NARAYANA IIT/PMT ACADEMY
INDIA XIIP IIT LJ (MAINS MODEL)
Exam Date:01-10-2016 Max Marks: 360
Time:3:00
INSTRUCTIONS : 1) There are 3 sections in this paper, consisting Physics, Chemistry, Chemistr y, Mathematics. Mathemat ics. There will be objective type questions with four options having single correct answer. For each correct answer 4 marks awarded. For each incorrect response one fourth (1/4) of the total marks allotted to the question would be deducted. No deduction from the total score will, however, be made if no response is indicated for an item in the answer sheet. The candidates are advised not to attempt such item in the answer sheet if they are not sure of the correct response. More than one answer indicated against a question will be deemed as incorrect response and will be negatively marked. All objective type questions are required to be answered on OMR sheet provided provided with the question question paper. paper. PHYSICS
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A marble going at a speed of 2 ms –1 hits another marble of equal mass at rest. If the collision is perfectly elastic, then the velocity of the first marble after collision is (1) 4 ms –1 (2) 0 ms –1 (3) 2 ms –1 (4) 3 ms –1 A body of mass m moving at a constant velocity v hits another body of the same mass moving with a velocity v/2 but in the opposite direction and sticks to it. The common velocity after collision is (1) v (2) v/4 (3) 2v (4) v/s An 8 gm bullet is is fired horizontally into into a 9 kg block of wood and and sticks in it. The block which is free to move, has a velocity of 40 cm/s after impact. The initial velocity of the bullet is (1) 450 m/s (2) 450 cm/s (3) 220 m/s (4) 220 cm/s A ball is dropped onto a horizontal floor. It reaches a height of 144 cm on the first bounce and 81 cm on the second bounce. The coefficient of restitution is (1) 0 (2) 0.75 (3) 81/144 (4) 1 A stationary body explodes into two fragments of masses m 1 and m2. If momentum of one fragment is p, the energy of explosion is 2 2 p 2 m1 m 2 p 2 p p (1) (2) (3) (4) 2 m1 m 2 2m1m 2 2 m1 m 2 2 m1m 2 A railway truck of mass 16000 kg moving with a velocity of 5 ms –1 strikes another truck of mass 4000 kg at rest. If they move together after impact, their common velocity is (1) 2 ms –1 (2) 4 ms –1 (3) 6 ms –1 (4) 8 ms –1 A particle part icle falls from a height ‘h’ upon a fixed horizontal plane and rebounds. If ‘e’ is the coefficient of restitution, then the total distance travelled before it comes to rest is
1 e2 (1) h 2 1 e
1 e2 (2) h 2 1 e
(3)
h 1 e2
2 1 e2
(4)
h 1 e2
2 1 e2
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Three identical particles moving with velocities v 0 ˆi, 3v 0 ˆj and 5v 0kˆ collide successively with each other in such a way that they form a single particle. The velocity of resultant particle in i, j, k form is v v v (1) v 0 ˆi 3jˆ 5kˆ (2) 0 ˆi 3jˆ 5kˆ (3) 0 ˆi 3jˆ 5kˆ (4) 0 ˆi 3jˆ 5kˆ 3 2 3 In two separate collisions, the coefficient of restitutions e 1 and e2 are in the ratio 3 : 1. In the first collision the relative velocity of approach is twice the relative velocity of separation. Then, the ratio between relative velocity of approach and relative velocity of separation in the second collision is (1) 1 : 6 (2) 2 : 3 (3) 3 : 2 (4) 6 : 1 A sphere of mass m moving with constant velocity u, collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second sphere is 1 e 1 e e 1 e (1) (2) (3) (4) 1 e 1 e 1 e e A ball of mass ‘m’ moving with a horizontal velocity ‘v’ strikes the bob of mass ‘m’ of a pendulum at rest. During this collision, the ball sticks with the bob of the pendulum. The height to which the combined mass raises is (g = acceleration due to gravity) v2 v2 v2 v2 (1) (2) (3) (4) 4g 8g g 2g A 3 kg sphere makes an inelastic collision with another sphere at rest and they stick after
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the collision. If the composite mass moves with a speed of
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1 4
th
of the initial speed of 3 kg
sphere, the mass of second sphere is (1) 12 kg (2) 9 kg (3) 6 kg (4) 3 kg A moving sphere P collides another sphere Q at rest. If the collision takes place along the line joining their centres of mass such that their total kinetic energy is conserved and the 8 fraction of K.E. transferred by the colliding particle is , then the mass of P and the mass 9 of Q bears a ratio (1) 8 : 3 (2) 9 : 8 (3) 2 : 3 (4) 2 : 1 Two spheres A and B of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ‘t’, ‘A’ impinges on ‘B’. If ‘e’ is the coefficient of restitution, the second impinge will occur after a time 2t t t t (1) (2) (3) (4) e e e e A sphere A of mass m moving with certain velocity hits another stationary sphere B of VA 1 e different mass. If the ratio of velocities of the spheres after collision is , where e VB 1 e is coefficient of restitution. The initial velocity of sphere A with which it strikes is VB VA (1) VA + VB (2) VA – VB (3) VB – VA (4) 2
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A rigid body consists of a 3kg mass located at r1 2iˆ 5ˆj m and a 2 kg mass located at
r2 4iˆ 2ˆj m . The position of centre of mass is
14 ˆ 19 ˆ j i m 5 5
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14 ˆ 19 ˆ i j m 5 5
(2)
19 ˆ 14 ˆ i j m 5 5
(3)
(4) 0
Two blocks of masses 10 kg and 30 kg are placed along a vertical line if the first block is raised through a height of 7 cm then the distance through the second mass should be moved to raise the centre of mass of the system by 1 cm is (1) 1 cm up (2) 1 cm down (3) 2 cm down (4) 2 cm up 10iˆ 2ˆj 5kˆ Two bodies of 6 kg and 4 kg masses have their velocity 5iˆ 2ˆj 10kˆ and respectively. Then the velocity of their centre of mass is (1) 5iˆ 2ˆj 8kˆ (2) 7iˆ 2ˆj 8kˆ (3) 7iˆ 2ˆj 8kˆ (4) 5iˆ 2ˆj 8kˆ A dog weighing 5kg is standing on a flat boat so that it is 10 metres from the shore. It walks 4m on the boat towards the shore and then halts. The boat weights 20 kg and one can assume that there is no friction between it and water. The dog from the shore at the end of this time is (1) 3.4 m (2) 6.8 m (3) 12.6 m (4) 10 m The distance of centre of mass from ‘O’ is 5g
4g
6g
0
0.3 m
lm
(1) 0.21 m (2) 0.35 m (3) 0.42 m (4) 0.48 m Particles of masses 1 kg and 3 kg are at (2i + 5j + 13k) m and (–6i + 4j – 2k) m then instantaneous position of their centre of mass is 1 1 (1) 16i 17 j 7k m (2) 8i 17 j 7k m 4 4 1 1 (3) 6i 17 j 7k m (4) 6i 17 j 5k m 4 4 Two bodies of masses 5 kg and 3 kg are moving towards each other with 2ms –1 and 4 ms –1 respectively. Then velocity of centre of mass is (1) 0.25 ms –1 towards 3 kg (2) 0.5 ms –1 towards 5 kg (3) 0.25 ms –1 towards 5 kg (4) 0.5 ms –1 towards 3 kg A circular disc of radius 20 cm is cut from one edge of a larger circular disc of radius 50 cm. The shift of centre of mass is (1) 5.7 cm (2) –5.7 cm (3) 3.2 cm (4) –3.2 cm A uniform metre rod is bent into L shape with the bent arms at 90 o to each other. The distance of the centre of mass from the bent point is L L L L m m m m (1) (2) (3) (4) 4 2 2 2 2 8 2 A bomb of mass ‘m’ at rest at the coordinate origin explodes into three equal pieces. At a certain instant one piece is on the x-axis at x = 40 cm and another is at x = 20 cm, y = –60 cm. The position of the third piece is (1) x = 60 cm, y = 60 cm (2) x = –60 cm, y = –60 cm (3) x = – 60 cm, y = 60 cm (4) x = 60 cm, y = –60 cm
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Particles of masses m, 2m, 3m ….. nm gram are placed on the same line at distance, l, 2l, 3l, …. nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in cm in n n 2 l l 2n 1 l l 2l (1) (2) (3) (4) 3 n 1 2 n n 2 l l
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Figure shows a square plate of uniform thickness and side length 2m . One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is O
(1) 1/3 m
(2) 1/2 m
(3) 1/6 m
(4) 1/8 m Kx 2
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The centre of mass of a non uniform rod of length L whose mass per unit length
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Where k is a constant and x is the distance from one end is : 3L L K 3K (1) (2) (3) (4) 4 8 L L Four identical planks each of lengths ‘L’ are arranged one above the other over a table as shown. Each projects a distance ‘a’ beyond the edge of the one that is below it. What is the maximum possible value of ‘a’ for the system to be in equilibrium without tripping forward?
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L
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(1) L/5 (2) L/4 (3) L/3 (4) L Two bodies of masses m1 and m2 are moving with velocity v 1 and v2 respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is (v is relative velocity between the masses) m1m 2 v 2m1m 2 v 4m1m 2 v (1) (2) (3) zero (4) m1 m 2 m1 m2 m1 m 2 CHEMISTRY
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When molecules of type A react with molecules of type B in one-step process to given AB 2, the rate law is (1) rate = K[A] 1 [B]2 (2) rate = K[A]2[B]1 (3) rate = K[2A] [B] (4) rate = K[A] [B] The units of rate of reaction and rate constant are identical for a (1) fraction-order reaction (2) zero-order reaction (3) first-order reaction (4) second-order reaction The decomposition of H 2O2 is represented as H2O2 H2O + O(slow) (O) + (O) O2 (fast) Then the order of the reaction is
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(1) 1 (2) 2 (3) 0 (4) 3 For the reaction A B the rate law is, rate = K[A]. Which of the following statement is incorrect? (1) The reaction follows first order kinetics (2) The t 1 of reaction depends upon initial concentration of reactants 2
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(3) K is constant for the reaction at a constant temperature (4) The rate law provides a simple way of predicting the concentration of reactants and products at any time after the start of the reaction The time for half change for a zero order reaction is ……….. (1) proportional to the initial concentration (2) proportional to the square root of the initial concentration (3) independent of initial concentration (4) inversely proportional to the initial conc. Which of the following statements regarding molecularity of the reaction is correct? (1) Molecularity relates to mechanism of reaction (2) It cannot be negative or fractional (3) Molecularity of a complex reaction has two (or) more steps and each individual step has its own molecularity. (4) All are correct The rate of gaseous reaction is given by K[A] [B]. If the volume of reaction vessel is 1 reduced to of initial volume the reaction rate relative to the original rate is 4 1 1 (1) (2) (3) 8 (4) 16 16 8 For the reaction 4NH3 5O2 4NO 6H2 O, the rate of reaction with respect to NH 3 is
2 103 Ms1. Then the rate of the reaction with respect to oxygen in Ms –1 (1) 2 103 (2) 103 (3) 103 (4) 103 The rate of formation of SO 3 in the reaction 2SO 2 + O2 2SO3 is 100 g min –1. Hence rate of disappearance of O 2 is (1) 50 g min –1 (2) 100 g min –1 (3) 20 g min –1 (4) 40 g min –1 The rate of a certain reaction at different times is as follows Time 0 10 20 30 2 2 2 10 10 10 102 Rate The order of the reaction is (1) 1 (2) zero (3) 2 (4) 3 Which of the following relation is correct for a first order reaction? (K = rate constant; r = rate of reaction ; c = conc. of reactant) c r (1) K = r × c2 (2) K = r × c (3) K (4) K r c If the rate of reaction A B triples on increasing the concentration of A by 9 times, then the order of reaction is (1) 2 (2) 1 (3) 1/2 (4) 4
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The initial rates for gaseous reaction A + 3B AB3 are given below [A] (M) [B](M) Rate(M sec –1) 0.1 0.1 0.002 0.2 0.1 0.002 0.3 0.2 0.008 0.4 0.3 0.018 order of the reaction is (1) zero (2) three (3) one (4) two Half life of a zero order reaction is 250 sec. t 75%, t100% of the reaction respectively in sec. are (1) 500, 375 (2) 375, 500 (3) 300, 575 (4) 575, 300 In the equilibrium A + B C + D, the activation energy for forward reaction is 25 k. cal/mole and that of backward reaction is 15 k. cal/mole. Which one of the following statement is correct (1) It is an exothermic process (2) It is an endothermic process (3) It is reaction for which H = 0 (4) It is a sublimation process For a reversible reaction A B, which one of the following statements is wrong from the given energy profile diagram B E
A Re action coordinate
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(1) Activation energy of forward reaction is greater than backward reaction (2) The forward reaction is endothermic (3) The threshould energy is less than that of activation energy (4) The energy of activation of forward reaction is equal to the sum of heat of reaction and the energy of activation of backward reaction. 1 For a chemical reaction Y2 2Z Product, rate controlling step is Y Z Q. If then 2 the concentration of Z is doubled, the rate of reaction will (1) Remain the same (2) Become four times (3) Become 1.414 times (4) Become double Observe the following reaction 2A + B C. The rate of formation of C is d A 2.2 × 10 –3 mol L –1 min –1. What is the value of (in mol L –1 min –1)? dt –3 –3 (1) 2.2 × 10 (2) 1.1 × 10 (3) 4.4 × 10 –3 (4) 5.5 × 10 –3 2A + B D + E for this reaction proposed mechanism A + B C + D(slow), A + C E(fast). The rate law expression for the reaction is 2
(1) r K A B 50.
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(2) r K A B
2
(3) r K A
(4) r K A C
For a reaction A + 2B products, when B is taken in excess, then the rate law expression can be written as (1) Rate = K[A]1[B]0 (2) Rate = K[A]1[B]2 (3) Rate = K[A][B] (4) Rate =K[A]2[B]1 The unit of rate constant obeying the rate expression r = K[A] 1[B]2/3 is
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(1) mole –2/3 lit2/3time –1 (2) mole2/3 lit –2/3 time –1 (3) mole –2/3 lit –2/3 time –1 (4) mole2/3 lit2/3 time –1 For the reaction A + B products, it is found that order of A is 1 and order of B is ½. When concentrations of both A & B are increased four times the rate will increase by a factor (1) 6 (2) 8 (3) 4 (4) 16 The product of half life (t 1/2) and the square of initial concentration of the reactant (a) is constant. Then the order of reaction is (1) 2 (2) 3 (3) 0 (4) 1 50% completion of a first order reaction takes place in 16 minutes, then the fraction that would react in 32 minutes from the beginning (1) 1/2 (2) 1/4 (3) 1/8 (4) 3/4 75% of a first order process is completed in 30 min. The time required for 93.75% completion of same process (in hr)? (1) 1 (2) 120 (3) 2 (4) 0.25 The rate of the reaction CH3COOC2H5 + NaOH CH3COONa + C2H5OH is given as rate = K[CH3COOC2H5] [NaOH]. If three times water is added to the reaction mixture, the rate of the reaction compared to the original rate will be 1 1 1 th (1) rd (2) th (3) (4) 16 times 3 9 16 If doubling the concentration of the reactant A increases the rate by 4 times and tripling the concentration of A increases the rate by 9 times, the rate is proportional to (1) concentration of A (2) square of concentration of A (3) under root of conc. of A (4) cube of concentration of A Give the following data for the reaction: X + Y Z [X] [Y] Rate × 10 –1 ms –1 1.0 M 1.0 M 0.25 2.0 M 1.0 M 0.50 1.0 M 2.0 M 0.25 1.0 M 3.0 M 0.25 Which one is the rate law equation ? (1) Rate = K[X][Y] (2) Rate = K [X]0[Y]1 (3) Rate = K[X][Y] 0 (4) Rate = K[X][Y] 2 For the reaction system: 2NO (g) + O2(g) 2NO2(g) volume is suddenly reduced to half of its value by increasing the pressure on it. If the reaction is of first order with respect to O 2 and second order with respect to NO, the rate of reaction will (1) diminish to one-eight of its initial value (2) increase to eight times of its initial value (3) increase to four times of its initial value (4) diminish to one fourth of its initial value For N 2O5 2NO 2 1/ 2O2 , it is found that
d
d
N 2 O5 K1 N2 O5 , NO2 K2 N2 O5 ;
dt (1) K 1 = 2K 2 = 3K 3
dt (2) 2K 1 = 4K 2 = K 3
d
O 2 K3 N 2 O5 then dt (3) 2K 1 = K 2 = 4K 3 (4) K 1 = K 2 = K 3
MATHEMATICS
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1 If the points (a, 1), (2, –1) and , 2 are collinear, then a is equal to 2 (1) 1
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(2) 0
(3) 2
(4)
1
4 If Points A(x1, y1), B(x2, y2) and C(x3, y3) are such that x 1, x2, x3 and y1, y2, y3 are in A.P., then (1) A, B and C are concylic points (2) A, B and C are collinear points (3) A, B and C are vertices of an equilateral triangle (4) none of the above If Points A(x1, y1), B(x2, y2) and C (x3, y3) are such that x 1, x2, x3 and y1, y2, y3 are in G.P. with same common ratio, then (1) A, B and C are concylic points (2) A, B and C are collinear points (3) A, B and C are vertices of an equilateral triangle (4) none of the above If 3a + 4b + c = 0, then the lines ax + by + c = 0 always passing through: (1) (3, 4) (2) (4, 3) (3) (3, 3) (4) none of these Set of lines (x – 2y + 1) + (x + y) = 0 (where is a parameter) passing through a fixed point: 1 1 (1) , (2) , (3) 1,1 (4) none of these 3 3 3 3 The equation of line equidistant from the lines 2x + 3y + 5 = 0 and 4x + 6y = 11 is : (1) 2x + 3y – 1 = 0 (2) 4x + 6y – 1 = 0 (3) 8x + 12 y – 1 = 0 (4) none of these A ray of light along x 3y 3 gets reflected upon reaching x-axis, the equation of reflected ray is : (1) y = x + 1 (2) 3y x 3 (3) y 3x 3 (4) none of these If orthocenter and circumcentre of triangle are respectively (1, 1) and (3, 2) then the coordinates of its centroid are : 7 5 5 7 (1) , (2) , (3) (7, 5) (4) none of these 3 3 3 3 The angle bisector of two intersecting lines L 1 = 0 and L2 = 0 (1) are always perpendicular (2) are at 60 o (3) are perpendicular if L 1 = 0 and L2 = 0 are perpendicular (4) make equal angle as is the angle between L 1 = and L2 = 0 Obtuse angled bisector of lines 3x + 4y = 5 and 5x + 12y = 5 is (1) 37x + 56y = 45 (2) 7x + 4y = 20 (3) 7x – 4y = 20 (4) 37x + 56y = 49 o If a point P(4, 3) is rotated through an angle 45 in anticlockwise direction about origin, then co-ordinates of P in new position are 1 7 1 7 7 1 7 1 (1) (2) (3) (4) , , , , 2 2 2 2 2 2 2 2
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If a point P(4, 3) is shifted by a distance 2 units parallel to the line y = x, then coordiantes of P in new position are: (1) (5, 4) (2) (5 + 2 , 4 + 2 ) (3) (5 – 2 , 4 – 2 ) (4) none of these The orthocenter of a triangle formed by the lines 2x + y = 2, x – 2y = 1 and x + y = 1 is 1 2 2 1 (1) , (2) (0, 1) (3) , (4) (1, 0) 3 3 3 3 The point (4, 1) undergoes the following three transformations successively (i) reflection about the line y = x. (ii) translation through a distance 2 units along the positive direction of x-axis. (iii) rotation through an angle
about the origin the anticlockwise direction. 4 (iv) The final position of the point is given by the co-ordinates. 1 7 1 7 (1) (2) 2, 7 2 (3) (4) 2, 7 2 , , 2 2 2 2 Line L has intercepts a and b on the co-ordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line has intercepts p and q then : 1 1 1 1 1 1 1 1 (1) a2 + b2 = p2 + q 2 (2) 2 2 2 2 (3) a 2 p 2 b 2 q 2 (4) 2 2 2 2 a b p q a p b q P, Q R and S are the points on line joining the points P(a, x) and T(b, y) such that PQ = QR 5a 3b 5x 3y , = RS = ST, then is the mid-point of : 8 8 (1) PQ (2) QR (3) RS (4) ST The incentre of the triangle formed by lines x = 0, y = 0 and 3x + 4y = 12 is at: 1 1 1 1 (1) , (2) (1, 1) (3) 1, (4) ,1 2 2 2 2 Circumcentre of triangle whose vertices are (0, 0), (3, 0) and (0, 4) is : 3 3 (1) , 2 (2) 2, (3) (0, 0) (4) none of these 2 2 If origin is shifted to (7, –4), then point (4, 5) shifted to (1) (–3, 9) (2) (3, 9) (3) (11, 1) (4) none of these
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If the line y 3x cuts the curve x 3 + y3 + 3xy + 5x2 + 3y2 + 4x + 5y – 1 = 0 at the points A, B, C then OA. OB. OC is, (O is origin) 2 4 7 3 3 1 (1) (2) 3 3 1 (3) (4) none of these 13 3 If p and p ' be the perpendicular from the origin upon the straight lines
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x sec + y cosec = a and x cos – y sin = a cos 2, then 4p2 + p '2 is equal to : 1 2 1 2 (1) a (2) a (3) a2 (4) none of these 2 4 x y The incentre of the triangle formed by the axes and the line 1 is a b
a b ab a b ab ab ab (4) , 2 2 2 2 a b a b a b a b
a b (1) , 2 2
(2)
a b (3) , 3 3 83.
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ab
,
ab
If a straight line passes through (x 1, y1) and its segment between the axes is bisected at this point, then its equation is given by: x y (1) (2) 2 xy1 x 1y x 1y 1 2 x1 y1 (3) xy1 yx1 x1y1 (4) none of these Equation of a line which passes through the point (–3, 8) and cut off positive intercepts on the axes whose sum is 7 is (1) 3x – 4y = 12 (2) 4x + 3y = 12 (3) 3x + 4y = 12 (4) 4x – 3y = 12 If the line (x – y + 1) + k(y – 2x + 4) = 0 makes equal intercept on the axes then the value of k is (1) 1/3 (2) 3/4 (3) 1/2 (4) 2/3 2
The distance between the parallel lines given by x 7y 4 2 x 7y 42 0 is (1) 1 (2) 5 (3) 6 (4) 2 For all values of ‘a’ the set of straight lines (3a + 1) x – (2a + 3)y + 9 – a = 0 passes through the point (1) (3, 4) (2) (4, 2) (3) (3, 3) (4) (1, 2) If 2x + 3y + 4 = 0 & x + ky + 2 = 0 are identical lines then 3 – 2k = (1) 1 (2) 0 (3) –1 (4) 2 The distance between the parallel lines 8x + 6y + 5 = 0 and 4x + 3y – 25 = 0 is (1) 7/2 (2) 9/2 (3) 11/2 (4) 5/4 If the point of intersection of kx + 4y + 2 = 0, x – 3y + 5 = 0 line on 2x + 7y – 3 = 0 then k = (1) 2 (2) 3 (3) –2 (4) –3 PAPER SETTER – KALU SRAI BRANCH
PHYSICS
: Mr. Vikas Kaushik
CHEMISTRY
: Dr. Mohit Saxena
MATHEMATICS
: Mr. Dharmendra Singh
NEXT WEEK CPT DETAILS 15.10.16 CPT-8 JEE MAINS MODEL
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Physics
Chemistry
Mathematics
Rotational kinematics, moment of inertia, Rotational K.E. Dynamics of rigid body
Chemical equilibrium
Locus problem + Pair of Straight Lines
