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IIT JEE Exam Sample / Model Paper 2025 : Main

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Sparsh Saraogi
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20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP Sec: SR.IIT_*CO-SC(MODEL-A& APEX) Time: 3HRS GTM-2 PHYSICS Date:20-12-24 Max. Marks: 300 MAX.MARKS: 100 SECTION I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 1. Two polarizers are oriented with transmission planes making an angle of 60 . The percentage of incident unpolarized light that passes through the system is A) 50% 2. B) 100% C) 12.5% D) 37.5% If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is 1 103 kg / m3 and g 10m / s 2 , then the volume elasticity in N / m 2 will be: A) 108 Page. No. 1 B) 2 108 C) 109 D) 2 109 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 3. A uniform electric field of 200V / m is directed at 45 with x axis as shown in figure. The coordinates of point P and point Q are 1,0 and 0,2 . Find the potential difference VP VQ (in volts). y(m) Q 45 P A) 4. 200 2 B) 200 2 C) x (m) 200 2 D) 200 2 What is the resistance of voltmeter shown in the circuit? 50V V 100V A) 5. 800 3 B) 800 C) 1000 D) 200 A steel wire of diameter 2 mm has a breaking strength of 4 105 N . What is the breaking force of similar steel wire of diameter 1.5 mm ? A) 2.25 105 N 6. B) 2.6 105 N C) 3 105 N D) 1.5 105 N A car runs at constant speed on a circular track of radius 100m taking 62.8 s on each lap. What is the average speed and average velocity on each complete lap? A) Velocity 10 m / s speed 10 m / s B) Velocity zero, speed 10 m / s C) Velocity zero, speed zero D) velocity 10 m / s, speed zero Page. No. 2 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 7. The deflection in a galvanometer falls from 50 divisions to 20 divisions, when a 12 shunt (resistance connected in parallel to galvanometer) is applied. The galvanometer resistance is A) 18 8. B) 24 C) 30 D) 36 A block of mass 2kg is at rest on an inclined plane of inclination angle 37 . Calculate the force of friction acting on the block [take g 10 m / s 2 ] 2k g 37 A) 20N 9. B) 12N C) 16N D) Zero For a particle moving under the action of a variable force, kinetic energy K versus position x graph is given, then k A B D C O X A) At A , particle is decelerating B) At B , particle is decelerating C) At C , particle has maximum velocity D) At D , particle has maximum acceleration 10. A bob of mass m is pulled along a circular arc by means of a constant horizontal force P as shown. Work done by the force P while lifting the bob from A to B is Page. No. 3 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP O 30 l B P P A A) mgl 11. B) Pl 2 C) Pl D) 3Pl 2 In the situation shown, what is the value of resistance connected between A and D in addition to 12 resistance, so that galvanometer shows no deflection? C 10 50 I I G B A 12 20 D A) 12 12. B) 6 C) 4 D) 5 Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the rms velocity of hydrogen molecule is 13. A) Equal to that of helium B) Twice that of helium C) Half that of helium D) 2 times that of helium A uniform ladder of length 3.25m and weighing 240N is placed against smooth vertical wall with its lower end 1.25m from the wall. If coefficient of friction is 0.3. Find the friction force between ladder and floor (Take normal reaction perpendicular to wall and floor) A) 20 N Page. No. 4 B) 30N C) 50 N D) 40 N 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 14. A movable piston separates a sample of gas from vacuum. In this state, pressure of gas is P, then find pressure after piston is released. 5 m3 of gas A) P B) 6P 6 m3 vacuum C) Adiabatic Wall 5P 11 D) Pressure is not defined because it is a free expansion. 15. In a thermodynamic process on an ideal diatomic gas, work done by the gas is times the heat supplied ( 1). The molar heat capacity of the gas for the process is A) 16. 5R 2 B) 5 R 2 C) 5R 2 1 D) 5 R 1 2 Assertion: The time period of revolution of a satellite close to surface of earth is smaller then that revolving away from surface of earth. Reason: The square of time period of revolution of a satellite is directly proportional to cube of its orbital radius. A) If both assertion and reason are true and reason is the correct explanation of assertion. B) If both assertion and reason are true but reason is not the correct explanation of assertion C) If assertion is true but reason is false D) If both assertion and reason are false 17. Assertion (A): The accuracy of a standard screw gauge is more than the accuracy of a standard vernier caliper. Reason (R) : The least count of standard screw gauge is more than the least count of standard vernier caliper. A) A and R are true and R is the correct explanation of A B) A and R are true, but R is not the correct explanation of A C) A is true but R is false D) Both A and R are false Page. No. 5 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 18. t Given that y a sin qx , where t represents time in second and x represents p distance in meter. Which of the following statement is true? A) Dimension of t is same as that of q B) Dimension of x is same as that of p C) Dimension of x is same as that of q D) Dimension of t is same as that of p 19. A nucleus disintegrates into two parts which have their velocities in the ratio 2 : 1 The ratio of their nuclear sizes will be 1 A) 2 3 :1 20. B) 1: 3 1 1 2 C) 3 2 :1 D) 1: 2 1 3 In a photo-emissive cell, with exciting wavelength 1 , the maximum kinetic energy of electron is K . If the exciting wavelength is changed to 2 , the maximum kinetic energy of electron is 2K then A) 1 2 2 B) 1 2 2 D) 1 C) 1 2 2 2 2 SECTION-II (NUMERICAL VALUE ANSWER TYPE) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals , Round off to the nearest Integer only. Have to Answer all 5 questions and question will be evaluated according to the following marking scheme: Marking Scheme: +4 for correct answer, 0 if not attempted and 1 if not correct. 21. A solid sphere is released from rest on a curved surface as shown in figure. Left half of the surface is rough and right half is smooth. If sphere is released from rough side, then the maximum height attained by it on smooth side is (Rough surface has sufficient friction for pure rolling) h=7m Page. No. 6 R ou gh Sm th oo 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 22. Consider an imaginary cube with different vertices of the cube marked as shown. A point charge is placed at vertex H and flux through the face ABCD is in this case. Now, the charge is shifted to centre of the cube. Flux through the face AEHD in this case is k . What is the value of k ? G H C D F E B A 23. In the figure shown below, a fluid of density 2 103 kg m 3 is flowing in a horizontal pipe. The speed of water at point A is 4cm s 1 , what is its speed at point B (in cm s 1 ). Round off the answer to the nearest integer. 2.5 mm A 24. B In a stationary wave represented by y a sin t cos kx , amplitude of the component progressive wave is na . The value of 10n _______ 25. The torque acting upon the following structure carrying current i due to the magnetic field B is p R 2iB. Find p q . (Magnetic field is in the plane of loop) q B 2R 30 R Page. No. 7 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP CHEMISTRY MAX.MARKS: 100 SECTION I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 26. For the homogeneous 1st order gaseous reaction. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z The initial pressure was P0 while after time t , total pressure was P . The expression for rate constant k in terms of P0 , P and t is 27. A) k 2.303 P0 log t P0 P B) k 2.303 25 P0 log t 26 P0 P C) k 2.303 24 P0 log t 25 P0 P D) k 2.303 24 P0 log t P0 25 P In the following reaction, the number of monochloro derivatives possible for the compound D is CH 3CN A) 3 28. H2O /H+ Ca dry distillabtion A B B) 4 C C) 2 Zn - Hg + HCl D) 5 What is product of following reaction? Hex 3 ynal (i) NaBH 4 (ii) PBr3 (iii) Mg/ether (iv) CO2 / H3O+ A) COOH B) COOH O C) Page. No. 8 C OH D) COOH D 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 29. An organic compound P C6 H 6O gives violate colouration with ferric chloride. On treatment with CHCl3 and KOH , followed by acidification gives compound Q . Compound Q can also be obtained from compound R on reaction with pyridinium chlorochromate (PCC). Identify P, Q and R OH OH CH2OH CHO P= Q= OH R= A) OH CH2OH OH P= Q= OH CHO R= B) CH2OH OH P= OH OH CHO Q= R= C) OH CHO P= CH2OH OH Q= OH R= D) 30. Which of the following statement is incorrect? A) Glucose give schiff s test and forms the hydrogen sulphite addition product with NaHSO3 B) The pentacetate of glucose does not react with hydroxyl amine indicating the absence of free CHO group C) On oxidation with conc. HNO3 , both glucose and gluconic acid yield saccharic acid D) Glucose reacts with hydroxylamine to form an oxime Page. No. 9 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 31. Which of the following doesn t produce an ether compound as a major product? H2SO4 A) CH3CH2OH 140 C CH3 CH3 O- Na+ + CH3Br C CH3 B) NH2 NaNO2 (i) H2O warm (ii) NaOH (iii) CH 3Br +HCl C) N2+ Cl+ CH3CH2OH D) 32. Assertion: Phenoxide ion is more stable than carboxylate ion hence phenol is more acidic than carboxylic acids. Reason: The negative charge is delocalized over two electronegative oxygen atoms in carboxylate ion. A) Both A and R are true and R is the correct explanation of A B) Both A and R are true and R is not the correct explanation of A C) A is true but R is false D) A is false but R is true Page. No. 10 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 33. 34. Match the following. List I List-II (Complex) (Hybridisation) a) Ni CO 4 I. sp3 b) Ni CN 4 2 II. sp 3d 2 c) Co CN 6 3 III. d 2 sp3 d) CoF6 IV. dsp 2 3 A) a IV , b I , c III , d II B) a I , b IV , c III , d II C) a I , b IV , c II , d III D) a IV , b I , c II , d III Consider the complex ions, trans - Co en 2 Cl2 A and cis- Co en 2 Cl2 B The correct statement regarding them is A) Both (A) and (B) can be optically active B) Both (A) and (B) cannot be optically active C) (A) can be optically active, but (B) cannot be optically active D) (A) cannot be optically active, but (B) can be optically active 35. Which of the following electronic configuration of the corresponding element is wrongly matched? 36. A) Thulium - Xe 4 f 13 6 s 2 B) Americium - Rn 5 f 7 7 s 2 C) Uranium - Rn 5 f 4 7 s 2 D)Terbium - Xe 4 f 9 6 s 2 Consider the ions/molecule O2 , O2 , O2 , O22 for increasing bond order the correct option. A) O22 O2 O2 O2 B) O2 O22 O2 O2 C) O2 O22 O2 O2 D) O2 O2 O22 O2 Page. No. 11 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 37. Correct order of stability of halogen oxides A) I Br Cl 38. B) Br Cl I C) Cl Br I D) I Cl Br First and second ionization energies of magnesium are 7.646 and 15.035eV respectively. The amount of energy in kJ needed to convert all the atoms of magnesium into Mg 2 ions present in 12 mg of magnesium vapours is nearly: [Given: 1eV 96.5 kJ mol 1 ] A) 1.1 39. B) 1.5 C) 2.0 D) 0.5 5 moles of PCl5 and 2 moles of N 2 are placed in 200 Lt vessel maintained at 600 K . The equilibrium pressure is 2.46 atm. The equilibrium constant K p for the dissociation of PCl5 is nearly ________ atm. (Given R 0.082 lit atm mol 1 K 1 ) A) 3.3 40. B) 2.2 C) 1.1 D) 1.6 The freezing point of benzene decreases by 0.45 C when 0.2g of acetic acid is added to 20g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be: ( K f for benzene = 5.12 K kg mol 1 ) 41. A) 74.6% B) 94.6% Consider the following changes C) 64.6% D) 80.4% 1. Sublimation energy of M P 2. Sublimation energy I .E1 I .E2 of M Q 3. I .E1 of M R 4. I .E2 of M S 5. I .E1 I .E2 of M T The enthalpy change of the reactions (i) M s M g2 2e ,(ii) M g M g2 e respectively are A) (i) Q P T , (ii) R T B) (i) P R , (ii) T R C) (i) Q , D) (i) P R S , (ii) R S Page. No. 12 (ii) T 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 42. A solution of 15 mL contained NaHCO3 and Na2CO3 mixture. It required 5 ml of M /10 HCl for neutralization using phenolphthalein indicator. To the same solution after adding methyl orange indicator it required more 15 mL of acid for neutralization. The amount of NaHCO3 present in 500 mL of solution is A) 2.8g 43. B) 3.53g C) 5.6g Arrange in decreasing order or reactivity with HCl (i) (iii) (ii) NO2 OCH3 A) I II III 44. D) 0.42g B) III II I C) II III I D) I III II Correct decreasing order of bond angle x, y and z in given structure. Cl Cl Cl x Al A) x y z 45. y Al Cl Cl B) z y x C) x y z z Cl D) z x y Arrange the following in decreasing order of ionic size. A) Ce 3 Lu 3 Gd 3 Eu 3 B) Ce 3 Eu 3 Gd 3 Lu 3 C) Eu 3 Ce 3 Gd 3 Lu 3 D) Gd 3 Eu 3 Ce 3 Lu 3 SECTION-II (NUMERICAL VALUE ANSWER TYPE) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals , Round off to the nearest Integer only. Have to Answer all 5 questions and question will be evaluated according to the following marking scheme: Marking Scheme: +4 for correct answer, 0 if not attempted and 1 if not correct. Page. No. 13 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 46. The minimum pH required to prevent the precipitation of ZnS in a solution containing 0.01M ZnCl2 and saturated with 0.10 M H 2S is (Given K sp ZnS 10 21 , Ka1 Ka2 of H 2 S 10 20 ) 47. A tetrapeptide on hydrolysis produced glycine (gly), Leucine (Leu.), Alanine (Ala), Valine (Val.). Count number of possible tetrapeptides (structural isomers only) Which can produce above four amino acids with the following both conditions. i) Glycine is not present at N-terminal ii) Alanine in present at C-terminal 48. 14 1 For a first order reaction A B . The rate constant K 5.5 10 sec . The time 1 required for 67% completion of reaction is x 10 times the half life of reaction. Then ' x ' (nearest integer) is ______ ( log3 0.48 ) 49. 2MnO4 bC2O42 cH xMn2 yCO2 zH 2O If the above equation is balanced with integer coefficients, the value of b c x y z __________ 50. For the elementary reaction M N , the rate of disappearance of M increase by a factor of 8 upon doubling the concentration of M . The order of the reaction with respect of M is Page. No. 14 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP MATHEMATICS MAX.MARKS: 100 SECTION I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 51. tan 2 x , x 0 2 x x Given a real valued function f x , defined as f x 1, x 0 where x .cot x , x 0 x and x represents greatest integer function and fractional part of x, respectively, then which is incorrect? A) lim f x 1 x 0 C) tan 1 lim f x 52. x 0 2 B) cot 1 lim f x 4 Let z be a complex number such that x 0 1 D) lim f x exists x 0 5 z i 1 and z . Then the value of z 3i 2 z 2i is A) 10 53. B) 7 2 C) 15 4 D) 2 3 A square is inscribed in the circle x 2 y 2 10 x 6 y 30 0 . One side of this square is parallel to y x 3. If xi , yi are the vertices of the square, then equal to A) 148 Page. No. 15 B) 156 C) 160 D) 152 x 2 i yi2 is 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 54. Four points having position vectors a, b, c, d are coplanar and sin a 2sin 2 b 3sin 3 c d 0 , then the least value of sin 2 sin 2 2 sin 2 3 is A) 55. 1 14 B) 14 C) 6 D) 1 6 5x 3 y 5 f x 3 f y , x, y R and f 0 3, If f x satisfies the relation f 2 2 f ' 0 2, then the fundamental period of sin f x is A) 56. B) 2 C) 3 D) 4 Let P be the point 10, 2, 1 and Q be the foot of the perpendicular drawn from the point R 1,7,6 on the line passing through the points 2, 5,11 and 6,7, 5 . Then the length of the line segment PQ is equal to A) 14 57. C) 12 D) 17 cos 2 x x 2 n sin x 1 The function f x lim is continuous for all x in x 1 x 2 n 1 x 2 n A) R 1 58. B) 13 B) R 1,1 C) R 1 D) R 0 The total number of 3 3 matrices A having entries from the set 0,1,2,3 such that the sum of all the diagonal entries of AAT is 9, equal to _____ A) 765 59. C) 766 D) 757 2100 C) 101 ! 251 D) 101 ! 1 1 1 1 ... 1!.100! 3!.98! 5!.96! 101 ! 2100 A) 100! 60. B) 756 2101 B) 101! If vertex of a parabola is 2, 1 and the equation of its directrix is 4 x 3 y 21 , then the length of its latus rectum is A) 2 Page. No. 16 B) 8 C) 12 D) 16 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 61. x 2 xy The general solution of the differential equation x y .e e y dy xy y e y 2 .e xy dx is xy x y A) e e c 62. xy y x B) e e c xy x y C) e e c xy y x D) e e c If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is A) 63. 13 32 B) The integral 1 4 C) dx x 4 x 3 8/7 6/7 1 x 3 7 x 3 A) C B) x 4 x 4 64. 1 7 1 32 D) 3 16 is equal to (Where C is a constant of integration) 3 1 x 3 7 1 x 3 C C) C D) 2 x 4 13 x 4 13 7 C Let x denote the total number of one-one functions from set A with 4 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A B then A) y 969 x 65. B) 2 y 91 x C) y 91x D) 2 y 273x A ray of light through 2,1 is reflected at a point P on the y -axis and then passes through the point 5,3 . If this reflected ray is the directrix of an ellipse with eccentricity 1 16 and the distance of the near focus from the directrix is then the 3 53 equation of the directrix can be A) 2 x 7 y 25 0 B) 2 x 7 y 25 0 C) 2 x 7 y 47 0 D) 2 x 7 y 47 0 Page. No. 17 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 66. Let F : 3,5 R be a twice differential function on 3,5 such that x F x e x 3t 2 2t 4 F ' t dt Then F x ________ 3 x 3 x 2 36 A) ex 4 C) 67. x 3 x 2 36 B) ex 4 x 3 x 2 36 ex 4 Let u D) x 3 x 2 36 ex 4 2z i , z x iy and k 0 . If the curve represented by Re u Im u 1 z ki intersects the y axis at the points P and Q where PQ 5, then the value of k is: A) 1 / 2 68. 69. B) 3 / 2 C) 4 D) 2 x2 x 1 The true solution set of log 2 is equal to tan x 2 6 A) 1 x 5 B) 2 x 5 C) x 2 1 x 5 D) x 5 If the mean deviation of number 1,1 d ,1 2d ,...1 100d from their mean is 255, then d is equal to A) 10.0 70. B) 20.0 C) 10.1 D) 20.2 Unit vector c is inclined at an angle to unit vectors a and b which are perpendicular. If c a b a b where , be real, then belongs to A) ,0 4 B) 0, 4 C) , 4 3 D) , 4 4 SECTION-II (NUMERICAL VALUE ANSWER TYPE) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals , Round off to the nearest Integer only. Have to Answer all 5 questions and question will be evaluated according to the following marking scheme: Marking Scheme: +4 for correct answer, 0 if not attempted and 1 if not correct. Page. No. 18 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP 71. xe ax , x 0 Let f x , where a is a positive constant. The interval in 2 3 x ax x , x 0 k a which f ' x is increasing is , . Then k l is equal to. a l 3 72. The value of 12 x 2 3 x 2 dx is 0 73. The area (in sq. units) of the region bounded by the curve x 2 4 y and the straight line x 4 y 2 is k , then 8k is 74. For a unique value of & , the system of equations given by x y z 6 x 2 y 3z 14 2x 5 y z has infinitely many solutions, then 75. is equal to 4 Four persons can hit a target correctly with probabilities 1 1 1 1 , , and respectively. 2 3 4 8 If all hit at the target independently, then the probability that the target would be hit, is n . Then 192n is _____ Page. No. 19 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP Page. No. 20 20.12.24_SR.STAR CO-SC(MODEL-A& APEX)_Jee_Main_GTM-2_QP Page. No. 21

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