Practice Test 02 Test Papers (PCM) Prayas JEE 2.0 2025.pdf

Prayas JEE 2.0 (2025) PRACTICE TEST - 02 DURATION ::180 DURATION Minutes 90 Minutes DATE : 04/08/2024 M.MARKS : 300...

Prayas JEE 2.0 (2025) PRACTICE TEST - 02 DURATION ::180 DURATION Minutes 90 Minutes DATE : 04/08/2024 M.MARKS : 300 Topics Covered Physics: Work, Energy and Power (Complete Chapter), Circular Motion (Complete Chapter) Chemistry: Periodic Table (Complete Chapter), Chemical Bonding (Complete Chapter), Coordination Chemistry (Without isomerism) Mathematics: Sequence and Series, Trigonometric functions General Instructions: 1. Immediately fill in the particulars on this page of the test booklet. 2. The test is of 3 hours duration. 3. The test booklet consists of 90 questions. The maximum marks are 300. 4. There are three sections in the question paper, Section I, II & III consisting of Section-I (Physics), Section-II (Chemistry), Section-III (Mathematics) and having 30 questions in each Section in which first 20 questions are compulsory and are of Objective Type and last 10 questions are integer type with answers ranging from ‘0’ to ‘999’ where answer needs to be rounded off to the nearest integer. Only 5 questions have to be attempted out of the last 10 questions of each section. 5. There is only one correct response for each question. 6. Each correct answer will give 4 marks while 1 Mark will be deducted for a wrong response. 7. No student is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. inside the examination room/hall. 8. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 9. Do not fold or make any stray mark on the Answer Sheet (OMR). OMR Instructions: 1. Use blue/black dark ballpoint pens. 2. Darken the bubbles completely. Don't put a tick mark or a cross mark where it is specified that you fill the bubbles completely. Half-filled or over-filled bubbles will not be read by the software. 3. Never use pencils to mark your answers. 4. Never use whiteners to rectify filling errors as they may disrupt the scanning and evaluation process. 5. Writing on the OMR Sheet is permitted on the specified area only and even small marks other than the specified area may create problems during the evaluation. 6. Multiple markings will be treated as invalid responses. 7. Do not fold or make any stray mark on the Answer Sheet (OMR). Name of the Student (In CAPITALS) : _______________________________________________________________ Roll Number : _____________________________________________________________________________________________ OMR Bar Code Number : ________________________________________________________________________________ Candidate’s Signature : _______________________________ Invigilator’s Signature _____________________  Section-I (PHYSICS) Single Correct Type Questions (2) Tension 1. A force acts on a 30gm particle in such a way that (3) Normal the position of the particle as a function of time is (4) None of these given by x  3t  4t 2  t 3 , where x is in metres 6. A particle is moving in a vertical circle the tension and t is in seconds. The work done during the first in the string when passing through two position at 4 seconds is angle 30° and 60° from vertical from lowest (1) 5.28 J (2) 450 mJ position are T1 and T2 respectively then: (3) 490 mJ (4) 530 mJ (1) T1  T2 (2) T1  T2 10 (3) T1  T2 (4) T1  T2 2. A particle A of mass kg is moving in the 7 positive x -direction. Its initial position is x  0 & 7. Potential energy function along x -axis in a certain initial velocity is 1 m/s. The velocity at x  10m is force field is given as x4 11 : (use the graph given) U  x   2 x3  x 2  6 x. 4 2 For the given force field :- (i) the points of equilibrium are x  1, x  2 and x  3. (ii) the point x  2 is a point of unstable equilibrium. (iii) the points x  1 and x  3 are points of stable (1) 4 m/s (2) 2 m/s equilibrium. (3) 3 2 m/s (4) 100/3 m/s (iv) there exists no point of neutral equilibrium. The correct option is :- 3. A particle moves in a straight line with retardation (1) (i), (ii), (iv) (2) (i), (ii), (iii), (iv) proportional to its displacement. Its loss of kinetic (3) (iii), (iv) (4) (ii), (iii) energy for any displacement x is proportional to 8. A body of mass 2 kg is moving under the influence (1) x2 (2) ex of a central force whose potential energy is given (3) x (4) log e x by U = 2r3 J. If the body is moving in a circular orbit of 5 m, its energy will be 4. A body of mass m was slowly hauled up the hill (1) 625 J (2) 250 J by a force F which at each point was directed (3) 500 J (4) 125 J along a tangent to the path. The work done by this force, if the height of the hill is h , the length of its 9. If atmosphere exerts only frictional force on a base is and the coefficient of friction is  , is- moving block which is given as F   kv then what is the maximum possible rate of heat loss if a ball of mass m is dropped from sufficient height under gravity:- m2 g 2 mg (1) (2) k k k m4 g 4 (3) (4) (1) mgh  mg m2 g 2 k3 (2) mgh  mg (3) mgh  mg 2  b2 10. If U  x2  2 y  3z , find the force F  (4) Can't determined corresponding to it. (1) 2xiˆ  2 ˆj  3kˆ (2) 3xiˆ  2 ˆj  3kˆ 5. Which of the following forces can never, under (3) 3xiˆ  2 ˆj  3kˆ (4) 2 xiˆ  2 ˆj  3kˆ any circumstances, does work? (1) Static friction 11. A small ball B of mass m is suspended with radius in horizontal plane about O with light inelastic string of length L from a block A constant speed v , as shown in the figure. The of same mass m which can move on smooth average force exerted by string on the bob during horizontal surface as shown in the figure. The ball its :- is displaced by angle  from lower most position & then released. Maximum velocity of block during subsequent mv 2 (A) half revolution will be motion of the system after release of ball is  (1) [ gl 1  cos]1/2 (B) half revolution will be 2mv 2  (2) [2 gl 1  cos ]1/2 2mv 2 [ glcos]1/2 (C) one fourth revolution will be (3)  (4) informations are insufficient to decide (D) one revolution will be zero Select correct alternative :- 12. A particle of mass m describes a circle of radius (1) Only (A) and (D) (2) Only (A), (C) and (D) (3) Only (B) and (D) (4) Only (B), (C) and (D) (r). The centripetal acceleration of the particle is 4. The momentum of the particle is 17. A pendulum of mass m and length l is released r2 from rest in a horizontal position. A nail at 2m 2m a distance d below the pivot, causes the mass (1) (2) r r to move along the path indicated by the dotted line. 4m 4m The minimum distance such that the mass will (3) (4) swing completely round in the circle shown in r r 5d figure is d then is 13. The particle moving in a circle of radius of 10 cm with uniform speed completing the circle in 4 s. Find magnitude of linear acceleration. (1) 5 cm/s2 (2) 2.5 cm/s2 (3) 52 cm/s2 (4) Zero 14. A body is moving in a circle at a uniform speed v. (1) 2 (2) 3 What is the magnitude of the change in velocity (3) 4 (4) 5 when the radius vector describes an angle   (1) v cos  (2) 2v cos   18. As shown in the figure a mass m is rotating freely 2 in a horizontal circle of radius 20 cm in a smooth  (3) v sin  (4) 2v sin   fixed cone which supports a stationary mass m, 2 attached to the other end of the string passing through smooth hole O in cone, hanging 15. A heavy particle hanging from a string of length vertically. Find the angular velocity of rotation. is projected horizontally with speed g. Find speed of particle at point where the tension equals weight of particle. 2g (1) (2) g 3 g (3) (4) 2g 3 16. A bob of mass m is attached at one end of a (1) 5 rad/s (2) 2 rad/s string of length. Other end of the string is fixed (3) 10 rad/s (4) 15 rad/s at point O. Bob is rotating in a circular path of 19. A uniform cable of mass ‘M’ and length ‘L’ is 24. Two bars of masses m1 = 4 kg and m2 = 8 kg placed on a horizontal surface such that its (1/n)th connected by a non-deformed light spring rest on a part is hanging below the edge of the surface. To horizontal plane. The coefficient of friction lift the hanging part of the cable upto the surface, between bars and surface is m = 0.2. What the work done should be: minimum constant force has to be applied in the 2MgL horizontal direction to the bar of mass m1 in order (1) nMgL (2) n2 to shift the other bar? MgL MgL (3) 2 (4) 2n n2 20. A particle is given a certain velocity v at point P as shown on a hemispherical smooth surface. The 25. When the bob of a simple pendulum swings, the value of v in m/s, such that particle when reaches work done by tension in the string is (in J) Q the normal reaction of surface is equal to particle's weight, is [R = 1.6 m, g = 10 m/s2] 26.   A force F  5  3 y 2 acts on a particle in the y - direction, where F is in newton and y is in meter. The work done by the force during a displacement from y  2 m to y  5 m is _____ J (1) 2 (2) 3 (3) 8 (4) 4 27. Power applied to a particle varies with time as Integer Type Questions   P  3t 2  2t  1 watt, where t is in second. Find 21. A simple pendulum oscillates in a vertical plane. the change in its kinetic energy between time When it passes through the mean position, the t  2 s and t  4 s. (in J) tension in the string is 3 times the weight of the pendulum bob. What is the maximum angular 28. A particle is moving in a circle of radius r under displacement of the pendulum of the string with the action of a force F = αr2 which is directed respect to the downward vertical? (in degrees) towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the 22. A mass m slides from rest at height h down a particle is k r 3. Find the value of 6k. smooth curved surface which becomes horizontal (take potential energy = 0 for r = 0): at zero height (see figure). A spring is fixed horizontally on the level part of the surface. The 29. A body is slowly lowered on to a massive platform spring constant is k N/m. When the mass moving horizontally at a speed of 4 m/s. Through encounters the spring it compresses it by an what distance (in m) will the body slide relative to amount x = h/10. If m = 1 kg, h = 5m then find the platform? (The coefficient of friction is 0.2; g = k /100. 10 m/s2) 30. A ball falls under gravity from a height 10 m with an initial velocity v0. It hits the ground, loses 50% of its energy in collision and it rises to the same height. What is the value of v0? 23. A particle moves in a circle of radius 1.0 cm at a (Round off to nearest integer). speed given by v  2.0t where v is in cm/s and t in seconds. Find the radial acceleration in cm/s2 of the particle at t  1s.  Section-II (CHEMISTRY) Single Correct Type Questions 37. Primary and secondary valency of Pt in 31. The IUPAC name for the complex [Pt(en)2Cl2]Cl2 are [Co(NO2)(NH3)5]Cl2 is (1) 4, 4 (2) 4, 6 (1) nitrito-N-pentaamminecobalt (III) chloride (3) 6, 6 (4) 4, 2 (2) nitrito-N-pentaammineocobalt (II) chloride (3) pentaaminenitrito-N-cobalt (II) chloride 38. Which of the following oxide is most acidic? (4) pentaaminenitrito-N-cobalt (III) chloride (1) CO2 (2) Cl2O7 (3) P2O5 (4) SO2 32. The element which has highest third ionization energy is: 39. Which of the following order of lattice energy is not (1) Na correct? (2) Mg (1) NaCl < Na2S (2) KF < LiF < MgO (3) Al (3) MgO < AlN (4) NaCl > MgO (4) Ar  4 40. Ti3 aq.  is purple while Ti aq. is colourless because 33. The correct order of increasing bond angles in the following species is: (1) There is not crystal field effect in Ti4+ (1) CH4 < NH3 < H2O (2) The energy difference between t2g and eg of Ti4+ (2) SO2 < SO3 < CO2 is quite high and does not fall in the visible (3) CO2 < SO2 < SO3 region (3) Ti4+ had d0 configuration (4) CH4 < H2O < NH3 (4) Ti4+ is very small in comparison to Ti3+ and hence does not absorb any radiation 34. Which of the following is a  -acid ligand? (1) NH 3 41. Considering the elements B, Al, Mg and K, the correct order of their metallic character is (2) CO (1) B > Al > Mg > K (3) F (2) Al > Mg > B > K (4) H 2 N  CH 2  CH 2  NH 2 (3) Mg > Al > K > B (4) K > Mg > Al > B 35. Statement I: Newland's law of octaves is valid only 42. According to MO theory, which of the following lists up to mass number 20. rank the nitrogen species in terms of increasing bond Statement II: Li, Na, K forms a Dobereiner's triad. order? N2  N22  N2 (1) Both statement I and statement II are true but (1) statement II is not the correct explanation of statement I. (2) N2  N2  N22 (2) Statement I is true but statement II is false. (3) Statement I is false but statement II is true. (3) N22  N2  N2 (4) Both statement I and statement II are true and statement II is the correct explanation of (4) N2  N22  N2 statement I. 43. Match List-I with List-II and select the correct answer using codes given ahead in the lists: 36. Match the following: List-I List-II List-I List-II (Metal ions) (Spin only Magnetic (Molecule) (Shape) moments of the ions) I. NH 2– P. Square pyramidal I. Cr3+ P. 35 B.M. II. Q V-shaped II. Fe2+ Q. 30 B.M. XeOF2 2+. III. Ni R. 24 B.M. III. ICl4– R. T-shaped 2+ IV. Mn S. 15 B.M. T. IV. SbF5 2 S. Square planar 8 B.M. (1) I-P, II-R, III-T, IV-S (1) I-S, II-Q, III-R, IV-P (2) I-Q, II-R, III-T, IV-P (2) I-Q, II-R, III-S, IV-P (3) I-S, II-R, III-T, IV-P (3) I-R, II-S, III-Q, IV-P (4) I-S, II-T, III-R, IV-P (4) I-Q, II-R, III-P, IV-S 44. The element that shows anomalous behaviour in group (1) O > S > Se > Te (2) Te > Se > S > O 13 is: (3) S > O > Se > Te (4) S > Se > Te > O (1) Boron (2) Aluminium Integer Type Questions (3) Gallium 51. The total number of unpaired electrons in t2g orbitals (4) Thallium of central atom in [CoF6]3– is ____. 45. Among the following molecules: 52. Electronic configuration of an element is 1s2 2s2 2p6 (i) XeO3 3s2 3p6 3d10 4s1. What is atomic number of next (ii) XeOF4 element of same group which is recently discovered? (iii) XeF6 Those having same number of lone pairs on Xe are:  (1) (i) and (ii) only 53. How many atom(s) of BF2 , lie in the same plane? (2) (i) and (iii) only (3) (ii) and (iii) only 54. The EAN of a metal carbonyl, M(CO) x is 36. The (4) (i), (ii) and (iii) only atomic number of metal is 24. The value of x is_____. 46. What is the crystal field stabilisation energy (CFSE) 55. How many elements from the following are not for d7 configuration for strong ligand field? transition element? Zr, Co, Cd, Hg, Au, Cu (1) 1.6 Δ 0 (2) 2 Δ 0 56. How many of the following has sp3 hybridisation? (3) 2.4 Δ 0 (4) 1.8 Δ 0 PCl3, I3+, H2S, H2Se, PH3, OCl2 47. What will be the group number and period number 57. The CFSE for [CoCl6]4– is 18000 cm–1. The Δ for respectively for atomic number 42? [CoCl4]2– is ____ × 103 cm–1. (1) 4, 5 (2) 5, 6 (3) 6, 5 (4) 5, 4 58. How many of the following molecule has bond angle greater than 100°? 48. Statement I: Scandium and zinc are two members of NH3, H2O, H2S, PH3, AsH3, OF2, OCl2, BF3 first transition series which do not form coloured compounds. 59. How many of the following oxides is/are amphoteric Statement II: Scandium compounds have 3d0 oxides? configuration while zinc compounds have 3d10 I. CaO II. SO2 configuration, i.e. there is not d-d transition. III. SO3 IV. B2O3 In the light of above statements, choose the V. BeO VI. Al2O3 appropriate answer from the options given below. VII. Ga2O3 VIII. CO2 (1) Statement-I is true, statement-II is true and statement-II is correct explanation for statement- I. 60. How many of the following atomic orbital (2) Statement-I is true, statement-II is true and overlappings are not allowed? statement-II is not the correct explanation for statement-I. (3) Statement-I is true, statement-II is false. P. Q. (4) Statement-I is false, statement-II is true. 49. Among following molecule N-Si bond length is shortest: R. S. (1) N(SiH3)3 (2) NH(SiH3)2 (3) NH2(SiH3) (4) All have equal N-Si bond length T. 50. The correct order of electron gain enthalpy is:  Section-III (MATHEMATICS) Single Correct Type Questions 68. The minimum value of the function sin1  sin2  sin3  3 2sinx 4cosx f  x  61. If then value of   cos1  cos2  cos3 is 1  cos x 1  sin 2 x 2 (1) 0 (2) 1 8tanx 16cotx  (whenever it is defined) is (3) 1 (4) 2 sec 2 x  1 cosec 2 x  1 (1) 34 (2) 30     (3) 26 (4) 22 62. The value of cos 2      sin 2     is 4  4  (1) 0 (2) cos2 69. If K  sin 6 x  cos6 x , then K belongs to the interval (3) sin2 (4) cos 7 5 1 5 (1) 8 , 4 (2) 5 , 8     63. The sum of the first 2n terms of an A.P. is x and the sum 1  of the next n terms is y, then its common difference is (3)  4 ,1 (4) None of these   x  2y 2y  x (1) 2 (2) 3n 3n 2 3  cot76o cot16o 70. The value of is x  2y 2y  x cot76o  cot16o (3) (4) 3n 3n (1) cot 44o (2) tan 44o (3) tan 2o (4) cot 46o 64. The minimum value of  a2  a  1b2  b  1 c2  c  1 d 2  d  1 where a, b, 71. If tan, tan are the roots of the equation x  px  q  0 , then the value of 2 abcd sin2 ( + ) + p sin ( + ) cos ( + ) c, d > 0, is + q cos2 ( + ) is 1 1 (1) Independent of p but dependent on q (1) 4 (2) (2) Independent of q but dependent on p 3 24 (3) Independent of both p and q (3) 24 (4) 34 (4) dependent on both p and q 3 5 7 65. If sin  cosec  2 , then the value 72. Sum of the series   ..... upto n terms is 4 36 144 of sin10  cosec10 is equal to equal to (1) 2 (2) 210 1 n  n  2 9 (1) 1 (2) (3) 2 (4) 10  n  12 2 n n 2  2n  2 1 66. If 32sin5  243cos5  3  30sin  cos  ; (3) (4) 1  n  1 2 n2   ,  0,  , then the value of cos2  cos2 is  2 73. If cos       a and sin ( – ) = b, 5 5 (1) (2)     0    ,      then cos ( – ) + 2ab sin ( – 2 18 18  2 7 7 (3)  (4) ) is equal to 9 9 (1) 4a 2b2 (2) a 2  b2 67. The sum of the series (3) a 2  b2 (4) a2b2  a  b  a  b   a 2  b2  1 74. The range of is  a  b  a  b    3sin  4cos  2 2!  1 1 (1)  3 , 7   a  b  a  b   a 4 b a b 4 2 2  +....  is equal to    1 1  3! (2) 3 , 7  2 2 2   b2 (1) ea  eb (2) ea  1 1   ,     ,     2 2 (3) (3) log 1  a 2  b 2 (4) ea  eb  3 7  (4) None of these  1 89o  n  2  n  3 for n = 1, 2, 3,......, tn  75. If 4 82. The value of o  3  cos4 x  cos2 x is equal to x 1 1 1 1 1 then   .....  is equal to t1 t2 t3 t2011 4022 2011 83. The value of (1) (2) 3021 3021 1   3tan1o 1  3tan2o  tan1o  tan59o  tan2o  tan58o  (3) 4006 (4) None of these 1  tan 21o 1  tan 2 2o  2011 is 76. The series of natural numbers is divided into groups as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10)………. 19 3  r  1 r  1 a 84.    r  1  r 5  2r 4  r 3  If sum of elements in the 20th group is m, then m is equal If (a and b are co- r 1 b to (1) 1368 (2) (38)2 prime numbers), then (b  a) is (3) (39)2 (4) 38 × 39 77. The largest perfect square that divides 20143  20133 + 85. The sum of infinite terms of the series, 20123  20113 +......+ 23  13 is 2 6 10 14 1    .... upto  terms, is (1) 12 (2) 22 3 32 33 34 2 (3) (1007) (4) (2014)2 78. Value of expression 86. Value of cos6 x  6cos4 x  15cos2 x  10 cos20o cos50o cos110o is   is cos5 x  5cos3 x  10cosx sin50o sin110o sin110o.sin20o sin20o sin50o (1) cos 2x (2) cos2 x (3) 2 cos x (4) 1 + cos x 87. If tanx  tan 2 x  1 , then the value 79. The sum of first two terms of a geometric progression is of tan x  2tan x  tan x  2tanx  1 is equal to 4 3 2 12. The sum of third and fourth terms is 48. If the terms are alternately positive and negative, then 88. The largest possible value of the expression (1) common ratio of G.P. is 2 S = sin x1  cos x2 + sin x2  cos x3 + …. + sin x99  cos (2) common ratio of G.P. is 3 x100 + sin x100  cos x1, (where x1, x2, x3,….x100 are (3) sixth term of G.P. is 128 arbitrary real numbers) is (4) none of these 360   p 1 a a a  a3 If 2 3  2 a a   3  2 3  , then a1 , a2 , a3 , a4 89. If   n n  1   n  1 n   q (where p and q 80. n 1   a1a4 a1  a4  a1  a4  relatively prime integers), the |p  q| is are in (1) A.P. (2) G.P. 90. The value of (1 + tan1°) (1 + tan 22°) (1 + tan 23°) (3) H.P. (4) none of these (1 + tan 44°) is equal to Integer Type Questions 81. If sin5  a sin5  b sin3  c sin  d ,  R , then a + b + c + d is equal to PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if