, tea ceremony, flower arrangements, proper etiquette, cooking and famous places.
But the transition was not so simple. Books could be read only be the literate and the rates of literacy in most European countries were very low till the twentieth century. How then, could publishers persuade the common people to welcome the printed book? To do this, they had to keep in mind the wider reach of the printed work: even those who did not read could certainly enjoy listening to books being read out. So printers began publishing popular ballads and folk tales, and such books would be profusely illustrated with pictures. These were then Bung and recited at gatherings in villages and in taverns in towns.
PRINT COMES TO EUROPE The Production of handwritten manuscripts could not satisfy the ever-increasing demand for books. Copying was an expensive, laborious and time-consuming business. Manuscripts were fragile, awkward to handle, and could not be carried around or read easily. Their circulation therefore remained limited. With the growing demand for books, wood block printing gradually became more and more popular. By the early fifteenth century; woodblocks were being widely used in Europe to print textiles, playing cards, and religious pictures with simple, brief texts. There was clearly a great need for even quicker and cheaper reproduction of texts. This could only be with the invention of a new print technology. The breakthrough occurred at 8trasbourg where Johann Gutenberg developed the first-known printing press in the 1430s. Gutenberg and the Printing Press: Gutenberg adapted existing technology to design his innovation. The olive press provided the model for the printing press and moulds were used for casting the metal types for the letters ofthe alphabet. By 1448, Gutenberg perfected
A New Reading Public: Access to books created a new culture of reading. Earlier, reading was restricted to the elites. Common people lived in a world of oral culture. They heard sacred texts read out, ballads recited, and folk tales narrated. Knowledge was transferred orally. People collectively heard a story or saw a performance. As you will see in Chapter 8, they did not read a book individually and silently. Before the age of print books were not only expensive but they could not be produced in sufficient numbers. Now books could reach out to wider sections of people. If earlier there was a hearing public, now a reading public came into being.
(ii)
Religions Debates and the Fear of Print : Print created the possibility of wide circulation of ideas and introduced a new world of debate and discussion. Even those who disagreed with established authorities could now print and circulate their ideas. Through the printed message, they could persuade people to think differently, and move them to action. This had significance in different spheres of life. In 1517, the religious reformer Martin Luther wrote Ninety Five Theses criticising many of the practices and rituals of the Roman Catholic Church. A printed PAGE # 46
copy of this was pasted on a church door in Wittenberg. It challenged the Church to debate his ideas. Luther's writings were immediately reproduced in vast numbers and read widely. This lead to a division within the Church and to the beginning of the Protestant Reformation. Luther's translation of the New Testament sold 5,000 copies within a few weeks and a second edition appeared within three months. Deeply grateful to print, Luther said, 'Printing is the ultimate gift of God and the greatest one.' Several scholars, in fact, think that print brought about a new intellectual atmosphere and helped spread the new ideas that led to the Reformation. (iii) Print and Dissent : In the sixteenth century, Manocchio, a miller in Italy, began to read books that were available in his locality: he reinterpreted the message of the Bible and formulated a view of God and Creation that enraged the Roman Catholic Church. When the Roman Church began its inquisition to repress heretical ideas. Manocchio was hauled up twice and ultimately executed. The Roman Church, troubled by such effects of popular readings and questionings of faith, imposed severe cont over publishers and booksellers and began to maintain an Index rohibited Books from 1558.
THE READING MANIA The seventeenth and eighteenth centuries literacy rates went up in most parts of Europe. Churches of different denominations set up schools in villages, carrying literacy to peasants and artisans. By the end of the eighteenth century, in some parts of Europe literacy rates were is high as 60 to 80 per cent. As literacy and schools spread in European countries, there was a virtual reading mania. People wanted books to read and printers produced books ever increasing numbers.
Voltaire and Rousseau, they were also exposed to monarchical and Church propaganda. They were not influenced directly by everything they read or saw. They accepted some ideas and rejected oth~rs. They interpreted things their own way. Print did not directly shape their minds, but it did open up the possibility of thinking differently.
THE NINETEENTH CENTURY (i)
Children, Women and Workers : A children's press, devoted to literature for children alone, was set up in France in 1857. This press published new works as well as old fairy tales and folk tales. The Grimm Brothers in Germany spent years compiling traditional folk tales gathered from peasants. What they collected was edited before the stories were published in a collection in 1812. Anything that was considered unsuitable for children or would appear vulgar to the elites, was not included in the published version. Rural folk tales thus acquired a new form. In this way; print recorded old tales but also changed them. When novels began to be written in the nineteenth century, women were seen as important readers. Some of the best-known novelists were women: Jane Austen, the Bronte sisters, George Eliot. Their writings became important in defining a new type of women: a person with will, strength of personality, determination and the power to think. In the nineteenth century, lending libraries in England became instruments for educating whitecollar workers, artisans and lower-middle-class people. Sometimes, self-educated working class people wrote for themselves. After the working day was gradually shortened from the mid-nineteenth century, workers had some time for selfimprovement and self-expression. They wrote political tracts and autobiographies in large numbers.
New forms of popular literature appeared in print, targeting new audiences. Bookseller employed padlars who roamed around villages, carrying little books for sale. There we almanacs or ritual calendars, along with ballads and folktale. But other forms of reading matter, largely for entertainment, began to reach ordinary readers as well. In England penny chapbooks were carried by petty pedlars known as chapmen, and sold for a penny, that even the poor could buy them. In France, were the 'Biliotheque Blue', which were low priced small books printed on poor quality paper and bound in cheap blue covers. Then the were the romances, printed on four to six pages and the more substantial 'histories' whi were stories about the past. Books were of various sizes, serving many different purpose an interests.
(ii) Further innovations : By the mid-nineteenth century, Richard M. Hoe of New York had perfected the power-driven cylindrical press. This was capable of printing 8,000 sheets per hour. This press was particularly useful for printing newspapers. In the late nineteenth century, the offset press was developed which could print up to six colours at a time. From the turn ofthe twentieth century, electrically operated presses accelerated printing operations. A series of other developments followed. Methods of feeding paper reels and photoelectric controls of the colour register were introduced. The accumulation of several individual mechanical improvements transformed the appearance of printed texts.
There can be no doubt that print helps the spread of ideas. But we must remember that people did not read just one kind of literature. If they read the ideas of
Nineteenth century periodicals serialised important novels, which gave birth to a particular way of writing novels. In the 1920s in England, popular works were sold in cheap series, called PAGE # 47
the Shilling Series. The dust cover or the book jacket is also a twentieth century innovation. With the onset of the Great Depression in the 1930s, publishers feared a decline in book purchases. To sustain buying, they brought out cheap paperback editions.
INDIA AND THE WORLD OF PRINT (i)
Manuscripts before the Age of Print : India had a very rich and old tradition of handwritten manuscripts-in Sanskrit, Arabic, Persian, as well as in various vernacular languages. Manuscripts were copied on palm leaves or on handmade paper. Pages were sometimes beautifully illustrated. They would be either pressed between wooden covers or sewn together to ensure preservation. Manuscripts continued to be produced till well after the introduction of print, down to the late nineteenth century. Manuscripts were not widely used in everyday life. Even though pre-colonial. Bengal had developed an extensive network of village primary schools, students very often did not read texts. They only learnt to write. Teachers dictated portions of texts from memory and students wrote them down. Many thus became literate without ever actually reading any kinds of texts.
(ii) Print Comes to India : The printing press first came to Goa with Portuguese missionaries in the midsixteenth century. Jesuit priests learnt Konkani and printed several tracts. By 1674, about 50 books had been printed in the Konkani and in Kanara languages. Catholic priests printed the first Tamil book in 1579 at Cochin and in 1713 the first Malayalam book was printed by them. By 1710, Dutch Protestant missionaries had printed 32 Tamil texts, many of them translations of older works. The English language press did not grow in India till quite late even though the English East India Company began to import presses from the late seventeenth century. Governor-General Warren Hastings persecuted Hickey, and encouraged the publication of officially sanctioned newspapers that could counter the flow of information that damaged the image of the colonial government. By the close of the eighteenth century, a number of newspapers and journals appeared in print. There were Indians, too, who began to publish Indian newspapers. The first to appear was the weekly Bengal Gazatte, brought out by Gangadhar Bhattacharya, who was close to Rammohan Roy.
RELIGIOUS REFORMS AND PUBLIC DEBATES This was 'a time of intense controversies between social and religious reformers and the Hindu orthodoxy over matters like widow immolation, monotheism, Brahmanical priesthood and idolatry. In Bengal, as the debate developed, tracts and newspapers proliferated, circulating a variety of arguments. To reach a wider audience, the ideas were printed in the everyday, spoken language of ordinary people. Rammohan Roy published the Sam bad Kammaudi from 1821 and the Hindu orthodoxy commissioned the Samachar Chandrika to oppose his opinions. From 1822, two Persian newspapers were published. Jan-i-Jahan Nama and Shainsah Akhbar. In the same year, a Gujarati newspaper, the Bombay Samachar; made its appearance. In north India the ulama were deeply anxious about the collapse of Muslim dynasties. They feared that colonial rulers would encourage conversion, change the Muslim personal laws. To counter this, they used cheap lithographic presses, published Persian and Urdu translations of holy scriptures, and printed religious newspapers and tracts. The Deoband Saminary, founded in 1867, published thousands upon thousands of fatwas telling Muslim readers how to conduct themselves in their everyday lives, and explaining the meanings of Islamic doctrines. All through the nineteenth century, a number of Muslim sects and seminaries appeared, each with a different interpretation of faith, each keen on enlarging its following and countering the influence of its oponents. Urdu print helped them conduct these battles in public. Religious texts, therefore, reached a very wide circle of people, encouraging discussions, debates and controversies within and among different religions. Print did not only stimulate the publication of conflicting opinions amongst communities, but it also connected communities and people in different parts of India. Newspapers conveyed news from one place to another creating pan-Indian identities.
NEW FORMS OF PUBLICATION Other new literary forms also entered the world of reading-lyrics, short stories, essays about social and political matters. In different ways, they reinforced the new emphasis on human livel;l and intimate feelings, about the political and social rules that shaped such things. By the end of the nineteenth century, a new visual culture was taking shape. With the setting up of an increasing number of printing presses, visual images could be easily reproduced in multiple copies. Painters like Raja Ravi Varma produced images for mass circulation. Poor wood engravers who made woodblocks set up shop near the letterpresses, and were employed by print shops. Cheap prints and calendars, easily available in the bazaar, could be bought even by the poor to PAGE # 48
decorate the walls of their homes or places of work. These prints began shaping popular ideas about modernity and tradition, religion and politics and society and culture. (i)
Women and Print : Lives and feelings of women began to be written in particularly vivid and intense ways. Women's reading, therefore, increased enormously in middle-class homes. Liberal husbands and fathers began educating their womenfolk at home, and sent them to schools when women's schools were set up in the cities and towns after the mid· nineteenth century. Many journals began carrying writings by women and explained why women should be educated. They also carried a syllabus and attached suitable reading matter which could be used for homebased schooling. Since social reforms and novels had already created a great interest in women's lives and emotions, there was also an interest in what women would have to say about their own lives. From the 1860s, few Bengali women like Kailashbashini Debi wrote books highlighting the experiences of women-about how women were optioned at home, kept in ignorance, forced to hard domestic about and treated unjustly by the very people they served. In the 1880s, in present-day Maharashtra, Tarabia Shinde and Pandita amabai wrote with passionate anger about the miserable lives upper-caste Hindu women, especially widows. In Punjab, too, a similar folk literature was widely printed from the early twentieth century. Ram Chaddha published the fast-selling Istri Dharm Vichar to teach wom~n how to be obedient wives. The Khalsa Tract Society published cheap booklets with a similar message. Many of these were in the form of dialogues about the qualities of a good woman.
(ii) Print and the poor people : From the late nineteenth century, issues of caste discrimination began to be written about in many printed tracts and essays Jyotiba Phule, the Maratha pioneer of 'low caste' protest movements, wrote about the injustices of the caste system in his Gulamgiri (1871). In the twentieth century. B.R. Ambedkar in Maharashtra and E,V. Ramaswamy Naicker in Madras, better known as Periyar, wrote powerfully on caste and their writings were read by people all over India. Local protest movements and sects also created a lot of popular journal and tracts criticising ancient scriptures and envisioning a new and just future. Workers in factories were too overworked and lacked the education to write much about their experiences. But Kashibaba, a Kanpur mill worker, wrote and published Chhote Aur Bade Ka Sawal in 1938 to show the links between caste
and class exploitation. The poems of another Kanpur mill worker, who wrote under the name of Sudarshan ,Chakr between 1935 and 1955, were brought together and published in a collection called Sachi Kavitayan. By the 1930s Bangalore cotton mill workers set up libraries to educate themselves, following the example of Bombay workers. These were sponsored by social reformers who tried to restrict excessive drinking among them, to bring literacy and sometimes to propagate the message of nationalism.
PRINT AND CENSORSHIP By the 1820s, the Calcutta Supreme Court passed certain regulations to control press freedom and the Company began encouraging publications of newspapers that would celebrate British rule. In 1835, faced with urgent petitions by editors of English and vernacular Dewspapers, Governor-General Bentinick agreed to revise press laws. Thomas Macaulay a liberal colonial official, formulated new rules that restored the earlier freedoms. After the revolt of 1857, the attitude to freedom of the press changed. Enraged Englishmen demanded a clamp down on the 'native' press. As vernacular newspapers became assertively nationlist, the colonial government began debating measures of stringent control. In 1878, the Vernacular Press Act was passed, modelled on the Irish Press Laws. It proviged the JOvernment with extensive rights to censor reports and editorial in the vernacular press. From now on the government kept regular track of the vernacular newspapers published in .different provinces. When a report was judged as seditious, the newspaper was warned, and if the warning was ignored, the press was liable to be seized and the printing machinery confiscated.
1. The first biography, ‘Amar Jiban’ in 1876 in Bengali language was written by (A) Bibi Fatima. (B) Pandita Ramubai. (C) Kumardevi. (D) Rashsuindari Debi. 2. What led to the production of children’s literature in nineteenth century in Europe? (A) Primary education became compulsory from the nineteenth century. (B) Demand increased for children’s books. (C) New schools were opened. (D) New story books were published. 3. The first printed edition of the Ramcharitmanas of Tulsidas, came out from Calcutta in the year (A) 1810 (B) 1813 (C) 1816 (D) 1817 4. Kitagawa Utamaro contributed to an art form called (A) Jomon (B) Kofun (C) ukiyo (D) Yayoi PAGE # 49
5. The oldest Japanese book printed in AD 868 is the Buddhist (A) Bronze Sutra (B) Diamond Sutra (C) Gold Sutra (D) Silver Sutra 6. The term, ‘Vellum’ refers to the (A) paper made from wood (B) parchment made from the skin of animals (C) parchment made of leaves (D) wood-pulp material 7. Erasmus, a Latin scholar and a Catholic reformer, who criticised the excesses of Catholicism, expressed a deep anxiety about printing in his book (A) Adages (B) Confessiones (C) De Doctrina Christiana (D) De civitate dei 8. The Gita Govinda was written by (A) Jayadeva (B) Jayagonda (C) Kalhana (D) Valmiki 9. Criticizing many of the practices and rituals of the Roman Catholic Church, in 1517 the religious reformer Martin Luther wrote (A) Sixty Five Theses (B) Seventy Five Theses (C) Eighty Five Theses (D) Ninety Five Theses 10. “The Gita Govinda” was written by Jayadeva in the (A) Sixteenth century. (B) Seventeenth century. (C) Eighteenth century (D) Nineteenth century. 11. The collected works known as “Diwan” were written by (A) Hafiz. (B) Hajj Zayn. (C) Iraj Bashiri. (D) Mubariz Muzaffar. 12. Penny chapbooks were sold by petty pedlars known as chapmen in (A) England (B) France. (C) Germany. (D) Italy. 13. ‘Almanacs’ are the (A) astronomical calendars. (B) astrological calendars. (C) regional calendars. (D) ritual calendars. 14. “The Forbidden Best- Sellers of Pre-Revolutionary France” was a book written by (A) Maxim Gorky. (B) Robert Darnton. (C) William Bolts. (D) John Kingston. 15. The first Indian weekly “Bengal Gazette” was edited by (A) Gangadhar Bhattacharya. (B) James Augustus Hickey (C) Rammohun Roy. (D) Raja Ravi Varma 16. The Penny magazine was published especially for the (A) business men (B) children (C) women (D) workers
17. Who of the following published first weekly magazine in India, Bengal Gazette in 1780? (A) James Augustus Hickey. (B) Warren Hastings. (C) Gangadhar Bhattacharya. (D) Ram Mohan Roy. 18. Jyotiba Phule, the Maratha pioneer of ‘low caste’ protest movements, wrote about the injustices of the caste system in his (A) Brahmananche Kasab (B) Gulamgiri (C) Shetkarayacha Aasud (D) Tritiya Ratna 19. The Chinese city that became a new centre of printing technology in the nineteenth century was (A) Beijing (B) Tonkin (C) Shanghai (D) Yenan 20. Who introduced woodblock printing from China to Europe, especially in Italy? (A) Nicolo Conti. (B) Abdul Razzak. (C) Marco Polo. (D) Chrisher Columbus. 21. Who developed first known printing press in Strasbourg, Germany? (A) John Shelly. (B) John Suleiman. (C) Johann Guttenberg. (D) John S. Mill. 22. Which was the first book published by Gutenberg by using printing technology? (A) Quran (B) Bible (C) Hebrew book (D) Story book 23. Which one of the following led to the print revolution in world? (A) Hand printing. (B) Manuscript writing. (C) Calligraphy. (D) Mechanical printing. 24. The first Tamil book was printed in 1579 at Cochin by the (A) Buddhist monks (B) Catholic priests (C) Hindu priests (D) Muslim Maulavis 25. The old name of Tokyo was (A) Edo (B) Hokkaido (C) Nippon -Koku (D) Nippon 26. The number of Tamil texts printed by the Dutch Protestant missionaries by 1710 was (A) 32 Tamil texts (B) 37 Tamil texts (C) 39 Tamil texts (D) 40 Tamil texts 27. The folk tales and stories from the peasants in Germany in 1812 were published by the (A) Graham Brothers (B) Grimm Brothers (C) Hnery Brothers (D) Stephen Brothers 28. Who of the following, by the end of nineteenth century, produced mass images for circulation among the public? (A) V.B. Cama. (B) T.B. Rangachari. (C) Raja Ravi Verma. (D) Hari Sen. 29. Which one of the following journals was published in the late nineteenth century? (A) Bombay Gazzette. (B) Bengal Gazzette. (C) Indian Charivari. (D) Al-Hilal. PAGE # 50
30. The first biography, ‘Amar Jiban’ in Bengali language was written by (A) Bibi Fatima (B) Pandita Ramubai (C) Kumardevi (D) Rashsuindari Debi 31. In Bengal, an entire area in central Calcutta devoted to the printing of popular books was (A) Battala (B) Bga Bazaar (C) Boroline House (D) Girish Avenue 32. The book Istri Dharm Vichar was published by (A) Ram Chaddha (B) Ram Sharan Sharma (C) Ram Chandra Guha (D) Ram Shivashankar 33. Rammohun Roy published the ‘Sambad Kaumudi’ in (A) 1821. (B) 1822. (C) 1823. (D) 1824. 34. Folk tales and stories from the peasants in Germany in 1812 were published by the (A) Graham Company. (B) Grimm Brothers. (C) Music Germany. (D) Queens Publishing Company. 35. Begum Rokeya Sakhawat Hossein addressed the Bengal Women’s Education Conference in (A) 1926. (B) 1927. (C) 1928. (D) 1929. 36. Meaning of the term “Despotism” is (A) Rule of law (B) Absolute Individual power (C) Peopels’ power (D) Power of clergies 37. In the 1880s, in Maharashtra, Tarabai Shinde and Pandita Ramabai wrote about the miserable lives of (A) converted –Hindu women. (B) lower-caste Hindu women. (C) uneducated Hindu women. (D) upper-caste Hindu women. 38. The news paper ‘Kesari’ was started by the Indian freedom fighter (A) Balgangadhar Tilak. (B) Bipin Chandra Pal. (C) Dadabhai Naoroji. (D) Sri Aurobindo.
41. The meaning of “Calligraphy” is (A) kind of writing (B) ancient library (C) cultural practice (D) book binding 42. Who introduced hand-printing technology into Japan? (A) Buddhist missionaries (B) Christian missionaries (C) Muslim mulavis (D) Jainist missionaries 43. The Calcutta Supreme Court had passed certain regulations to control press freedom by (A) 1820’s. (B) 1830’s. (C) 1840’s. (D) 1850’s 44. The Statesman newspaper was established in the year (A) 1875. (B) 1876. (C) 1877. (D) 1878. 45. The Indian newspaper that refused a colonial government subsidy was the (A) Deccan Herald. (B) Hindu. (C) Friend of India. (D) Times of India. 46. “The Ramcharitmanas” was written by (A) Kambar. (B) Thiruvalluva. (C) Tulsidas. (D) Ved Vyas. 47. The power-driven cylindrical press was perfected by (A) J.V. Schley. (B) Johann Gutenberg. (C) Marco Polo. (D) Richard M. Hoe. 48. Bangalore cotton millworkers set up libraries to educate themselves following the example of (A) Bengal mill workers. (B) Bombay mill workers. (C) Kanpur mill workers. (D) Madras mill workers. 49. Bangalore cotton millworkers set up libraries to educate themselves by the (A) 1920s. (B) 1930s. (C) 1940s. (D) 1950s. 50. Raja Ravi Varma produced innumerable mythological paintings that were printed at the (A) Naval Kishore Press. (B) Navakali Press. (C) Ravi Varma Press. (D) Shri Venkateshwar Press.
39. In England, penny chapbooks were carried by petty pedlars known as (A) chapmen. (B) dealmen. (C) papermen. (D) salesmen.
51. Caricatures and cartoons published in journals and newspapers in India ridiculed (A) conventional Hindus. (B) educated Indians. (C) peasants. (D) orthodox women.
40. E.V. Ramaswamy Naicker from Madras is better known as (A) Acharya. (B) Guru. (C) Saint. (D) Periyar.
52. The Indian Charivari was a journal of caricature and satire published in the late (A) sixteenth century. (B) seventeenth century. (C) eighteenth century. (D) nineteenth century. PAGE # 51
53. The “Sacchi Kavitayan” a collection of poems was written by (A) Kailashbashini Debi (B) Kashibaba. (C) Ram Chaddha. (D) Sudarshan Chakr. 54. A new visual culture was taking shape in India by the end of the (A) sixteenth century. (B) seventeenth century. (C) eighteenth century. (D) nineteenth century. 55. The books “My Childhood” and “My University” were written by (A) Leo Tolstoy. (B) Maxim Gorky. (C) Mikhail Bhaktin. (D) Nikolai Gogol. 56. Punjab revolutionaries were deported in (A) 1905. (B) 1906. (C) 1907. (D) 1908. 57. The colonial rule’s attitude to freedom of the press in India changed after the (A) Chauri-Chaura incident of 1922. (B) Jallianwalla Bagh of 1919. (C) Non Cooperation Movement of 1920. (D) Revolt of 1857. 58. The Vernacular Press Act was passed in the year (A) 1875. (B) 1876. (C) 1877. (D) 1878. 59. The Vernacular Press Act of 1878 was modelled on the (A) Irish Brehon Laws. (B) Irish Coercion Laws. (C) Irish Restrictive Laws. (D) Irish Press Laws. 60. “Amar Jiban” is the autobiography of (A) Begum Rokeya Sakhawat. (B) Pandita Ramabai. (C) Rashsundari Debi. (D) Tarabai Shinde. 61. Rashsundari Debi wrote her autobiography “Amar Jiban” which was published in (A) 1875. (B) 1876. (C) 1877. (D) 1878. 62. The first full-length autobiography published in the Bengali language was (A) Amar Jiban. (B) Chhote Aur Bade Ka Sawal (C) Gulamgiri. (D) Istri Dharm Vichar. 63. Bengali women wrote books highlighting the experiences of women during the (A) 1850s. (B) 1860s. (C) 1870s. (D) 1880s.
64. The novel “Istri Dharm Vichar” was written by (A) Begum Rokeya Sakhawat. (B) Pandita Ramabai. (C) Ram Chaddha. (D) Tarabai Shinde. 65. The publication commissioned by the Hindu orthodoxy, to oppose Rammohun Roy’s opinions was the (A) Jam-i-Jahan Nama. (B) Samachar Chandrika. (C) Sambad Kaumudi. (D) Shamsul Akhbar. 66. Two Persian newspapers “Jam-i-Jahan Nama” and “Shamsul Akhbar” were published in the year (A) 1821. (B) 1822. (C) 1823. (D) 1824. 67. The Deoband Seminary was founded in (A) 1865. (B) 1866. (C) 1867. (D) 1868. 68. In the pre-revolution France, the print popularised the ideas of the (A) Christian thinkers. (B) conventional thinkers. (C) enlightenment thinkers. (D) traditional thinkers. 69. Kashibaba’s poems “Chhote Aur Bade Ka Sawal” showed the links between (A) caste and class exploitation. (B) illiteracy and caste. (C) illiteracy and class exploitation. (D) religion and caste. 70. The power-driven cylindrical press was capable of printing (A) 5,000 sheets per hour. (B) 6,000 sheets per hour. (C) 7,000 sheets per hour. (D) 8,000 sheets per hour. 71. The offset press developed in the late nineteenth century could print up to (A) five colours. (B) six colours. (C) seven colours. (D) eight colours. 72. In the 1920s, popular works were sold in cheap series, called the Shilling series in (A) England (B) France. (C) Germany. (D) Italy. 73. The art of beautifull and stylised writing is known as (A) calligraphy. (B) cartography. (C) lithography. (D) typography. 74. Hand-printing technology was introduced into Japan by (A) Buddhist missionaries. (B) Christian missionaries. (C) Muslim mulavis. (D) Jainist missionaries. PAGE # 52
75. Buddhist missionaries from China introduced handprinting technology in Japan around (A) AD 766-770. (B) AD 767-770. (C) AD 768-770. (D) AD 769-770.
78. The first book published by Gutenberg, by using printing technology was the (A) Avesta. (B) Bible. (C) Quran (D) Torah.
76. The Chinese city that became a new centre of printing technology was (A) Beijing. (B) Tonkin. (C) Shanghai. (D) Yenan.
79. The Penny magazines were written especially for (A) children. (B) women. (C) workers. (D) peasants.
77. ‘Vellum’ was a (A) paper made from wood. (B) parchment made from the skin of animals. (C) wood-pulp material. (D) product for paper making.
80. The first weekly magazine in India, ‘Bengal Gazette’ was published in 1780 by (A) Gangadhar Bhattacharya. (B) James Augustus Hickey. (C) Ram Mohan Roy. (D) Warren Hastings.
PAGE # 53
POWER SHARING Some of the elements of the Belgian model are–
BELGIUM AND SRI LANKA
(i)
(a) Ethnic composition of Belgium : A small country in Europe, It has borders with Netherlands, France and Germany. It has a population of a little over one crore. The ethnic composition of this small country is very complex. Of the country’s total population, 59 percent lives in the Flemish region and speaks Dutch language. Another 40 percent people live in the Wallonia region and speak French. Remaining 1 percent of the Belgians speak German. Problems– The minority French-speaking community was relatively rich and powerful. This led to tensions between the Dutch-speaking and French-speaking communities during the 1950s and 1960s. Brussels presented a special problem: The Dutch-speaking people constituted a majority in the country, but a minority in the capital.
(ii) Many powers of the central government have been given to state government of the two regions of the country. The state governments are not subordinate to the Central Government. (iii) Brussels has a separate government in which both the communities have equal representation. (iv) Apart from the Central and the State Government, there is a third kind of government. This ‘community government’
IS POWER SHARING DESIRABLE ? (a) Prudential Reason : Power sharing is good because it helps to reduce the possibility of conflict between social groups. Power sharing is a good way to ensure the stability of political order.
(b) Ethnic composition of Sri Lanka : The major social groups are the Sinhalaspeakers (74 percent) and the Tamil-speakers (18 percent). Among Tamils there are two subgroups. Tamil natives of the country are called ‘Sri Lankan Tamils’ (13 percent). The rest, are called ‘Indian Tamils’.There are about 7 percent Christians, who are both Tamil and Sinhala.
MAJORITARIANISM IN SRI LANKA Majoritarian measures to establish Sinhala supremacy : In 1956, an Act was passed to recognise Sinhala as the only official language, thus disregarding Tamil.A new constitution stipulated that the state shall protect and foster Buddhism. Outcomes/Problems that emerged : Majoritarianism has increased the feeling of alienation among the Sri Lankan Tamils. They felt that the constitution and government policies denied them equal political rights, discriminated against them in getting jobs and other opportunities and ignored their interests. By 1980s several political organisation were formed demanding an independent Tamil Eelam (state) in northern and eastern parts of Sri Lanka.
ACCOMMODATION IN BELGIUM Between 1970 and 1993, they amended their constitution four times so as to work out an arrangement that would enable everyone to live together
Constitution prescribes that the number of Dutch and French-speaking ministers shall be equal in the central government.
(b) Moral Reasons : Power sharing is the very spirit of democracy. A democratic rule involves sharing power with those affected by its exercise, and who have to live with its effects. People have a right to be consulted on how they are to be governed.
POWER SHARING Forms of Power Sharing :
Power sharing Among different organs of government
Among different social groups
Among Governments at different levels
(i)
Political Parties pressure groups and movements
Power is shared among different organs of government such as the legislature, executive and judiciary. Is also termed as horizontal distribution of power because it allows different organs of government placed at the same level.
(ii) Power can be shared among governments at different levels – A general government for the entire country and governments at the provincial or regional level. Such a general government for the entire country is usually called federal government. PAGE # 54
(iii) Power can be shared among different social groups, such as the religious and linguistic groups. In some countries there are constitutional and legal arrangements whereby socially weaker sections and women are represented in the legislatures and administration. (iv) Power sharing arrangements can also be seen in the way political parties, pressure groups and movements control or influence those in power.
1.
The power sharing arrangement among different organs of the government is (A) horizontal. (B) vertical. (C) multiple. (D) indirect.
2.
An important principle under which the three organs of the government work, is (A) each organ can work freely. (B) balance of power. (C) power-management. (D) easy administration.
3.
4.
5.
6.
The group, which is fighting with arms for the demands of Sri Lankan Tamil is (A) Dravida Munnettra Kazhagam. (B) All-Ceylon Tamil Congress. (C) Liberation Tigers of Tamil Eelam. (D) Pattali Makkal Katchi. Belgium has borders with (A) Netherlands, France and Germany. (B) France, Germany and Spain. (C) Spain, Nethwelands and France. (D) Germany, Spain and Netherlands. The role played by the ‘pressure groups’ in politics is to (A) influence policies and decisions. (B) launch political struggles. (C) finance and mobilize political parties . (D) organize armed struggle. Belgium has a (A) bicameral legislature. (B) unicameral legislature. (C) dictatorship form of government. (D) autocratic form of government.
7.
The United Progressive Alliance is a (A) pressure group. (B) coalition party. (C) regional party. (D) interest group.
8.
In Sri Lanka, Sinhala was recognized as an official language in (A) 1956. (B) 1968. (C) 1978. (D) 1996.
9.
The concept of seperate, soverign national and state governments is known as (A) unicameralism. (B) federalism. (C) aristocracy. (D) oligarchy.
10. The Indian democracy functions on the basis of (A) one man and unlimited votes. (B) one man one vote. (C) only elite adults can vote. (D) only educated people can vote.
11. Member of Parliament are representatives of (A) party. (B) judiciary. (C) government. (D) people. 12. The basic principle of democracy is (A) majority rule. (B) people are the ultimate source of power. (C) only leaders are powerful. (D) political parties are powerful. 13. UPA stands for (A) United Power Association. (B) United Professional Alliances. (C) United Progressive Alliance. (D) United Progression Alliance. 14. An example of a one-party system is (A) Myanmar. (B) Pakistan. (C) China. (D) Belgium. 15. The country with unicameral legislature is (A) Belgium. (B) Germany. (C) Finland. (D) U.S.A. 16. The main objective of the federal system is to (A) promote diversity. (B) make centre more powerful. (C) accomodate regional diversity. (D) distribute finances to different organs. 17. The major objective of LTTE in Sri Lanka is to (A) establish autonomy for Buddhist people. (B) attain independence for Christians. (C) end Sinhala rule. (D) demand separate homeland for Tamils. 18. The institution that can bring changes in the existing laws in India is (A) Executive. (B) Judiciary. (C) Parliament. (D) Press. 19. The first UPA alliance came to the power in (A) 1996. (B) 1999. (C) 2004. (D) 2006. 20. The state that protects and fosters Buddhism is (A) Nigeria. (B) Finland. (C) Sri Lanka. (D) Belgium. 21. Executive is responsible to (A) Lok Sabha. (B) Judiciary. (C) Parliament. (D) President. 22. The voting age in India was reduced from 21 to 18 years by (A) Indira Gandhi Government. (B) Rajiv Gandhi Government. (C) Moraji Desai Government. (D) V.P.Singh Government. 23. The state in Canada that has agreed to settle land claims made by Aboriginal Community was (A) Ohio. (B) Ottowa. (C) Ontario. (D) Dakota. 24. The following government operates on the principle of ‘Collective Responsibility’ (A) Federal Government. (B) Parliamentary Government. (C) Presidential Government. (D) Unitary Government. PAGE # 55
25. Democracy originated in the (A) UK, after the signing of Magna Carta. (B) France after the Revolution. (C) Ancient Greece. (D) US after freeing itself from British tyranny.
36. In Sri Lanka, the two sub groups of Tamils are (A) Sinhala Tamils and Sri Lankan Tamils. (B) Sri Lankan Tamils and Indian Tamils. (C) Colombo Tamils and Indian Tamils. (D) Sinhala Tamils and Colombo Tamils.
26. The first general elections held in India was in the year (A) 1971. (B) 1964. (C) 1951. (D) 1947.
37. The major cause of the civil war in Sri Lanka was the distrust between the two communities namely, (A) Sri Lankan Tamils and the Indian Tamils. (B) Hindus and Muslims. (C) Sinhalas and Moors. (D) Sinhalas and the Tamils.
27. In India the leader of ruling party in the Lok Sabha is (A) Prime Minister. (B) President. (C) Speaker of Lok Sabha. (D) Secretary of Lok Sabha. 28. The responsible party model (A) makes it easier for voters to hold parties accountable for their actions. (B) causes campaigns to be less negative. (C) makes legislatures less divisive. (D) increases citizen interest in politics. 29. Apart from the Central and the State government there is the third type of government in Belgium called the (A) Regional government. (B) Ethnic government. (C) Community government. (D) Federal government. 30. Power sharing is desirable because it (A) ensures the stability of political order. (B) imposes the will of the majority community over others. (C) helps in promoting the communal feeling. (D) helps the people of different communities to celebrate their festivals freely. 31. In 1830 Belgium declared its independence from (A) France. (B) Netherlands. (C) Norway. (D) Germany. 32. The diverse groups and views are given due respect in (A) Totalitarianism. (B) Autocracy. (C) Democracy. (D) Dictatorship. 33. The Sri Lankan Tamils felt that the major political parties led by the Buddhist Sinhala leaders were (A) sensitive to their language and culture. (B) insensitive to their people and culture. (C) supportive to their customs and traditions. (D) different to their colour and culture. 34. In Belgium, 40% people living in the Wallonia region speaks (A) English language. (B) German language. (C) French language. (D) Dutch language. 35. In Sri Lanka , the democratically elected government adopted a series of (A) reforms to establish Tamils power and to protect Buddhism. (B) majoritarian measures to establish Sinhala supremacy. (C) repressive measures to establish the supremacy of Indian Tamils. (D) preferential policies to establish a strong democracy.
38. Ethnic communities of Sri Lanka are composed of (A) Sinhalese, Indian Tamil and Muslim Communities. (B) Sinhalese, Sri Lankan Tamil, Indian Tamil and Muslim Communities. (C) Muslim, Sinhalese and Indian Tamil Communities. (D) Sri Lankan Tamils and Indian Tamils. 39. Prudential reason of power sharing is based on careful calculation of (A) gains and losses. (B) money and man power. (C) profit and gains. (D) total income and losses. 40. In Belgium, 59% people living in the Flemish region speaks (A) Spanish language. (B) English language. (C) Dutch language. (D) Sinhala language. 41. European Union Parliament is in (A) Switzerland. (B) Denmark. (C) Belgium. (D) Germany. 42. In Belgium, Constitution (1970-1993). prescribes that the number of (A) Dutch and French speaking ministers shall be equal in the central government. (B) German and English speaking people shall be equal in the state government. (C) Spanish and French speaking leaders shall be unequal in the local government. (D) German and Dutch speaking ministers shall be equal in union government. 43. The vertical division of power takes place in (A) presidential rule. (B) dictatorship. (C) unitary government. (D) federalism. 44. Belgium is made up of (A) German Region, the Flemish Region and the Brussels Region. (B) Walloon Region, the Flemish Region and the Brussels Region. (C) Walloon Region, the Flemish Region and the German Region. (D) German Region, the Flemish Region and Walloon Region. 45. The period in which acute tension existed between Dutch and French-speaking people in Brussels was (A) 1940s and 1950s (B) 1950s and 1960s (C) 1970s and 1980s (D) 1980s and 1990s 46. Belgium is made up of three Communities namely (A) French Community, Flemish Community, and European Community. (B) French Community, English Community, and German-speaking Community. (C) French Community, Dutch Community, and German-speaking Community. (D) Spain Community, Flemish Community, and German-speaking Community. PAGE # 56
47. Power sharing is necessary for (A) vote bank. (B) rules and freedom. (C) dictatorship and diversity accommodation (D) prudential and moral. 48. The two functions of parties are (A) electioneering and lobbying. (B) electioneering and governing. (C) fundraising and governing. (D) lobbying and governing. 49. The distribution of powers among Central, State and Local governments in India depicts the power sharing arrangement among different (A) departments. (B) levels of governments. (C) socio-political groups. (D) political groups and movements. 50. The concept of power sharing is based on the principle of (A) sovereignty. (B) distribution of powers. (C) individuality. (D) concentration of power. 51. The unitary government is best defined as (A) checks and balance. (B) no constitutional division of powers between central and state government. (C) balance of powers. (D) seperation of powers between executive and parliament. 52. The horizontal distribution of power sharing takes place between the (A) legislature and executive. (B) executive and judiciary. (C) legislature, executive and judiciary. (D) legislature, executive, judiciary and press. 53. In a coalition government, power sharing takes place among different (A) organs of government. (B) levels of government. (C) religious groups. (D) political parties. 54. Inclusion of representatives of labour union, in the Management Board of an industry is an example of power sharing among different (A) levels of government.(B) social groups. (C) pressure groups. (D) organs of government. 55. During 1956 the Tamils feels alienated because government (A) give due importance to Tamil elites only. (B) followed preferential policies. (C) was exercising its emergency powers. (D) was not increasing their wages. 56. In Sri lanka the Sri Lankan Tamils are concentrated in the (A) north and east part of the country. (B) south and east part of the country. (C) west and north part of the country. (D) south and east part of the country. 57. Sharing of power among different levels of government is known as the (A) Vertical power sharing. (B) Horizontal power sharing. (C) Organizational power sharing. (D) Regional power sharing.
58. Indian Tamils are those people whose forefathers came from India as (A) explorers. (B) artisans. (C) industralist. (D) plantation workers. 59. Vertical power sharing helps in (A) concentration of power. (B) decentralization of power. (C) creating differences. (D) motivating leaders. 60. Indian Parliament consists of (A) Cabinet and President. (B) Prime Minister and President. (C) President, Council of States and House of the People. (D) Ruling party, Opposition party and Cabinet. 61. Majoritarianism is a belief that the majority community should be able to rule a country by disregarding the (A) Minority community. (B) Ethnic group. (C) Sinhala community. (D) Muslim Community. 62. AITUC and INTUC are regarded as (A) political parties. (B) pressure groups. (C) social movement. (D) ethnic groups. 63. Sri Lanka has a (A) presidential system. (B) semi-presidential system. (C) parliamentary system. (D) monarchical system. 64. The factor which led to the civil war in Sri Lanka is (A) tyranny of majority. (B) mismanagement. (C) partial policies. (D) economic inequalities. 65. The country where a Grand Coalition came into being after the elections of 2005 is (A) Belgium. (B) Lebanon. (C) Sri Lanka. (D) Germany. 66. Wallonia region is the predominantly (A) Dutch-speaking southern region of Belgium. (B) French-speaking southern region of Belgium. (C) German speaking northern region of Belgium. (D) Dutch-speaking northern region of Belgium. 67. Between 1970 and 1993, Belgian government amended their constitution (A) two times. (B) three times. (C) four times. (D) five times. 68. Sri Lanka’s name before 1972 was (A) Ceylon. (B) South India Island. (C) East Holland Colony.(D) Oceania. 69. The Dutch and French speaking ministers were equal in the central government of (A) Bangladesh (B) Belgium (C) Sri Lanka (D) Russia 70. The rules of power distribution among the different levels of government are laid down by the (A) Central government. (B) Supreme Court. (C) Constitution. (D) Legal laws. 71. Civil war is a violent conflict among various (A) different countries. (B) political parties. (C) organs of government. (D) opposing groups within a country. PAGE # 57
72. The term ethnic implies (A) people living in harmony. (B) a social division based on shared culture. (C) people fighting for their community. (D) people fighting for power. 73. The social and ethnic crisis in Sri Lanka can be solved through power sharing among different (A) political parties. (B) organs. (C) social groups. (D) pressure groups. 74. The meaning of the term ‘coalition government’ is (A) alliances of various political parties. (B) grouping of two state government. (C) government formed during state emergency. (D) united government. 75. The principle of ‘’Hindutva’’ is advocated by (A) FICCI. (B) Lok Dal. (C) BJP. (D) Congress. 76. The voting age in Sri lanka is (A) 24 years. (B) 21 years. (C) 18 years. (D) 16 years. 77. Sri Lanka emerged as an independent country in the year (A) 1942. (B) 1944. (C) 1947. (D) 1948. 78. The percentage of Dutch-speaking people in Flemish region of Belgium is (A) 40 %. (B) 55%. (C) 59%. (D) 63%. 79. The percentage of French speaking population in Brussels is (A) 75. (B) 80. (C) 90 (D) 98. 80. The population of Sri Lanka is divided into (A) Sinhala 55 % and Tamil 40%. (B) Sinhala 68 % and Tamil 25%. (C) Sinhala 74 % and Tamil 18%. (D) Sinhala 80 % and Tamil 15%. 81. In Belgium the federal executive power, as regulated by the Constitution, belongs to the (A) Prime Minister. (B) House of Representatives. (C) Senate. (D) King. 82. Tamil natives of Sri Lanka are called (A) Sri Lankan Tamilian Group. (B) Tamils of Sri Lanka. (C) Sri Lankan natives. (D) Sri Lankan Tamils. 83. The religion followed by the majority of Sinhala speaking people is (A) Hinduism. (B) Buddhism. (C) Islam. (D) Christianity.
84. The religion which is practiced by 7 percent of Sri Lankan population is (A) Hinduism. (B) Buddhism. (C) Christianity. (D) Islam. 85. The 1993 constitutional revisions, Belgium government waschanged from a (A) republican to monarchy. (B) unitary government to a federal system. (C) dictatorship to democractic system. (D) military to participatory democracy. 86. Sri Lankan Tamils launched a struggle for (A) language recognition, autonomy and equal opportunities. (B) language based division of country and major jobs. (C) equal distribution of resources and separate land. (D) government jobs and equal representation in government. 87. Christian Democratic Union is a political party in (A) Srl Lanka. (B) Germany. (C) Netherlands. (D) Denmark. 88. The first countrywide pressure group of the organized Indian working class (A) Hind Mazdoor Sabha. (B) Indian Mining Federation (C) All India Trade Union Congress. (D) Indian National Trade Union Congress. 89. Belgian leaders amended their constitution four times between (A) 1950 and 1983. (B) 1970 and 1993. (C) 1975 and 1995. (D) 1980 and 1999. 90. The term Eelam means (A) country. (B) state. (C) nation. (D) territory. 91. The powers of three organs of Indian government are defined by the (A) majority party. (B) opposition. (C) members of parliament. (D) constitution. 92. The division of powers between different organs of Indian government is based on the principle of (A) separation of powers. (B) centralization of powers. (C) delegation of authority. (D) decentralization of powers. 93. The capital of Belgium is (A) Walloon. (B) Brussels. (C) Paris. (D) Melbourne. 94. The head of the Sri Lankan government is (A) Prime Minister. (B) President. (C) Governor. (D) Secretary of State. 95. The concept of Gram Swaraj was conceived by (A) Jaya Prakash Narain. (B) Vinoba Bhave. (C) Swami Dayanand. (D) Mahatma Gandhi.
PAGE # 58
WATER RESOURCES Freshwater is mainly obtained from surface run off and ground water that is continually being renewed and recharged through the hydrological cycle. All water moves within the hydrological cycle ensuring that water is a renewable resource.
WATER SCARCITY Water scarcity is a situation wherein adequate water is not available to meet its requirement in different uses. Broadly speaking, water scarcity may be caused by (i) over-exploitation, (ii) excessive use, and (iii) unequal access to water among different social groups. Another situation when water is sufficiently available to meet the needs of the people, but, the areas still suffers from water scarcity, due to bad quality of water. Increasing population a cause of water scarcity (i)
Greater demands of water, and unequal access to it.
(ii) Water resources are being overexploited to expand irrigated areas and dry-season agriculture.
(iv) Generates electricity. (v) Provides inland navigation. (vi) Provides facilities for recreation. (vii) Preservation of wildlife, forests and development of fisheries. Negative features of Multi-purpose River Valley project : (i)
Affect river’s natural flow causing poor sediment flow and excessive sedimentation at the bottom of the reservoir, resulting in rockier stream beds and poorer habitats for the rivers’ aquatic life.
(ii) Makes it difficult for aquatic fauna to migrate, especially for spawning. Also submerge’s the existing vegetation and soil. (iii) Large-scale displacement of local communities. (iv) Has changed the cropping pattern of many regions. (v) Ecological consequences like salinisation of the soil .
(iii) Leads to falling groundwater levels, adversely affecting water availability and food security of the people.
(vi) Has transformed the social landscape i.e. increasing the social gap, creates conflicts between people wanting different uses and benefits from the same water resources.
Urbanisation and Industrialisation adversely affect the availability of water -
(vii) Inter-state water disputes are also becoming common.
(i)
(viii) Failure to achieve the purposes for which they were built. Ironically, mostly been unsuccessful in controlling floods at the time of excessive rainfall.
Industry itself is a heavy user of water, in its different processes.
(ii) Industry requires power to run machinery and equipment. Power is generated from water. (iii) Multiplying urban centres with large and dense populations and urban lifestyles add to water and energy requirements. (iv) Growing water requirements are met by pumping underground water, it results in decline in the level of underground water. MULTI-PURPOSE RIVER PROJECTS AND INTEGRATED WATER RESOURCES MANAGEMENT
Dams were traditionally built to impound rivers and rainwater that could be used later to irrigate agricultural fields. Multi-Purpose River Projects - A dam or a series of dam are built on a river and its tributaries to solve various purposes. (i) Control on flood and drought. (ii) Checks soil erosion. (iii) Provides water for irrigation, drinking and industrial purposes.
(ix) Sedimentation also meant that the flood plains were deprived of silt. (x) The multi-purpose projects induced earthquakes, caused water borne diseases and pests and pollution resulting from excessive use of water.
RAINWATER HARVESTING In ancient India, there existed an extraordinary tradition of water-harvesting system. (i)
‘Guls’ & ‘kuls’ of the Western Himalayas for agriculture.
(ii) Roof top rainwater harvesting was commonly practised to store drinking water particularly in Rajasthan. (iii) In the flood plains of Bengal, people developed inundation channels to irrigate their fields. (iv) ‘Khadins’ in Jaisalmer and ‘Johads’ in other parts of Rajasthan. Rainwater Harvesting in semi-arid regions of Rajasthan - In the semi-arid and arid regions of PAGE # 59
(D) Falling ground water level.
Rajasthan, particularly in Bikaner, Phalodi and Barmer, almost all the houses traditionally had underground tanks or tankas for storing drinking water. The rainwater can be stored in tankas till the next rainfall making it an extremely reliable source of drinking water when all other sources are dried up. In Gendathur, a remote backward village in Mysore, Karnataka, villagers have installed, in their household’s rooftop, rainwater harvesting system to meet their water needs. Gendathur receives an annual precipitation of 1000 mm, and with 80 per cent of collection efficiency and of about 10 fillings, every house can collect and use about 50000 litres of water annually.
1.
Which one of the following is the correct percentage of contribution of hydroelectric power to India’s total electricity produced? (A) 15% (B) 20% (C) 22% (D) 25%
2.
The uses of multi-purpose projects is (A) rain water harvesting. (B) scenic beauty. (C) electricity generation. (D) All of the above
3.
The state receiving rainfall less than 100 cm rainfall is (A) Assam (B) Rajasthan (C) Delhi (D) Bihar
4.
Hirakud dam is situated on River (A) Narmada. (B) Mahanadi. (C) Sutlej. (D) Ganga.
5.
Water in atmosphere is recharged through which one of the following process ? (A) Carbon cycle (B) Nitrogen cycle (C) Hydrological cycle (D) Hydrogen cycle
6.
7.
8.
9.
The ecologists and the environmentalists are against big dams and multi purpose projects as it (A) produces hydroelectricity. (B) produces more vegetation and soil. (C) affects their natural flow causing excessive sedimentation on the river beds resulting in poor habitat for the rivers’ aquatic life. (D) easy for the aquatic fauna to migrate. The state prone to floods is (A) Rajasthan. (B) Madhya pradesh. (C) Assam. (D) Delhi. A large population affecting water resources adversely due to (A) building of dams. (B) digging of canals. (C) prayers offered for rain. (D) higher food grain production. Which one of the following is fixed as water stress level, when availability is less than cubic meter per person per day? (A) 2000 (B) 3000 (C) 1000 (D) 500
10. The total renewable water resources of India are estimated at (A) 897 sq. km. per annum. (B) 1897 sq. km. per annum. (C) 2897 sq. km. per annum. (D) 3897 sq. km. per annum.
11. The states in India to rainwater harvesting Act (A) Andhra Pradesh. (C) Tamil Nadu.
introduce compulsory roof is (B) Karnataka. (D) Kerala.
12. Which one of the following village has adopted rain water harvesting techniques completely in South India? (A) Mettur village in Karnataka (B) Gulberga in Karnataka (C) Gendathur in Mysore-Karnataka (D) Mithapur in Kerala 13. The increase in urbanization and industrialization has effected not only the quantity , but also the (A) salinity of water resources. (B) quality of water resources. (C) accumulation of water resources. (D) potential of water resources. 14. Which one of the following is the correct meaning of palar pani ? (A) Rain water in areas of Rajasthan (B) Drinking water in hilly regions (C) Underground water in Kashmir (D) Harvesting water in fields 15. In which one of the following areas, farmers in Gujarat were agitated over priority given to water supply in urban areas? (A) Mahi river basin farmers (B) Sabarmati basin farmers (C) Narmada basin farmers (D) Luni basin farmers 16. Which one of the following rank is attributed to India in terms of water availability per person per annum? (A) 121 (B) 127 (C) 133 (D) 136 17. What among the following is the common factor between the leeward side of the western Ghats, Ladakh and western India(deserts of Rajasthan)? (A) These areas face floods every year (B) These are the drought prone areas of India (C) These areas have ample forest cover (D) It rains throughout the year in these areas 18. In which state did Narmada Bachao Andolan, an NGO, launch movement against river valley project ? (A) Madhya Pradesh (B) Maharashtra (C) Karnataka (D) Gujarat 19. Which one of the following is right option for ‘guls’ or ‘kuls’ Himalayan region ? (A) These are water bodies in western Himalayan region. (B) These are water channels in western Himalayan region. (C) These are diversion channels for agriculture in Himalayas. (D) They were names of daughters of Himalayas. 20. The states using roof rain water harvesting on extensive scale is (A) Punjab. (B) Delhi. (C) Haryana. (D) Rajasthan. PAGE # 60
GLOBALISATION AND THE INDIAN ECONOMY PRODUCTION ACROSS COUNTRIES Multinational Corporations - A company that owns or controls production in more than one nation. The goods and services are produced globally. Production is organized in increasingly complex ways.
INTERLINKING PRODUCTION ACROSS COUNTRIES MNCs set up production where it is close to the markets; where there is skilled and unskilled labour available at low costs; and where the availability is assured. MNCs might look for government policies that look after their interests. Ways in which the MNCs spread their production across the globe (i)
Joint production with local companies
(ii) Buy up local companies (iii) Place orders for production with small producers
Liberalisation of foreign trade and foreign investment policy Trade Barrier - Restrictions on export and import. Governments can use trade barrier to increase or decrease foreign trade and to decide what kinds of goods and how much of each should come into the country. After independence, the Indian government had put barriers to protect the Indian producers from international competition. Starting around 1991, the government decided that the time had come for Indian producers to compete with producers around the globe. Thus barriers on foreign trade and foreign investment were removed to a large extent. Removing barriers or restrictions set by the government is what is known as liberalisation.
WORLD TRADE ORGANISATION A group of 149 countries (2006), this organisation say that all the barriers to foreign trade and investment are harmful. There should be no barriers. Trade between countries should be free. All countries in the world should liberalise their policies.
FOREIGN TRADE AND INTEGRATION OF MARKETS
Foreign trade creates an opportunity for the
(i) Producers to reach beyond the domestic markets (ii) For buyers, expanding the choice of goods beyond what is domestically produced (iii) Prices of similar goods in the two markets tend to become equal. Producers in two countries closely compete against each other even though they are separated by thousands of miles. WHAT IS GLOBALISATION ? Globalisation is the process of rapid integration or interconnection between countries.
IMPACT OF GLOBALISATION IN INDIA Positive Impacts
(i) MNCs have increased their investments in India, new jobs have been created. Local companies supplying raw materials, etc. to these industries have prospered. (ii) Several of the top Indian companies have been able to benefit from the increased competition. (iii) Globalisation has enabled some large Indian companies to emerge as multinationals themselves. (iv) Created new opportunities for companies providing services, particularly those involving IT.
More and more goods and services, investments and technology are moving between countries.
Negative Impacts
People usually move from one country to another in search of better income, better jobs or better education.
For a large number of small producers and workers globalisation has posed major challenges. Small manufacturers have been hit hard due to competition. Several of the units have shut down rendering many workers jobless.
Factors That Have Enabled Globalisation (i) Rapid improvement in technology has been one major factor that has stimulated the globalization process. (ii) Even more remarkable have been the developments in information and communication technology.
(i)
Small producers : Compete or perish:
(ii) Competition and uncertain employment: Globalisation and the pressure of competition have substantially changed the lives of workers. Faced with growing competition, most employers these days prefer to employ workers ‘felxibly’. This means that workers jobs are no longer secure. Workers also have to put in very long working hours and work night shifts PAGE # 61
THE STRUGGLE FOR A FAIR GLOBALISATION Not everyone has benefited from globalisation. People with education, skill and wealth have made the best use of the new opportunities. On the other hand, there are many people who have not shared the benefits. Steps that can be taken by the Government to ensure a fair globalisation :
(i) Policies to protect the interests of all the people in the country. (ii) Proper implementation of labour laws. (iii) Support to small producers, use of trade and investment barriers. (iv) Negotiation at the WTO for ‘fairer rules’.
1.
Liberalization means (A) removing trade barriers. (B) adding more trade barriers. (C) protecting domestic industries. (D) closing domestic economy.
10. The aim of WTO is (A) to keep watch on trade of less developing countries (B) to support only the least developed countries (C) to promote trade in developed countries (D) to liberalize international trade 11. According to 2006, the member countries of WTO are (A) 129. (B) 139. (C) 149. (D) 159. 12. Government has set trade barriers (A) to increase foreign trade. (B) to protect international companies. (C) to regulate foreign trade. (D) to increase the production of wheat. 13. Companies that own and control production in more than one country are called (A) Multiple National Companies (B) Multiple Nation Companies (C) Multi National Corporations (D) Multiple Nation Corporations 14. Name an MNC dealing in medicines (A) Ranbaxy (B) Asian Paints (C) Tata Motors (D) Tata Indicom
2.
In India, the first plant set up by Ford Motors was established in (A) Kashmir (B) Punjab (C) Bangalore (D) Chennai
3.
Indian government has put barriers to foreign trade and foreign investment known as (A) trade restrictions. (B) trade barriers. (C) trade transactions. (D) trade deficit.
16. The restriction imposed on imports is known as (A) tade formality (B) trade barrier (C) trade control (D) trade shortage
4.
Cargill Foods, an American MNC, had bought smaller Indian companies such as (A) Pillsbury Foods. (B) Parakh Foods. (C) Aashirwad Foods. (D) MTR Foods.
17. In India, the first plant set up by Ford Motors was established in______. (A) Kashmir (B) Punjab (C) Bangalore (D) Chennai
5.
Within a year, 70% to 80% of toy shops have replaced Indian toys with Chinese toys due to (A) cheaper prices. (B) good material. (C) easy availability. (D) better quality.
6.
World Trade Organisation is the organisation whose aim is to liberalise (A) internal trade. (B) international trade. (C) external trade. (D) national trade.
18. What is the benefit of container used in transportation of goods? (A) Reduction in port handling costs (B) Reduction in delays (C) Reduction in damaged goods (D) All of them
7.
Ford Motors came to India in (A) 1994 (B) 1995 (C) 1996 (D) 1997
8.
Investment made by MNCs is called (A) foreign investment. (B) direct investment. (C) indirect investment. (D) domestic investment.
9.
The aim of WTO is (A) to keep watch on trade of less developing countries (B) to support only the least developed countries (C) to promote trade in developed countries (D) to liberalize international trade
15. Rapd integration or inter-connection between countries is called (A) urbanisation. (B) liberalisation. (C) globalisation. (D) migration.
19. Tax on imports is an example of __________. (A) Indirect tax (B) Trade barrier (C) Sales tax (D) Direct tax 20. How can government use a trade barrier? (A) To increase foreign trade (B) To protect international companies (C) To decide how much of any commodity should come into the country (D) To increase production of wheat 21. What do you mean by liberalization? (A) Removing trade barriers (B) Adding more trade barriers (C) Protecting domestic industries (D) Closing domestic economy
PAGE # 62
22. What does WTO stand for? (A) World Telecommunication Organization (B) World Toll Organization (C) World Trade Organization (D) World Trade Orientation 23. What is the aim of WTO? (A) To keep watch on trade of less developing countries (B) To support only the least developed countries (C) To promote trade in developed countries (D) To liberalize international trade 24. Started at the initiative of ______ countries, WTO established rules regarding international trade. (A) Least developed (B) Developing (C) Developed (D) Poor 25. How many countries are members of WTO according to 2006 data? (A) 130 (B) 149 (C) 150 (D) 206 26. What special step has been taken by the central and state goverenments to attract foreign companies in India? (A) SEZs (B) EU (C) NPO (D) JSY 27. Companies who set up production units in SEZ’s do not have to pay taxes for an initial period of _____ years. (A) 2 (B) 3 (C) 4 (D) 5 28. Who are the most affected from WTO rules? (A) Indian farmers (B) Farmers of USA (C) Industrialist in India (D) Industrialist in China 29. How can government of a country play a major role in making Globalization fairer? (A) Government can ensure that labour laws are properly implemented (B) Government can support large producers to improve their performance (C) Government can negotiate at UNO for fairer rules (D) Government should negotiate with USA 30. Which of the following is an MNC dealing in medicines? (A) Ranbaxy (B) Asian Paints (C) Tata Motors (D) Infosys 31. How is an MNC defined? (A) A MNC is a company that owns or controls production in more than one district in a country (B) A MNC is a company that owns or controls production in more than one state in a country (C) A MNC is a company that owns or controls production in more than one nation (D) All of the above1.
32. What is the basic function of foreign trade? (A) Connects markets of two countries only (B) Creates opportunity for only the buyer to approach foreigh goods (C) Connects markets of different countries (D) Foreign trade connects developed countries only 33. The past decades of globalization has seen rapid movements in ______. (A) goods, services and people (B) goods, technology, investments and services (C) goods and people (D) Technology and goods 34. Cargill Foods, an American MNC, has bought smaller Indian companies such as ________. (A) Pillsbury Foods (B) Parakh Foods (C) Aashirwad Foods (D) MTR Foods 35. What is the major benefit to the local company of a joint production with MNC? (A) Domestic labours get high wages (B) Production reduces (C) MNC’s can provide money for additional investments (D) Domestic companies started following labour laws 36. What do you mean by investment? (A) Money spent for investment (B) Money that is spent to buy assets such as land, building, machines and other equipment (C) Money used by owners for luxuries (D) The money used to build the factory only 37. In general, where does MNC prefer to set up production units? (A) Where tax rate is high (B) Where labour is available at low costs (C) Where other MNC’s exist (D) Countries who are member of WTO 38. How is an MNC defined? (A) Company that owns production unit in more than one district in a country (B) Company that owns production unit in more than one state in a country (C) Company that owns production units in more than one nation (D) Company that owns production unit in one state of a country 39. Globalization has mostly affected ______. (A) Developed countries (B) MNC’s (C) Large producers (D) Small producers 40. What is Globalisation? (A) Process of rapid integration between countries (B) Process of rapid integration of various states of a country (C) Rapid integration of people of various countries only (D) Integration of technologies of different countries only
PAGE # 63
NUMBER SERIES Number series problems deal with numbers. While attempting to solve the question, you have to check the pattern of the series. Series moves with certain mathematical operations. You have to check the pattern. Type of questions asked in the examination : (i) Find the missing term(s). (ii) Find the wrong term(s).
Ex 6.
Sol.
Number Series In this type of series, the set of given numbers in a series are related to one another in a particular pattern or manner. The relationship between the numbers may be • Consecutive odd/even numbers,
Ex 7.
Sol.
• Consecutive prime / composite numbers, • Squares/cubes of some numbers with/without variation of addition or substraction of some number,
Ex 8.
• Sum/product/difference of preceding number(s), • Addition/subtraction/multiplication/division by some number, and
Sol.
• Many more combinations of the relationship given above. Directions : (1 to 13) Find the missing numbers : Ex 1.
Sol. Ex 2.
Sol. Ex 3.
Sol.
Ex 4.
Sol.
Ex 5.
Sol.
3, 5, 7, 9, 11, 13, 15, 17, ? (A) 14 (B) 19 (C) 15 (D) 21 (B) Each term has a common difference = + 2. Hence, next term = 17 + 2 = 19. 2, 3, 5, 7, 11, ?, 17 (A) 14 (B) 13 (C) 10 (D) 12 (B) The series is made up of consecutive prime numbers. Therefore, the missing term is 13. 1, 4, 9, 16, 25, ? (A) 35 (B) 36 (C) 37 (D) 49 (B) Each term is a square of 1, 2, 3, 4 and so on 12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25. Hence, next term = 62 = 36. 2, 5, 10, 17, ? (A) 24 (B) 25 (C) 26 (D) 27 (C) Each term is a square of 1, 2, 3, 4 and so on and 1 is added to it, i.e. 12 + 1, (2)2 +1, (3)2 +1,..........= 2, 5, 10, 17.... Hence, next term = (5)2 + 1 = 26. 2, 3, 10, 15, 26, 35, ? (A) 48 (B) 51 (C) 49 (D) 50 (D) The series exhibits the pattern of n2 + 1, n2 – 1, alternately, n taking values 1, 2, ......
Ex 9.
Sol. Ex 10.
Sol.
Ex 11.
Sol.
Ex 12.
1, 8, 9, 64, 25, 216, ?, ? (A) 49, 64 (B) 343, 64 (C) 49, 512 (D) 343, 512 (C) Odd positioned digits are squares of 1, 3, 5 and so on, i.e. 12 = 1, 32 = 9, 52 = 25 and so on. Similarly, even positioned digits are cubes of 2, 4, 6, etc., i.e. 23 = 8, 43 = 64, 63 = 216. Therefore, the next term would be 72 i.e. 49 and 83 = 512 respectively. 0, 7, 26, ?, 124, 215 (A) 51 (B) 37 (C) 63 (D) 16 (C) Each term is a cube of 1, 2, 3, 4 and so on and 1 subtracted from it, i.e. 13 – 1, 23 – 1, 33 – 1, 43 – 1, 53 – 1, 63 – 1. Therefore, the term replacing the question mark would be 43 – 1 = 64 – 1 = 63. 3, 4, 10, 33, 136, ? (A) 240 (B) 430 (C) 685 (D) 820 (C) The terms of the series are, previous term × 1 + 1, previous term × 2 + 2, previous term × 3 + 3 and so on. Hence, the next term will be 136 × 5 + 5 = 680 + 5 = 685. 11, 15, 21, 29, ? (A) 40 (B) 41 (C) 37 (D) 39 (D) This series consists of increasing numbers. The pattern is +4, +6, +8,........ 3, 6, 18, 72, 360, ? (A) 720 (B) 1080 (C) 1600 (D) 2160 (D) The sequence in the given series is × 2, × 3, × 4, × 5, × 6. Hence, the missing number is 360× 6 =2160. 6, 12, 7, 11, 8, 10, 9, ? (A) 8 (C) 11 (B) Alternate series (i) 6, 7, 8, 9 (ii) 12, 11, 10, ? 0, 5, 22, 57, 116, ? (A) 205 (C) 192 0
Sol.
Difference
(B) 216 (D) 207
5
(A) Difference 5
22 17
12
(B) 9 (D)10 [Difference series]
57 35
18
116 59
24
205 89
30
Hence, the next term = 205
PAGE # 64
Ex 13.
Sol.
151, 158, 172, 182, ? (A) 210 (B) 193 (C) 197 (D) 203 (B) 1 + 5 + 1 = 7, The difference between 151 & 158 is seven (7) 1 + 5 + 8 = 14, The difference between 158 & 172 is (14). 1 + 7 + 2 = 10 .......... and so on, Missing term = 182 + 11 = 193.
Directions : (14 to 15) In each of the following questions, a number series is given. After the series, below it in the next line, a number is given followed by (P), (Q), (R), (S) and (T). You have to complete the series starting with the number given following the sequence of the given series. Then answer the question given below it. Ex 14. 12 28 64 140 37 (P) (Q) (R) (S) (T) Which number will come in place of (T) ? (A) 1412 (B) 164 (C) 696 (D) 78
17.
Sol.
111000 is wrong. The correct term is 121000. 18.
Sol.
+4
37
(P)
(Q)
(R)
(S)
(T)
78
164
340
696
1412
×2+4
×2+8
×2+12
×2+16
Ex 15.
Sol.
2 9 57 3 (P) (Q) Which number will come (A) 113 (C) 3912 ( A
×2+20
337 (R) (S) in place of (Q) ? (B) 17 (D) 8065
(T)
3.
4.
5. ) 6.
Similarly, 3 ×8–7
(P)
(Q)
17
113 ×7–6
(R)
(S)
673 ×6–5
3361
7.
×5–4
Therefore, the number 113 will come in place of (Q).
8.
Direction : (16 to18) Find the wrong term : 16.
Sol.
2, 5, 9, 11, 14 (A) 2 (B) 5 (C) 9 (D) 11 (C) Series : + 3, + 3, + 3, .......... The next term is got by adding 3 in preceeding term. 2 + 3 = 5, 5 + 3 = 8 9 is wrong term.
+5 +6 +7
+8
+9
Directions : (1 to 50) Find the missing numbers :
2.
Therefore, the number 1412 will come in place of (T).
(B) 17 (D) 32
EXERCISE-1
(A)
Similarly
2, 6, 11, 17, 23, 32, 41 (A) 6 (C) 23 (C) Given series is :
24 2, 6, 11, 17, 23, 32, 41
1. Sol.
10, 100, 1100, 11000, 111000, 1210000. (A) 1210000 (B) 11000 (C) 100 (D) 111000 (D) Given series is :
9
10.
2, 3, 5, 7, ? (A) 9 (C) 11
(B) 10 (D) 14
0, 6, 20, 42, ? (A) 64 (C) 80
(B) 72 (D) 84
3, 8, 35, 48, ?, 120 (A) 72 (C) 80
(B) 64 (D) 99
4, 25, 64, 121, 196, ? (A) 384 (C) 225
(B) 256 (D) 289
210, 120, ?, 24, 6, 0 (A) 64 (C) 35
(B) 48 (D) 60
2, 12, 36, 80, 150, ? (A) 194 (C) 252
(B) 210 (D) 258
4, 10, 22, 46, ? (A) 56 (C) 76
(B) 66 (D) 94
8, 15, 28, 53, ? (A) 120 (C) 104
(B) 106 (D) 102
4, 8, 12, 24, 36, 72, ? A) 98 (C) 144
(B) 100 (D) 108
12, 15, 18, 21, ? (A) 24 (C) 22
(B) 23 (D) 25
PAGE # 65
11.
3, 6, 12, 24, ?, 96 (A) 84 (C) 52
26.
5, 6, 13, 26, 45, ? (A) 68 (C) 70
27.
190, 94, 46, 22, 10, 4, ? (NTSE Stage-I / Raj./ 2008) (A) 3 (B) 2 (C) 1 (D) 0
28.
128, 110, 90, 68, ? (A) 36 (C) 44
29.
1, 2, 4, 7, ?, 16 (A) 9 (C) 12
30.
6, 8, 9, 12, 14, 18, ? (NTSE Stage-I / Raj./ 2008) (A) 21 (B) 19 (C) 23 (D) 20
31.
4, 9, 19, 34, 54, ? (A) 66 (C) 79
(NTSE Stage-II, 2008) (B) 75 (D) 84
32.
31, 29, 24, 22, 17, ?, ? (A) 15, 13 (C) 14, 12
NTSE Stage-II, 2008) (B) 10, 8 (D) 15, 10
(B) 50 (D) 48
12.
2, 10, 19, 29, 40, 52, 65, 79, 94, ? (A) 110 (B) 109 (C) 108 (D) None of these
13.
4, 7, 3, 6, 2, 5, ? (A) 6 (C) 3
(B) 5 (D) 1
14.
4, 7, 10, 11, 22, 17, 46, 25, ? (A) 58 (B) 69 (C) 86 (D) 94
15.
2, 2, 4, 4, 6, 8, 8, ? (A) 10 (C) 14
(B) 12 (D) 16
(NTSE Stage-I / Raj./ 2008) (B) 42 (D) 48 (NTSE Stage-I / Raj./ 2008) (B) 11 (D) 13
16.
2, 3, 10, 15, 26, ? (A) 34 (C) 36
17.
1, 4, 27, 16, 125, 36, ? (NTSE Stage-I / Raj./2007) (A) 216 (B) 343 (C3) 64 (D) 49
33. 18..
336, 210, 120, ?, 24, 6, 0 (NTSE Stage-I / Raj./2007) (A) 40 (B) 50 (C) 60 (D) 70
3, 6, 11, 18, ? (A) 19 (C) 30
(NTSE Stage-II, 2008) (B) 27 (D) 37
34.
3, 4, 8, 17, 33, ? (A) 58 (C) 49
3, 8, 15, 24, ? (A) 30 (C) 36
(NTSE Stage-II, 2008) (B) 35 (D) 49
35.
4, 10, 23, 50, 105, ? (NTSE Stage-I / Raj./ 2009) (A) 215 (B) 210 (C) 216 (D) 439
36.
912, 303, 102, 33, ?, 3, 2 (NTSE Stage-I / Raj./ 2009) (A) 12 (B) 10 (C) 8 (D) 6
37.
1, 4, 9, ?, 25, 36 (A) 11 (C) 21
38.
7, 12, 22, 37, ?, 82, 112 (NTSE Stage-I / Raj./ 2009) (A) 62 (B) 57 (C) 52 (D) 42
39.
11, 13, 17, 19, ?, 25 (NTSE Stage-I / Raj./ 2009) (A) 20 (B) 21 (C) 23 (D) 22
40.
5, 9, 17, 33, ?, 129 (A) 72 (C) 65
41.
2, 5, 4, 10, 7, 15, 11, 20, ?, ? (NTSE Stage-II, 2009) (A) 12, 21 (B) 16, 25 (C) 13, 25 (D) 17, 30
19.
20.
(NTSE Stage-I / Raj./2007) (B) 35 (D) 37
(NTSE Stage-I / Raj./ 2008) (B) 74 (D) 82
(NTSE Stage-I / Raj./ 2007) (B) 69 (D) 98
8, 13, 21, 34, 55, ? (NTSE Stage-I / Raj./ 2007) (A) 60 (B) 68 (C) 89 (D) 76
21.
480, 480, 240, 80, 20, ?
22.
(NTSE Stage-II, 2007) (A) 4 (B) 1 (C) 5 (D) 10 1, 1, 2, 2, 3, 4, 4, 8, 5, 16, ? (NTSE Stage-II, 2007) (A) 6 (B) 32 (C) 8 (D) 7
23.
24.
25.
2, 5, 11, 23, 47, ? (A) 92 (C) 95
(NTSE Stage-II, 2007) (B) 90 (D) 91
12, 21, 23, 32, 34, 43, 45, ? (NTSE Stage-II, 2007) (A) 54 (B) 48 (C) 77 (D) 9 14, 1, 21, 4, 28, 9, ?,? (A) 9, 42 (C) 35, 16
(NTSE Stage-II, 2007) (B) 16, 35 (D) 16, 36
(NTSE Stage-I / Raj./ 2009) (B) 19 (D) 16
(NTSE Stage-II, 2009) (B) 67 (D) 58
PAGE # 66
42.
0, 6, 24, 60, 120, ? (A) 180 (C) 196
43.
57, 54, 58, 55, 59, 56, 60, ? (NTSE Stage-II,2011) (A) 64 (B) 63 (C) 58 (D) 57
44.
(NTSE Stage-II, 2009) (B) 224 (D) 210
52.
53.
27, 31, 40, 56, 81, 117, ? (A) 156 (C) 166
(NTSE Stage-II,2011) (B) 165 (D) 169
5 18 48 112 7 (P) (Q) (R) (S) (T) Which number will come in place of (S) ? (A) 172 (B) 276 (C) 270 (D) 376 15 159 259 323 7 (P) (Q) (R) (S) (T) Which of the following numbers will come in place of (R) ? (A) 251 (B) 315 (C) 176 (D) 151
EXERCISE-2 45.
46.
47.
48.
49.
55, 168, 57, 120, 60, 80, 62, 48, 65, 24, ?, ? (NTSE Stage-II,2011) (A) 69, 11 (B) 67, 8 (C) 8, 71 (D) 6, 72 8, 7, 16, 5, 32, 3, 64, 1, 128, (?) (NTSE Stage-I / Raj./ 2012) (A) 18 (B) 13 (C) –1 (D) 3 16, 33, 65, 131, (?), 523 (NTSE Stage-I / Raj./ 2012) (A) 261 (B) 521 (C) 613 (D) 721 5, 2, 17, 4, (?) , 6, 47, 8, 65 (NTSE Stage-I / Raj./ 2012) (A) 29 (B) 30 (C) 31 (D) 32 1, 2, 4, 8, (?), 32 (NTSE Stage-I / Raj./ 2012) (A) 10 (B) 12 (C) 14 (D) 16
Directions : (1 to 21) Find the wrong term of the series : 1.
3, 7, 9, 21, 27, 66, 81, 189, 243 (NTSE Stage-I / Raj./ 2007) (A ) 27 (C) 243
2.
27, 34, 40, 45, 49, 53, 54 , 55 (NTSE Stage-I / Raj./ 2007) (A) 53 (C) 56
3.
2, 3, 10, 15, 26, (?)(NTSE Stage-I / Raj./ 2012) (A) 36 (B) 35 (C) 39 (D) 48
Directions : (51 to 53) In each of the following questions, a number series is given. After the series, below it in the next line, a number is given followed by (P), (Q), (R), (S) and (T). You have to complete the series starting with the number given following the sequence of the given series. Then answer the question given below it. 51.
2 3 8 27 5 (P) (Q) (R) (S) (T) Which of the following numbers will come in place of (T) ? (A) 184 (B) 6 (C) 925 (D) 45
(B) 45 (D) 34
0, 2, 3, 6, 6, 20, 9, 54, 12 (NTSE Stage-I / Raj./ 2007) (A) 3 (C) 20
4.
(B) 6 (D) 54
0, 2, 10, 36, 68, 130 (NTSE Stage-I / Raj./ 2007) (A) 10 (B) 36 (C) 68
5.
(D) 130
9, 54, 44, 264, 254, 1520, 1514 (A) 1514
50.
(B) 66 (D) 21
(NTSE Stage-I / Raj./ 2007) (B) 1520
(C) 264 6.
10, 15, 26, 35, 48, 63, 82 (A) 48 (C) 63
7.
(D) 82
(B) 66 (D) 218
7, 9, 17, 42, 91, 172, 293 (NTSE Stage-I / Raj./2008) (A) 91 (C) 17
9.
(NTSE Stage-I / Raj./2008) (B) 26
3, 10, 30, 66, 127, 218 (NTSE Stage-I / Raj./2008) (A) 3 (C) 30
8.
(D) 44
(B) 42 (D) 9
2, 12, 24, 34, 68, 78, 158, 166 (NTSE Stage-I / Raj./2008) (A) 68 (C) 158
(B) 78 (D) 166 PAGE # 67
10.
2, 6, 10, 20, 30, 42, 56
16.
320, 254, 200, 155, 122, 100, 89
(NTSE Stage-I / Raj./2008)
11.
(NTSE Stage-I / Raj./ 2009)
(A) 6
(B) 10
(A) 155
(B) 320
(C) 20
(D) 30
(C) 254
(D) 200
7, 9, 16, 25, 41, 68, 107, 173
17.
6, 8, 9, 12, 14, 18, 22, 26, 30
(NTSE Stage-II, 2008)
12.
13.
(B) 41
(A) 12
(B) 22
(C) 68
(D) 107
(C) 26
(D) 30
3, 9, 27, 82, 243
(NTSE Stage-I / Raj./ 2009)
(A) 27
(B) 54
(C) 82
(D) 162
3, 7, 9, 28, 27, 84, 81, 448, 243 (A) 84
(B) 81
(C) 28
(D) 7
5, 9, 17, 35, 65, 129
(A) 65
19.
190, 94, 46, 22, 10, 3 (NTSE Stage-I / Raj./ 2012)
(B) 35
(C) 17
(D) 9
1, 5, 6, 11, 17, 27, 45, 73 (NTSE Stage-I / Raj./ 2009)
15.
18.
(NTSE Stage-I / Raj./ 2012)
(NTSE Stage-I / Raj./ 2009)
14.
(NTSE Stage-I / Raj./ 2012)
(A) 16
(A) 27
(B) 45
(C) 17
(D) 11
3, 6, 11, 18, 28, 38, 51, 66
20.
(A) 94
(B) 46
(C) 22
(D) 3
0, 5, 15, 50, 128 (NTSE Stage-I / Raj./ 2012)
21.
(A) 5
(B) 17
(C) 35
(D) 128
9, 63, 5, 35, 1, 8
(NTSE Stage-I / Raj./ 2009) (A) 18 (C) 38
(NTSE Stage-I / Raj./ 2012)
(B) 28
(A) 63
(B) 5
(D) 51
(C) 35
(D) 8
PAGE # 68
ALPHABET SERIES Alphabet Series problems deals with alphabets and Alpha-Numeric. While attempting to solve the question, you have to check the pattern of the series. Type of questions asked in the examination : (i) Find the missing term(s). (ii) Find the wrong term(s).
Alphabet Series In these types of questions, a series of single or pairs of groups of letters is given. The terms of the series form a certain pattern as regards the position of the letters in the English alphabet.
Position of Alphabet : (i) Alphabet in order :
(ii) Alphabet in reverse order :
Z Y X W V U T S R Q P O N M L K J I H G F E D C B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Directions : (1 to 7) Find the missing term : Ex 1.
Sol. Ex 2.
Sol.
Ex 3.
A, C, ?, G, I (A) E (B) D (C) F (D) H (A) Series consists of alternate letter in order . So, the missing term would be E. V, T, R, ?, N, ? (A) O,M (B) P,M (C) L,P (D) P,L (D) Given series consists of alternate letters in reverse order. So, the missing terms would be P and L . A, C, F, ?, O (A) G (C) H C
A
F
J
(B) Hint
Ex 4.
DC, DE, FE, ?, HG, HI (A) FE (C) GF (B) +2 DC 0
Ex 5.
Sol.
Ex 6.
Sol.
Sol.
+2
+3
Ex 8.
Sol.
FE +2
O
(B) FG (D) GH
Sol. Hint
+2
0 FG
0
Ex 9.
+5
+2
0
DE
+4
+2
HG
HI 0
CIR, GMV, KQZ, OUD, ? (A) RYH (B) SYH (C) SZI (D) SYI (B) There is a continuous difference of 4 letters between the first letter of each group, second letter of each group and third letter of each group. So the missing term would be SYH. ZSD, YTC, XUB, WVA, ? (A) VWZ (B) UVW (C) VXY (D) UWZ (A) The first letter of each group is in continuation in backward direction. The second letter of each group is in continuation in forward direction. The third letter of each group is in continuation in backward direction. Therefore, the missing term would be VWZ.
KTE, SBM, AJU, IRC, ? (A) OZL (B) QYZ (C) QZL (D) QZK (D) First letter of each group differ by 8 letters. Second letter of each group differ by 8 letters. Third letter of each group differ by 8 letters. Therefore, the missing term would be QZK.
Directions : (8 to 9) Find the wrong term (s) :
(B) J (D) K
Sol.
Sol.
Ex 7.
DOU, EPV, FQW, GRX, HTY, ITZ (A) EPV (B) FQW (C) GRX (D) HTY (D) In every term first, second and third letter is in alphabetical order to its next term respectively. Fourth term is not following the same rule. Hence, HTY is the wrong term and should be replaced by HSY. ABC, DGJ, HMR, NTA, SBK, ZKV (A) DGJ (B) HMR (C) NTA (D) SBK (C) First letter of first, second, third,.........terms is moved three, four, five, ........steps forward respectively. Similarly, second letter is moved five, six, seven,......steps forward respectively and third letter is moved seven, eight, nine,........steps forward respectively. Hence, NTA is the wrong term and should be replaced by MTA.
Alpha-Numeric Series A series in which both alphabets and number are used. Direction : (10) Find the missing term : Ex 10.
Sol.
F3X, H7U, J15R, L31O, ? (A) M46L (B) N44L (C) N63L (D) N44M (C) The first letter of each term is moved two steps forward and the last letter is moved three steps backward to obtain the corresponding letters of the next term. The numbers form the sequence 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, 31 × 2 + 1 = 63. So, the missing term would be N63L.
69
PAGE # 69
Direction : (11) Find the wrong term : Ex 11.
Sol.
D4V, G10T, J20R, M43P, P90N (A) G10T (B) J20R (C) M43P (D) P90N (A) First letter of every term is moved three steps forward in each next term. Second number of every term of the pattern × 2 + 1, × 2 + 2,× 2 + 3,............and third letter of every term is moved two steps backward. Hence, G10T is the wrong term and should be replaced by G9T.
13.
UTRQU, QPNMT, MLJIS, IHFER, ? (NTSE Stage-I / Raj./2007) (A) EDCAQ (B) EDBAQ (C) IHFGP (D) KJHGP
14.
CDFI, EFHK, IJLO, KLNQ, OPRU, ? (NTSE Stage-I / Raj./2007) (A) QRTW (B) MNPS (C) QRST (D) RSUX
15.
CFIJ, RUXY, EHKL, PSVW, ? (NTSE Stage-I / Raj./2007) (A) HILM (B) UXZA (C) SVYZ (D) MOSV BCFH, ?, HILN, KLOQ, NORT (NTSE Stage-I / Raj./2008) (A) MNQS (B) EFIK (C) NOPQ (D) PQTV
EXERCISE-1 Directions : (1 to 36) Find the missing letters : 1.
2.
3.
4.
5.
6.
7.
8.
9.
B, E, H, ? (A) K (C) J
(B) L (D) M
Y, W, U, S, Q, ? (A) A (C) O
(B) P (D) B
AH, DL, GP, JT, ? (A) MY (C) MX
(B) NX (D) NY
LO, IL, FI, CF, ? (A) ZB (C) ZC
(B) AB (D) ZO
ZYX, BAZ, DCB, FED, ? (A) GHF (C) FFG
(B) FGH (D) HGF
ATL, BUM, CVN, DWO, ? (A) EZP (C) EFP
(B) EYQ (D) EXP
TYU, NSO, HMI, ? (A) AGC (C) GBC
(B) CGC (D) BGC
MAAL, AALM, ALMA, LMAA, ? (A) AMLA (B) MAAL (C) AAML (D) LAAM A3P, C5N, E8K, G12G, ? (A) I16D (C) I17D
16.
17.
KMON, NPRQ, ?, TVXW, WYAZ (NTSE Stage-I / Raj./2008) (A) QSUT (B) QTUS (C) UWYX (D) SUWV
18.
GRPT, HSQS, ITRR, ?, KVTP, LWUO (NTSE Stage-I / Raj./2008) (A) USJQ (B) QSUJ (C) JSQR (D) JUSQ
19.
XBI, JNU, VZG, HLS, ? (NTSE Stage-I / Raj./2008) (A) TYE (B) TXE (C) PTA (D) UYE
20.
AYCXB, EWGVF, IUKTJ, MSORN, ? (NTSE Stage-I / Raj./2008) (A) QOPPR (B) RPSQO (C) QQSPR (D) PQRPQ
21.
AAZY, DDVU, GGRQ, ?, MMJI, PPFE (NTSE Stage-II, 2008) (A) KKMN (B) MMJN (C) KKMM (D) JJNM
22.
ZDOA, VHNF, ?, NPLP, JTKU, FXJZ (NTSE Stage-II, 2008) (A) RLKM (B) MLRK (C) RKML (D) RLMK
23.
ZOA, XMF, ?, TIP, RGU, PEZ (NTSE Stage-II, 2008) (A) YXX (B) WLL (C) UKK (D) VKK
24.
CGJL, FJMO, IMPR, LPSU, ? (NTSE Stage-I / Raj./ 2009) (A) ORUW (B) OSVX (C) JMPR (D) KORS
25.
ADCG, ?, JMLP, QTSW, UXWA (NTSE Stage-I / Raj./ 2009) (A) PSRV (B) PTSV (C) PRVS (D) PVRS
(B) I17B (D) J16B
10.
Q1F, S2E, U6D, W21C, ? (A) Y66B (B) Y44B (C) Y88B (D) Z88B
11.
BYDW, FUHS, JQLO, NMPK, ? (NTSE Stage-I / Raj./ 2007) (A) RITG (B) RJGH (C) IRGT (D) HPIN
12.
BYCXA, EVFUD, HSIRG, KPLOJ, ? (NTSE Stage-I / Raj./2007) (A) MNLOL
(B) NMOLM
(C) QJRIP
(D) PKQJO
70
PAGE # 70
26.
?, CAFH, YWBD, USXZ, QOTV
EXERCISE-2
(NTSE Stage-I / Raj./ 2009) (A) GELJ
(B) INLN
(C) GEJL
(D) PSNP
Directions (1 to 10) : There is a wrong term in the following numbers / letters series. Find the wrong term of
27.
AYBX, EUFT, IQJP, MMNL, ? (NTSE Stage-I / Raj./ 2009)
28.
(A) QIRH
(B) NLOK
(C) GSHR
(D) PJQI
(A) KLHI
(B) MNJK
(C) GHIJ
(D) JKGH
31.
32.
2.
(A) QRLM
(B) QRST
(C) QULM
(D) QRLF
BDF, HKN, QUY, ?, RXD (NTSE Stage-II, 2009)
3.
34.
(A) BCD
(B) CDE
(C) DEF
(D) FEG
ZOA, XMF, VKK, THP, RGU, PEZ (A) THP
(B) XMF
(C) VKK
(D) RGU
4.
AACC, BBED, CCHE, DDMF, EEQG (A) AACC
(B) DDMF
(C) BBED
(D) EEQG
ECA, JHF, OMK, TQP, YWU (A) ECA (B) JHF
(A) CHM
(B) BGL
(C) CIO
(D) BHN
AZYB, CXVE, FURI, ?
(NTSE Stage-II, 2009)
(A) KQPL
(B) JRNM
DKY, FJW, HIT, JHS, LGQ (A) FJW (B) LGQ
(C) JQMN
(D) ISPM
(C) JHJ
(C) TQP 5.
6.
DOZ, GRC, (?), ALW, BMX (NTSE Stage-I / Raj./ 2012)
33.
ABC, BCD, CDE, DEF, FEG
ABHR, EFIO, IJJL, MNKI, ?, UVMC (NTSE Stage-II, 2009)
30.
1.
PQMN, NOKL, LMIJ, ?, HIEF (NTSE Stage-I / Raj./ 2009)
29.
the series.
(A) BGL
(B) LWH
(C) DLT
(D) GJM
fed, ihg, lkj, (?) , rqp (NTSE Stage-I / Raj./ 2012) (A) npq
(B) onm
(C) oqp
(D) nom
(D) ZKW
EPV, FQW, GRX, HTY, ITZ (A) FQW (B) GRX (C) HTY
ABYZ, ADWZ (?), AHSZ
(D) LJO
ABD, DGK, HMS, NTB, SBL, ZKW (A) NTB (B) DGK (C) SBL
8.
(D) HIT
DVG, FSI, HPK, JNM, LJO (A) DVG (B) JNM (C) HPK
7.
(D) YWU
(D) ITZ
(NTSE Stage-I / Raj./ 2012)
35.
(A) AFUZ
(B) AUFZ
(C) ZFUA
(D) ZUFA
VTRP, NLJH, FDBZ, XVTR, (?) (NTSE Stage-I / Raj./ 2012)
36.
(A) JLPN
(B) LJPN
(C) NPLJ
(D) PNLJ
9.
PON, RQP, TSR, VVT, XWV, ZYX (A) VVT (B) TSR (C) XWV
10.
(D) RQP
P 3 C, R 5 F, T 8 I, V 12 L, X 18 O, Z 23 R (A) V 12 L (B) X 18 O (C) Z 23 R
(D) R 5 F
OBDR, QACT, SZBV, (?), WXZZ (NTSE Stage-I / Raj./ 2012) (A) WUWZ
(B) YTVB
(C) UYAX
(D) ASVD
71
PAGE # 71
1. FORCE AND LAWS OF MOTION (PHYSICS) Que.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ans.
A
B
A
C
A
A
D
B
D
B
D
C
A
D
C
Que. 16
17
18
19
20
21
22
23
24
25
26
27
28
C
A
B
C
A
B
B
C
C
A
C
C
B
Ans.
2. STRUCTURE OF ATOM(CHEMISTRY)
Ques Ans Ques Ans Ques Ans Ques Ans
1 D 12 D 23 B 34 A
2 C 13 A 24 B 35 D
3 B 14 C 25 B
4 C 15 D 26 A
5 B 16 A 27 C
6 A 17 C 28 B
7 C 18 C 29 B
8 B 19 D 30 B
9 A 20 B 31 D
10 C 21 B 32 A
11 B 22 D 33 B
3. PERCENTAGE (MATHEMATICS) Q. Ans. Q. Ans. Q. Ans. Q. Ans. Q. Ans.
1 B 11 C 21 B 31 A 41 A
2 C 12 C 22 B 32 A 42 D
3 C 13 D 23 A 33 D 43 B
4 C 14 C 24 B 34 C 44 D
5 C 15 D 25 B 35 A 45 B
6 D 16 A 26 C 36 C 46 B
7 C 17 B 27 A 37 A 47 D
8 B 18 B 28 C 38 B 48 D
9 A 19 D 29 C 39 B 49 C
10 B 20 C 30 C 40 B 50 B
4. RATIO & PROPORTION, PARTNERSHIP, MIXTURE & ALLIGATION(MATHEMATICS) Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans.
1 C 11 B 21 C 31 D 41 A 51 B
2 B 12 B 22 B 32 A 42 C 52 A
3 B 13 C 23 A 33 A 43 C 53 B
4 D 14 D 24 B 34 B 44 D 54 C
5 B 15 A 25 B 35 D 45 A 55 C
6 C 16 C 26 B 36 B 46 C 56 B
7 C 17 D 27 C 37 B 47 D 57 B
8 A 18 B 28 B 38 C 48 D 58 B
9 D 19 D 29 C 39 C 49 C 59 A
10 D 20 C 30 C 40 C 50 B 60 B
PAGE # 72
5.CONTROL & COORDINATION (BIOLOGY) Ques.
1
2
3
4
5
6
7
8
9
10
Ans.
A
D
A
B
C
D
A
C
B
C
Ques.
11
12
13
14
15
16
17
18
19
20
Ans. Ques. Ans.
D 21 A
A 22 A
A
A
C
D
D
B
A
C
6.PRINT CULTURE AND MODERN WORLD (SOCIAL SCIENCE) Ques
1
2
3
4
5
6
7
8
9
10
Ans.
D
A
A
C
B
B
A
A
D
C
Ques
11
12
13
14
15
16
17
18
19
20
Ans.
A
A
D
B
B
D
A
B
C
C
Ques
21
22
23
24
25
26
27
28
29
30
Ans.
C
B
D
B
A
A
B
C
C
D
Ques
31
32
33
34
35
36
37
38
39
40
Ans.
A
A
A
B
A
B
D
A
A
D
Ques
41
42
43
44
45
46
47
48
49
50
Ans.
A
B
A
D
C
C
D
B
B
C
Ques
51
52
53
54
55
56
57
58
59
60
Ans.
B
D
D
D
B
C
D
D
D
C
Ques
61
62
63
64
65
66
67
68
69
70
Ans.
B
A
B
C
B
B
C
C
A
D
Ques
71
72
73
74
75
76
77
78
79
80
Ans.
B
A
A
A
C
C
B
B
C
B
7.POWER SHARING (SOCIAL SCIENCE)
Ques
1
2
3
4
5
6
7
8
9
10
Ans.
A
B
C
A
A
A
B
A
B
B
Ques
11
12
13
14
15
16
17
18
19
20
Ans.
D
B
C
C
C
C
D
C
C
C
Ques
21
22
23
24
25
26
27
28
29
30
Ans.
C
B
C
B
C
C
A
A
C
A
Ques
31
32
33
34
35
36
37
38
39
40
Ans.
B
C
A
C
B
B
D
B
A
C
Ques
41
42
43
44
45
46
47
48
49
50
Ans.
C
A
D
B
B
C
D
B
B
B
Ques
51
52
53
54
55
56
57
58
59
60
Ans.
B
C
D
C
B
A
A
D
B
C
Ques
61
62
63
64
65
66
67
68
69
70
Ans.
A
B
B
A
D
B
C
A
B
C
Ques
71
72
73
74
75
76
77
78
79
80
Ans.
D
B
C
A
C
C
D
C
B
C
Ques
81
82
83
84
85
86
87
88
89
90
Ans.
D
D
B
C
B
A
B
C
B
B
Ques
91
92
93
94
95
Ans.
D
A
B
B
D
PAGE # 73
8.WATER RESOURCES (SOCIAL SCIENCE)
Ques
1
2
3
4
5
6
7
8
9
10
Ans.
C
D
B
C
C
C
C
D
C
B
Ques
11
12
13
14
15
16
17
18
19
20
Ans.
C
C
B
A
B
C
B
D
C
B
9.GLOBALISATION AND THE INDIAN ECONOMY (SOCIAL SCIENCE)
Ques
1
2
3
4
5
6
7
8
9
10
Ans.
A
D
B
B
A
B
B
A
D
D
Ques
11
12
13
14
15
16
17
18
19
20
Ans.
C
C
C
A
C
B
D
D
B
C
Ques
21
22
23
24
25
26
27
28
29
30
Ans.
A
C
D
C
B
A
D
A
A
A
Ques
31
32
33
34
35
36
37
38
39
40
Ans.
C
C
B
B
C
B
B
C
D
A
10. NUMBER SERIES(MENTAL ABILITY) EXERCISE-1 Que.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ans.
C
B
D
D
D
C
D
D
D
A
D
A
D
D
D
Que.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Ans.
B
B
C
A
C
A
A
C
A
C
C
C
C
B
A
Que.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
C
C
B
D
D
C
B
Ans.
C
D
B
B
A
A
D
B
Que.
46
47
48
49
50
51
52
53
Ans.
C
A
C
D
B
C
B
B
EXERCISE-2 Que.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Ans.
B
A
C
B
B
A
C
D
C
B
C
C
B
A
B
D
Que. 17
18
19
20
21
Ans.
A
D
D
D
B
11. ALPHABET SERIES(MENTAL ABILITY) EXERCISE-1 Que.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ans.
A
C
C
C
D
D
D
B
B
C
A
B
B
A
C
Que.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
D
D
B
A
C
A
D
D
A
Ans.
B
A
D
B
C
D
Que.
31
32
33
34
35
36
Ans.
C
B
B
A
D
C
EXERCISE-2 Que.
1
2
3
4
5
6
7
8
9
10
Ans.
D
A
B
C
D
B
A
C
A
B
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