Ai Aieee Modeltest 06

MODEL TEST TEST CODE - FXI

AIEEE 180 QUESTIONS TIME ALLOWED : 180 MINUTES

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STUDENT’S NAME :

Read the instructions on the ANSWER SHEET. Fill in your NAME, TEST CODE and AIEEE Application form Number. Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. Mark only ONE answer for each question. Q. 1 to 8, 61 to 68 & 121 to 130 carries1 12 marks each, Q. 9 to 52, 69 to 112 & 131 to 170 carries 3 marks each and Q. 53 to 60,113 to 120 & 171 to 180 carries 412 marks each. For each incorrect response,one-third of the total marks alloted to the question would be deducted from the total score. You are NOT allowed to use a calculator

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TM

Questions - 180

1.

PHYSICS

The dimensions of frequency is a) [T −1 ]

2.

Time - 180 Min

b) [M 0 L0 T]

c)

[M 0 L0 T -2 ]

d) none of these

A particle is moving on a straight line path with constant acceleration directed along the direction of instantaneous velocity. Which of following statements are flase about the motion of particle ? a) Particle may reverse the direction of motion b) Distance covered is nto equal to magnitued of displacement c) The magnitude of average velocity is less than average speed d) all the above

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3.

Half life of a radioactive material is 1day. If starting material is 16mg, how much of it will be left after 4 days a) 12 mg b) 8mg c) 4 mg d) 1 mg

4.

In the circuit given V (t) is the sinusoidal voltage source, voltage drop VAB (t) across the resistor R is 1) is half wave rectified

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2) is full wave rectified

3) has the same peak value in the positive and negative half cycles

4) has different peak values during positive and negative half cyles. D1

D2

R i = 100Ω VAB R V(t)

a) 2, 4 5.

R2

b) 2, 3

c)

1, 2

d) 1, 4

Real image of an object lying at a distance d1 from the focus of a concave mirror is formed at distance d 2 from the foucs, then focal length of the mirror will be

a)

d1 d2

b)

d2 d1

c)

d1d 2

d)

d1 d 2

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6.

Ratio of amplitudes of the waves coming from two slits having width in the ratio 4 : 1 will be a) 1 : 2 b) 2 : 1 c) 1 : 4 d) 4 : 1

7.

A closed loop is placed in a non- uniform magnetic field a) The force experienced by it is always zero

b) The force acting on the loop is zero only when the loop is parallel to the field

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c) The torque experienced by the loop is zero only when the loop is perpendicular to the field. d) The loop always experiences a torque

for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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2

8.

G G

For an electromagnetic wave the direction of the vector E × B gives : a) the direction of the electric field b) the direction of magnetic field c) the direction of wave propagation d) the direction of the electromagnetic force on a proton

9.

10.

What work must be done to rotate an electric dipole through an angle θ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E a) W = pE(1 - cos θ)

b) W = pE(1 + cos θ)

c) W = 2PE(1 - cos θ)

d) none of these

A solid cube is placed on a horizontal surface. The coefficiet of friction between them is µ, where

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µ < 1 . A variable horizontal force is is applied on the cube’s upper face, perpendicular to one edge 2

and passing through the midpoint of that edge. The maximum acceleration with which it can move without topping is

Force

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a) µg 11.

b) 2µg

c)

 

1

d) µ + 2  g

g(1 - 2µ )



Two identical rods are made of different materials whose thermal conductivities are k1 and k 2 . They are placed end to end between two heat reservoirs at temperatures Q1 and Q2 , The temperature of the junction of the rods is

θ1 a)

θ1 + θ 2 2

c)

k 1θ 2 + k 2 θ1 k1 + k 2

k2

k1

θ2

PAGE b)

d)

k 1θ1 + k 2 θ 2 k1 + k 2

k 1θ1 + k 2 θ 2 k1 + k 2

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3

12.

A circular cylinder of radius R and heigh H is filed with water to a height

2 H . It starts rotating about 3

its axis with constantly increasing angular speed.

H

2 H 3

a) 1, 2, 4 13.

At all speeds, shape of the free surface is parabolloid

2)

The free surface touches first the brium of cylinder and then the base of the cylinder

3)

The free surface cannot touch the base without spillig water

4)

The free surface touches the brim as well as base at the same instant.

b) 2, 3, 4

c)

1, 2

d) 1, 2, 3

A long solenoid of self-inductance, L, not carrying any current, is placed in a uniform magnetic filed, with its axis parallel to the direction of the field. The total magnetic flux linked with the solenoid is φ. The energy of the magnetic field contained inside the solenoid is a) zero

14.

1)

b)

PAGE φ2 L

c)

φ 2L

d)

1 Lφ 2

A milliammeter of range 10 mA and resistance 9Ω is joined in a circuit as shown. The meter gives fullscale deflection for current I when A and B are used as its terminals, i.e., current enters at A and leaves at B (C is left isolated). The value of I is

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9Ω 10mA 0.1Ω

A 15.

B

0.9Ω

a) 100mA

b) 900mA

c) 1A

d) 1.1A

C

G

Calculate the work done by a force F = (î + 2ˆj + 3kˆ)N, to displace a body from position A to position B. G

The position vector of A is r1 = (î + 3ˆj + kˆ) m and the position of vector of B is r2 = (2î + 2ˆj + 3kˆ)m a) 5J 16.

b) 3J

c)

2J

d) 10J

Consider the situation in which the horizontal suface accelrates towards right with a0 with respect to ground, as shown in fig. Choose the correct statement. If the acceleration a 0 starts increasing uniformly from zero

m1 Rough µ

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m2

a0

a)

the block m1 starts moving first.

b)

both block m2 starts moving first

c)

both the blocks start moving together because the blocks are in contact with each other.

www.aieeepage.com d)

both the blocks will always move together irrespective of the fact whether they are in contact or not.


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4

17.

An engine whistling at a constant frequency n 0 and moving with a constant velocity goes past a stationaryobserver, As the engine crosses him, the frequency of the sound heard by him changes by a factor f. The actual differency in the frequencies of the sound heard by him before and after the engine crosses him is a)

18.

1 n0 (1 − f ) 2 2

b) 1.5 ve

 1− f   n0  1+ f 

1

 1− f f

d) 2 n0  1 + 

  

c)

1.5 ve

d) 2ve

Choose the correct statement(s) related to the initial and final conditions of pressure.

c)

PAGE b) P =

a) P = p1 + p 2

20.

c)

The escape velocity for a planet is ve . A particle starts from rest at a large distance from, the planet, reaches the planet only under gravitation attraction, and passes through a smooth tunnel through its centre. Its speed at the centre of the planet will be a) ve

19.

1 (1 − f ) 2 n0 b) f 2

p1 + p 2 < p < p1 + p 2 2

p1 + p 2 2

d) Insufficient data

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Choose the correct statement(s) related to the initial and final temperature of the gas

a) T = T1 + T2

b)

T=

T1 + T2 T1 T2 + P1 P2

c)

T=

P1 + P2 P1 P2 + T1 T2

d) Insufficient data

21.

The earths magnetic field at a certain point is 0.70 gauss. This field is to be annulled by the magnetic field at the centre of a circulr conducting loop 5.0 cm in radius. the required current is about a) 0.66 A b) 5.6 A c) 0.28 A d) 2.8 A

22.

The motion of a body falling from rest in a resisting medium is described by the equation dt = a − bv. Where a and b are constnat. The velocity at any time t is

dv

a) a (1 − b 2t ) 23.

a

b) b (1 − e

−bt

c) abe−t

)

d) ab 2 (1 − t )

When a voltage source that is inducing voltage into a large number of coils is disconnected, and a switch that is in series with the coils of wire is also opened, a spark is observed to jump across the switch terminals as the switch begins to open up. What is the cause of this spark ? a) Free electrons from the voltage source

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b) Free electrons from the coils of wire

c) Collapse of the magnetic field in the coils of wire d) Secondary electron flow from the source 24.

A ball is allowed to fall freely from a height of h meters on a fixed plate. If the successive rebound heights are h1, h 2 , h3...., the distance covered by the ball before coming to rest if e = 0.5 will be a) zero

www.aieeepage.com b) 5 h/3

c) 3 h/5

d) 3 h/4


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5

25.

A block A of mass m1 rests on a block B of mass m2 . B rests on fixed surface. The coefficient of friction between any two sufaces is µ. A and B are connected by a massless string passing around a frictionless pulley fixed to the wall as shown in fig. With what force should A be dragged so as to keep both A and B moving with uniform speed.

F

A

f1 f2 a) µg (2m1 + m2 ) 26.

f1 B

T

PAGE

b) µg (3m1 + m2 )

c) µg (m1 + 2m2 )

c)

b) (4/3)Gm 2

d) zero

(4/3 Gm 2 )

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Water flows through a frictionless tube with a varying cross - section as shown in fig. Pressure P at points along the axis is represented by

P

a)

P

b)

x P

c) 28.

d) µg (m1 + 3m2 )

Identical point masses each equal to m are placed at x = 0, x = 1, x = 2, x = 4,... The total gravitational force on mass m at x = 0 due to all other masses is : a) infinite

27.

T

x P

d)

x

x

The spring constant from the adjoing combination of spring is

PAGE 2K

m

K

K

www.aieeepage.com a) K

b) 2K

c)

4K

d) 5 K/2


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6

29.

A particle of mass m is fixed to one end of a light spring of froce constant K and unstreched length l. The system is rotated about the other end of the spring with an angular velocity ω, in gravity free space. The increase in length of the spring will be

ω

K m

a) 30.

32.

n λ v , and µ µ µ

mω2l

PAGE c)

k − mω2

k + mω2

d) None of these

λ

v

v µ

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b) n, µ and µ

c)

n,2λ and

d)

2n λ , and v µ µ

A metal ball immersed in alcohol weighs W1 at 0°C and W2 at 59°C. The coefficient of cubical expansion of the metals is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be show that a) W1 > W2

b) W1 = W2

c) W1 < W2

d) W1 = (W2/2)

The maximum energy in the thermal rediation from a hot source occurs at a wavelength of 11×10-5 cm. According to Wien’s law, the temperature of this source (on Kelving scale) will be n times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is 5.5 × 10-5 cm.

The value n is

a) 2 33.

mω2l

b)

An electromagnetic radiation of frequency n, wavelength λ, travelling with velocity v in air, enters a glass slab of refractive index µ. The frequency, wavelength and velocity of light in the glass slab will be respevtively. a)

31.

mω 2l k

b) 4

c)

1/2

d) 1

The four capacitors, each of 25µ Fared connected a shown in Fig. The dc voltmeter reads 200 V. The charge on each plate of capacitor is

PAGE V

a) ± 2 × 10-3 C

b) www.aieeepage.com ± 5 × 10-3 C

c) ± 2 × 10-2 C

d) ± 5 × 10-2 C


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7

34.

If in the experiment of wheatstone’s bridge , the positions of cells and galvanometer are interchanged, then balance points will a) change b) remain unchnnged c) depend on the internal resistance of cell and resisof cell and resistance of galvanometer d) none of these

35.

You have the following appliance each of 500 watt running on 220 volts a. c (1) electric iron (2) an electric lamp ( 3 ) an electronic room heater . The electric resistance is a) maximum for the heater b) maximum for the electric lamp c) maximum for the electric iron

36.

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the nth sec to the distance covered in n sec is 2

1

a) n − 2 n 37.

d) same in all the three cases

b)

PAGE 1

n2

−

1 n

c)

If the potential energy of the molecule is given by U =

2

n2 A

r

6

−

−

1

n2

B . 12

2

1

d) n + 2 n

Then at equilibrium

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position its potential energy is equal to a) − A /4B 2

38.

d) A/2B

2 A/B

b) 682.4 m/s

c)

684.4 m/s

d) 684.3 m/s

Light takes t1 sec to travel a distance 1cm in vacuum and the same light takes t 2 sec to travel 10 cm in a medium. Critical angle for corresponding medium will be  10t 

-1 2 a) sin  t   1 

40.

c)

A pipe of length 1.5 m closed at one end is filled with a gas and it resonates in its fundamental mode with a tuning fork. Another pipe of the same length but open at both ends is filled with air and it resonates in its fundamental mode with the same turning fork. Calculate the velocity of sound at 0°C the gas, given that velocity of sound in air at room temp. (30°C), where expt is carred out is 360 m/ s. a) 683.4 m/s

39.

b) A 2 /4B

 t



-1 2 b) sin  10t   1

c)

 10t  sin -1 1   t2 

 t



-1 1 d) sin  10t   2

An infinitely long straight conductor is bent into shape as shown below on fig. It carries a current of i ampere and the radius of the circular loop is r, metre. Then the magnetic induction at the centre of the circular part is

PAGE r

i www.aieeepage.com a) zero

b) Infinite

c)

µ 0 2i . (π + 1) 4π r

µ

2i

d) 4π0 . r (π - 1)


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8

41.

A fuse wire with a radius of 1mm blows at 1.5A. If the fuse wire of the same material should blow at 3.0A, the radius of the wire must be a) 41/4 mm

42.

b) 2 2 mm

c)

d) 8.0 mm

The ratio of momentum of an electron and an alpha particle which are accelerated from rest by a potential difference of 100 V is a) 1 c)

43.

5 mm

(m e /m α )

b)

(2me /2m α )

d)

(m e /2m α )

A radioactive material has a mean lives of 16 years and 520 year for α and β emission respectively. The material decays by simultaneous α and β emission. The time in which 1/4th of the material intact is a) 4675 year b) 720 year c) 648 year

PAGE d) 324 year

44.

The velocity of light c measured by an observer moving with velocity equal to that of light in the direction of propagation of light is a) 0 b) c c) 2c d) uncertain

45.

In the spring - block system shown, the block of mss m moves over a smooth horizontal surface, and under goes SHM with time period = T and amplitude = A.A constnat horizontal force F not begins to acts on the block. The motion of the block will now be

www.aieeepage.com m

K a) Periodic but not SHM

b) SHM with time period = T

c) SHM with time period = 46.

F

 F  T+   mA 

−1 2

−1

d) SHM with time period =

 F 2 T-   mA 

When the filament of a light bulb is heated slowly, its colour changes from red to orange to yellow and eventually to white. It never appears green or blue. This is because a) The maximum temperature attainable gives maximum intensity of emmison in the ultraviolet part of the spectrum

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b) The temperature range in which green and blue light predominate is too narrow c) The filament is not black at high temperatures and Wien’s displacement law does not apply d) any green and blue light emitted is always accompained by more intense red and orange emission. 47.

A dip circle lying initially in the magnetic meridian is rotated through angle θ in the horizontal plane. The tangent of angle of dip is increased in the ratio a) cos θ : 1

www.aieeepage.com b) sin θ : 1

c) 1 : cos θ

d) 1 : sin θ


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9

48.

The figure shows a transparent sphere of radius R and refractive index µ. An object O is placed at a distance X from the pole of the first surface so that a real image is fromed at the pole of the exactly opposite surface. If an object is placed at a distance R from the pole of first surface, then the real image is formed at a distance R from the pole of the second surface. The refractive index µ of the sphere is given by

Air

Air

I

O

X

a) 1.5 49.

2R

b) 2

c)

d) none of these

2

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Two resistance thermometers are made, one of the platinum wire and the other of germanium wire. The resistance of both the thermometers are equal at toom temperaturem. The two resistor wires are connected in series to a battery. Now two resistance wires are heated to 100°C. The potential drop in the two resistance is measured. Which of the following statement is correct a) The potential drop across the platinum wire is equal to the potential drop across the germanium wire

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b) The potential drop across the platinum wire is greater than that across germanium c) The potential drop across the platinum wire is lessthan that across germanium d) The natre of potential drop cannot be ascertained unless the magnitude of current is known. 50.

The magnet in figure rotates as shown on a pivot through its center. At the instant shown, what are the directions of the induced currents

A

51.

D

C

B

a) A to B and C to D

b) B toA and C to D

c) A to B and D to C

d) B to A and D to C

A particle moving in a straight line with uniform acceleration is observed to be at a distance ‘a’ from a fixed point initially. It is at distances b, c, d from the same point after n,2n, 3n second. The acceleration of the particle is a)

c − 2b + a n2

c)

c + 2b + a 4n 2

PAGE b)

c+b+a 9n 2 c−b+ a

d) www.aieeepage.com n 2


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52.

A block of mass m is kept in elevation which starts moving down ward with an acceleration a as shown

in fig. The block is observed by two observers A and B for time interval t 0 .

A

m

a

B

PAGE

The observer B finds that the work done by pseudoforce is

b) − ma 2t 0

a) zero c) + ma 2t 0 53.

d) −mgat0

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A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. The angular speed will approximately a) increase by 1% b) decrease by 1% c) decrease by 0.67%

54.

d) decrease by 0.33%

The molar heat capacity of an ideal gas at constant pressure is greater than that at constant volume because a) work has to be done against intermolecular forces as the gas expands b) work has to be done against external pressure as the gas expands c) the molecules gain rotational kinetic energy as the gas expands d) when the molecules are farther apart, they collide less frequently and the average molecular energy decreases

55.

In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed u. The pulleys A and B are fixed. The mass M moves upwards with a speed.

A P

a) 2u cos θ

2a

B

x

PAGE Q

θ

www.aieeepage.com b) u/cos θ

c) 2u/cos θ

d) u cos θ


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11

56.

Two masses each equal to m are lying on X-axis at (-a, 0) and (+a, 0) respectively as shown in fig. They are connected by a light string. A force F is applied at the origin and along the Y-axis. As result, the masses move towards each other. What is the accelreation of each mass ? Assume the instaneous position of the masses as (-x, 0) and (x, 0) respectively.

F

-x 57.

(a, 0)

(-a, 0)

m

m

O

2F

c) m

x

F

x F . m (a 2 − x 2 )

a) .

b) 2m

x 2

(a − x )

2

(a − x 2 )

2F 2 F ( a 2 − x 2 ) . m x

d)

2

x

.

The curcuit is as shown in the fig. the cell is ideal with e.m.f = 15 V, each resistance is of 3Ω . The potential difference across the capacitor is

PAGE C

R

2µF

R

R

a) zero R www.aieeepage.com

R

c)

b) 9 V

12 V

d) 15 V

15V 58.

Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string. The time period of assembly in magnetic field of strength H is 3 seconds. If now the polarity of one of teh magnets is reversed and the combination is again made to oscillate in the same field, the time of oscillation is a) 3 sec

59.

c)

b) 3 3 sec

d) 6 sec

3 / 3 sec

The figure shows the displacement-time graph of a body moving in a stright line Which of the graph shown in the fig., represents the velocity-time graph of the motion of the body ?

Y s

Y

Y

v

v

O 1

2

3 4 t

X

a)

PAGE O

1

2

3

4

X

b)

O

1

2

3

4

X

4

X

v

v

O

t

Y

Y

c) www.aieeepage.com t

3

2

1

t

d)

O

1

t

2

3

4


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12

X

Jack and Jill are skating on a pond so that they are moving with the same speed v in the same straight line. Jack is skating backwards facing Jill. Jack throws a ball to Jill at time t1 and receives it back at time t2.

Speed

Speed

Assuming that the time of flight is negligible and that Jack and Jill weigh the same, which one of the sketches gives the correct speed – time relationship for the two skaters?

Jack Jack

PAGE

Jill

Jill

t1

t2

t1

Time

t2

Time

www.aieeepage.com(b)

(a)

Speed

Speed

60.

Jack Jack Jill Jill

t1

t2

t1

Time

(c)

t2

Time

(d)

PAGE

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13

Chemistry 61.

For a covalent solids, the units which occupy lattice point are : a) atoms b) ions c) molecule

d) electron

62.

The following quantum numbers are possible for how many orbital n = 3, l = 2 a) 4 b) 3 c) 2 d) 1

63.

The electronic configuration of an element is 1s2, 2s2 2p6, 3s2 3p3. The atomic number of element just below this element in the periodic table is : a) 49 b) 31 c) 33 d) 34

64.

If a molecule MX has dipole moment zero then the sigma (s) bonding orbitals used by M(Z< 21) is : a) sp2-hybridized b) pure p-orbitals c) sp3 hybridized d) sp-hybridized

65.

Which type of hydrocarbon is present in commercial gasoline : a) Straight chain hydrocarbon b) Aromatic hydrocarbon like toluene

PAGE

c) Branched hydrocarbon 66. 67. 68. 69. 70.

d) Linear unsaturated hydrocarbon

Which of the following does not give iodoform test : a) 3-Pentanone b) 2-Pentanone c) Ethanol

d) Ethanal

Nitrous acid on reaction with primary aliphatic amine gives : a) Alkyl nitrite b) Secondary amine c) Alcohol

d) Nitro alkane

Reactive species in the nitration of benzene is : a) HNO3 b) NO3-

c)

NO2-

d) NO2+

Cyclone collector is used for reducing : a) Water pollution b) Air pollution

c)

Soil pollution

d) All the above

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Which of the following does not give Claisen condensation reaction : a) C6H5COOC2H5 b) C6H5CH2COOC2H5 c) CH3COOC2H5

71.

Element A changes to element C by the following tow step process : (i)

72.

d) None of these

A → B + 2He

(ii) B → C + 2e- then : a) A and C are isotopes

b) A and C are isobars

c) A and B are isobars

d) A and B are isotopes

PAGE

The hypothetical reaction A 2 + B 2 → 2AB; follows the following mechanism A 2 Fast  → A + A, → AB + B, A + B Fast A + B 2 Slow  → AB. The order of the overall reactions is

a) 0 73.

b) 1

c)

2

d) 3/2

The standard reduction potential of Pb and Zn electrodes are -0.126 and -0.763 volts respectively. The

www.aieeepage.com c) > 0.637 V

emf of the cell Zn/Zn+2 (0.1M) || Pb +2 (1M)/Pb is a) 0.637 V

b) < 0.637 V

d) 0.889


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14

74.

The relationship between the values of osmotic pressure of solutions obtained by dissolving 6.00 g L−1 of CH 3 COOH (π1 ) and 7.45 g L−1 of KCl ( π 2 ) is

a) π1 < π 2 75.

76.

b) π1 > π 2

78.

π

+

C H 5 Mgl H O/H → B 2 → tert. Pentyl alcohol What is ‘A’? A 2ether

b) Acetaldehyde

c)

Acetone

d) Propanal

PAGE

Correct order of -I effect is : a) - NR3+ > OR- > F

b) F > - NR3+ > - OR

c) - NR3+ > F > - OR

d) - OR > - NR3+ > F

2-bromopentane reacts with alcoholic KOH to give : a) Cis - 2 - pentene b) Trans - 2 - pentene

www.aieeepage.com Aniline is a reactive system for electrophilic substitution. The compound formed by heating aniline c) 1-Pentene

79.

π

1 2 d) π + π = π + π 1 2 1 2

Calculate the temperature at which ∆G = −5.2 kJ mol-1 , ∆H = 145.6 kJ mol-1 and ∆S = 116 JK -1 mol-1 for a chemical reaction a) 1300°C b) 1300 K c) 130 K d) 130°C

a) pentanone 77.

π1 = π 2

c)

d) None of the above

with acetic anhydride will be :

a)

b)

O

c)

80. 81.

NH

C

CH 3

d)

PAGE

Iodine on oxidation with this thiosulphate gives : a) tetrathionate ion b) sulphide ion c)

sulphate ion

d) sulphite ion

Sodium is prepared by the electrolysis of liquid mixture of 40% NaCl and 60% CaCl2 because : a) Ca2+ can reduce NaCl to Na

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b) CaCl2 helps in electrical conduction

c) this mixture has low melting point than NaCl d) Ca2+ can displace Na from NaCl


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15

82.

Cr in [Cr(NH3)6] Br3, has how many unpaired electrons : a) 4 b) 3 c) 2

d) 1

83.

The molar freezing point constant for water is 1.86°C/mole. If 342 gm of cane 100 g of water the solution will freeze at a) -1.86° b) 2.42°C c) -3.92°C d) 1.86°C

84.

Atoms with the same mass number but having different nuclear charge are called a) Isobars b) isotones c) Isochores d) Isotopes

85.

The simplest way to check whether a system is colloidal is by a) Brownian movement b) Electrodialysis c) Tyndall effect

86.

d) finding out particle size

Which of the following halogens exist in the solid state ?

PAGE

a) F2 87.

b) Cl2

I2

d) Br2

c)

Na 2O

d) Na 2CO3

Chroine oxidises Na 2 S2 O3 to form a) Na2SO4

88.

c)

b) Na2SO3

A substance which decomposes at or below its boiling point can be best purified by a) Fractional distillation b) Simple distillation

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c) Distillation under reduced pressure 89.

90.

How many

σ and π

bonds are there in the molecule of tetracyanoethene ?

a) nine σ and nine π bonds

b) Five σ and eight π bonds

c) Nine σ and seven π bonds

d) Five π and nine π bonds

Which substance chars when heated with conc. H2SO4 a) Fat

91.

b) Protein

c)

Hydrocarbon

d) Carbohydrate

The value of molar conductivity of HCl is greater that of NaCl at a particular temperature because a) molecular mass of HCl is less than that of NaCl b) velocity of H + ions is more than that of Na + ions c) HCl is strongly acidic d) ionisation of HCl is larger than that of NaCl

92.

Which one of the following substance is used in the labratory for fast drying of neutral gases ? a) Phosphrous pentoxide b) Active charcoal

PAGE

c) Anhydrous calcium chloride 93.

d)

Na 3 PO 4

Concentrated nitric acid passivates iron due to

a) formation of Fe(NO 3 ) 2 , which does not reach with iron , on the surface of the ioron b) formation of a protective coating of the oxide of iron which does not react with nitric acid , on the surface of the iron c) formation of a stable complex on the surface of the iron

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d) decomposition of nitric acid into NO 2 and O 2 for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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16

94.

For the square planar complex [M (a) (b) (c) (d)] (where M=central metal and a, b, c and d are monodenate ligands), the number of possible geometrical isomrs are a) 1 b) 2 c) 3 d) 4

95.

If H 2SO4 ionises as H 2SO4 + 2H 2O → 2H3O+ + SO24 −

then total number of ions produced by 0.1 M H2SO4 will be a) 9.03×1021 96.

c)

6.02×1022

d) 1.8×10-23

If a dilute solution has N1 mole of the solute and N2 moles of both solute and solvent, then the ratio of the decrease in the vapour pressure with the vapour of a solvent is equal to a)

97.

b) 3.01×10 22

N1 N2

b)

N1 + N 2 N2

N1 N1 + N 2

c)

PAGE

d)

N 2 − N1 N1

The colour of K2Cr2O7 changes from red orange to lemon yellow on treatment with aqueous KOH because of a) reduction of Cr (VI) to Cr (III) b) Formation of chromium hydroxide

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c) Conversion of dichrromate to ion to chromate ion

d) Oxidation of potassium hydrozide to potassium peroxide 98.

Identify the correct statement with respect to carbon monoxide; a) It combines with water to given carbonic acid b) It reacts with haemoglobin in red blood cells c) It is a powerful oxidizing agent

99.

d) It is used to prepare aerated drinks

Pale blue colour of liquid oxgen is due to a) Electronic transitions from triplet ground statement to excited singlet state b) Electronic transitions from singlet ground state to excited triple state c) Excitation of π* 2p1X and π* 2p1Y electrons to π* 2pZ M.O’s d) None of these

100. A compound contains 15.05% nitrogen by wiehgt if the molecular of the compound is 93, then the number of nitrogen atoms present in one molecule of the compound, is/are a) 3 b) 1 c) 2 d) 4 101. Reaction of acetaldehyde with HCN followed by hydrolysis gives compound which shows a) Optical isomers b) Geometrical isomerism c) Metamerism d) Tautomerism

PAGE

102. Which of the following statements is/are not correct 1) A compound with D-configuration will always be dextrorotatory 2) A compound with D-configuration may be dextrorotatory or laevorotaiory 3) A compound with L-configuration will always be laevorotatory 4) A compound with L-configuration may be dextrorotatory or laevorotatory a) 1, 3 b) 2, 1 c) 3, 4 d) 2, 3

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103. Which of the following statement is wrong ? a) α - D-Glucose and β - D-Glucose are anomers c) Glucose and mannose are C2 − epimers

b) Sucrose contains fructose in the pyranose form d) Maltose and lactose form osazones.


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17

104. During dialysis a) solvent molecules and ions can diffuse b) solvent molecules, ions and colloidal particle can diffuse c) all kinds of particles can diffuse through the semipermeable membrane d) only solvent molecules can diffuse 105. Ge (II) compounds are powerful reducing agent, where as Pb (IV) compounds are strong oxidants. It can be due to a) lead is more electropositive than germanium b) the ionizaton potential of lead is less than that of germanium c) the ionic radii of Pb 2 + and Pb 4 + are larger than those of Ge 2 + and Ge 4 + d) more pronounced inert pair effect in lead than in germanium

PAGE

106. In the reaction 411 H →42 He + 210 e, the energy released is 26×108 kJ/mol of He. The value of the change in mass (mass of products - mass of reactants) in g/mol of He is a) 0.029 b) -0.029 c) -0.058 d) 0.058 107. The hair dyes available in the market generally contain two bottles, one containing due and the other hydrogen peroxide. Before applying the dye, the two solutions are mixed. The hydrogen peroxide. a) is added to dilute the solution of the dye b) oxidises the dye to given the desired colour

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c) reduces the due to given the desireid colour

d) acidifies the solutionof the dye

108. For the reaction : H 2 (g) + Br2 (g) → 2HBr(g), the experimental data suggests Rate = K[H 2 ][Br2 ]1/2 The molecularity and order of reaction for the reaction is b) 2 and 1

a) 2 and 2 respectively c) 1

1 and 2 respectively 2

1 2

1 respectively 2

d) 1 and 1

1 respectively 2

109. Which of the following does not respond to iodoform test ? a) CH3COCH2COOC2H5

b) CH3COCH2CH2COOC2H5

c) CH3COCH2CH2COCH3

d) CH3COCH2CH3

110. Bakelite is prepared by the reaction between a) Urea and formaldehyde b) Tetramethylene glycol and hexamethylene isocynate c) Phenol and formaldehyde d) Ethylene glycol and dimethylterephthalate

PAGE

111. A solution containing one mole per litre each of Cu(NO3 )2 , AgNO3 , Hg2 (NO3 )2 and Mg(NO3 )2 is being electrolysed by using inert electrodes. The value of standard electrodes potentials (reduction potentials) +

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in volts are : Ag | Agh = 0.80V; 2Hg | Hg 22+ = 0.79V Cu | Cu 2+ = 0.34V; Mg | Mg2+ + 2.37V with increasing voltage the sequence of deposition of metals on the cathode will be : a) Ag, Hg, Cu, Mg b) Mg,Cu, Hg, Ag c) Ag, Hg, Cu d) Cu, Hg, Ag for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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18

112. Equivalent weight of KMnO 4 at pH = 12 is a) M/5

b) M/2

c)

M

d) M/3

113. 50 ml of hydrogen diffuses in 20 minutes from a small hole in a tube then 40 ml of oxygen will diffuse in : a) 12 minutes b) 8 minutes c) 64 minutes d) 32 minutes 114. What is the molarity of H2SO4 solution which is 98% by weight and the density of solution at 35° C is 1.84j gm/cm3: a) 4.18 M b) 8.14 M c) 18.4 M d) 18 M 115. When one mole is heated at constant volume temperature is raised from 298 to 308 K. Heat supplied to the gas is 500 J. Then which statement is correct : a) q = W = 500 J, ∆ U = 0

b) q = ∆ U = 500 J, W = 0

PAGE

c) q ≠ W = 500 J , ∆ U = 0 116. XeF6 + H2O º xeOF4 + 2HF constant = K1

d) ∆ U = 0, q = W = - 500 J

XeO4+ + XeF6 º XeOF4 + XeO3F2 constant = K2 then equilibrium constant for the following reaction XeO4 + 2HF º XeO3F2 + H2O will be : a)

K1 K2

K1

b) K1 + K2

c)

K2 K1

d)

b) SN1

c)

SN°

d) SN2

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(K 2 )2

117. Following reaction is :

a) SE1

118. From the following the number of atoms is greatest in : a) 4 g hydrogen b) 71 g chlorine c) 48 g magnesium

d) 127 g iodine

119. 0.20 g of an organic compound containing carbon, hydrogen and oxygen yields on combustion 0.147 g carbon dioxide and 0.12 g water. The percentage composition of the substance respectively is a) 20.04, 66.6 & 73.30 b) 20.04, 6.66 & 73.30 c) 21.05, 66 & 23.95 d) 24.59, 25.32 & 50.12

PAGE

120. Match List-I with List-II and select the correct answer using the options given below the lists List-I List-II (A) Rosenmund’s reaction 1. Rearrangement of oximes to amides. (B) Reimer-Tiemann’s reaction 2. Conversion of an aldohexose into an aldopentose. (C) Kiliani - Fisher’s synthesis 3. Catalytic reduction of an acid halide to an aldehyde. (D) Beckmann’s rearrangement 4. Conversion of an aldopentose into two aldohexoses. 5. Formylation of a phenol with chloroform and strong base. a) A–3; B–5; C–2; D–1 b) A–3; B–5; C–4; D–1 c) A–3; B–4; C–2; D–5 d) A–5; B–3; C–1; D–4

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19

MATHEMATICS 121.

Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relation from A to B is:

a) 4 b) 8 c) 64 2 122. The next term of the geometric progression x, x + 2, x3 + 10 is : a) 0

b) 54

c)

729 16

d) none

d)

16 729

 x, if x is rational

123. If f ( x) = - x, if x is irrational' then  a)

1

b) f(x) is continuous at x = 2 d) f(x) is a periodic function

f(x) is an odd function

PAGE

c) f(x) is continuous at x = 0 124.

3π / 4 dx is equal to : ∫π / 4 1+ cosx

a) 2

b) -2

c)

1 2

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d) −

125. Equation of curve passing through (1, 1) and satisfying the differential equation is given by : a) x2 = y

b) x = y2

c)

x = 2y

1 2

dy 2y = ; (x > 0, y > 0) dx x

d) y = 2x

126. Let AB be a chord of the circle x 2 + y 2 = r 2 subtending a right anlge at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is a) a parabola b) a circle c) an ellipse d) a pair of straight lines 127. The coordinates of the foot of the perpendicular from the point (1, 3, 4) upon the plane 2x - y + z + 3 = 0 are: a) (1, 1, -4) b) (4, -3, 1) c) (1, -3, -4) d) (-1, 4, 3) 128. If the letter of the word SUCCESS are arranged, then the probability that similar letters occurs together is a)

4 35

b)

3 35

c)

1 35

d)

2 35

129. The minimum value of the expression sin α + sin β + sin γ , where α , β , γ are real number satisfying α + β + γ = π is : a) positive

PAGE

b) zero

c)

negative

d) -3

130. Let f(x) = cos π x + 10x + 3x 2 + x 3 ,−2 ≤ x ≤ 3 .The absolute minimum value of f ( x ) is a) 0 b) - 15 c) 3 - 2 π d) none of these 2 131. The equation (cos p - 1) x + (cos p) x + sin p = 0, in the variable x has real roots. Then, p can take any value in the interval :

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a) (0, 2π)

b) (−π, 0)

c)

 π π − ,   2 2

d)

(0, π )


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20

3

5

7

132. Sum of the series 1 + 1 ! + 2 ! + 3 ! + ..... is a) e-1

b) 2e

c)

3e

d) 5e-7

 1   133. The term independent of a in the expansion of 1 + a + a − 1  

a)

30

b) 0

C 20

c)

30

−30

is d) none of these

C15

134. Differential equation for y = A cos α x + B sin α x, where A and B are arbitrary constants is : a) c)

d2y dx

2

d2y d x2

−α 2 y = 0

b)

+α y = 0

d)

d2y dx

2

+α 2 y = 0

d2y −α y = 0 d x2

PAGE

135. Two masses m1, m2 are connected by a light inextensible string and suspended over a smooth fixed light pulley. Then : b) pressure = m2 a) pressure on the pully = m1 c) pressure < (m1 + m2) d) pressure > (m1 + m2) G

G

G

G

G

G

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136. If the projection of the vector i + j + k on the vector ai + j − 2k be

1 then a is 3

a) 7 b) 0 c) 1/2 d) 2 137. The equation of a diameter of a circle passing through the origin is x + y = 1 and the greatest distance of any point of the circle from the diameter is 5 . Then an equation of the circle is

138.

a) x 2 + y 2 − 2 x + 4 y = 0

b) x 2 + y 2 − 4 x + 2 y = 0

c) x 2 + y 2 + 4 x − 2 y = 0

d) x 2 + y 2 + 2 x + 4 y = 0

Let φ (x) =

∫

x

0

cos3 x dx . The function φ (x) is

 π

a) monotonic increasing in [0, π ]

b) monotonic increasing in 0,   2

c) monotonic decreasing in [0, 2π ]

d) monotonic decreasing in − ,

 π 3π    2 2

139. In a right-angled isosceles triangle the ratio of the circumradius and inradius is a) 2( 2 + 1) : 1

b) ( 2 + 1) : 1

c)

2:1

PAGE 1 2

140. Let f(x) be a periodic function of the period 1 and f   = 3 φ '   is equal to 2

a)

3 2

b)

1 . Lt φ ( x) = 2

1 c) 2 www.aieeepage.com 2

d) x

2 :1

∫ f ( x + n) dx, n ∈ N . 0

Then

d) 1


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21

x3 − x

lim

141.

x→-∞

1+ x6

is equal to

a) -1

b) 1

c)

142. If tan θ = 5 , sin4 θ is a a) positive rational number c) positive irrational number

0

d) 3

b) negative rational number d) negative irrational number

143. If f(x) = x 2 − 3x + 1 and f (2α ) = 2f (α ) , then α is equal to a)

1

b) −

2

1

c)

2

1 2

or −

1 2

d) none of these

144. If in a triangle ABC, if, a, c and angle A is given and c sin A < a < c, then a) b1 + b2 = 2c cos A

b) b1 + b2 = c cos A

c) b1 + b2 = 3c cos A 145.

∫

PAGE

d) b1 + b2 = 4c sin A

ex [1 + (x + 2) log (x + 2)]dx = x+2

a) e x log( x + 2) + c

b)

ex +c x+2

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e x ( x + 2) + c

d) e x ( x − 2) + c

146. If two squares are chosen at random on a chess board, the probability that they have a side in common is a) 147. ∫

1 9

2 7

b)

c)

1 18

d) none of these

c)

sin x

d) 2sin x

cos x dx = x

a) 2 cos x

cos x x

b) 

   2x − 1 1

−1 148. Derivative of sec 

2

1 2

a) 0b)

1

w.r.t 1 + 3 x at x = − 3 is 1 3

c)

d) does not exist

149. If the direction cosines of a straight line are k, k, k, then : a) k > 0 150. If the coefficient of

PAGE

b) 0 < k < 1 m th , ( m + 1) th

and

c)

( m + 2) th

k=1

d) k =

1 3

or −

1 3

terms in the expansion (1 + x) n are in A.P., then

a)

n 2 + 4( 4m + 1) + 4 m 2 − 2 = 0

b)

n 2 + n ( 4 m + 1) + 4 m 2 + 2 = 0

c)

(n − 2 m ) 2 = n + 2

d)

(n + 2m ) 2 = n + 2

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151. In a 12-storey house ten people enter a lift cabin. It is known that they will leave the lift in groups of 2, 3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is a) 78 b) 112 c) 720 d) 132 for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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22

1

2 152. The domain of the function [ x] + 2 x − x is

a) [1, 2] b) [0, 2] c) [0, 1) d) [1, 2) 153. The two points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y = 10 are : a) (-3, 1); (7, 11) b) (3, 1); (-7, 11) c) (3, 1); (7, 11) d) none 154. A man who can swim at the rate of 3 km/hr. in still water wishes to cross the river 1.5 km wide flowing at the rate of 5 km/hr. The direction, to the direction of current, in which he should swim in order to reach the opposite bank as soon as possible is : b) 60o c) 90o d) 120o a) 30o 155. Two students while solving a quadratic equation in x with leading coefficient ‘1’, one copied the constant term incorectly and got the roots 3 and 2. The other copied the constant term corretly -6. The correct roots are a) -2, 3 b) -3, 2 c) -6, -1 d) -1, 6

PAGE

156. The angle between the asymptotesof b

−1  a) 2 tan  a   

x2

a

2

−

y2

b2

=1

b

−1  b) tan  a 

is equalt o c)

 

a 2 tan−1  b

a

−1  d) tan  b   

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157. The product of the perpendiculars drawn from the two foci of an ellipse to the tangent at any point of the ellipse is b) b 2

a) a 2

 1 3   − 1 , then 4 + 5 − 2 + i 2   

158. If i =

a) 1 - i 3

c) 334

 1 3  + 3 − + i  2 2  

b) -1 + i 3

d) 4b 2

4a 2

365

is equals to

c)

i 3

d) -i 3

159. The differential equation of the family of curve y = Ae3x + Be5x, where AB are arbitrary constants is : a) c)

d2y dx

2

d2y dx

2

+8

−

dy + 15y = 0 dx

b)

dy +y = 0 dx

d2y dx

2

−8

dy + 15y = 0 dx

d) none of these

−1 x(x + 1) + sin −1 (x 2 + x + 1) = 160. The number of real solutions of tan

PAGE

π is : 2

a) zero b) one c) two d) infinite 161. Two like parallel forces 5N and 15N, act on a light rod at two points A and B respectively, 6m apart. The resultant forces and the distance of its point of action from the point A are : a) 10N; 4.5 m b) 20 N; 4.5 m c) 20 N; 1.5 m d) 10 N; 1.5 m 162. A particle moves from rest at a distance c from a fixed O with an acceleration

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µ x2

away from O at a

distance x. Then the velocity of the particle at distance 2c from is : a)

µ c

b)

c)

µc

µ c

d) none


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23

−1  2 163. The range of f ( x) = sin  2 + x  is ( [•] denotes greatest integer function)

1



 π

 π

π

a) − 2 ,0, 2    164. The value of tan



b) 0, 2   

c)

π   2

d) none of these

π π + 2 tan + 4 is equal to 16 8

π

π

π

c) cot 16 − 4

b) cot 16

a) cot 8

0

 2 4

d) none of these

5 

165. If A = 3 1 , A 2 − λA + 415 − 5  = 0 then λ is equal to    4 4  a) 2

b) 4

c)

8

d) none of these

PAGE

166. If sin 2 θ - 2sinθ - 1 = 0 is to be satisfied for exactly 4 distinct values of θ ∈ [0, nπ], n ∈ N, then the least value of n is a) 2 b) 6 c) 4 d) 1 167. The centroid of the triangle whose three sides are given by the combined equation is (x 2 + 7 xy + 2 y 2 )( y − 1) = 0 2



a)  3 , 0   

c) www.aieeepage.com 7 2

 7 2 − ,   3 3

b)  3 , 3   

d) none of these

G

G 168. If the sides of a triangle are given by vectors a = iˆ − 2 ˆj + 2kˆ and b = 2iˆ + ˆj + 2kˆ, then the internal bisector is :

a) 3iˆ − ˆj + 4kˆ

b)

1 ˆ ˆ (3i − j + 4kˆ ) 3

c)

3iˆ + ˆj − 4kˆ

d) none of these

G G G G G 169. For any three non zero non coplanar vectors a, b and cG (aG - 2b + cG) • (b - 2cG + aG) × (cG - 2aG + b)) is equal to

GG

a) 3[a b c]

GG

b) 2[a b c]

c)

GG [ a b c]

d) none of these

170. India and pakistan play a 5 match test series, the probablity that India is ahead 2-1after 3 matches is a)

1 2

b)

1   2

2

c)

1   2

3

d) none of these

171. An automobile driver travels from plain to a hill station 120 km distant at an aveage speed of 30 km per hour . He then makes the return trip at an average speed of 25 km per hour .He covers another 120 km distance on plane at an average speed of 50 km per hour . His average speed over the entire distance of 360 km will be a)

30 + 25 + 50 km/hr 3

c)

3 km/hr 1 1 1 + + 30 25 50

PAGE

1

b) (30 + 25 + 50) 2 km/hr d) none of these

172. A particle is moving with a velocity of 30m/sec. The components of the velocity in m/sec at angles 30o and 45o in opposite sides to its directions are : a)

3 − 1, 3 + 1

www.aieeepage.com b) 30( 3 −1),15( 6 −

c) 30( 3 + 1),30( 3 − 1)

2)

d) none of them


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24

173. A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6 meter and weight 3 units. Its centre of gravity G is at a distance 0.4 meter from A. Then the tension of the string at A, in the same unit is : a) 0.2 b) 1.4 c) 0.8 d) 1.0 174. In a triangle ABC, ∠B =

π sin ∠BAD π and ∠C = . Let D divide BC internally in the ratio 1 : 3 then 3 sin ∠CAD 4

equals : a)

1

b)

6

1 3

c)

1 3

d)

2 3

175. A sphere is inscribed in a cube of side 2a. If the cube is bounded by the coordinate planes as its three faces, then the equation of the sphere is a) x 2 + y 2 + z 2 − 2ax − 2ay − 2az + a 2 = 0

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b) x 2 + y 2 + z 2 − 2ax − 2ay − 2az + 2a 2 = 0 c) x 2 + y 2 + z 2 − ax − ay − az + a 2 = 0 d) x 2 + y 2 + z 2 = 4a 2

176. Let a = cos 2 π  + i sin  2 π , α = a + a 2 + a 4 and β = a 3 + a5 + a 6 , then α, β are the roots of the equation  7 

 7 

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a) x 2 − x + 2 = 0 b) x 2 + x − 2 = 0 c) x 2 + x + 2 = 0 d) none of these 177. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sumof three terms and each elements of the the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value a) 1 b) 9 c) 16 d) 24 G G 178. If aG, b, cG are three non-coplanar unit vectors cG is inclined at an angle α to the plane of aG and b, aG

G G G G G G G and cG are equally inclined at an angle β to b . The vector {(a ×b ) × (b × c) × (c × a)} is equal to :

a)

G G 1 sin 2 α cos β (c - a) 2

b)

G G 1 sin 2 β cos α (c - a) 2

c)

G G 1 sin α sin 2 β (c - a) 2

d)

G G 1 sin 2α sin β (c - a) 2

179. Let AB be a chord of the parabola y 2 = 4ax. If the pole of AB with respect to the parabola be (2a, 3a) then the length of AB is a)

13 a

b) 4a

c)

5a

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d) 2 13 a

180. The ratio of the areas between the curves y = cos x and y = cos 2 x and x - axis from x = 0 to x = a) 1 : 2

b) 2 : 1

c)

3 :1

π is 3

d) none of these

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