JEE MAIN REVISION MODEL (Unit -1) PDF

Name................................................ TEST ID REVISION MODEL EXAM Batch.................... Roll No................ 05- 10- 2023...

Name................................................ TEST ID REVISION MODEL EXAM Batch.................... Roll No................ 05- 10- 2023 UNIT - I 181 24V/JM/R/(G1&G2) Physics + Chemistry + Mathematics Mark : 300 Time : 3.00 Hr PHYSICS Section 1 - Only one correct option type (4, –1) 1. The circular divisions of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is 1) 2.25 mm 2) 2.20 mm 3) 1.20 mm 4) 1.25 mm 2. Find the dimension of B2 2 0 : 1) ML1T 2 2) ML2 T 2 3) ML1T 2 4) ML2 T 1 3. The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is 1) 3.07 cm 2) 3.11 cm 3) 3.15 cm 4) 3.17 cm a 2b2 3 4. A physical quantity z depends on four observables a, b, c and d, as z . The percentage of error cd 3 in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is 1) 13.5% 2) 16.5% 3) 14.5% 4) 12.25% 5. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistance, its velocity v varies with the height h above the ground is 1) 2) 3) 4) 24V/TP/MOD/J/R- 2 J - MODEL 6. A small block slides without friction down an inclined plane starting from rest. Let Sn be the distance Sn travelled from time t = n-1 to t = n. Then S is n 1 2n  1 2n  1 2n  1 2n 1) 2) 3) 4) 2n 2n  1 2n  1 2n  1 7. Two bodies A and B of masses 1 kg and 3 kg respectively are dropped from heights 16 m and 25 m. The ratio of the time taken by them to reach the ground is : 4 5 12 5 1) 2) 3) 4) 5 4 5 12 8. The position x of a particle with respect to time t along X-axis is given by x  9t 2  t 3 where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction ? 1) 54 m 2) 81 m 3) 24 m 4) 32 m  9.   At a height 0.4m from the ground, the velocity of a projectile is, v  6iˆ  2ˆj ms. The angle of projec- 1 tion is (g = 10 ms ) -2 1  3  1) 450 2) 600 3) 300 4) tan   4 g 2 10. The equation of projectile is y  3x  x. The angle of projection and initial velocity is 2 1) 300, 4 ms-1 2) 600, 2 ms-1 3) 600, 4 ms-1 4) 900, 4 ms-1 11. A particle is projected with a ceratin velocity at an angle  above the horizontal from the foot of an inclined plane of inclination 300. If the particle strikes the plane normally then  is equal to 1  1  1) 30  tan  0  2 3 0 1 2) 30  tan 2 3   1  3 4) 30  tan  2  0 3) 600   12. A ball is thrown from the top of a staircase which just touches the ceiling and finally hits the bottom of the steps. The initial speed of the ball is 1) 6.3 ms-1 2) 7.6 ms-1 3) 63 ms-1 4) 76 ms-1 24V/TP/MOD/J/R- 3 J - MODEL 13. A ball is thrown vertically upward with a speed v from a point h metre above the ground. The time taken for the ball to hit the ground is  v  2hg   2hg   1) g   1  1   2) 1   2    v 2   v  v  2hg  v  2hg  3)   1   2  4)   1   2  g  v  g  v    14. Two particles A and B, move with constant velocities v1 and v 2. At the initial moment their position   vectors are r1 and r 2 respectively. The condition for particle A and B for their collision is :-         r1  r 2 v 2  v1 1) r1  r 2  v1  v 2 2)      r1  r 2 v 2  v1         3) r1  v1  r 2  v 2 4) r1  v1  r 2  v 2 15. The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to north is given by : 1) 300 west 2) 00 3) 600 west 4) 450 west 16. A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction =  ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is : (Assume m1 = m2 = m3 = m) g 1  g  2g 1) 2) 9 3 g 1  2  g 1  2  3) 4) 3 2 17. A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward. (take g = 10 m/s2) 1) 32 N 2) 23 N 3) 25 N 4) 18 N 24V/TP/MOD/J/R- 4 J - MODEL 18. Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown in the figure. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is : 1) 80N 2) 120N 3) 150N 4) 100N 19. In the following figure the position time graph of a particle of mass 0.1 kg is shown. The impulse at t = 2 sec is : 1) 0.2 kg ms-1 2) 0.02 kg ms-1 3) 0.1 kg ms-1 4) 0.4 kg ms-1 20. Two forces 12 N and 8 N act on a body of mass 24 kg. Whatever may be the directions of the forces, the acceleration of the body cannot be less than : 5 2 1 2 1 2 1 2 1) ms 2) ms 3) ms 4) ms 6 6 3 2 Section II - Integer type Questions (4, -1) [This section contains 10 Questions. Attempt any five Questions. For each question enter the correct interger value. Rounded off to the next integer if the answer is decimal. Eg: If the answer is 25.67, rounded off to 26. If the answer is 9.35, rounded off to 9. If the answer is 0.75, r ounded off to 1. I f the answer is 0.45, r ounded off to 0. I f the answer is 0.50 r ounded off to 1] 21. Mass (M) of the largest stone that can be moved by flowing river depends on the velocity of flow of river (v), density of water    and acceleration due to gravity (g). If M depends on nth power of velocity then calculate n. 22. Consider the following equation F  a x  bt 2. If the dimensions of a/b are MPLqTr then calculate value of : -qr 23. A balloon starts from the state of rest from the ground with constant acceleration g/n. After time T, a stone is dropped from the balloon. If stone takes time T to reach the ground then calculate the value of n. 24. A particle is moving in a straight line and its velocity varies with its displacement as v  4  4s m / s. Assume s = 0 at t = 0. Find the displacement of the particle in metres at t = 1s.     25.   Two vectors A and B are defined A  aiˆ and B  a cos tiˆ  sin tjˆ , where a is a constant and        6 rad s 1. If A  B  3 A  B at time t   for the first time, the value of  , in second, is 26. A particle is projected with a speed u at an angle  with the horizontal. If R1 is radius of curvature of trajectory at the initial point and R2 is the radius of curvature at the highest point. Value of R2/R1 is found to be cos n . What is the value of n ? 24V/TP/MOD/J/R- 5 J - MODEL 27. A small block of mass m is placed on inclined surface of wedge which accelerates with an acceleration a 0  g in a direction shown in figure. If length of the inclined plane is 1m, then find time taken by the block in seconds to cover the distance from A to B. 28. In the following figure find force of friction in newtons acting between 3 kg block and the floor. 29. A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 300 with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle  with the line AB should be that of the river. The angle  with the line AB should be _____0, so that the swimmer reaches point B. 30. Position of two particles A and B as a function of time are given by X A  3t 2  8t  c and YB  10  8t 3. The velocity of B with respect to A at t = 1 is v. Find v : CHEMISTRY Section 1 - Only one correct option type (4, –1) 31. In which case is the number of molecules of water maximum? 1) 18 mL of water 2) 0.18 g of water 3) 10-3 mol of water 4) 0.00224 L of water vapours at 1 atm and 273 K 32. The number of moles of hydrogen required to produce 20 moles of ammonia through Haber’s process is: 1) 10 2) 20 3) 30 4) 40 24V/TP/MOD/J/R- 6 J - MODEL 33. Concentrated aqueous sulphuric acid is 98% H2SO4 by mass and has a density of 1.80 g mL-1. Volume of acid required to make one litre of 0.1 M H2SO4 solution is: 1) 16.65 mL 2) 22.20 mL 3) 5.55 mL 4) 11.10 mL 34. What mass of 95% pure CaCO3 will be required to neutralise 50 mL of 0.5 M HCl solution? 1) 1.32 g 2) 3.65 g 3) 9.50 g 4) 1.25 g 35. What is the mass of precipitate formed when 50 mL of 16.9% solution of AgNO3 is mixed with 50 mL of 5.8% NaCl solution? 1) 28g 2) 3.5g 3) 7g 4) 14g 36. If uncertainty in position and momentum are equal then uncertainty in velocity is 1 h 1 h h 1) 2) 3) 4) None of these 2m  m   37. The orientation of an atomic orbital is governed by 1) Principal quantum number 2) Orbital angular momentum quantum number 3) Magnetic quantum number 4) None of these 38. Which of the following is not correct according to Bohr’s atomic theory? 1) Larger the value of n, the larger is the orbitradius 2) Velocity of electron is lower in higher orbits 3) The electron is more loosely bound in the smallest allowed orbit 4) The energy of electron bound to nucleus is lower than that would be if the electron was at infinite distances from the nucleus 39. If radius of second Bohr orbit of He+ is 105.8 pm, what is the radius of third Bohr orbit of Li2+ 1) 15.87 pm 2) 1.587 pm o 3) 158.7 A 4) 158.7 pm 40. The energy absorbed per molecule (X2) of a substance is 4.4 × 10-19 J and bond energy per molecule is 4.0 × 10-19 J. The kinetic energy of the molecule per atom will be: 1) 2.2 × 10-19 J 2) 2.0 × 10-19 J 3) 2.2 × 10-20 J 4) 2.0 × 10-20 J 41. Identify the correct order of electron gain enthalpy for C, Ca, Al, F and O 1) F  O  C  Al  Ca 2) Ca  Al  C  O  F 3) F  O  C  Ca  Al 4) Al  Ca  C  O  F 42. Statement I: The process of formation of O2- in gas phase is favourable because O2- isoelectronic with Ne Statement II: The electronic configuration of the element Z =114 is  Rn  5f 14 6d10 7s 2 7p2 1) Both Statement I and Statement II are correct 2) Statement I is correct but Statement II is incorrect 3) Both Statement I and Statement II are incorrect 4) Statement I is incorrect but Statement II is correct 24V/TP/MOD/J/R- 7 J - MODEL 43. The metal that has very low melting point and its periodic position is closer to a metalloid is 1) Al 2) Ga 3) Se 4) ln 44. The total number of acidic oxides among the following list is: NO, N2O, B2O3, N2O5, CO, SO3, P4O10, BeO, BaO 1) 3 2) 4 3) 2 4) 5 45. The number of completely filled orbitals with m   0 in the ground state electronic configuration of Ge is: 1) 6 2) 7 3) 9 4) 8 46. The correct IUPAC name of the following compound is: Cl OH Br 1) 6-bromo-2-chloro-4-methylhexan-4-ol 2) 1-bromo-4-methyl-5-chlorohexan-3-ol 3) 6-bromo-4-methyl-2-chlorohexan-4-ol 4) 1-bromo-5-chloro-4-methylhexan-3-ol 47. The correct structure of 2,6-dimethyldec-4-ene is: 1) 2) 3) 4) 48. The IUPAC name of the compound is: O O H C 1) 5-formylhex-2-en-3-one 2) 5-methyl-4-oxohex-2-en-5-al 3) 3-keto-2-methylhex-5-enal 4) 3-keto-2-methylhex-4-enal 24V/TP/MOD/J/R- 8 J - MODEL 49. The structure of the compound whose IUPAC name is 3-ethyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid is: OH OH COOH 1) 2) OH COOH 3) 4) COOH OH 50. The structure of isobutyl group in an organic compound is: | | 1) CH 3 C HCH 2 CH 3 2) CH 3 C  CH 3  CH3 3) CH 2 CH  CH3 2 4) CH 2  CH 2 2 CH3 Section II - Integer type Questions (4, -1) [This section contains 10 Questions. Attempt any five Questions. For each question enter the correct interger value. Rounded off to the next integer if the answer is decimal. Eg: If the answer is 25.67, rounded off to 26. If the answer is 9.35, rounded off to 9. If the answer is 0.75, rounded off to 1. If the answer is 0.45, rounded off to 0. If the answer is 0.50 rounded off to 1] 51. Suppose the elements X and Y combine to form two compounds XY2 and X3Y2. When 0.1 mole of XY2 weighs 10g and 0.05 mole of X3Y2 weight 9g, the atomic weights of X is............. g mol-1. 52. The volume occupied by one molecule of water is............ × 10-24 cm3 [Given: density of water = 1 g mL-1] 53. When 22.4 litres of H2(g) is mixed with 11.2 litres of Cl2(g), each at STP, the moles of HCl(g) formed is........... × 10-2 mol. 54. The wavelength for an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is............... × 102. [Mass of electron is 9.1 ×10-31 kg and mass of neutron is 1.6 × 10-27 kg] 55. A source of monochromatic radiation of wavelength 400nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, x × 1020 electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of x is............. (h = 6.626 × 10-34 Js) 3 56. Consider an imaginary ion 48 22 Z. The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of a is........................... 57. The azimuthal quantum number for the valence electron of Ga+ is x. The magnetic quantum number of the outermost electron of Zn+ is y. The value of x-y is......... 58. How many of the following is/are exothermic in nature? i) H g   e H g  ii) Ar g   e Ar  g   2  iii) O g   e O g  iv) Na  g  Na  g   e 24V/TP/MOD/J/R- 9 J - MODEL 59. The total number of ethyl groups present in 3,5-diethyl-4-propylhept-1-en-6-yne is.............. 60. The total number of allylic hydrogen atom(s) present in 4-bromo-3-methylpent-2-ene is............ MATHEMATICS Section 1 - Only one correct option type (4, –1) 61. If the equation  k  2  x 2   k  4  x  2  0 has difference of roots as 3 then the value of k is 3 3 3 1) 1,3 2) 3, 3) 2, 4) ,1 2 2 2  62. If z1, z2 are two complex numbers such that z1z 2  2 and arg  z1   arg  z 2   , then z1 z 2 is equal 4 to 1) 1  i 2) 1  i 3) 1  i 4) 1  i a b c a1 b1 c1 63. If a,b,c,a1,b1,c1 are non zero complex numbers satisfying a  b  c  1  i and    0, then 1 1 1 a b c a 2 b2 c2   is equal to a12 b12 c12 1) 2  2i 2) 2i 3) 2  2i 4) 2  zz  64. If z lies in 4th quadrant, then arg   is  2019    1) 0 2) 3)  4)  2 2 65. It is given that complex numbers z1 and z 2 satisfy z1  2 and z 2  3. If the included angle of their z1  z 2 corresponding vectors is 60°, then z  z  1 2 133 131 19 134 1) 2) 3) 4) 7 7 7 7 66.     Let A  z : 1  2i  z  1  2i  z  2  0 and B  z :  3  2i  z   3  2i  z  3  0 , then 1) n  A  B   0 2) A  B 3) n  A  B   1 4) B  A 67. Let f  x   9 x  3x  1 x   ,1 , then range of f(x) is ([.] denotes the greatest integer function) 1) 0,1, 2,3, 4,5,6 2) 0,1, 2,3, 4,5, 6, 7 3) 1, 2,3, 4,5, 6 4) 1, 2,3, 4,5, 6, 7 24V/TP/MOD/J/R- 10 J - MODEL x 2  2x  5 68. Let f : R R be a function defined by f  x   is x2  x 1 1) one-one and into 2) one-one and onto 3) many one and onto 4) many one and into 69. If g  x  be a function defined on  1,1 if the area of the equilateral triangle with two of its vertices at (0,0) and  x,g  x   is 3 / 4 , then 1) g  x    1  x 2  2) g  x    1  x 2  3) g  x    1  x  2 4) g  x    1  x  2 a b 1 70. If * is a binary operation defined by a * b    for positive integers a and b, then 2 * 5 is equal b a ab to 1) 4 2) 3 3) 2 4) 1 71. Let R1 and R2 be two relations defined as follows: R 1   a, b   R 2 : a 2  b 2  Q and R 2   a, b   R 2 : a 2  b 2  Q , where Q is the set of all rational numbers. Then 1) Neither R1 nor R2 is transitive 2) R2 is transitive but R1 is not transitive 3) R1 is transitive but R2 is not transitive 4) R1 and R2 are both transitive x 72. Let f : R R be defined by f  x   , x  R. Then the range of f is 1 x2  1 1  1 1 1)  1,1  0 2) R   1,1 3)   ,  4) R    ,   2 2  2 2 1 73. Let a function f :  0,    0,   be defined by f  x   1 . Then f is x 1) injective only 2) both injective as well as surjective 3) not injective but it is surjective 4) neither injective nor surjective 3  2 2   1  sin 9  i cos 9  The value of   is  1  sin 2  i cos 2  74.  9 9  1) 1 2  1 i 3  2) 1 2  3 i  3)  1 2  3 i  4)  1 2  1 i 3  24V/TP/MOD/J/R- 11 J - MODEL x 2  2x  1 75. Let f :   2, 6  be real valued function defined as f  x  . Then range of f is x 2  8x  12  21   21  1)  ,     0,   2)  ,     0,    4  4  21   21   21  3)  ,     ,   4)  ,    1,    4  4   4 i 1 z 76. The complex number   cos  i sin is equal to 3 3  5 5    1) 2  cos  i sin  2) cos  i sin  12 12  12 12     5 5  3) 2  cos  i sin  4) 2i  cos  i sin   12 12   12 12  77. Let a,b,c are real numbers with a 2  b 2  c2  0. Then the equation x 2   a  b  c  x   a 2  b 2  c2   0 has 1) 2 positive real roots 2) 2 negative real roots 3) 2 real roots with opposite sign 4) no real roots 78. Let a,b are two different positive integers and the two quadratic equations  a  1 x 2   a 2  2  x   a 2  2a   0 and  b  1 x 2   b 2  2  x   b 2  2b   0 have one common a b  ba root. Then the value of  b is equal to a  ba 1) 256 2) 64 3) 16 4) 72 79. Three real numbers x,y,z are such that x 2  6y  17, y 2  4z  1 and z 2  2x  2. Then the value of x 3  y3  z3 is equal to 1) 30 2) –24 3) –36 4) –28 80. The degree of the polynomial p(x) which satisfies the condition  x  p  x  1   x  15  p  x  is 1) 4 2) 15 3) 7 4) can not be determined Section II - Integer type Questions (4, -1) [This section contains 10 Questions. Attempt any five Questions. For each question enter the correct interger value. Rounded off to the next integer if the answer is decimal. Eg: If the answer is 25.67, rounded off to 26. If the answer is 9.35, rounded off to 9. If the answer is 0.75, rounded off to 1. If the answer is 0.45, rounded off to 0. If the answer is 0.50 rounded off to 1] 81. Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If  is the number of one- 1 one functions from X to Y and  is the number of onto functions from Y to X, then the value of     5! is..... 24V/TP/MOD/J/R- 12 J - MODEL 82. Let p be the product of the non real roots of the equation x 4  4x 3  6x 2  4x  2008 where [*] denotes t he greatest integer function, then find  p  83. Number of real values of x satisfying the equation log 2     x  1  log 3 1  x is equal to   6  8 If  and  are the roots of the equation x  6x  12  0 and the value of    2  24 84. 2   1 is a b 8 where a and b are natural numbers then find least value of  a  b  85. Let A  a, b, c and B  1, 2,3, 4. Then the number of elements in the set C  f : A B | 2  f  A  and f is not one  one is 86. Let X  n  N :1  n  50. If A  n  X : n is a multiple of 2 and B  n  X : n is a multiple of 7 , then the number of elements in the smallest subset of X containing both A and B is m n  1 i  2  1 i 3 87. If      1,  m, n  N  then the greatest common divisor of the least values of m and n is  1 i   i 1  88. Let L be any line not passing through origin and P  z1  be the foot of perpendicular from origin to the line. z2 z2 Let Q  z 2  be any point different from P on L. Then  is equal to z1 z1 Let a,b,c are given distinct numbers, then the number of distinct values of the expression      2  , 3 89.  1 3 where  , ,   is a permutation of a,b,c is equal to     2  i 2    90. If z1 , z 2 , z3 be the vertics of ABC , taken in anticlockwise direction and z0 its circumcentre, then  z 0  z1  sin 2A  z 0  z 3  sin 2C    is equal to  z 0  z 2  sin 2B  z 0  z 2  sin 2B Name................................................ TEST ID REVISION MODEL EXAM Batch.................... Roll No................ 05- 10- 2023 UNIT - I 181 24V/JM/R/(G1&G2) P + C + M - Key with Hints PHYSICS 0.5 1. 3 Zero error = 5   0.05 mm 50 0.5 Actual measurement  2  0.5 mm  25   0.05 mm 50  1mm  0.25 mm  0.05 mm  1.20 mm B2 Force  displacement MLT 2 L 2. 1 Energy density in magnetic field = ;    ML1T 2 2 0  displacement  L3 3. 3 Given 10 VSD = 9 MSD; Here MSD - Main scale division 9 1 VSD = MSD ; VSD - Vernier scale division 10  9 Least count = 1 MSD - 1 VSD = 1   MSD = 0.1 MSD = 0.1 × 0.1 = 0.01 cm  10  As ‘0’ of VS lie before ‘0’ of MS Zero error = -[10-6]L.C = -4×0.01 = -0.04 cm Reading = 3.1 cm + 1×LC = 3.4 cm + 1×0.01 = 3.11 cm True diameter = Reading - zero error = 3.11-(-0.04) cm = 3.15 cm t 2 a 2 b 1 c d 4. 3    3 t a 3 b 2 c d 2 1  2  2   1.5   4  3  2.5  4  1  2  7.5  14.5% 3 2 5. 1 For the given condition initial height h = d and velocity of the ball is zero. When the ball moves downward its velocity increases and it will be maximum when the ball hits the ground and just after the collision it becomes half and in opposite direction. As the ball moves upward its velocity again decreases and becomes zero at height d/2. This explanation match with graph (A). 2n  1 6. 3 2n  1 7. 1 Both balls are dropped so, u A  0 , u B  0 1 1 SA t A2 tA S 16 4 SA  g  t A  , SB  g  t B  ;  2 ;  A   2 2 2 2 SB t B tB SB 25 5 8. 1 Given, x is the position with respect to time t dx dv x  9t 2  t 3 ; v  18t  3t 2 ;  18  6t dt dt dv For maxima or minima,  0 , the time 18-6t = 0; t = 3 seconds dt The distance covered in time t = 3 seconds; x = 9(3)2-(3)3 = 54 m 9. 3 ; 24V/TP/MOD/J/R- 2 J - MODEL 10. 2 Standard equation of projectile is and the given equation is Comparing (1) and (2) , we get 11. 4 If T be the time of flight, then For the projectile to hit the plane normally, vx = 0 12. 1 ; ; From (2) ; 13. 1 14. 2 For two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle. ; 24V/TP/MOD/J/R- 3 J - MODEL 15. 1 16. 3 17. 1 Total upward force on inclined plane is equal to total downward force ; ; ; 18. 2 Let us make free body diagram The frictional force by block B on wall is calculated as : 19. 1 24V/TP/MOD/J/R- 4 J - MODEL 20. 2 21. 6 22. 1 ; 23. 3 Velocity attained by the balloon in time T will be same as initial velocity of stone. Let us assume downward direction as positive direction for the stone.We can write the following for the stone. 24. 3 Squaring the above equation we get the following : We can seen that the above equation is same as that for constant acceleration. We can compare the above equation with v2 = u2 + 2as to get the following : 24V/TP/MOD/J/R- 5 J - MODEL 25. 2 ; 26. 3 Centre of curvature lies on the line perpendicular to instantaneous velocity of the particle. At the initial point, component of mg perpendicular to the velocity will act as centripetal force and let R1 be the radius of curvature for initial point. Let radius of curvature for highest point be R2. On dividing we get, ; We can see that n = 3 27. 1 Force diagram for the block with respect to wedge is shown in figure. Note that pseudo force on the block is applied opposite to the acceleration. Let a be the acceleration of block up the plane. We can write the following equation : We can apply equation of kinematics Initial velocity (u) is zero and length of incline (S) is 1m. 28. 9 No friction is applied by the upper block as long as 3 kg block remains stationary. Normal reaction from the floor on 3kg block is 50B; hence maximum friction that can act is as follows : f  N  0.3  50  15 Newton Maximum friction is greater than applied force hence friction between 3 kg block and floor is equal to 9N, which is same as applied force. 24V/TP/MOD/J/R- 6 J - MODEL 29. 30 Both velocity vectors are of same magnitude therefore resultant would pass exactly midway through them   300 30. 580 CHEMISTRY 31. 1 18 ml water = 18g water; 10-3 mol water = 18 × 10-3 g water 22.4 × 10-4 L = 10-4 mol = 18 × 10-4 g water 32. 3 N  3H 2NH 2 2 3 1mol 3mol 2 mol 10 10 30 mol 20 mol 10 33. 3 In 1L 0.1mol H 2SO 4  9.8g H 2SO 4  10 g solution  mL 1.8 34. 1 2 HCl  CaCO3 2 mol 1mol or 100g 95 25m mol 1.25 g 1.32   1.25 100 35. 3 AgNO3  NaCl AgCl   NaNO3 1 mol 1 mol 1 mol 170g 48.5g 143.5g 8.45g 2.9g 7.1g (LR) h h h h 36. 1 V     V 2  4mx 4m  P 4m V 2 4m 2 37. 3 38. 3 n2 39. 4 r Z 40. 4 41. 2 42. 4 Second electron gain enthalpy of O is +ve. 43. 2 44. 2 B2 O3 ,SO3 , N 2O5 and P4 O10 are acidic 45. 2 Cl OH 1 4 46. 4 5 3 6 2 Br 47. 2 48. 4 49. 1 24V/TP/MOD/J/R- 7 J - MODEL 50. 3 51. 40 1mol XY2  100g ; 1mol X3 Y2  180 g 52. 30 18g  6.02 10 molecules  18 mL 23 18  1molecule  mL 6.02  1023 53. 100 H 2  Cl 2 24 Cl 1mol 0.5mol 1mol (LR ) h h m 54. 18   ve  n vn m n vn me ve me 55. 2 1 second  100J hc Energy required to eject each electron  400  10 9 100 Number of electrons ejected   2  1020  hc   9   4000  10  26  25 56. 4 no. of neutrons = 26; no. of electrons = 25; % of extra neutrons   100  4% 25 57. 0 Valence electron: 4p1 (Ga+), 4s1 (Zn+) 58. 1 Only (i) is exothermic 59. 3 60. 7 MATHEMATICS 61. 2 62. 4 63. 2 24V/TP/MOD/J/R- 8 J - MODEL 64. 2 65. 1 66. 3 67. 3 68. 4 69. 1 2 5 1 70. 2 2*5    3 5 2 25 71. 1 24V/TP/MOD/J/R- 9 J - MODEL 72. 3 73. 3 74. 3 75. 1 24V/TP/MOD/J/R- 10 J - MODEL 76. 1 77. 4 78. 1 79. 3 80. 2 24V/TP/MOD/J/R- 11 J - MODEL 81. 119 82. 45 83. 1 84. 16 85. 19 24V/TP/MOD/J/R- 12 J - MODEL 86. 29 87. 4 88. 2 89. 2 90. 1