COURSE : ALL INDIA TEST SERIES (VIKALP) Duration : 3 Hours Max. Marks : 258

Transcription

1 PART TEST-3 (PT-3) TARGET : IIT-JEE 011 CLASS-XII/XIII COURSE : ALL INDIA TEST SERIES (VIKALP) Duration : 3 Hours Max. Marks : 58 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General : Distance Learning Programmes Division (A Unit of Resonance Eduventures Pvt. Ltd.) 1. This Question Paper contains 78 questions. PAPER - 1. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. No additional sheets will be provided for rough work. CODE 4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 6. Do not Tamper / mutilate the ORS or this booklet. 7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators Write your Name, Roll No. and Sign in the space provide on the back page of this booklet. B. Filling the bottom-half of the ORS : 9. The ORS has CODE printed on its lower and upper Parts. 10. Make sure the CODE on the ORS is the same as that on this booklet. If the Codes do not match, ask for a change of the Booklet. 11. Write your Roll No., Name and Name of centre and sign with pen in appropriate boxes. Do not write these anywhere else. 1. Darken the appropriate bubbles below your registration number with HB Pencil. 13. Fill the test cities code in ORS Sheet and for details of cities code see last page this test paper booklet. C. Question paper format and Marking scheme : 14. The question paper consists of 3 parts (Chemistry, Mathematics & Physics). Each part consists of five Sections. 15. For each question in Section I, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one ( 1) mark will be awarded. DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR 16. For each question in Section II, you will be awarded 4 marks if you darken the bubble(s) corresponding to the correct choice(s) for the answer and zero mark if no bubbled is darkened. There is no negative marking for incorrect answer for this this section. 17. For each question in Section III, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one ( 1) mark will be awarded. 18. For each question in Section IV, you will be awarded marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one ( 1) mark will be awarded. 19. For each question in Section V, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one ( 1) mark will be awarded.

2 PART-I Atomic masses : [H = 1, D =, Li = 7, C = 1, N = 14, O = 16, F = 19, Na = 3, Mg = 4, Al = 7, Si = 8, P = 31, S = 3, Cl = 35.5, K = 39, Ca = 40, Cr = 5, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75, Br = 80, Ag = 108, I = 17, Ba = 137, Hg = 00, Pb = 07] SECTION - I Straight Objective Type This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct. 1. For the reaction, NO(g) + H (g) N (g) + H O(g) the rate expression can be written in the following ways : {d[n ] / dt} = k 1 [NO][H ] ; {d[h O] / dt) = k[no][h ] ; { d[no] / dt} = k 1 [NO] [H ] ; { d[h ] / dt} = k 1 [NO][H ] The relationship between k, k 1, k 1 and k 1. is : (A) k = k 1 = k 1 = k 1 (B) k = k 1 = k 1 = k 1 (C) k = k 1 = k 1 = k 1 (D) k = k 1 = k 1 = k 1. For the reaction, A + B + C Products. Conc. at t = 0 a b c Let rate = k C A C B C C. Let b > > a and c > > a then rate is given by rate = k C A. Choose the correct option. (A) k = kac (B) k = kab (C) k = kbc (D) None of these VIKALP_XII-XIII - 1 _ C 0-1

3 3. For a reaction A + B + C Products. On doubling the concentration of A rate becomes times. On doubling the concentration of A and B both rate becomes times and on doubling the concentration of B and C both rate becomes.8 times. Overall order of the reaction is : (A) 7 (B).41 (C) 5 (D) 3 4. For a reaction A B + C, it was found that at the end of 10 minutes from the start the total optical rotation of the system was 50 and when the reaction is complete, it was 100. Assuming that only B and C are optically active and dextrorotatory. calculate the time where optical rotation of first order reaction system become (A) 0 min (B) 30 min (C) 40 min (D) 37.5 min 5. Which of the following statement is not correct for the molecule Cl BBCl? (A) Molecule is planar at each boron atom. (B) Molecule is non-polar. (C) Each boron atom has a complete octet. (D) The hybridisation of boron is the same as that of nitrogen in CNO molecule. VIKALP_XII-XIII - 1 _ C 0 -

4 moles of NaNH 6. A, the product A will be : (A) (B) (C) (D) VIKALP_XII-XIII - 1 _ C 0-3

5 7. Write the basicity order of the following : CH 3 CH H (I) (II) (III) (IV) (A) (II) > (I) > (III) > (IV) (B) (I) > (III) > (IV) > (II) (C) (III) > (I) > (II) > (IV) (D) (I) > (II) > (III) > (IV) 8. The correct acidity order of the following is : (A) (IV) > (I) > (III) > (II) (B) (IV) > (I) > (II) > (III) (C) (IV) > (III) > (II) > (I) (D) (IV) > (III) > (I) > (II) SECTION - II Multiple Correct Answer Type This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 9. For the gas phase reaction C H 4 + H C H 6 (H = 3.7 kcal) carried out in a vessel, the equilibrium concentration of C H 4 can be increased by (A) Increasing the temperature (B) Decreasing the pressure (C) Removing some H (D) Adding some C H 6 VIKALP_XII-XIII - 1 _ C 0-4

6 10. At a certain temperature T 1, some hydrazine (N H 4 ) gas is placed in a sealed flask where the following equilibrium is established : 3N H 4 (g) 4NH 3 (g) + N (g) ; Hº > 0 If the temperature is increased to T, some ammonia gas also decomposes as : NH 3 (g) N (g) + 3H (g) ; Hº > 0 What would be observed as temperature is increased from T 1 to T. (A) Some more hydrazine would decompose. (B) If K 1 << K at T temperature,concentration of NH would decrease. 3 (C) Partial pressure of N would increase. (D) Partial pressure of H would decrease. 11. Which of the following is/are correct : (A) Carbon-carbon bond length in CaC will be more than that in CH CCH (B) O O bond length in KO will be more than that in Na O. (C) O O bond length in O [PtF 6 ] will be less than that in KO (D) N O bond length in NO gaseous molecule will be smaller than that bond length in NOCl gaseous molecule. 1. Find the correct option/s. (I) (II) (III) (IV) (A) II is most basic compound (B) In II lone pairs of nitrogen are less involved in resonance (C) The extent of resonance in I, III is same (D) IV is most basic due to + I effect of two methyl groups. VIKALP_XII-XIII - 1 _ C 0-5

7 SECTION - III Comprehension Type This section contains paragraphs. Based open each paragraph, there are 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 13 to 15 Reactions Tending To Equilibrium Not all chemical reactions proceed to a stage at which the concentrations of the reactants become vanishingly small. Here we consider the kinetics of such reactions. Let a reaction be represented in general terms by the scheme A k 1 B k 1 where k 1 and k 1 represent the rate constants for the forwards and reverse reactions, respectively. The equilibrium constant for this reaction may be written as K = [B] /[A] = k 1 /k 1...(1) where the subscript refers to a time t, sufficiently long to establish equilibrium at the given temperature. The initial concentration of species A is [A] 0, and that of B is [B] 0. After a time t, let the concentration of species A be [A] t and that of B be [B] t. The total rate of change of [A] t is given by d[a] t / dt = k 1 [A] t + k 1 [B] t If, as is usual, [B] 0 is initially zero, it follows from a mass balance that at any time t, [B] t = [A] 0 [A] t, whence d[a] t /dt = k 1 [A] t + k 1 ([A] 0 [A] t ) k or d[a] t /dt = (k 1 + k 1 ) 1 [ A] t [A] 0...() k1 k 1 Now, from (1) we have [B] /[A] = ([A] 0 [A] )/[A] = k 1 /k 1, or [A] = [A] 0 k 1 /(k 1 + k 1 ) Introducing this result into (), we obtain d[a] t /dt = (k 1 + k 1 )([A] t [A] ) VIKALP_XII-XIII - 1 _ C 0-6

8 Integrating In([A] t [A] ) = (k 1 + k 1 )t + f For t = 0, f = In ([A] 0 [A] ) ; hence, In [A] t [A] [A] 0 [A] = (k 1 + k 1 )t 13. For the reaction A k f k b C (having both 1 st order reactions), the concentration as a function of time are given for a certain experimental run along with a tangent to the graph at the origin. The ratio of the magnitude of the slopes of the graph of [A] and [C] at the origin would be : (A) 1 (B) 4 3 (C) 3 4 (D) None of these Conc. 0.6 (M) [A] [C] Time (min.) 14. At what time is the rate of change of concentration of A equal to rate of change of concentration of C in magnitude? (A) t = 0 only (B) t t equilibrium only (C) t = 10 only (D) at all times 15. What is the K C of the reaction C A? (A) 3 (B) 3 (C) 1 (D) None of these VIKALP_XII-XIII - 1 _ C 0-7

9 Paragraph for Question Nos. 16 to 18 The lone pair of amines makes them basic. They react with acids to form acid-base salts. Amines are more basic than alcohols, ethers or water when an amine is dissolved in water, an equilibrium is established where water acts as an acid and transfer a proton to the amine. The basic strength of an amine can be measured by basicity constant K b. Arylamines are less basic than alkylamines because the nitrogen lone pair are delocalised by interaction with the aromatic ring and are less available for donation. Substituted arylamines can be either more basic or less basic than aniline, depending on the substitutent. ERG substituent, such as CH 3, NH and OCH 3 increases the basicity and EWG substituent, such as Cl, NO and CN decreases arylamine basicity. Thus sp -hybridlzed nitrogen atom in pyridine is less basic than the sp 3 -hybridized nitrogen in an alkylamine. 16. Select the correct order of K b. (A) CH 3 NH > NaOH (B) > (C) p-methyl aniline > p-chloroaniline > p-amino acetophenone (D) p-bromoaniline > p-nitroaniline > p-amino benzaldehyde 17. Observe the following sequence of reactions. + CH 3 NH + + CH ( 1) 3 NH + + VIKALP_XII-XIII - 1 _ C 0-8

10 Select the correct option regarding the relative basic strength. (A) > CH3 C NH... (K b ) (B) > NH CH3 C NH... (K b ) NH (C) CH3 C NH > CH 3 NH... (K b ) (D) CH 3 NH >... (K b ) NH 18. Which of the following statement is incorrect (A),4,6-Trinitro-N,N-dimethyl aniline is 40,000 times stronger base than,4,6-trinitro aniline (B) > (K b ) (C) The basic strength of an amine in water is determined only by electron availability on the nitrogen atom (D) is sufficiently acidic to form salts with alkali metal. SECTION - IV True & False Type This Section Contains 4 questions. Each statement is either true (T) or false (F). VIKALP_XII-XIII - 1 _ C 0-9

11 19. If initial concentration of reactants is in stoichiometric ratio then half life of all reactants is same, irrespective of the order of reaction. 0. For gaseous reactions with n g > 0, equilibrium constant increases with the increase in pressure. 1. For a chemical reaction at equilibrium at standard state, standard Gibbs energy of reaction is zero.. In following compounds the acidity order is : & 1 > > 3 > 4 SECTION - V Integer Answer Type This section contains 4 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened. VIKALP_XII-XIII - 1 _ C 0-10

12 3. A and B are two different chemical species undergoing 1 st order decomposition with half lives equal to 5 sec. C and 7.5 sec. respectively. If the initial concentration of A and B are in the ratio 6 : 1. Calculate C half lives of A. 4. A non volatile solid P is dissolved in liquid X and progress of first order decomposition P(in solution phase) X () + Q (g) is monitored by total pressure measurement at 7 C. Date collected is : A t Bt after three Time Totalpressure t 0 0 mm Hg 1 t hr mmhg t after long time 100 mm Hg Calculate Half life of decomposition in minute. 5. A sample of mixture of A (g), B(g) and C(g) under equilibrium has mean molecular mass equal to 80 g/mole. The equilibrium is : A(g) B(g) + C(g) If initially 4 mole of 'A' gas is present then total number of mole at equilibrium is : [M A = 100, M B = 60, M C = 40] 6. Which of the following group is most basic : VIKALP_XII-XIII - 1 _ C 0-11

13 PART- II SECTION - I Straight Objective Type This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct. d y 7. If x = cost and y = nt, then at t =, + dx dy dx equals to (A) 0 (B) 1 (C) 1 (D) 8. If = lim x 0 sinax sin x x exists and finite then the values of ' ' and 'a' are respectively equal to x 3 (A) 6 7, (B) 3 4, (C) 6 7, (D) 6 7, 9. Range of g(x) = cos 1 sin x 3 1 cos x, where [. ] denotes the greatest integer function, is (A) 6 (B) (, ) (C), 0, 6 (D) (0, ] VIKALP_XII-XIII - 1 _ C 0-1

14 cos ecx If domain of f(x) = log x (sin x) + cos 1 ((1 {x}) {x}) +, where {.} denotes the fractional part log (1 4x ) 5 function, is (a, b), then (A) a + b = 1 (B) (a + b) = 1 (C) a b = 0 (D) a + b = 31. lim x n x 1x 1 e 1 is equal to x (A) 1 (B) 1 (C) 3 (D) g(x), 3. Let fog(x) = g(x) 1, 5 g(x), The graph of f(g(x)) is 0 g(x) 1 1 g(x) 3 and graph of g(x) is as shown. 3 g(x) 4 (A) (B) (C) (D) VIKALP_XII-XIII - 1 _ C 0-13

15 4x 5 x If the function satisfying the functional equation 5 fx 4 f 9x 1, x R 4 equal to (A) 7 (B) 11 (C) 9 (D) 17. Then f(7) is 34. With usual notations in ABC, if A = and a + b + c =, then b + c a is equal to (A) 1 (B) (C) 3 (D) 4 SECTION - II Multiple Correct Answer Type This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 35. The graph of a function y = f(x) is as shown. Then which of the following statements is(are) true? (A) f(x) has non-removable discontinuity at x =. (B) f(x) has missing point discontinuity at x = 0. (C) f(x) has isolated point discontinuity at x = 1. (D) f(x) is continuous at x = 3. VIKALP_XII-XIII - 1 _ C 0-14

16 x 5x The function f(x) = is x x 6 (A) one-one (B) many one (C) into (D) onto 37. Which of the following pair of functions does not have same graph? (A) f(x) = sin (sin 1 x) ; g(x) = cos (cos 1 x) (B) f(x) = cot 1 x ; g(x) = e n (cot 1 x) (C) f(x) = cos8x cos7x, g(x) = cos 3x cos x 1 cos5x (D) f(x) = lim n x x n n 1 1 ; g(x) = sgn (1 x ) 38. A period of the function f(x) = sin 4 x + cos 4 x is (A) 6 (B) 3 (C) (D) 4 VIKALP_XII-XIII - 1 _ C 0-15

17 SECTION - III Comprehension Type This section contains paragraphs. Based open each paragraph, there are 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 39 to 41 For x 0, 4 n Let = r 1 sin(sin 1 x 3r1 n ), m = r 1 n 1 3r cos(cos x ), r 1 1 n tan(tan x ), n N, n 3 3r 39. Which of the following is true? (A) > m > n (B) m > > n (C) < m < n (D) n > > m 40. lim ( + m + n) is equal to n (A) does not exist (B) x x 1 1 (C) 1 x x (D) 1 x 41. The value of x, satisfying the equation m = + n is (A) sin (B) cos (C) cos (D) 1 sin 10 VIKALP_XII-XIII - 1 _ C 0-16

18 Paragraph for Question Nos. 4 to 44 Let f(x) = x x 1, x R and f : (, a] [b, ), where 'a' is the largest real number for which f(x) is bijective. 4. The value of a b is equal to (A) 3 (B) 1 (C) (D) Let g(x) : [ 1, 7] R, then number of integers in domain of g(f(x)) is (A) 3 (B) 6 (C) 9 (D) infinite 44. If g(x) is the inverse of f(x), then g( 1) is equal to (A) (B) (C) 3 (D) not defined SECTION - IV True & False Type This Section Contains 4 questions. Each statement is either true (T) or false (F). VIKALP_XII-XIII - 1 _ C 0-17

19 45. The function f(x) = cos 1 x + sec 1 x is even function as well as odd function Complete solution set of the inequation sec 1 x is x 1, sec. 47. With usual notation in a ABC, cos A + cos B + cos C is equal to + R r. 48. The equation log 1.5 (cot 1 x sgn (e x )) = has no real solution. (where sgn(.) denotes signum function) SECTION - V Integer Answer Type This section contains 4 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened. VIKALP_XII-XIII - 1 _ C 0-18

20 cos x 49. Total number of points of discontinuity in f(x) = [sinx] + 4 integer function) in the interval (0, 4) is + x nx (where [.] denotes greatest 50. If the complete solution set of the inequation cos (cos 1 x ) sin (sin 1 (x + 1)) is [p, q], then the value of 1 sin 1 (q p) is equal to 51. Let f(x) and g(x) be two functions such that f(0) = 1, g(0) = 0 and f(x) = g(x), g (x) = f(x). Find lim x / 4 5 (f(tanx) + g(cotx)). e 5. Let f(x) = 5 A cos x Bx sin x k, (x 0) is continuous at x = 0. If f(0) = 4, then find the value of k. x 4 VIKALP_XII-XIII - 1 _ C 0-19

21 PART - III SECTION - I Straight Objective Type This section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 53. A shell is fired from a canon with a velocity V at an angle with the vertical direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is (A) 3V cos (B) V cos (C) 3 V cos (D) V sin 54. There are hundred identical sliders equally spaced on a frictionless track with magnitude of velocity of each slider numbering from 1 to 100 is (v, v, v,v, 3v, 3v... so on) as shown in the figure. All the blocks continue to collide elastically till a constant velocity is acquired by each block then, final velocity of block number will be : (A) v (B) v (C) 49v (D) 50v 55. In a vertical plane inside a smooth hollow semicircular thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube, velocity of the tube will be (where R is mean radius of tube). Assume that the tube remains in vertical plane. (A) gr (B) gr (C) Zero (D) None of these VIKALP_XII-XIII - 1 _ C 0-0

22 56. A ball is bouncing down a set of stairs. The height of each step is d and the ball bounces one step at each bounce. After each bounce the ball rebounds to a height as shown in figure. Coefficent of restitution will be : (A) e = 1 (B) e = 1 (C) e 1 (D) 3 e Look at the drawing given in the figure which has been drawn with ink of uniform linethickness. The mass of ink used to draw each of the two inner circles, and a missing line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle ( a, a), right inner circle (a, a). The centre of mass of the whole ink in this drawing is at origin then the coordinates of centre of mass of the missing line are : (A) (0, a) (B) (0, a) (C) (0, a ) (D) (0, 0) 58. Three parallel forces are acting on a rod (as shown in figure) at distances of 0 cm, 40 cm, 60 cm and 80 cm respectively from one end of the rod. Assuming no motion in the rod under the influence of these forces the rod : (A) is at rest (C) experiences a linear motion (B) experiences a torque (D) experiences a torque and also a linear motion VIKALP_XII-XIII - 1 _ C 0-1

23 59. A uniform rod of mass m is hinged at a smooth, horizontal, fixed axis as shown in the figure and is released from a horizontal position. The force applied by the hinge on the rod when it becomes vertical is: (A) 19mg 7 (B) 5mg 4 13mg (C) 7 (D) mg 60. A thin string is wrapped several times around a cylinder kept on a rough horizontal surface. A boy standing at a distance from the cylinder draws the string towards him as shown in figure. The cylinder rolls without slipping. The length of the string unbound from the cylinder while the cylinder reaches to the boy is : (A) (B) (C) 3 (D) 4 SECTION - II Multiple Correct Answers Type This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 61. A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact lasts for a time t. m(u v) (A) The average elastic force acting on the ball is t (B) The average elastic force acting on the ball is m(u v) t (C) The kinetic energy of the ball increases by mu (u + v) (D) The kinetic energy of the ball remains the same after the collision. VIKALP_XII-XIII - 1 _ C 0 -

24 6. Which of the following is correct always? (A) Work done by all forces is equal to change in kinetic energy. (B) Work done by all forces is equal to the sum of the work done by each force individually. (C) Work done by all forces is equal to the work done by the resultant force. (D) conservative force can not change mechanical energy of the system 63. A car is moving along a circle with constant speed on an inclined plane as shown in diagram. Then friction force on car will be in horizontal direction at least at one point : (A) in portion 'AB' including pont A and B (C) in portion 'CD' including pont C and D (B) in portion 'BC' including pont B and C (D) in portion 'DA' including pont D and A 64. A particle collides with a rod which is hinged at one end. Rod is kept on smooth horizontal surface and particle has velocity in horizontal plane and normal to the rod. Which of the following will be true : (A) Linear momentum of rod and particle system will not be conserved. (B) Linear momentum of rod and particle system may be conserved. (C) Energy of rod and particle system (SPACE will decrease. FOR ROUGH WORK) (D) Linear momentum of rod and particle system may increase. VIKALP_XII-XIII - 1 _ C 0-3

25 SECTION - III Comprehension Type This section contains paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 65 to 67 Two friends A and B (each weighing 40 kg) are sitting in a frictionless well having vertical circular smooth wall. They subtend angle 90 at the centre of well. 'A' rolls a ball of mass 40 kg in clockwise direction on the platform towards B along the wall of the well which B catches. Then similarly B rolls the ball towards 'A' anticlockwise and A catches it. The ball has a fixed speed of 5 m/s. (Neglect catching and throwing time.) 65. Find the total impulse by the wall of well on whole system by the time ball travels from A to B (A) 00 kg-m/s (B) 400 kg-m/s (C) zero (D) None of these 66. Find the angular displacement of A till he meets B : (A) 150 (B) 60 (C) 90 (D) When A meets B they catch each other and now they move together i.e. perfectly inelastic collision. What will be the velocity when they (A + B) throw the ball after catching it : 5 50 (A).5 m/s (B) m/s (C) m/s, 5 m/s (D) None of these 3 11 VIKALP_XII-XIII - 1 _ C 0-4

26 Paragraph for Question Nos. 68 to 70 A uniform disc of mass M and radius R initially stands vertically on a horizontal plank of mass M and length L, as shown. The plank rests on smooth horizontal floor and friction between disc and plank is sufficiently high such that disc rolls on plank without slipping. The plank is pulled to right and disc is pulled to left with constant horizontal force of magnitude F on each. F M R M smooth horizontal floor L F 68. The ratio of magnitudes of acceleration of plank and acceleration of highest point of the disc is : (A) 1 : 1 (B) 1 : (C) 1 : 3 (D) : The magnitude of frictional force acting between disc and plank is : F F (A) F (B) (C) 3 F (D) Work done by friction on plank in time in which disc rotates by one revolution on plank is : (A) F F F R (B) FR (C) R (D) R 4 SECTION - IV True & False Type This Section Contains 4 questions. Each question is either true (T) or false (F). VIKALP_XII-XIII - 1 _ C 0-5

27 71. Whenever a stationary object explodes in absence of external force into three parts, all parts will surely move in a plane. 7. In a circular motion centripetal force can never be constant. 73. In variable mass system when some mass adds with non zero relative velocity and moves together with the system then in this case mechanical energy conservation cannot be applied for the system including the mass which is going to attach this system. 74. Centre of gravity always coincides with centre of mass. SECTION - V Integer Answer Type This section contains 4 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened. 75. Two particles A and B each of mass m are connected by a massless string. A is placed on the rough table. The string passes over a small, smooth peg. B is left from a position making an 60ºwith the vertical. Find the minimum coefficient of friction between A and the table so that A does not slip during the motion of mass B. VIKALP_XII-XIII - 1 _ C 0-6

28 76. String is wound on a cylinder and one end string is connected to a block as shown in figure. It is given that there is no slipping between cylinder and two horizontal fixed planks and string does not slip on the cylinder. Find the distance (in metre) travelled by the axis of the cylinder during the time block moves 8 metre downwards. VIKALP_XII-XIII - 1 _ C 0-7

29 77. Two oppositely charged particles of mass kg each are kept on a smooth horizontal surface at distance of 8m. When they starts moving towards each other at time t = 0 due to electrostatic force, a force of N is applied one of the charge as shown. Find the distance traveled by the positive charge (in metres) before it collides with negative charge. It is given that the two charges collide at t = seconds. 78. A particle is moving in a circle in vertical plane about a horizontal axis AB with help of two massless strings of length 10m each as shown in figure. Find the minimum possible speed (in m/s) of particle during that motion. (take g = 10 m/s ) VIKALP_XII-XIII - 1 _ C 0-8

30 Name of the Candidate Roll Number I have read all the instructions and shall abide by them. I have verified all the information filled in by the Candidate Signature of the Candidate Signature of the Invigilator Example for Filling Test Cities Code in ORS : If your Test centre is Bhatinda and test code is 06 then fill in ORS : (a) (b) Test Code Test Centre Test Code Test Centre Test Code Test Centre 01 Ahamedabad 0 Agra 03 Bengluru 04 Bikaner 05 Bhopal 06 Bhatinda 07 Bhubneshwar 08 Bokaro 09 Chandigarh 10 Dhanbad 11 Dehradun 1 Guwahati 13 Hyderabad 14 Indore 15 Jaipur 16 Kanpur 17 Kolkata 18 Kota 19 Lucknow 0 Mumbai-Andheri 1 Mumbai-Thane Mumbai-Nerul 3 Mumbai- Dadar 4 Mangluru 5 Muzaffarpur 6 Nagpur 7 New Delhi- East 8 New Delhi-West 9 New Dehi- North West 30 New Delhi- South 31 Patna 3 Raipur 33 Ranchi 34 Sri Ganganagar 35 Shakti Nagar (NTPC) 36 Udaipur 37 Udupi 38 Varanasi (Space for rough work)