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JEE Main Session 2 1st February 2023 Shift 2 Question Paper and Answer Key

May 10, 2023 by suresh84

JEE MAIN 1st February 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ‘ K ‘ is :

(1) −273°C

(2) −100°C

(3) −40°C

(4) −373°C

Answer: (1)

2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : For measuring the potential difference across a resistance of 600Ω, the voltmeter with resistance 1000Ω will be preferred over voltmeter with resistance 4000Ω.

Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.

In the light of the above statements, choose the most appropriate answer from the options given below.

(1) Both 𝐀 and 𝐑 are correct and 𝐑 is the correct explanation of 𝐀

(2) Both 𝐀 and 𝐑 are correct but 𝐑 is not the correct explanation of 𝐀

(3) 𝐀 is not correct but 𝐑 is correct

(4) 𝐀 is correct but 𝐑 is not correct

Answer: (3)

3. Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

(1) Fig (c)

(2) Fig (b)

(3) Fig (d)

(4) Fig (a)

Answer: (2)

4. An electron of a hydrogen like atom, having Z = 4, jumps from 4th energy state to 2nd energy state. The energy released in this process, will be :

(Given Rch=13.6eV)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck’s constant

(1) 40.8eV

(2) 3.4eV

(3) 10.5eV

(4) 13.6eV

Answer: (1)

5. The ratio of average electric energy density and total average energy density of electromagnetic wave is :

(1) 3

(2) 1/2

(3) 1

(4) 2

Answer: (2)

6. Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______.

(1) 100 cm

(2) 60 cm

(3) 160 cm

(4) 40 cm

Answer: (3)

7. Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

Answer: (3)

8. A Carnot engine operating between two reservoirs has efficiency 1/3. When the temperature of cold reservoir raised by x, its efficiency decreases to 1/6. The value of x, if the temperature of hot reservoir is 99°C, will be:

(1) 66 K

(2) 62 K

(3) 33 K

(4) 16.5 K

Answer: (2)

9. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason R: Capacitance of metallic spheres depend on the radii of spheres.

In the light of the above statements, choose the correct answer from the options given below.

(1) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(2) 𝐀 is true but 𝐑 is false

(3) 𝐀 is false but 𝐑 is true 4.

(4) Both 𝐀 and 𝐑 are true but 𝐑 is not the correct explanation of 𝐀

Answer: (3)

10. If the velocity of light c, universal gravitational constant G and Planck’s constant h are chosen as fundamental quantities. The dimensions of mass in the new system is :

(1) [h^1/2c⁻^1/2G¹]

(2) [h⁻^1/2c^1/2G^1/2]

(3) [n^1/2c^1/2G⁻^1/2]

(4) [h¹c¹G⁻¹]

Answer: (3)

11. Choose the correct statement about Zener diode :

(1) It works as a voltage regulator in forward bias and behaves like simple pn junction diode in reverse bias.

(2) It works as a voltage regulator only in forward bias.

(3) It works as a voltage regulator in both forward and reverse bias.

(4) It works as a voltage regulator in reverse bias and behaves like simple pn junction diode in forward bias.

Answer: (4)

12. The Young’s modulus of a steel wire of length 6 m and cross-sectional area 3 mm², is 2 × 10¹¹ N/m². The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 1/4 of its value on the earth. The elongation of wire is (Take g on the earth =10 m/s²) :

(1) 0.1 cm

(2) 0.1 mm

(3) 1 cm

(4) 1 mm

Answer: (2)

13. In an amplitude modulation, a modulating signal having amplitude of X V is superimposed with a carrier signal of amplitude Y V in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude 2Y V. The ratio of modulation index in the two cases respectively will be :

(1) 2 : 1

(2) 1 : 2

(3) 4 : 1

(4) 1 : 1

Answer: (1)

14. The threshold frequency of a metal is f₀. When the light of frequency 2f₀ is incident on the metal plate, the maximum velocity of photoelectrons is 𝑣₁. When the frequency of incident radiation is increased to 5f0, the maximum velocity of photoelectrons emitted is 𝑣₂. The ratio of 𝑣₁ to 𝑣₂ is:

Answer: (4)

15. A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:

(A) By changing the magnitude of the magnetic field within the coil.

(B) By changing the area of coil within the magnetic field.

(D) By reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below :

(1) A and B only

(2) A, B and D only

(3) A, B and C only

(4) A and C only

Answer: (3)

16. Choose the correct length (L) versus square of time period (T²) graph for a simple pendulum executing simple harmonic motion.

Answer: (1)

17. As shown in the figure, a long straight conductor with semicircular arc of radius π/10 m is carrying current I=3 A. The magnitude of the magnetic field. at the center O of the arc is : (The permeability of the vacuum =4π × 10⁻⁷NA⁻²)

(1) 1 μT

(2) 3 μT

(3) 4 μT

(4) 6 μT

Answer: (2)

18. As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30∘, with horizontal. For μ_s = 0.25, the block will just start to move for the value of F : [Given g = 10 ms⁻²]

(1) 20 N

(2) 33.3 N

(3) 25.2 N

(4) 35.7 N

Answer: (3)

19. The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be :

(1) 3/2

(2) 2/3

(3) 3/4

(4) 4/3

Answer: (3)

20. For a body projected at an angle with the horizontal from the ground, choose the correct statement.

(1) The vertical component of momentum is maximum at the highest point.

(2) The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.

(3) The horizontal component of velocity is zero at the highest point.

(4) Gravitational potential energy is maximum at the highest point.

Answer: (4)

SECTION-B

21. A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0 ) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0.25 J. The spring constant of the spring is ________ Nm⁻¹

Answer: (50)

22. A square shaped coil of area 70 cm² having 600 turns rotates in a magnetic field of 0.4 wbm⁻², about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at 60° with the field, will be ________ V. (Take π = 22/7)

Answer: (44)

23. As shown in the figure, in Young’s double slit experiment, a thin plate of thickness t = 10μm and refractive index μ = 1.2 is inserted infront of slit S1. The experiment is conducted in air (μ = 1) and uses a monochromatic light of wavelength λ = 500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of xβ₀.β₀ is the fringe-width before the insertion of the plate. The value of the x is ________.

Answer: (4)

24. Moment of inertia of a disc of mass 𝑀 and radius ‘R’ about any of its diameter is MR²/4. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, The value of x is ______.

Answer: (3)

25. For a train engine moving with speed of 20 ms⁻¹, the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed √x ms⁻¹. The value of x is ________. (Assuming same retardation is produced by brakes)

Answer: (200)

26. A cubical volume is bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a. The electric field in the region is given by Where E₀ = 4 × 10⁴ NC⁻¹ m⁻¹. If a = 2 cm, the charge contained in the cubical volume is Q × 10⁻¹⁴ The value of Q is _______. (Take ϵ₀ = 9 × 10⁻¹² C²/Nm²)

Answer: (288)

27. A force F = (5 + 3y²) 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.

Answer: (132)

28. The surface of water in a water tank of cross section area 750 cm2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross section area 500 mm² is 30 cm/s. At that instant, dh/dt is x × 10⁻³ m/s. The value of x will be _______.

Answer: (2)

In the given circuit, the value of is ________.

Answer: (2)

30. Nucleus A having Z = 17 and equal number of protons and neutrons has 1.2MeV binding energy per nucleon. Another nucleus B of Z = 12 has total 26 nucleons and 1.8MeV binding energy per nucleons. The difference of binding energy of B and A will be _______ MeV.

Answer: (6)

Chemistry

31. For electron gain enthalpies of the elements denoted as Δ_egH, the incorrect option is :

1) Δ_eg H(Te) < Δ_egH(PO)

(2) 2. Δ_egH(Se) < Δ_egH(S)

(3) Δ_egH(Cl) < Δ_egH(F)

(4) Δ_egH(I) < Δ_egH(At)

Answer: (2)

32. All structures given below are of vitamin C. Most stable of them is :

Answer: (1)

33. In figure, a straight line is given for Freundrich Adsorption (y = 3x + 2.505). The value of 1/n and log K are respectively.

(1) 0.3 and 0.7033

(2) 0.3 and log 2.505

(3) 3 and 0.7033

(4) 3 and 2.505

Answer: (4)

34. The correct order of bond enthalpy (kJmol⁻¹) is :

(1) C – C > Si – Si > Sn – Sn > Ge − Ge

(2) C − C > Si − Si > Ge − Ge > Sn − Sn

(3) Si – Si > C – C > Sn – Sn > Ge − Ge

(4) Si – Si > C – C > Ge – Ge > Sn − Sn

Answer: (2)

35. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : An aqueous solution of KOH when used for volumetric analysis, its concentration should be checked before the use.

Reason (R) : On aging, KOH solution absorbs atmospheric CO₂.

In the light of the above statements, choose the correct answer from the options given below :

(1) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(2) (A) is correct but (R) is not correct

(3) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(4) (A) is not correct but (R) is correct

Answer: (3)

36. O − O bond length in H₂O₂ is X than the O − O bond length in F₂O₂. The O − H bond length in H₂O₂ is Y than that of the O − F bond in F₂O₂.

Choose the correct option for X and Y from those given below

(1) X-shorter, Y-longer

(2) X-shorter, Y-shorter

(3) X-longer, Y-shorter

(4) X-longer, Y-longer

Answer: (3)

37. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Cu²⁺ in water is more stable than Cu⁺.

Reason (R) : Enthalpy of hydration for Cu²⁺ is much less than that of Cu⁺.

(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) (A) is not correct but (R) is correct

(3) (A) is correct but (R) is not correct

(4) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Answer: (1)

38.

Answer: (4)

39. The complex cation which has two isomers is :

(1) [Co(NH₃)₅NO₂]²⁺

(2) [Co(H₂O)₆]³⁺

(3) [Co(NH₃)₅Cl]⁺

(4) [Co(NH₃)₅Cl]²⁺

Answer: (1)

40. The graph which represents the following reaction is :

Answer: (3)

41. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : α-halocarboxylic acid on reaction with dil NH₃ gives good yield of 𝛼-amino carboxylic acid whereas the yield of amines is very low when prepared from alkyl halides.

Reason (R) : Amino acids exist in zwitter ion form in aqueous medium.

In the light of the above statements, choose the correct answer from the options given below :

(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) (A) is not correct but (R) is correct

(3) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(4) (A) is correct but (R) is not correct

Answer: (1)

42. The industrial activity held least responsible for global warming is :

(1) Industrial production of urea

(2) Electricity generation in thermal power plants

(3) steel manufacturing

(4) manufacturing of cement

Answer: (1)

43. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Gypsum is used for making fireproof wall boards.

Reason (R): Gypsum is unstable at high temperatures.

In the light of the above statements, choose the correct answer from the options given below :

(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(3) (A) is correct but (R) is not correct

(4) (A) is not correct but (R) is correct

Answer: (2)

44. The starting material for convenient preparation of deuterated hydrogen peroxide (D₂O₂) in laboratory is :

(1) BaO

(2) K₂S₂O₈

(3) BaO₂

(4) 2-ethylanthraquinol

Answer: (2)

45. The effect of addition of helium gas to the following reaction in equilibrium state, is :

PCl₅( g) ⇌ PCl₃( g) + Cl₂( g)

(1) helium will deactivate PCl₅ and reaction will stop.

(2) the equilibrium will shift in the forward direction and more of Cl₂ and PCl₃ gases will be produced.

(3) the equilibrium will go backward due to suppression of dissociation of PCl₅.

(4) addition of helium will not affect the equilibrium.

Answer: (2)

46. Which element is not present in Nessler’s reagent ?

(1) Oxygen

(2) Potassium

(3) Mercury

(4) Iodine

Answer: (1)

47. The structures of major products A,B and C in the following reaction are sequence.

Answer: (4)

48. In a reaction,

Reagents ‘X’ and ‘Y’ respectively are:

(1) (CH₃CO)₂O/H⁺ and (CH₃CO)₂O/H⁺

(2) CH₃OH/H⁺, Δ and (CH₃CO)₂O/H⁺

(3) CH₃OH/H⁺, Δ and CH₃OH/H⁺, Δ

(4) (CH₃CO)₂O/H⁺ and CH₃OH/H⁺, Δ

Answer: (4)

49. Which one of the following sets of ions represents a collection of isoelectronic species ? (Given: Atomic Number : F:9, Cl:17, Na=11, Mg=12, Al=13, K=19, Ca=20, Sc=21)

(1) Ba²⁺, Sr²⁺, K⁺, Ca²⁺

(2) Li⁺, Na⁺, Mg²⁺, Ca²⁺

(3) N³⁻, O²⁻, F⁻, S²⁻

(4) K⁺, Cl⁻, Ca²⁺, Sc³⁺

Answer: (4)

50. Given below are two statements :

Statement I : Sulphanilic acid gives esterification test for carboxyl group.

Statement II : Sulphanilic acid gives red colour in Lassigne’s test for extra element detection.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Statement I is incorrect but Statement II is correct

(2) Both Statement I and Statement II are incorrect

(3) Statement I is correct but Statement II is incorrect

(4) Both Statement I and Statement II are correct

Answer: (1)

SECTION B

51. 0.3 g of ethane undergoes combustion at 27°C in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by 0.5∘C. The heat evolved during combustion of ethane at constant pressure is_____________ kJmol⁻¹. (Nearest integer)

[Given : The heat capacity of the calorimeter system is 20 kJ K⁻¹, R = 8.3JK⁻¹ mol⁻¹.

Assume ideal gas behavior.

Atomic mass of C and H are 12 and 1 g mol⁻¹ respectively]

Answer: (1006)

52. Among the following, the number of tranquilizer/s is/are _______

(A) Chloroliazepoxide (B) Veronal

Answer: (3)

53. Among the following, the number of tranquilizer/s is/are

(A) CuCO₃ (B) Cu₂S (C) Cu₂O (D) FeO

Answer: (1)

54. A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2.0 and 2.5Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is___________ (Nearest integer)

Answer: (4)

55. The spin only magnetic moment of [Mn(H₂O)₆]²⁺ complexes is__________ B.M. (Nearest integer) (Given: Atomic no. of Mn is 25)

Answer: (6)

56. 1 × 10⁻⁵M AgNO₃ is added to 1 L of saturated solution of AgBr. The conductivity of this solution at 298 K is__________ × 10⁻⁸ S m⁻¹

[Given : K_SP(AgBr) = 4.9 × 10⁻¹³ at 298 K

Answer: (14)

57. 20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is___________ × 10⁻³°C Atomic mass of C,H and O are 12,1 and 16 a.m.u. respectively.

[Given : Molal depression constant and density of water are 1.86 K kg mol⁻¹ and 1 g cm⁻³ respectively.

Answer: (372)

58. A → B

20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is___________ × 10⁻³°C Atomic mass of C,H and O are 12, 1 and 16 a.m.u. respectively. [Given : Molal depression constant and density of water are 1.86 K kg mol⁻¹ and 1 g cm⁻³ respectively.

Answer: (75)

59. Testosterone, which is a steroidal hormone, has the following structure.

The total number of asymmetric carbon atom /s in testosterone is___________

Answer: (6)

60. The molality of a 10%(v/v) solution of di-bromine solution in CCl₄ (carbon tetrachloride) is ‘x’. x =_________ × 10⁻² (Nearest integer)

[Given : molar mass of Br₂ = 160 g mol⁻¹

atomic mass of C = 12 g mol⁻¹

atomic mass of Cl = 35.5 g mol⁻¹

density of dibromine = 3.2 g cm⁻³

density of CCl₄ = 1.6 g cm⁻³]

Answer: (139)

Mathematics

SECTION-A

61. Let αx = exp(x^βy^γ) be the solution of the differential equation 2x²y dy – (1 – xy²) dx = 0, x > 0, y(2) = √log_e 2. Then α + β + γ equals :

(1) 1

(2) −1

(3) 3

(4) 0

Answer: (1)

62. The sum

Answer: (4)

63. Let be two vectors. Then which one of the following statements is TRUE?

(1) Projection of and the direction of the projection vector is same as of

(2) Projection of and the direction of the projection vector is opposite to the direction of

(3) Projection of and the direction of the projection vector is same as of

(4) Projection of and the direction of the projection vector is opposite to the direction of

Answer: (*)

64. Let and be three given vectors. If is a vector such that then is equal to :

(1)

(2) √914/7

(3)

(4) 11/7

Answer: (3)

65. Let f : ℝ − 0, 1 → ℝ be a function such that Then f(2) is equal to

(1) 9/2

(2) 7/4

(3) 9/4

(4) 7/3

Answer: (3)

66. Let P(S) denote the power set of S = {1, 2, 3, ………., 10}. Define the relations R1 and R₂ on P(S) as AR₁B if (A ∩ B^C) ∪ (B ∩ A^C) = ∅ and AR₂B if A ∪ B^C = B ∪ A^C, ∀ A, B ∈ P(S). Then :

(1) only R₁ is an equivalence relation

(2) only R₂ is an equivalence relation

(3) both R₁ and R₂ are equivalence relations

(4) both R₁ and R₂ are not equivalence relations

Answer: (3)

67. The area of the region given by {(x, y) : xy ≤ 8, 1 ≤ y ≤ x²} is :

Answer: (2)

68. If then :

(1) A³⁰ + A²⁵ + A = I

(2) A³⁰ = A²⁵

(3) A³⁰ + A²⁵ –A = I

(4) A³⁰ – A²⁵ = 2I

Answer: (3)

69. Which of the following statements is a tautology ?

(1) p ⋁ (p ⋀ q)

(2) (p ⋀ (p → q)) → ~q

(3) (p ⋀ q) → (~(p) → q)

(4) p → (p ⋀ (p → q))

Answer: (3)

70. The sum of the absolute maximum and minimum values of the function f (x) = |x² – 5x + 6| − 3x + 2 in the interval [–1,3] is equal to :

(1) 12

(2) 13

(3) 10

(4) 24

Answer: (4)

71. Let the plane P pass through the intersection of the planes 2x + 3y – z = 2 and x + 2y + 3z = 6 and be perpendicular to the plane 2x + y – z = 0. If d is the distance of P form the point (–7, 1, 1,) then d² is equal to :

(1) 250/83

(2) 250/82

(3) 15/53

(4) 25/83

Answer: (1)

72. The number of integral values of k, for which one root of the equation 2x² – 8x + k = 0 lies in the interval (1,2) and its other root lies in the interval (2, 3), is :

(1) 3

(2) 0

(3) 2

(4) 1

Answer: (4)

73. Let P(x₀, y₀) be the point on the hyperbola 3x² – 4y² = 36, which is nearest to the line 3x + 2y = 1. Then √2(y₀ – x₀) is equal to:

(1) −9

(2) −3

(3) 3

(4) 9

Answer: (1)

74. Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st die is odd and that on the 2nd is even. Then :

(1) the number of favourable cases of the events A,B and C are 15,6 and 6 respectively

(2) the number of favourable cases of the event (A ∪ B) ∩ C is 6

(3) B and C are independent

(4) A and B are mutually exclusive

Answer: (2)

75. If y(x) = x^x, x > 0, then y”(2) – 2yʹ(2) is equal to :

(1) 4log_e 2 + 2

(2) 8log_e 2 – 2

(3) 4(log_e 2)² + 2

(4) 4(log_e 2)² – 2

Answer: (4)

76. Let

If n(S) denotes the number of elements in S then :

(1) n(S) = 2 and only one element in S is less then 1/2.

(2) n(S) = 1 and the element in S is more than 1/2.

(3) n(S) = 0

(4) n(S) = 1 and the element in S is less than 1/2.

Answer: (1)

77. The value of the integral is :

(1) π²/12√3

(2) π²/6√3

(3) π²/6

(4) π²/3√3

Answer: (2)

78. For the system of linear equations αx + y + z = 1, x + αy + z = 1, x + y + αz = β, which one of the following statements is NOT correct?

(1) It has infinitely many solutions if α = 2 and β = −1

(2) It has no solution if α = −2 and β = 1

(3) if α = 2 and β = 1

(4) It has infinitely many solutions if α = 1 and β = 1

Answer: (1)

79. Let 9 = x₁< x₂ < ….. < x₇ …….., x₇ be in an A.P. with common difference d. If the standard deviation of x₁ ∙ x₂ ………, x₇ is 4 and mean is is equal to

(1)

(2)

(3) 25

(4) 34

Answer: (4)

80. Let a, b be two real numbers such that ab < 0. IF the complex number is of unit modulus and a + ib lies on the circle |z – 1| = |2z|, then a possible value of where [t] is greatest integer function, is :

(1) −1/2

(2) −1

(3) 1

(4) 1/2

Answer: (*)

SECTION-B

81. Let αx + βy + yz = 1 be the equation of a plane through the point (3, –2, 5)and perpendicular to the line joning the points (1, 2, 3) and (–2, 3, 5). Then the value of αβy is equal to

Answer: (6)

82. If the term without x in the expansion of is 7315, then |α| is equal to

Answer: (1)

83. If the x – intercept of a focal chord of the parabola y²= 8x + 4y + 4 is 3, then the length of this chord is equal to

Answer: (16)

84. Let the sixth term in the binomial expansion of in the increasing powers of be 21. If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of A.P., then the sum of the squares of all possible values of x is

Answer: (4)

85. The point of intersection C of the plane 8x + y + 2z = 0 and the line joining the point A(–3, –61) and B(2, –4, –3) divides the line segment AB internally in the ratio k:. If a, b, c (|a|, |b|, |c|) are coprime are the direction ratios of the perpendicular form the point C on the line then |a + b + c| is equal to

Answer: (10)

86. The line x = 8 is the directrix of the ellipse with the corresponding focus (2, 0). If the tangent to E at the point P in the first quadrant passes through the point (0, 4√3) and intersects that x-axis at Q then (3PQ)² equal to

Answer: (39)

87. The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , is

Answer: (81)

88. Number of integral solutions to the equation x + y + z = 21, where x ≥ 1, y ≥ 3, z ≥ 4, is equal to

Answer: (105)

89. The sum of the common terms of the following three arithmetic progressions.

3, 7, 11, 15, ……., 399

2, 5, 8, 11, ……., 359 and

2, 7, 12, 17, …….., 197

is equal to

Answer: (321)

90. If

Then k is equal to

Answer: (13)

JEE Main Session 2 31st January 2023 Shift 2 Question Paper and Answer Key

May 10, 2023 by suresh84

JEE MAIN 31^st January 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. Given below are two statements:

Statement I: In a typical transistor, all three regions emitter, base and collector have same doping level.

Statement II: In a transistor, collector is the thickest and base is the thinnest segment. In the light of the above statements, choose the most appropriate answer from the options given below.

(1) Both Statement I and Statement II are correct

(2) Statement I is incorrect but Statement II is correct

(3) Statement I is correct but Statement II is incorrect

(4) Both Statement I and Statement II are incorrect

Answer: (2)

2. If the two metals A and B are exposed to radiation of wavelength 350 nm. The work functions of metals A and B are 4.8eV and 2.2eV. Then choose the correct option.

(1) Both metals A and B will emit photo-electrons

(2) Metal A will not emit photo-electrons

(3) Metal B will not emit photo-electrons

(4) Both metals A and B will not emit photo-electrons

Answer: (2)

3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :

(1) 525 J

(2) 441 J

(3) 572 J

(4) 735 J

Answer: (1)

4. Match List I with List II

Choose the correct answer from the options given below:

(1) A – III, B – I, C – IV, D – II

(2) A – II, B – III, C – IV, D – I

(3) A – IV, B – II, C – I, D – III

(4) A – I, B – IV, C – III, D – II

Answer: (1)

5. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :

(1) 40 ms⁻¹

(2) 400 ms⁻¹

(3) 20 ms⁻¹

(4) 10 ms⁻¹

Answer: (3)

6. A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 5/3 is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is :

(1) 12 cm

(2) 50 cm

(3) 18 cm

(4) 75 cm

Answer: (4)

7. The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be :

(1) 0%

(2) 75%

(3) 50%

(4) 100%

Answer: (1)

8. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4s. At the end of 3rd second, the displacement of body (in m) from its starting point is:

(1) 15π

(2) 10√2

(3) 30

(4) 5π

Answer: (2)

9. The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will be :

(1) H/4

(2) 16H

(3) 4H

(4) H

Answer: (2)

10. A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns. Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

(1) n: N

(2) n² : N²

(3) N² : n²

(4) N : n

Answer: (3)

11. A body weight W, is projected vertically upwards from earth’s surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be :

(1) W/100

(2) W/91

(3) W/3

(4) W/9

Answer: (1)

12. The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be

(1) R/3

(2) 3R

(3) 2.25R

(4) 9R

Answer: (3)

13. A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 16/81. Then ratio of c_p/c_v will be

(1) 1/2

(2) 4/3

(3) 3/2

(4) 3/1

Answer: (2)

14. For a solid rod, the Young’s modulus of elasticity is 3.2 × 10¹¹Nm⁻² and density is 8 × 10³ kg m⁻³. The velocity of longitudinal wave in the rod will be.

(1) 145.75 × 10³ ms⁻¹

(2) 18.96 × 10³ ms⁻¹

(3) 3.65 × 10³ ms⁻¹

(4) 6.32 × 10³ ms⁻¹

Answer: (4)

15. A body of mass 10 kg is moving with an initial speed of 20 m/s. The body stops after 5 s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity g = 10 ms⁻²)

(1) 0.3

(2) 0.5

(3) 0.2

(4) 0.4

Answer: (4)

16. Given below are two statements :

Statement I : For transmitting a signal, size of antenna (l) should be comparable to wavelength of signal (at least l = λ/4 in dimension)

Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged).

In the light of the above statements, choose the most appropriate answer from the options given below.

(1) Statement 𝐈 is correct but Statement II is incorrect

(2) Both Statement I and Statement II are correct

(3) Statement I is incorrect but Statement II is correct

(4) Both Statement I and Statement II are incorrect

Answer: (1)

17. An alternating voltage source V=260sin⁡(628t) is connected across a pure inductor of 5mH. Inductive reactance in the circuit is :

(1) 0.318Ω

(2) 6.28Ω

(3) 3.14Ω

(4) 0.5Ω

Answer: (3)

18. Under the same load, wire A having length 5.0 m and cross section 2.5 × 10⁻⁵ m² stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 × 10⁻⁵ m² The ratio of the Young’s modulus of wire A to that of wire B will be :

(1) 1 : 1

(2) 1 : 10

(3) 1 : 2

(4) 1 : 4

Answer: (1)

19. Match List I with List II

Choose the correct answer from the options given below:

(1) A−IV,B – III, C – I, D – II

(2) A−IV,B−I,C – II, D – III

(3) A – III, B – II, C – I, D – IV

(4) A – II, B – IV, C – III, D – I

Answer: (1)

20. Considering a group of positive charges, which of the following statements is correct?

(1) Both the net potential and the net electric field cannot be zero at a point.

(2) Net potential of the system at a point can be zero but net electric field can’t be zero at that point.

(3) Net potential of the system cannot be zero at a point but net electric field can be zero at that point.

(4) Both the net potential and the net field can be zero at a point.

Answer: (3)

SECTION-B

21. A series LCR circuit consists of R = 80Ω, X_L = 100Ω, and X_C= 40Ω. The input voltage is 2500 cos⁡(100πt)V. The amplitude of current, in the circuit, is _____A.

Answer: (25)

22. Two bodies are projected from ground with same speeds 40 ms⁻¹ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60°, with horizontal then sum of the maximum heights, attained by the two projectiles, is _____m. (Given g = 10 ms⁻²)

Answer: (80)

23. For the given circuit, in the steady state, |V_B – V_D| = ________ V.

Answer: (1)

24. Two parallel plate capacitors C₁ and C₂ each having capacitance of 10μF are individually charged by a 100 V D.C. source. Capacitor C₁ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor C₂ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor C₁ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ______V. (Assuming Dielectric constant =10)

Answer: (55)

25. Two light waves of wavelengths 800 and 600 nm are used in Young’s double slit experiment to obtain interference fringes on a screen placed 7 m away from plane of slits. If the two slits are separated by 0.35 mm, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ mm.

Answer: (48)

26. A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of _____ m

Answer: (5)

27. If the binding energy of ground state electron in a hydrogen atom is 13.6eV, then, the energy required to remove the electron from the second excited state of Li²⁺ will be : x × 10⁻¹ The value of x is ____.

Answer: (136)

28. A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹. The efficiency of heater is 70%. Time required to heat 2 kg of water from 10∘C to 60°C is _____s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Answer: (300)

29. Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of x/6. The value of x is ______.

Answer: (5)

30. The displacement equations of two interfering waves are given by y₂ = 5[sin ωt + √3 cos ωt]cm respectively. The amplitude of the resultant wave is ________ cm.

Answer: (20)

Chemistry

SECTION-A

31. Which one of the following statements is incorrect ?

(1) van Arkel method is used to purify tungsten.

(2) The malleable iron is prepared from cast iron by oxidising impurities in a reverberatory furnace.

(3) Cast iron is obtained by melting pig iron with scrap iron and coke using hot air blast.

(4) Boron and Indium can be purified by zone refining method.

Answer: (1)

32. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The first ionization enthalpy of 3 d series elements is more than that of group 2 metals

Reason (R) : In 3d series of elements successive filling of d-orbitals takes place.

In the light of the above statements, choose the correct answer from the options given below :

(1) Both (A) and (R) are true but (R) is not the correct explanation of (A)

(2) Both (A) and (R) are true and (R) is the correct explanation of (A)

(3) (A) is true but (R) is false

(4) (A) is false but (R) is true

Answer: (2)

33. Given below are two statements :

Statement I : H₂O₂ is used in the synthesis of Cephalosporin

Statement II : H₂O₂ is used for the restoration of aerobic conditions to sewage wastes.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Both Statement I and Statement II are incorrect

(2) Statement I is incorrect but Statement II is correct

(3) Statement I is correct but Statement II is incorrect

(4) Both Statement I and Statement II are correct

Answer: (4)

34. A hydrocarbon ‘X’ with formula C₆H₈ uses two moles H₂ on catalytic hydrogenation of its one mole. On ozonolysis, ‘X’ yields two moles of methane dicarbaldehyde. The hydrocarbon ‘X’ is :

(1) cyclohexa-1, 4-diene

(2) cyclohexa – 1, 3 – diene

(3) 1-methylcyclopenta-1, 4-diene

(4) hexa-1, 3, 5-triene

Answer: (1)

35. Evaluate the following statements for their correctness.

(A) The elevation in boiling point temperature of water will be same for 0.1MNaCl and 0.1M urea.

(B) Azeotropic mixtures boil without change in their composition.

(D) The density of 32% H₂SO₄ solution having molarity 4.09M is approximately 1.26 g mL⁻¹.

(E) A negatively charged sol is obtained when KI solution is added to silver nitrate solution.

Choose the correct answer from the options given below :

(1) A, B and D only

(2) B and D only

(3) B, D and E only

(4) A and C only

Answer: (2)

36. The Lewis acid character of boron tri halides follows the order :

(1) BI₃ > BBr₃ > BCl₃ > BF₃

(2) BBr₃ > BI₃ > BCl₃ > BF₃

(3) BCl₃ > BF₃ > BBr₃ > BI₃

(4) BF₃> BCl₃> BBr₃ > BI₃

Answer: (1)

37. When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of A ?

(1) C₅H₈

(2) C₁₁H₄

(3) C₉H₈

(4) C₁₁H₈

Answer: (3)

38. Arrange the following orbitals in decreasing order of energy.

(A) n = 3, l = 0, m = 0

(B) n = 4, l = 0, m = 0

(D) n = 3, l = 2, m = 1

The correct option for the order is :

(1) D > B > C > A

(2)D > B > A > C

(3)A > C > B > D

(4) B > D > C > A

Answer: (1)

39. The element playing significant role in neuromuscular function and interneuronal transmission is :

(1) Li

(2) Mg

(3) Be

(4) Ca

Answer: (4)

40. Given below are two statements :

Statement I : Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green

Statement II : The green colour observed is due to the formation of copper(I) metaborate

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Both Statement I and Statement II are true

(2) Statement I is true but Statement II is false

(3) Statement 𝐈 is false but Statement II is true

(4) Both Statement I and Statement II are false

Answer: (4)

41. Which of the following compounds are not used as disinfectants ?

(A) Chloroxylenol (B) Bithional

(E) Terpineol

Choose the correct answer from the options given below :

(1) C, D

(2) B, D, E

(3) A, B

(4) A, B E

Answer: (1)

42. Incorrect statement for the use of indicators in acid-base titration is :

(1) Methyl orange may be used for a weak acid vs weak base titration.

(2) Phenolphthalein is a suitable indicator for a weak acid vs strong base titration.

(3) Methyl orange is a suitable indicator for a strong acid vs weak base titration.

(4) Phenolphthalein may be used for a strong acid vs strong base titration.

Answer: (1)

43. An organic compound [A](C₄H₁₁N), shows optical activity and gives N₂ gas on treatment with HNO₂. The compound [A] reacts with PhSO₂Cl producing a compound which is soluble in KOH.

Answer: (4)

44. The normal rain water is slightly acidic and its pH value is 5.6 because of which one of the following?

(1) CO₂ + H₂O → H₂CO₃

(2) 2SO₂ + O₂ + 2H₂O → 2H₂SO₄

(3) 4NO₂ + O₂ + 2H₂O → 4HNO₃

(4) N₂O₅ + H₂O → 2HNO₃

Answer: (1)

45. Match List I with List II

Choose the correct answer from the options given below:

(1) A – II, B – I, C – IV, D – III

(2) A – IV, B – II, C – III, D – I

(3) A – II, B – III, C – I, D – IV

(4) A – III, B – IV, C – I, D – II

Answer: (1)

46. Cyclohexylamine when treated with nitrous acid yields (P).On treating (P) with PCC results in (Q). When (Q) is heated with dil. NaOH we get (R) The final product (R) is :

Answer: (2)

47. In the following halogenated organic compounds the one with maximum number of chlorine atoms in its structure is :

(1) Freon-12

(2) Gammaxene

(3) Chloropicrin

(4) Chloral

Answer: (2)

48. In Dumas method for the estimation of N₂, the sample is heated with copper oxide and the gas evolved is passed over :

(1) Copper oxide

(2) Ni

(3) Pd

(4) Copper gauze

Answer: (2)

49. Which of the following elements have half-filled f-orbitals in their ground state ? (Given : atomic number Sm = 62; Eu = 63; Tb = 65; Gd = 64, Pm = 61 )

(A) Sm (B) Eu (C) Tb (D) Gd (E) Pm

Choose the correct answer from the options given below:

(1) A and B only

(2) A and E only

(3) C and D only

(4) B and D only

Answer: (4)

50. Compound A, C₅H₁₀O₅, given a tetraacetate with AC₂O and oxidation of A with Br₂−H₂O gives an acid, C₅H₁₀O₆ .Reduction of A with HI gives isopentane. The possible structure of A is :

Answer: (3)

SECTION B

51. The rate constant for a first order reaction is 20 min⁻¹. The time required for the initial concentration of the reactant to reduce to its 1/32 level is ______ 10⁻² (Nearest integer)

Given : ln 10 = 2.303, log 2 = 0.3010)

Answer: (17)

52. Enthalpies of formation of CCl₄( g), H₂O(g), CO₂(g) and HCl(g) are −105, −242, −394 and − 92 kJ mol⁻¹ The magnitude of enthalpy of the reaction given below is kJmol⁻¹. (nearest integer)

CCl₄(g) + 2H₂O(g) → CO₂(g) + 4HCl(g)

Answer: (173)

53. A sample of a metal oxide has formula M₈₃O_1.00. The metal M can exist in two oxidation states + 2 and +3.In the sample of M_0.83O_1.00, the percentage of metal ions existing in + 2 oxidation state is %. (nearest integer)

Answer: (59)

54. The resistivity of a 0.8M solution of an electrolyte is 5 × 10⁻³ Ω cm. Its molar conductivity is ______ × 10⁴Ω⁻¹ cm² mol⁻¹ (Nearest integer)

Answer: (25)

55. At 298 K, the solubility of silver chloride in water is 1.434 × 10⁻³ g L⁻¹.The value of −log Ksp for silver chloride is ____ (Given mass of Ag is 107.9 g mol⁻¹ and mass of Cl is 35.5 g mol⁻¹)

Answer: (10)

56. If the CFSE of [Ti(H₂O)₆]³⁺ is −96.0 kJ/mol, this complex will absorb maximum at wavelength _____ nm. (nearest integer)

Assume Planck’s constant (h) = 6.4 × 10⁻³⁴ Js, Speed of light (c) = 3.0 × 10⁸ m/s and Avogadro’s Constant (N_A) = 6 × 10²³/mol

Answer: (480)

57. The number of alkali metal(s), from Li, K, Cs, Rb having ionization enthalpy greater than 400 kJ mol⁻¹ and forming stable super oxide is _____

Answer: (2)

58. The number of molecules which gives haloform test among the following molecules is

Answer: (3)

59. Assume carbon burns according to following equation :

2C_(g) + O_2(g) → 2CO(g)

When 12 g carbon is burnt in 48 g of oxygen, the volume of carbon monoxide produced is × 10⁻¹ L at STP [nearest integer]

[Given : Assume co as ideal gas, Mass of c is 12 g mol⁻¹, Mass of O is 16 g mol⁻¹ and molar volume of an ideal gas STP is 22.7 L mol⁻¹]

Answer: (227)

60. Amongst the following, the number of species having the linear shape is

Answer: (5)

Mathematics

SECTION-A

61. The equation e^4x + 8e^3x + 13e^2x − 8e^x + 1 = 0, x ∈ ℝ has :

(1) four solutions two of which are negative

(2) two solutions and only one of them is negative

(3) two solutions and both are negative

(4) no solution

Answer: (3)

62. Among the relations

and T = {(a, b): a, b ∈ ℝ, a² – b² ∈ ℤ},

(1) neither S nor T is transitive

(2) S is transitive but T is not

(3) T is symmetric but S is not

(4) both S and T are symmetric

Answer: (3)

63. Let α > 0. If then α is equal to :

(1) 4

(2) 2√2

(3) √2

(4) 2

Answer: (3)

64. The complex number is equal to :

Answer: (3)

65. Let y = y(x) be the solution of the differential equation (3y – 5x)y dx + 2x(x − y)dy = 0 such that y(1) = 1. Then |(y(2)) – 12y(2)| is equal to :

(1) 16√2

(2) 32√2

(3) 32

(4) 64

Answer: (2)

66.

(1) does not exist

(2) is equal to 27

(3) is equal to 27/2

(4) is equal to 9

Answer: (2)

67. The foot of perpendicular from the origin O to a plane P which meets the co-ordinate axes at the points A,B,C is (2, a ,4), a ∈ If the volume of the tetrahedron OABC is 144 unit, then which of the following points is NOT on P ?

(1) (0, 6, 3)

(2) (0, 4, 4)

(3) (2, 2, 4)

(4) (3, 0, 4)

Answer: (4)

68. Let (a, b) ⊂ (0, 2π) be the largest interval for which sin (sin θ)− cos⁻¹(sin θ) > 0, θ ∈ (0, 2π), holds. If αx + βx + sin (x – 6x + 10) + cos⁻¹(x – 6x + 10) = 0 and α – β = b − a, then α is equal to :

(1) π/16

(2) π/48

(3) π/12

(4) π/8

Answer: (3)

69. Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α ( > 0 ), and the mean and standard deviation of marks of class B of n students be respectively 55 and 30 −α. If the mean and variance of the marks of the combined class of 100 + n students are respectively 50 and 350, then the sum of variances of classes A and B is :

(1) 650

(2) 450

(3) 900

(4) 500

Answer: (4)

70. The absolute minimum value, of the function f(x) = |x² – x + 1| + [x² – x + 1], where [t] denotes the greatest integer function, in the interval [−1, 2], is

(1) 1/4

(2) 3/2

(3) 5/4

(4) 3/4

Answer: (4)

71. Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2. Then the length of its latus rectum is

(1) 3/2

(2) 2

(3) 3

(4) 5/2

Answer: (2)

72. Let a₁, a₂, a₃, … be an A.P. If a₇ = 3, the product a₁a₄ is minimum and the sum of its first n terms is zero, then n! – 4a_n(n+2) is equal to :

(1) 9

(2) 33/4

(3) 381/4

(4) 24

Answer: (4)

73. If a point P(α, β, γ) satisfying

lies on the plane 2x + 4y + 3z = 5, then 6α + 9β + 7γ is equal to :

(1) −1

(2) 11/5

(3) 5/4

(4) 11

Answer: (4)

74. Let : and be there vectors. If is a vector such that, then is equal to

(1) 560

(2) 449

(3) 339

(4) 336

Answer: (3)

75. Let the plane P : 8x + α₁y + α₂y + α₂z + 12 = 0 be parallel to the line If the intercept of P on the y-axis is 1, then the distance between P and L is :

(1)

(2)

(3) 6/√14

(4) √14

Answer: (4)

76. Let P be the plane, passing through the point (1, −1, −5) and perpendicular to the line joining the points (4, 1, −3) and (2, 4, 3). Then the distance of P from the point (3, −2, 2) is

(1) 5

(2) 4

(3) 7

(4) 6

Answer: (1)

77. The number of values of r ∈ {p, q, ~p, ~q} for which ((p ⋀ q) ⇒ (r ⋁ q)) ⋀ ((p ⋀ r) ⇒ q) is a tautology, is:

(1) 3

(2) 4

(3) 1

(4) 2

Answer: (4)

78. The set of all values of a² for which the line x + y = 0 bisects two distinct chords drawn from a point on the circle 2x² + 2y² – (1 + a)x – (1 – a)y = 0, is equal to:

(1) (0, 4]

(2) (4, ∞)

(3) (2, 12]

(4) (8, ∞)

Answer: (4)

79. If x > 0, then ∅ʹ(π/4) is equal to:

Answer: (1)

80. Let f : ℝ − {2, 6} → ℝ be real valued function defined as Then range of f is

Answer: (4)

SECTION-B

81. Let A = [a_ij], a_ij ∈ Z ∩ [0, 4], 1 ≤ i, j ≤ The number of matrices A such that the sum of all entries is a prime number p ∈ (2, 13) is

Answer: (204)

82. Let A be a n × n matrix such that |A| = 2. If the determinant of the matrix Adj(2 ∙ Adj(2 A⁻¹)) ∙ is 2⁸⁴, then n is equal to

Answer: (84)

83. If the constant term in the binomial expansion of is −84 and the coefficient of x⁻^3l is 2^αβ, where β < 0 is an odd number, then |αl – β| is equal to

Answer: (98)

84. Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent at the point P(b, c), b, c ∈ ℕ, on the parabola y = 2ax and the lines x = b, y = 0 is 16 unit², then is equal to

Answer: (146)

85. Let the area of the region {(x, y) : |2x – 1| ≤ y ≤ |x² – x|, 0 ≤ x ≤ 1} be A. Then (6A + 11)² is equal to

Answer: (125)

86. The coefficient of x⁻⁶, in the expansion of is

Answer: (5040)

87. Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space [0, 60] is less than or equal to a . If then a is equal to

Answer: (10)

88. If ²ⁿ⁺¹P_n₋₁ : ²ⁿ⁻¹P_n = 11 : 21, then n² + n + 15 is equal to :

Answer: (45)

89. Let be three vectors such that and If the angle between is equal to

Answer: (3)

90. The sum 1² – 2 ∙ 3² + 3 ∙ 5² – 4 ∙ 7² + 5 ∙ 9² − … + 15 ∙ 29² is

Answer: (6952)

JEE Main Session 2 30th January 2023 Shift 2 Question Paper and Answer Key

May 10, 2023May 10, 2023 by suresh84

JEE MAIN 30^th January 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. A current carrying rectangular loop PQRS is made of uniform wire. The length PR = QS =5 cm and = RS =100 cm. If ammeter current reading changes from I to 2I, the ratio of magnetic forces per unit length on the wire PQ due to wire RS in the two cases respectively is :

(1) 1 : 2

(2) 1 : 3

(3) 1 : 4

(4) 1 : 5

Answer: (3)

2. The output Y for the inputs A and B of circuit is given by

Truth table of the shown circuit is:

Answer: (3)

3. Given below are two statements: one is labelled as Assertion 𝐀 and the other is labelled as Reason R

Assertion A: Efficiency of a reversible heat engine will be highest at −273∘C temperature of cold reservoir.

Reason R: The efficiency of Carnot’s engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as

In the light of the above statements, choose the correct answer from the options given below

(1) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

(2) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(3) A is false but 𝐑 is true

(4) A is true but 𝐑 is false

Answer: (2)

4. As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II and III is given by: (I: r < a, II: a < r < b, III: r > b)

(1) E_I = 0, E_II = 0, E_III = 0

(2) E_I = 0, E_II = 0, E_III ≠ 0

(3) E_I ≠ 0, E_II = 0, E_III ≠ 0

(4) E_I ≠ 0, E_II = 0, E_III = 0

Answer: (3)

5. The equivalent resistance between A and B is

Answer: (4)

6. A vehicle travels 4 km with speed of 3 km/h and another 4 km with sped of 5 km/h, then its average speed is

(1) 3.50 km/h

(2) 4.25 km/h

(3) 4.00 km/h

(4) 3.75 km/h

Answer: (4)

7. In the given circuit, rms value of current (I_rms) through the resistor R is:

(1) 2√2A

(2) 2 A

(3) 20 A

(4)

Answer: (2)

8. A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is:

Answer: (4)

9. A block of √3 kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of 30° with the wall. The tension T is: (Given g = 10 ms⁻²)

(1) 20 N

(2) 10 N

(3) 15 N

(4) 25 N

Answer: (1)

10. Match List I with List II

Choose the correct answer from the options given below:

(1) A-IV, B-III, C-I, D-II

(2) A-I, B-II, C-III, D-IV

(3) A-IV, B-III, C-II, D-I

(4) A-II, B-III, C-IV, D-I

Answer: (3)

11. An electron accelerated through a potential difference V₁ has a de-Broglie wavelength of 𝜆. When the potential is changed to V₂, its de-Broglie wavelength increases by 50%. The value of (V₁/V₂) is equal to

(1) 3

(2) 3/2

(3) 4

(4) 9/4

Answer: (4)

12. A flask contains hydrogen and oxygen in the ratio of 2:1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

(1) 2 : 1

(2) 1 : 1

(3) 1 : 4

(4) 4 : 1

Answer: (2)

13. As shown in the figure, a current of 2 A flowing in an equilateral triangle of side 4√3 cm. The magnetic field at the centroid O of the triangle is

(Neglect the effect of earth’s magnetic field)

(1) 1.4√3 × 10⁻⁵ T

(2) 4√3 × 10⁻⁴ T

(3) 3√3 × 10⁻⁵ T

(4) √3 × 10⁻⁴ T

Answer: (3)

14. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be

Answer: (4)

15. Match List I with List II:

Choose the correct answer from the options given below:

(1) A−IV,B−I,C−III,D−II

(2) A−IV,B−III,C−I,D−II

(3) A−IV,B−I,C−II,D−III

(4) A−I,B−IV,C−III,D−II

Answer: (1)

16. Given below are two statements: one is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑

Assertion A: The nuclear density of nuclides can be arranged as

Reason R: The radius R of nucleus is related to its mass number A as R = R₀A^1/3, where R₀ is a constant.

In the light of the above statements, choose the correct answer from the options given below

(1) A is false but 𝐑 is true

(2) A is true but 𝐑 is false

(3) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

(4) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

Answer: (1)

17. A force is applied to a steel wire ‘A’, rigidly clamped at one end. As a result elongation in the wire is 0.2 mm. If same force is applied to another steel wire ‘B’ of double the length and a diameter 2.4 times that of the wire ‘A’, the elongation in the wire ‘ B ‘ will be (wires having uniform circular cross sections)

(1) 6.06 × 10⁻² mm

(2) 2.77 × 10⁻² mm

(3) 3.0 × 10⁻² mm

(4) 6.9 × 10⁻² mm

Answer: (4)

18. A thin prism, P₁ with an angle 6th and made of glass of refractive index 1.54 is combined with another prism P₂ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P₂ is

(1) 1.3°

(2) 6°

(3) 4.5°

(4) 7.8°

Answer: (3)

19. A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 ms⁻¹ The recoil velocity of the gun is

(1) 1.5 m/s

(2) 0.6 m/s

(3) 2.5 m/s

(4) 0.02 m/s

Answer: (2)

20. For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is ω₁. When the mass block is 2 kg the angular frequency is ω₂. The ratio ω₂/ ω₁ is

(1) 1/√2

(2) √2

(3) 2

(4) 1/2

Answer: (1)

SECTION-B

21. A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m/s at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be _______ 𝐉 (given, coefficient of friction is 0.3 and g = 10 m/s²).

Answer: (54)

22. If the potential difference between B and D is zero, the value of x is The value of n is _______.

Answer: (2)

23. A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is The value of x ________. (Take π = 22/7)

Answer: (125)

24. A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be The value of α is ________.

Answer: (300)

25. A faulty thermometer reads 5°C in melting ice and 95°C in stream. The correct temperature on absolute scale will be _______ K when the faulty thermometer reads 41°

Answer: (313)

26. In an ac generator, a rectangular coil of 100 turns each having area 14 × 10⁻² m² is rotated at 360rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be _______ V. (Take π = 22/7)

Answer: (1584)

27. A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is The value of α will be _______.

Answer: (4)

28. As shown in figure, a cuboid lies in a region with electric field The magnitude of charge within the cuboid is n ∈₀

The value of n is _______ (if dimension of cuboid is 1 × 2 × 3 m³).

Answer: (12)

29. In a Young’s double slit experiment, the intensities at two points, for the path differences λ/4 and λ/3 (λ being the wavelength of light used) are I₁ and I₂ If I₀ denotes the intensity produced by each one of the individual slits, then

Answer: (3)

30. The velocity of a particle executing SHM varies with displacement (x) as 4v²= 50 − 𝑥². The time period of oscillations is The value of x is _______. (Take π = 22/7)

Answer: (88)

Chemistry

SECTION-A

31. The Cl−Co−Cl bond angle values in a fac- [Co(NH₃)₃Cl₃] complex is/are:

(1) 90°

(2) 90° & 120°

(3) 180°

(4) 90° & 180°

Answer: (1)

32. The correct order of pK_a values for the following compounds is:

(1) c > a > d > b

(2) b > a > d > c

(3) b > d > a > c

(4) a > b > c > d

Answer: (3)

33. Given below are two statements:

Statement I : During Electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as cathode.

Statement II : During the Hall-Heroult electrolysis process, purified Al₂O₃ is mixed with Na₃AlF₆ to lower the melting point of the mixture. In the light of the above statements, choose the most appropriate answer from the options given below:

1) Statement I is correct but Statement II is incorrect

(2) Both Statement I and Statement II are incorrect

(3) Both Statement I and Statement II are correct

(4) Statement I is incorrect but Statement II is correct

Answer: (4)

34. Match List I with List II:

(1) A-IV, B-I, C-III, D-II

(2) A-III, B-IV, C-I, D-II

(3) A-III, B-I, C-IV, D-II

(4) A-II, B-I, C-III, D-IV

Answer: (2)

35. 1 L, 0.02M solution of [Co(NH₃)₅SO₄]Br is mixed with 1 L, 0.02M solution of [Co(NH₃)₅Br]SO₄. The resulting solution is divided into two equal parts (X) and treated with excess of AgNO₃ solution and BaCl₂ solution respectively as shown below:

1 L solution (X) + AgNO₃ solution (excess) → Y

1 L Solution (X) + BaCl₂ solution (excess) → Z

The number of moles of Y and Z respectively are

(1) 0.02, 0.01

(2) 0.01, 0.01

(3) 0.01, 0.02

(4) 0.02, 0.02

Answer: (2)

36. Decreasing order towards SN 1 reaction for the following compounds is:

(1) a > c > d > b

(2) b > d > c > a

(3) a > b > c > d

(4) d > b > c > a

Answer: (2)

37. Which of the following reaction is correct?

Answer: (4)

38. Boric acid is solid, whereas BF₃ is gas at room temperature because of

(1) Strong van der Waal’s interaction in Boric acid

(2) Strong covalent bond in BF₃

(3) Strong ionic bond in Boric acid

(4) Strong hydrogen bond in Boric acid

Answer: (4)

39. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason 𝐑.

Assertion A: Antihistamines do not affect the secretion of acid in stomach.

Reason : Antiallergic and antacid drugs work on different receptors.

In the light of the above statements, choose the correct answer from the options given below:

(1) A is false but R is true

(2) Both A and R are true but R is not the correct explanation of A

(3) Both A and R are true and R is the correct explanation of A

(4) A is true but R is false

Answer: (3)

40. Formulae for Nessler’s reagent is:

(1) HgI₂

(2) K₂HgI4

(3) KHgI₃

(4) KHg₂I₂

Answer: (2)

41. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: can be easily reduced using Zn-Hg/HCl to

Reason R: Zn−Hg/HCl is used to reduce carbonyl group to −CH₂− group.

In the light of the above statements, choose the correct answer from the options given below:

(1) A is true but R is false

(2) Both A and R are true and R is the correct explanation of A

(3) A is false but R is true

(4) Both A and R are true but R is not the correct explanation of A

Answer: (2)

42. Maximum number of electrons that can be accommodated in shell with n = 4

(1) 16

(2) 32

(3) 72

(4) 50

Answer: (2)

43. The wave function (Ψ) of 2 s is given by

At r = r₀, radial node is formed. Thus, r₀ in terms of a₀

(1) r₀ = 4a₀

(2) r₀ = a₀/2

(3) r₀ = a₀

(4) r₀ = 2a₀

Answer: (4)

44.

In the above conversion of compound (X) to product (Y), the sequence of reagents to be used will be:

(1) (i) Br₂(aq) (ii) LiAIH₄ (iii) H₃O⁺

(2) (i) Br₂, Fe (ii) Fe, H⁺ (iii) LiAIH₄

(3) (i) Fe, H⁺ (ii) Br₂ (aq) (iii) HNO₂ (iv) H₃PO₂

(4) (i) Fe, H⁺ (ii) Br₂ (aq) (iii) HNO₂ (iv) CuBr

Answer: (3)

45. Match List I with List II:

(1) A-I, B-II, C-IV, D-III

(2) A-II, B-I, C-III, D-IV

(3) A-II, B-I, C-IV, D-III

(4) A-I, B-II, C-III, D-IV

Answer: (1)

46. The most stable carbocation for the following is:

(1) a

(2) b

(3) c

(4) c

Answer: (3)

47. Chlorides of which metal are soluble in organic solvents:

(1) K

(2) Be

(3) Mg

(4) Ca

Answer: (2)

48. KMnO₄ oxidises I^– in acidic and neutral/faintly alkaline solution, respectively, to

(1) IO₃⁻ & IO₃⁻

(2) I₂ & IO₃⁻

(3) I₂ & I₂

(4) IO₃⁻ & I₂

Answer: (2)

49. Bond dissociation energy of “E-H” bond of the “H₂E ” hydrides of group 16 elements (given below), follows order.

(A) O

(B) S

(D) Te

Choose the correct from the options given below:

(1) B > A > C > D

(2) A > B > D > C

(3) A > B > C > D

(4) D > C > B > A

Answer: (3)

50. The water quality of a pond was analysed and its BOD was found to be 4. The pond has

(1) Highly polluted water

(2) Slightly polluted water

(3) Water has high amount of fluoride compounds

(4) Very clean water

Answer: (4)

SECTION B

51. Number of compounds from the following which will not dissolve in cold NaHCO₃ and NaOH solutions but will dissolve in hot NaOH solution is

Answer: (3)

52. 1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27° The work done is 3 kJ mol⁻¹. The final temperature of the gas is _______ K (Nearest integer). Given CV = 20 J mol–¹ K^–1

Answer: (150)

53. A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles of valine (V) per mole of peptide. The number of peptide linkages in it are

Answer: (6)

54. Lead storage battery contains 38% by weight solution of H₂SO₄. The van’t Hoff factor is 2.67 at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is __ (Nearest integer). Given K_f = 1.8 K kg mol⁻¹

Answer: (243)

55. The strength of 50 volume solution of hydrogen peroxide is ___________ g/L (Nearest integer).

Given:

Molar mass of H₂O₂ is 34 g mol⁻¹ Molar volume of gas at STP = 22.7 L.

Answer: (150)

56. The electrode potential of the following half cell at 298 K

X|X²⁺(0.001M||Y²⁺(0.01M)|Y is____________ × 10⁻² V (Nearest integer).

Answer: (275)

57. An organic compound undergoes first order decomposition. If the time taken for the 60% decomposition is 540 s, then the time required for 90% decomposition will be is______ s. (Nearest integer).

Given: ln 10 = 2.3; log 2 = 0.3

Answer: (1350)

58. Consider the following equation:

2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Δ𝐻=−190 kJ

The number of factors which will increase the yield of SO₃ at equilibrium from the following is

(A) Increasing temperature

(B) Increasing pressure

(D) Adding more O₂

(E) Addition of catalyst

Answer: (3)

59. Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0Å. If density of the FeO in the crystal is 4.0 g cm⁻³, then the number of FeO units present per unit cell is______ (Nearest integer)

Given: Molar mass of Fe and O is 56 and 16 g mol⁻¹ respectively. N_A = 6.0 × 10²³ mol⁻¹

Answer: (4)

60. The graph of for an adsorption process is a straight line inclined at an angle of 45° with intercept equal to 0.6020. The mass of gas adsorbed per unit mass of adsorbent at the pressure of 0.4 atm is_______ ×10⁻¹ (Nearest integer)

Answer: (16)

Mathematics

SECTION-A

61. A vector in the first octant is inclined to the x-axis at 60∘, to the y-axis at 45 and to the z-axis at an acute angle. If a plane passing through the points (√2, −1, 1) and (a, b, c), is normal to , then

(1) √2a + b + c = 1

(2) a + √2b + c = 1

(3) a + b + √2c = 1

(4) √2a – b + c = 1

Answer: (2)

62. Let a, b, c > 1, a³, b³ and c³ be in A.P., and loga_b, log_c a and log_b c be in G.P. If the sum of first 20 terms of an A.P., whose first term is and the common difference is then abc is equal to :

(1) 125/8

(2) 216

(3) 343

(4) 343/8

Answer: (2)

63. Let a₁ = 1, a₂, a₃, a₄, ….. be consecutive natural numbers. Then is equal to

Answer: (3)

64. Let λ ∈ ℝ,

If then is equal to

(1) 132

(2) 136

(3) 140

(4) 144

Answer: (3)

65. Let q be the maximum integral value of p in [0, 10] for which the roots of the equation are rational. Then the area of the region {(x, y): 0 ≤ y ≤ (x – q)², 0 ≤ x ≤ q} is

(1) 243

(2) 164

(3) 125/3

(4) 25

Answer: (1)

66. Let f, g and h be the real valued functions defined on ℝ as

and h(x) = 2[x] − f(x), where [x] is the greatest integer ≤ x.

Then the value of lim_x_→₁g(h(x – 1)) is

(1) −1

(2) 0

(3) sin(1)

(4) 1

Answer: (4)

67. Let S be the set of all values of a₁ for which the mean deviation about the mean of 100 consecutive positive integers a₁, a₂, a₃, …. a₁₀₀ is 25 . Then S is

(1) N

(2) ϕ

(3) {99}

(4) {9}

Answer: (1)

68. For α, β ∈ ℝ, suppose the system of linear equations

x – y + z = 5

2x + 2y + αz = 8

3x – y + 4z = β

has infinitely many solutions. Then α and β are the roots of

(1) x² + 14x + 24 = 0

(2) x² + 18x + 56 = 0

(3) x² – 18x + 56 = 0

(4) x² – 10x + 16 = 0

Answer: (3)

69. Let be two vectors, let If then the value of is

(1) −24

(2) −84

(3) −48

(4) −60

Answer: (3)

70. If the functions and have a common extreme point, then a + 2b + 7 is equal to :

(1) 3/2

(2) 3

(3) 4

(4) 6

Answer: (4)

71. If P is a 3×3 real matrix such that P^T = aP + (a − 1)I, where a > 1, then

(1) |Adj P| = 1/2

(2) |Adj P| = 1

(3) P is a singular matrix

(4) |Adj P| > 1

Answer: (2)

72. The number of ways of selecting two numbers a and b, a ∈ {2, 4, 6, …., 100} and b ∈ {1, 3, 5, …., 99} such that 2 is the remainder when a + b is divided by 23 is

(1) 268

(2) 108

(3) 54

(4) 186

Answer: (2)

73. is equal to

(1) 12

(2) 19/3

(3) 0

(4) 19

Answer: (4)

74. Let A be a point on the x-axis. Common tangents are drawn from A to the curves x² + y² = 8 and y² = 16x. If one of these tangents touches the two curves at Q and R, then (QR)² is equal to

(1) 81

(2) 72

(3) 76

(4) 64

Answer: (2)

75. If a plane passes through the points (−1, k, 0), (2, k, −1), (1, , 2) and is parallel to the line then the value of is

(1) 17/5

(2) 13/6

(3) 6/13

(4) 5/17

Answer: (2)

76. The range of the function is:

(1) [2√2, √11]

(2) [√5, √13]

(3) [√2, √7]

(4) [√5, √10]

Answer: (4)

77. The solution of the differential equation is

Answer: (2)

78. The parabolas : ax² + 2bx + cy = 0 and dx² + 2ex + fy = 0 intersect on the line y=1. If a, b, c, d, e, f are positive real numbers and a, b, c are in G.P., then

(1) d, e, f are in G.P.

(2) d/a, e/b, f/c are in A.P.

(3) d, e, f are in A.P.

(4) d/a, e/b, f/c are in G.P.

Answer: (2)

79. Consider the following statements:

P : I have fever

Q: I will not take medicine

R : I will take rest.

The statement “If I have fever, then I will take medicine and I will take rest” is equivalent to:

(1) ((∼P) ∨ ∼Q) ∧ ((∼P) ∨ R)

(2) (P ∨ Q) ∧ ((∼P) ∨ R)

(3) ((∼P) ∨ ∼Q) ∧ ((∼P) ∨ ∼R)

(4) (P ∨ ∼Q) ∧ (P ∨ ∼R)

Answer: (1)

80. x = (8√3 + 13)¹³ and y = (7√2 + 9)⁹. If [t] denotes the greatest integer ≤ t, then

(1) [x] is odd but [y] is even

(2) [x] + [y] is even

(3) [x] and [y] are both odd

(4) [x] is even but [y] is odd

Answer: (2)

SECTION-B

81. Let a line L pass through the point P(2, 3, 1) and be parallel to the line x + 3y − 2z – 2 = 0 = x – y + 2z. If the distance of L from the point (5, 3, 8) is α, then 3α² is equal to ______.

Answer: (158)

82. A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is q. If p : q = m : n, where m and n are coprime, then m + n is equal to ______.

Answer: (14)

83. Let P(a₁, b₁) and Q(a₂, b₂) be two distinct points on a circle with center C(√2,√3). Let O be the origin and OC be perpendicular to both CP and CQ.

If the area of the triangle OCP is √35/2, then a₁² + a₂² + b₁² + b₂² is equal to _______.

Answer: (24)

84. Let A be the area of the region {(x, y) : y ≥ x², y ≥ (1 − x)², y ≤ 2x(1−x)}. Then 540 A is equal to ______.

Answer: (25)

85. The 8th common term of the series

S₁ = 3 + 7 + 11 + 15 + 19 + …

S₂ = 1 + 6 + 11 + 16 + 21 + …

is _______.

Answer: (151)

86. Let A = {1, 2, 3, 5, 8,9}. Then the number of possible functions f:A→A such that f(m ⋅ n) = f(m) ⋅ f(n) for every m, n ∈ A with m ⋅ n ∈ A is equal to ______.

Answer: (1)

87. If constant, then β – α is equal to ______.

Answer: (1)

88. If the value of real number a>0 for which x²− 5ax + 1 = 0 and x² – ax – 5 = 0⁡have a common real root is 3/√2β then β is equal to _______.

Answer: (13)

89. 50th root of a number x is 12 and 50th root of another number y is 18 . Then the remainder obtained on dividing (x + y) by 25 is ______.

Answer: (23)

90. The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is ______.

Answer: (240)

JEE Main Session 2 29th January 2023 Shift 2 Question Paper and Answer Key

May 10, 2023May 10, 2023 by suresh84

JEE MAIN 29^th January 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance 𝐵 has atomic mass number 32 and half life of 1/2 day. If both 𝐴 and 𝐵 simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days

(1) 3.38 × 10²⁴

(2) 1.69 × 10²⁴

(3) 6.76 × 10²⁴

(4) 6.76 × 10²³

Answer: (1)

2. For the given logic gates combination, the correct truth table will be

Answer: (3)

3. The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45∘ incline plane. The coefficient of kinetic friction between the object and the incline plane is:

Answer: (3)

4. Heat energy of 184 kJ is given to ice of mass 600 g at −12∘ Specific heat of ice is 2222.3 J kg⁻¹C⁻¹ and latent heat of ice in 336 kJkg⁻¹

(A) Final temperature of system will be 0∘C.

(B) Final temperature of the system will be greater than 0∘C.

(D) The final system will have a mixture of ice and water in the ratio of 1:5. E. The final system will have water only.

Choose the correct answer from the options given below:

(1) A and D only

(2) A and E only

(3) A and C only

(4) B and D only

Answer: (1)

5. Identify the correct statements from the following:

(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.

(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero.

(E) Work done by the air resistance on an oscillating pendulum in negative.

Choose the correct answer from the options given below:

(1) B, D and E only

(2) A and C only

(3) B and D only

(4) B and E only

Answer: (4)

6. A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

(1) Increase the refractive index of the medium between the object and objective lens

(2) Decrease the diameter of the objective lens

(3) Increase the wave length of the light

(4) Decrease the focal length of the eye piece.

Answer: (1)

7. With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is

(A) directly proportional to the length of the potentiometer wire

(B) directly proportional to the potential gradient of the wire

(D) inversely proportional to the length of the potentiometer wire

Choose the correct option for the above statements:

(1) A only

(2) C only

(3) A and C only

(4) B and D only

Answer: (3)

8. A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

(1) 40 N

(2) 5 N

(3) 20 N

(4) 10 N

Answer: (2)

9. The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 mV and 6 mV respectively is:

(1) 0.4

(2) 0.6

(3) 0.2

(4) 1.4

Answer: (1)

10. Given below are two statements:

Statement I: Electromagnetic waves are not deflected by electric and magnetic field.

Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as

In the light of the above statements, choose the correct answer from the options given below :

(1) Statement I is true but statement II is false

(2) Both Statement I and Statement II are false

(3) Statement I is false but statement II is true

(4) Both Statement I and Statement II are true

Answer: (1)

11. A square loop of area 25 cm² has a resistance of 10 Ω. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1.0sec, will be

(1) 1.0 × 10⁻³ J

(2) 2.5 × 10⁻³ J

(3) 5 × 10⁻³ J

(4) 1.0 × 10⁻⁴ J

Answer: (1)

12. For the given figures, choose the correct options:

(1) At resonance, current in (b) is less than that in (a)

(2) The rms current in circuit (b) can never be larger than that in (a)

(3) The rms current in figure(a) is always equal to that in figure (b)

(4) The rms current in circuit (b) can be larger than that in (a)

Answer: (2)

13. A fully loaded boeing aircraft has a mass of 5.4 × 10⁵ Its total wing area is 500 m². It is in level flight with a speed of 1080 km/h. If the density of air ρ is 1.2 kg m⁻³, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. (g = 10 m/s²)

(1) 16

(2) 10

(3) 8

(4) 6

Answer: (2)

14. The ratio of de-Broglie wavelength of an α particle and a proton accelerated from rest by the same potential is 1/√m, the value of m is-

(1) 16

(2) 4

(3) 2

(4) 8

Answer: (4)

15. The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

(1) 4 hours

(2) 6 hours

(3) 3 hours

(4) 12 hours

Answer: (3)

16. The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

(1) 16 T

(2) 2 T

(3) 8 T

(4) 4 T

Answer: (2)

17. A point charge 2 × 10⁻² C is moved from P to S in a uniform electric field of 30NC⁻¹ directed along positive x-axis. If coordinates of P and S are (1, 2, 0)m and (0, 0, 0)m respectively, the work done by electric field will be

(1) 1200 mJ

(2) −1200 mJ

(3) −600 mJ

(4) 600 mJ

Answer: (3)

18. An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at =+2 m, its velocity is

The object’s velocity (v) and acceleration ( a ) at x = −2 m will be

Answer: (3)

19. At 300 K the rms speed of oxygen molecules is times to that of its average speed in the gas. Then, the value of α will be (used = 22/7)

(1) 28

(2) 24

(3) 32

(4) 27

Answer: (1)

20. The equation of a circle is given by x² + y² = a², where 𝑎 is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : The dimensions of t is given as [T⁻¹].

(1) A=[LT], B=[L⁻¹ T⁻¹]

(2) A=[L⁻¹ T⁻¹], B=[LT]

(3) A=[L⁻¹ T], B=[LT⁻¹]

(4) A=[L⁻¹ T⁻¹], B=[LT⁻¹]

Answer: (1)

SECTION-B

21. A particle of mass 100 g is projected at time t = 0 with a speed 20 ms⁻¹ at an angle 45∘ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kgm²/s. The value of K is ________. (Take g = 10 ms⁻²)

Answer: (800)

22. Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium −1) and 6.8 (medium −2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be the value of θ is ________.

(Given for dielectric media, μ_r = 1)

Answer: (7)

23. A particle of mass 250 g executes a simple harmonic motion under a periodic force F = (−25x)N. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ______ cm.

Answer: (40)

24. A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is t(1 – e^−π^/2)S. The value of t is ________.

Answer: (40)

25. When two resistances R₁ and R₂ connected in series and introduced into the left gap of a meter bridge and a resistance of 10Ω is introduced into the right gap, a null point is found at 60 cm from left side. When R₁ and R₂ are connected in parallel and introduced into the left gap, a resistance of 3Ω is introduced into the right-gap to get null point at 40 cm from left end. The product of R₁R₂ is _______ Ω²

Answer: (30)

26. In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is where x is _______.

Answer: (41)

27. An inductor of inductance 2μH is connected in series with a resistance, a variable capacitor and an AC source of frequency 7kHz. The value of capacitance for which maximum current is drawn into the circuit is where the value of x is _______. (Take π = 22/7)

Answer: (3872)

28. A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by 5Ω. When a resistance of 15Ω is used for shunting, null point moves to 300 cm. The internal resistance of the cell is _______ Ω.

Answer: (5)

29. For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2ar² + b. Here, 𝑎 and 𝑏 are constant and r is the distance from the center. The volume charge density inside the ball is −λaε. The value of 𝜆 is ________.

ε = permittivity of the medium

Answer: (12)

30. A metal block of base area 0.20 m² is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is 5.0 × 10⁻³ Pl, the speed of block is ________ × 10⁻³ m/s.

Answer: (25)

Chemistry

SECTION-A

31. According to MO theory the bond orders for O₂²⁻, CO and NO⁺ respectively, are

(1) 1, 2 and 3

(2) 1, 3 and 2

(3) 2, 3 and 3

(4) 1, 3 and 3

Answer: (4)

32. A doctor prescribed the drug Equanil to a patient. The patient was likely to have symptoms of which disease?

(1) Hyperacidity

(2) Anxiety and stress

(3) Depression and hypertension

(4) Stomach ulcers

Answer: (3)

33. Reaction of propanamide with Br₂/KOH(aq) produces :

(1) Propylamine

(2) Ethylnitrile

(3) Propanenitrile

(4) Ethylamine

Answer: (4)

34. The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is (excluding rearrangement)

(1) 2-Bromopropane

(2) 2-Bromo-3,3-dimethylpentane

(3) 1-Bromo-2-methylbutane

(4) 2-Bromopentane

Answer: (4)

35. An indicator ‘ X ‘ is used for studying the effect of variation in concentration of iodide : on the rate of reaction of iodide ion with H₂O₂ at room temp. The indicator ‘ X ‘ forms blue colored complex with compound ‘ A ‘ present in the solution. The indicator ‘ X ‘ and compound ‘A’ respectively are

(1) Methyl orange and H₂O₂

(2) Starch and iodine

(3) Starch and H₂O₂

(4) Methyl orange and iodine

Answer: (2)

36. The major component of which of the following ore is sulphide based mineral?

(1) Siderite

(2) Sphalerite

(3) Malachite

(4) Calamine

Answer: (2)

37. A solution of C_rO₅ in amyl alcohol has a _______ colour.

(1) Green

(2) Orange-Red

(3) Yellow

(4) Blue

Answer: (4)

38. The set of correct statements is :

(i) Manganese exhibits +7 oxidation state in its oxide.

(ii) Ruthenium and Osmium exhibit +8 oxidation in their oxides.

(iii) Sc shows +4 oxidation state which is oxidizing in nature.

(iv) Cr shows oxidising nature in +6 oxidation state.

(1) (ii) and (iii)

(2) (i), (ii) and (iv)

(3) (ii), (iii) and (iv)

(4) (i) and (iii)

Answer: (2)

39. Following tetrapeptide can be represented as

(F, L, D, Y, I, Q, P are one letter codes for amino acids)

(1) PLDY

(2) FIQY

(3) YQLF

(4) FLDY

Answer: (4)

40. Find out the major product for the following reaction.

Answer: (4)

41. Match List I with List II

Choose the correct answer from the options given below :

(1) A-I, B-III, C-II, D-IV

(2) A-III, B-I, C-IV, D-II

(3) A-III, B-I, C-II, D-IV

(4) A-III, B-II, C-I, D-IV

Answer: (3)

42. Correct order of spin only magnetic moment of the following complex ions is: (Given At.no. Fe: 26, Co : 27)

(1) [FeF₆]³⁻ > [Co(C₂O₄)₃]³⁻ > [CoF₆]³⁻

(2) [FeF₆]³⁻ > [CoF₆]³⁻ > [Co(C₂O₄)₃]³⁻

(3) [Co(C₂O₄)₃]³⁻ > [CoF₆]³⁻ > [FeF₆]³⁻

(4) [CoF₆]³⁻ > [FeF₆]³⁻ > [Co(C₂O₄)₃]³⁻

Answer: (2)

43. Match List I with List II

Choose the correct answer from the options given below :

(1) A-II, B-III, C-I, D-IV

(2) A-IV, B-III, C-I, D-II

(3) A-IV, B-I, C-III, D-II

(4) A-II, B-I, C-IV, D-III

Answer: (2)

44. The concentration of dissolved Oxygen in water for growth of fish should be more than X ppm and Biochemical Oxygen Demand in clean water should be less than Y X and Y in ppm are, respectively.

Answer: (2)

45. Find out the major products from the following reaction sequence.

Answer: (4)

46. When a hydrocarbon A undergoes combustion in the presence of air, it requirs 9.5 equivalents of oxygen and produces 3 equivalents of water. What is the molecular formula of A ?

(1) C₉H₉

(2) C₈H₆

(3) C₉H₆

(4) C₆H₆

Answer: (2)

47. Given below are two statements:

Statement I : Nickel is being used as the catalyst for producing syn gas and edible fats.

Statement II : Silicon forms both electron rich and electron deficient hydrides.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Statement I is correct but statement II is incorrect

(2) Both the statements I and II are incorrect

(3) Statement I is incorrect but statement II is correct

(4) Both the statements I and II are correct

Answer: (1)

48. Which of the following relations are correct?

(A) ΔU = q + pΔV (B) ΔG = ΔH −TΔS

Choose the most appropriate answer from the options given below:

(1) B and D Only

(2) A and B Only

(3) B and C Only

(4) C and D Only

Answer: (3)

49. Given below are two statements :

Statement I : The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga.

Statement II : The d orbitals in Ga are completely filled.

In the light of the above statements, choose the most appropriate answer from the options given below

(1) Statement I is incorrect but statement II is correct

(2) Both the statements I and II are correct

(3) Both the statements I and II are incorrect

(4) Statement I is correct but statement II is incorrect

Answer: (1)

50. Match List I and List II

Choose the correct answer from the options given below :

(1) A-I, B-III, C-IV, D-II

(2) A-III, B-I, C-IV, D-II

(3) A-III, B-I, C-II, D-IV

(4) A-I, B-III, C-II, D-IV

Answer: (2)

SECTION-B

51. Assume that the radius of the first Bohr orbit of hydrogen atom is 0.6Å. The radius of the third Bohr orbit of He⁺ is _______ picometer. (Nearest Integer)

Answer: (270)

52. Total number of acidic oxides among

N₂O₃, NO₂, N₂O, Cl₂O₇, SO₂, CO, CaO, Na₂O and NO is _______

Answer: (4)

53. The denticity of the ligand present in the Fehling’s reagent is _______

Answer: (4)

54. The equilibrium constant for the reaction Zn(s) + Sn²⁺(aq) ⇌ Zn²⁺(aq) + Sn(s) is 1 × 10²⁰ at 298 K. The magnitude of standard electrode potential of Sn/Sn²⁺ if is _______ × 10⁻² V (Nearest integer).

Answer: (17)

55. The volume of HCl, containing 73 g L⁻¹, required to completely neutralise NaOH obtained by reacting 0.69 g of metallic sodium with water, is _______ mL.( Nearest Integer) (Given : molar Masses of Na, Cl, O, H, are 23, 35.5, 16 and 1 g mol⁻¹ respectively)

Answer: (15)

56. For conversion of compound A→B, the rate constant of the reaction was found to be 6 × 10⁻⁵ L mol⁻¹ s⁻¹. The order of the reaction is _________.

Answer: (2)

57. On heating, LiNO₃ gives how many compounds among the following? _______ LiO₂, N₂, O₂, LiNO₂, NO₂

Answer: (3)

58. When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of CO₂ was produced. The molar mass of compound is _______ gmol⁻¹ (Nearest integer).

Answer: (200)

59. At 298 K

N₂(g) + 3H₂(g) ⇌ 2NH₃ ( g), K₁= 4 × 10⁵

N₂( g) + O₂( g) ⇌ 2NO(g), K₂ = 1.6 × 10¹²

K₃ = 1.0 × 10⁻¹³

Based on above equilibria, the equilibrium constant of the reaction, is _______ × 10⁻³³ (Nearest integer).

Answer: (4)

60. A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is _______ × 10²¹ (Nearest integer). (Given NA = 6.02 × 10²³ )

Answer: (36)

Mathematics

SECTION-A

61. The statement B ⇒ ((∼A) ∨ B) is equivalent to :

(1) A ⇒ (A ⇔ B)

(2) A ⇒ ((∼A) ⇒ B)

(3) B ⇒(A ⇒ B)

(4) B ⇒ ((∼A) ⇒ B)

Answer: (1, 3 or 4)

62. The value of the integral is

Answer: (4)

63. The set of all values of λ for which the equation cos²⁡2x − 2sin⁴⁡x − 2cos²⁡x = λ has a real solution x, is

(1) [−2, −1]

(2) [−1, −1/2]

(3) [−3/2, −1]

(4) [−2, −3/2]

Answer: (3)

64. Let R be a relation defined on ℕ as a R b if 2a + 3b is a multiple of 5, a, b ∈ ℕ. Then R is

(1) an equivalence relation

(2) transitive but not symmetric

(3) not reflexive

(4) symmetric but not transitive

Answer: (1)

65. Consider a function f : ℕ → ℝ, satisfying f(1) + 2f(2) + 3f(3) + … + xf(x) = x(x + 1) f(x); x ≥ 2 with f(1) = 1. Then is equal to

(1) 8100

(2) 8400

(3) 8000

(4) 8200

Answer: (1)

66. If and is equal to

(1) 32

(2) 30

(3) 36

(4) 34

Answer: (4)

67. The shortest distance between the lines and

(1) 5√3

(2) 2√3

(3) 3√3

(4) 4√3

Answer: (4)

68. The plane 2x – y + z = 4 intersects the line segment joining the points A(a, −2, 4) and B(2, b, −3) at the point C in the ratio 2:1 and the distance of the point C from the origin is √5. If ab < 0 and P is the point (a − b, b, 2b − a) then CP² is equal to

(1) 97/3

(2) 17/3

(3) 16/3

(4) 73/3

Answer: (2)

69. The value of the integral is equal to

Answer: (1)

70. The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is

(1) 84

(2) 79

(3) 89

(4) 86

Answer: (3)

71. The set of all values of t ∈ ℝ, for which the matrix is invertible, is

(1) ℝ

(2)

(3) {kπ, k ∈ ℤ}

(4)

Answer: (1)

72. The area of the region A = {(x, y): |cos x – sin x| ≤ y ≤ sin x, 0 ≤ x ≤ π/2} is

(1) √5 + 2√2 – 4.5

(2)

(3)

(4) √5 – 2√2 + 1

Answer: (4)

73. The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

(1) 507

(2) 432

(3) 472

(4) 400

Answer: (2)

74. If the lines and intersect at the point P, then the distance of the point P from the plane z = a is :

(1) 28

(2) 16

(3) 10

(4) 22

Answer: (1)

75. Let y = y(x) be the solution of the differential equation If y(2) = 2, then y(e) is equal to

Answer: (2)

76. Let f and g be twice differentiable functions on ℝ such that

fʹʹ(x) = gʹʹ(x) + 6x

fʹ(1) = 4gʹ(1) – 3 = 9

f(2) = 3g(2) = 12.

Then which of the following is NOT true?

(1) There exists x₀ ∈ (1, 3/2) such that f(x₀) = g(x₀)

(2) |fʹ(x) – gʹ(x)| < 6 ⇒ −1 < x < 1

(3) If −1 < x < 2, then |f(x) − g(x)| < 8

(4) g(−2) − f(−2) = 20

Answer: (3)

77. If the tangent at a point P on the parabola y² = 3x is parallel to the line x + 2y = 1 and the tangents at the points Q and R on the ellipse are perpendicular to the line x – y = 2, then the area of the triangle PQR is :

(1)

(2) 3√5

(3) 9/√5

(4) 5√3

Answer: (2)

78. Let If is a vector such that and projection of then the projection of equals

(1) 1/5

(2) 5/√2

(3) 3/√2

(4) 1/√2

Answer: (2)

79. Let S = {w₁, w₂, …….} be the sample space associated to a random experiment. Let Let A = {2k + 3l; k. l ∈ ℕ} and B = {w_n : n ∈ A}. Then P(B) is equal to

(1) 3/64

(2) 1/16

(3) 1/32

(4) 3/32

Answer: (1)

80. Let K be the sum of the coefficients of the odd powers of x in the expansion of (1 + x)⁹⁹. Let a be the middle term in the expansion of where m and n are odd numbers, then the ordered pair (l, n) is equal to

(1) (50, 51)

(2) (50, 101)

(3) (51, 99)

(4) (51, 101)

Answer: (2)

SECTION-B

81. The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is

Answer: (3000)

82. Let a₁ = b₁ = 1 and a_n = a_{n – 1}+ (n – 1), b_n = b_{n – 1}+ a_{n – 1,}∀n ≥ If then 2⁷ (2S – T) is equal to

Answer: (461)

83. A triangle is formed by the tangents at the point (2, 2) on the curves y² = 2x and x² + y² = 4x, and the line x + y + 2 = 0. If r is the radius of its circumcircle, then r² is equal to

Answer: (10)

84. Let α₁, α₂, …., α₇ be the roots of the equation x⁷ + 3x⁵– 13x³ – 15x = 0 and |α₁| ≥ | α₂| ≥ ⋯ ≥ | α₇|. Then α₁ α₂ − α₃ α₄ + α₅α₆ is equal to

Answer: (3)

85. Let X = {11, 12, 13, …, 40, 41} and Y = {61, 62, 63, …, 90, 91} be the two sets of observations. If are their respective means and σ² is the variance of all the observations in X ∪ Y, then is equal to

Answer: (603)

86. If the equation of the normal to the curve at the point (1, −3) is x – 4y = 13, then the value of a + b is equal to

Answer: (−6)

87. Let A be a symmetric matrix such that |A| = 2 and If the sum of the diagonal elements of A is s, then βs/α² is equal to

Answer: (5)

88. Let α = 8 – 14i, and B = {z ∈ ℂ: |z + 3i| = 4}. Then ∑_Z_∈_A_∩_B(Re z = Im z) is equal to

Answer: (14)

89. A circle with centre (2, 3) and radius 4 intersects the line x + y = 3 at the points P and Q. If the tangents at P and Q intersect at the point S(α, β), then 4α − 7β is equal to

Answer: (11)

90. Let {a_k} and {b_k}, k ∈ ℕ, be two G. P.s with common ratios r₁ and r₂ respectively such that a₁ = b₁ = 4 and r₁ < r₂. Let c_k = a_k + b_k, k ∈ ℕ. If c₂ = 5 and c₃ = 13/4 then is equal to

Answer: (9)

JEE Main Session 2 25th January 2023 Shift 2 Question Paper and Answer Key

May 10, 2023May 10, 2023 by suresh84

JEE MAIN 25^th January 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-

Answer: (3)

2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The magnitude of induced emf, between the ends of wire will be

(1) 20 V

(2) 8 V

(3) 12 V

(4) 16 V

Answer: (4)

3. The energy levels of an atom is shown in figure.

Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? Given (h = 6.62 × 10⁻³⁴Js)

(1) D

(2) B

(3) C

(4) A

Answer: (1)

4. Given below are two statements :

Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.

Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.

In the light of above statements, choose the most appropriate answer from the options given below

(1) Statement I is incorrect but statement II is correct

(2) Statement 𝐈 is correct but statement 𝐈𝐈 is incorrect

(3) Both Statement 𝐈 and statement II are correct

(4) Both Statement I and Statement II are incorrect

Answer: (3)

5. The distance travelled by a particle is related to time t as x = 4t². The velocity of the particle at t = 5 s is:-

(1) 40 ms⁻¹

(2) 20 ms⁻¹

(3) 8 ms⁻¹

(4) 25 ms⁻¹

Answer: (1)

6. Match List I with List II

Choose the correct answer from the options given below: options

(1) A-I, B-II, C-III, D-IV

(2) A-II, B-III, C-IV, D-I

(3) A-I, B-III, C-IV, D-II

(4) A-III, B-I, C-II, D-IV

Answer: (4)

7. Match List I with List II

Choose the correct answer from the options given below:

(1) A-III, B-IV, C-II, D-I

(2) A-III, B-II, C-I, D-IV

(3) A-I, B-IV, C-III, D-II

(4) A-I, B-II, C-IV, D-III

Answer: (1)

8. The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:-

(A) Real

(B) Erect

(D) Laterally inverted

Choose the most appropriate answer from the options given below:

(1) A, C, and D only

(2) B and D only

(3) A and D only

(4) B and C only

Answer: (2)

9. The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by:-

Answer: (4)

10. Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (μ) is equal to :

(1) 0.25

(2) 0.50

(3) 0.60

(4) 0.33

Answer: (4)

11. Every planet revolves around the sun in an elliptical orbit:-

(A) The force acting on a planet is inversely proportional to square of distance from sun.

(B) Force acting on planet is inversely proportional to product of the masses of the planet and the sun.

(D) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below:

(1) B and C only

(2) A and C only

(3) A and D only

(4) C and D only

Answer: (3)

12. For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is 4.0 × 10⁻⁵ N m rad⁻¹, the magnetic field is 0.01 T and the number of turns in the coil is 200 , the area of each turn (in cm²) is :

(1) 1.0

(2) 2.0

(3) 1.5

(4) 0.5

Answer: (1)

13. Match List I with List II

Choose the correct answer from the options given below:

(1) A-IV, B-I, C-II, D-III

(2) A-II, B-III, C-IV, D-I

(3) A-III, B-IV, C-I, D-II

(4) A-I, B-II, C-III, D-IV

Answer: (1)

14. Two objects are projected with same velocity ‘u’ however at different angles α andβwith the horizontal. If α + β = 90°, the ratio of horizontal range of the first object to the 2nd object will be:

(1) 2 : 1

(2) 1 : 2

(3) 1 : 1

(4) 4 : 1

Answer: (3)

15. A particle executes simple harmonic motion between x = −A and x = +A. If time taken by particle to go from x = 0 to A/2 is 2 s; then time taken by particle in going from x = A/2 to A is

(1) 4 S

(2) 1.5 S

(3) 2 S

(4) 3 S

Answer: (1)

16. Match List I with List II

Choose the correct answer from the options given below:

(1) A-I, B-II, C-III, D-IV

(2) A-II, B-I, C-IV, D-III

(3) A-II, B-I, C-III, D-IV

(4) A-I, B-II, C-IV, D-III

Answer: (2)

17. Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.

Statement II: When such P-type and N-type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.

In the light of above statements, choose the most appropriate answer from the options given below

(1) Both Statement I and statement II are correct

(2) Statement 𝐈 is incorrect but statement II is correct

(3) Both Statement I and Statement II are incorrect

(4) Statement I is correct but statement II is incorrect

Answer: (4)

18. A point charge of 10μC is placed at the origin. At what location on the X-axis should a point charge of 40μC be placed so that the net electric field is zero at x = 2 cm on the X-axis?

(1) x = −4 cm

(2) x = 6 cm

(3) x = 4 cm

(4) x = 8 cm

Answer: (2)

19. The resistance of a wire is 5Ω. It’s new resistance in ohm if stretched to 5 times of it’s original length will be :

(1) 25

(2) 125

(3) 5

(4) 625

Answer: (2)

20. A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R_e), the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth)

Answer: (3)

SECTION-B

21. Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _____× 10⁻⁶ T

(Given : √2=1⋅4)

Answer: (60)

22. A spherical drop of liquid splits into 1000 identical spherical drops. If u_i is the surface energy of the original drop and u_f is the total surface energy of the resulting drops, the (ignoring evaporation), Then value of x is _______.

Answer: (1)

23. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be (x/3)^1/3. The value of ‘x’ is:-

Answer: (2)

24. A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound =330 ms⁻¹) _______ Hz.

Answer: (400)

25. A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ________ ms⁻¹.

Answer: (4)

26. A series LCR circuit is connected to an AC source of 220 V,50 Hz. The circuit contains a resistance R= 80Ω, an inductor of inductive reactance X_L= 70Ω, and a capacitor of capacitive reactance X_C = 130Ω. The power factor of circuit is x/10. The value of x is :

Answer: (8)

27. If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be x/7. The value of x is _____.

Answer: (5)

28. An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is cm

Answer: (30)

29. A capacitor has capacitance 5𝜇F when it’s parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d/2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will be μ

Answer: (6)

30. Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3Ω. Cell 2 has emf of 6 V and internal resistance of 6Ω. An external resistor R of 4Ω is connected across A and B. The current flowing through R will be __________ A.

Answer: (1)

Chemistry

SECTION-A

31. When the hydrogen ion concentration [H⁺]changes by a factor of 1000 , the value of pH of the solution

(1) increases by 2 units

(2) increases by 1000 units

(3) decreases by 2 units

(4) decreases by 3 units

Answer: (4)

32. Find out the major product from the following reaction.

Answer: (4)

33. Given below are two statements, one is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑

Assertion A: Carbon forms two important oxides – CO and CO₂.CO is neutral whereas CO₂ is acidic in nature

Reason 𝐑: CO₂ can combine with water in a limited way to form carbonic acid, while CO is sparingly soluble in water.

In the light of the above statements, choose the most appropriate answer from the options given below

(1) Both A and R are correct but R is NOT the correct explanation of A

(2) A is correct but R is not correct

(3) Both A and R are correct and R is the correct explanation of A

(4) A is not correct but R is correct

Answer: (3)

34. Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: The alkali metals and their salts impart characteristic colour to reducing flame.

Reason R: Alkali metals can be detected using flame tests.

In the light of the above statements, choose the most appropriate answer from the options given below

(1) A is not correct but R is correct

(2) Both A and R are correct but R is NOT the correct explanation of A

(3) A is correct but R is not correct

(4) Both A and R are correct and R is the correct explanation of A

Answer: (1)

35. Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from

(1) +2 to +1

(2) +3 to +1

(3) +6 to +2

(4) +6 to +3

Answer: (4)

36. Match List I with List II

Choose the correct answer from the options given below:

(1) A-III, B-IV, C-I, D-II

(2) A-III, B-II, C-IV, D-I

(3) A-III, B-I, C-IV, D-II

(4) A-III, B-IV, C-II, D-I

Answer: (4)

37. Which of the following represents the correct order of metallic character of the given elements ?

(1) Si < Be < Mg < K

(2) Be < Si < K < Mg

(3) Be < Si < Mg < K

(4) K < Mg < Be < Si

Answer: (1)

38. Match List I with List II

Choose the correct answer from the options given below:

(1) A-IV, B-I, C-II, D-III

(2) A-IV, B-III, C-II, D-I

(3) A-II, B-III, C-IV, D-I

(4) A-IV, B-III, C-I, D-II

Answer: (2)

39. Match List I with List II

Choose the correct answer from the options given below:

(1) A-III, B-IV, C-II, D-I

(2) A-III, B-II, C-I, D-IV

(3) A-I, B-IV, C-II, D-III

(4) A-III, B-II, C-IV, D-I

Answer: (1)

40. Match List I with List II

Choose the correct answer from the options given below:

(1) A-II, B-III, C-I, D-IV

(2) A-III, B-I, C-IV, D-II

(3) A-III, B-IV, C-I, D-II

(4) A-IV, B-III, C-I, D-II

Answer: (2)

41. What is the mass ratio of ethylene glycol (C₂H₆O₂, molar mass =62 g/mol) required for making 500 g of 0.25 molal aqueous solution and 250 mL of 0.25 molal aqueous solution?

(1) 1 : 1

(2) 2 : 1

(3) 1 : 2

(4) 3 : 1

Answer: (2)

42. Match list I with List II

Choose the correct answer from the options given below:

(1) A-III, B-I, C-II, D-IV

(2) A-IV, B-I, C-III, D-II

(3) A-III, B-II, C-I, D-IV

(4) A-II, B-III, C-IV, D-I

Answer: (3)

43. Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A : Butylated hydroxy anisole when added to butter increases its shelf life.

Reason R : Butylated hydroxy anisole is more reactive towards oxygen than food.

In the light of the above statements, choose the most appropriate answer from the options given below

(1) A is correct but R is not correct

(2) A is not correct but R is correct

(3) Both A and R are correct and R is the correct explanation of A

(4) Both A and R are correct but R is NOT the correct explanation of A

Answer: (3)

44. The isomeric deuterated bromide with molecular formula C₄H₈DBr having two chiral carbon atoms is

(1) 2 – Bromo – 2 – deuterobutane

(2) 2 – Bromo-1-deuterobutane

(3) 2 – Bromo – 1 – deutero – 2 – methylpropane

(4) 2 – Bromo −3 – deuterobutane

Answer: (4)

45. A chloride salt solution acidified with dil. HNO₃ gives a curdy white precipitate, [A], on addition of AgNO₃⋅[A] on treatment with NH₄OH gives a clear solution, B. A and B are respectively

(1) AgCl & (NH₄)[Ag(OH)₂]

(2) AgCl & [Ag(NH₃)₂]Cl

(3) H[AgCl₃] & (NH₄)[Ag(OH)₂]

(4) H[AgCl₃] & [Ag(NH₃)₂]Cl

Answer: (2)

46. Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre.

Statement II : The crossed arrow of the dipole moment symbolizes the direction of the shift of charges in the molecules.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Statement I is incorrect but Statement II is correct

(2) Statement I is correct but Statement II is incorrect

(3) Both Statement I and Statement II are incorrect

(4) Both Statement I and Statement II are correct

Answer: (2)

47. ꞌA’ in the given reaction is

Answer: (4)

48. (A) Ammonium salts produce haze in atmosphere.

(B) Ozone gets produced when atmospheric oxygen reacts with chlorine radicals.

(D) ‘Blue baby’ syndrome occurs due to the presence of excess of sulphate ions in water.

Choose the correct answer from the options given below:

(1) A and D only

(2) A, B and C only

(3) A and C only

(4) B and C only

Answer: (3)

49. Given below are two statements:

Statement I: In froth floatation method a rotating paddle agitates the mixture to drive air out of it.

Iron pyrites are generally avoided Statement II: for extraction of iron due to environmental reasons.

In the light of the above statements, choose the correct answer from the options given below:

(1) Statement I is false but Statement II is true

(2) Both Statement I and Statement II are false

(3) Statement I is true but Statement II is false

(4) Both Statement I and Statement II are true

Answer: (1)

50. Which one among the following metals is the weakest reducing agent?

(1) Li

(2) K

(3) Rb

(4) Na

Answer: (4)

Section B

51. Total number of moles of AgCl precipitated on addition of excess of AgNO₃ to one mole each of the following complexes [Co(NH₃)₄Cl₂]Cl,[Ni(H₂O)₆]Cl₂,[Pt(NH₃)₂Cl₂] and [Pd(NH₃)₄]Cl₂ is ____

Answer: (5)

52. The number of incorrect statement/s from the following is/are

(A) Water vapours are adsorbed by anhydrous calcium chloride.

(B) There is a decrease in surface energy during adsorption.

(D) Adsorption is accompanied by decrease in entropy of the system.

Answer: (2)

53. Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is ____ (Given: Molar mass of A = 84 g mol⁻¹)

Answer: (12)

54. The number of given orbitals which have electron density along the axis is ________

Answer: (5)

55. 28.0 L of CO₂ is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at 25°C and 1 atm. Heat evolved during the combustion process is________ kJ.

Given : ∆H_C(CH₄) = −900 kJ mol⁻¹

∆H_c(C₂H₄) = −1400 kJ mol⁻¹

Answer: (847)

The E_cell for the given cell is 0.1115 V at 298 K when

The value of a is

Given : E^θM³⁺/M⁺ = 0.2 V

Answer: (3)

57. The number of pairs of the solutions having the same value of the osmotic pressure from the following is (Assume 100% ionization)

(A) 0.500 M C₂H₅OH (aq) and 0.25 M KBr (aq)

(B) 0.100 M K4[Fe(CN)₆] (aq) and 0.100 M FeSO₄(NH₄)₂SO₄ (aq)

(D) 0.15 M NaCl(aq) and 0.1 M BaCl2(aq)

(E) 0.02 M KCl⋅MgCl₂⋅6H₂O(aq) and 0.05 M KCl(aq)

Answer: (4)

58. A first order reaction has the rate constant, = 4.6 × 10⁻³ s⁻¹. The number of correct statement/s from the following is/are

Given: log 3 = 0.48

(A) Reaction completes in 1000 s.

(B) The reaction has a half-life of 500 s.

(D) The degree of dissociation is equal to (1 – e^−kt)

(E) The rate and the rate constant have the same unit.

Answer: (1)

59. Based on the given figure, the number of correct statement/s is/are ___________

(A) Surface tension is the outcome of equal attractive and repulsive forces acting on the liquid molecule in bulk.

(B) Surface tension is due to uneven forces acting on the molecules present on the surface.

(D) The molecules on the surface are responsible for vapours pressure if system is a closed system.

Answer: (2)

60. Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is

Answer: (3)

Mathematics

SECTION-A

61. Let Δ, ∇ ∈ {∧, ∨} be such that (p → q) Δ (p ∇ q) is a tautology. Then

(1) Δ = V, ∇ = V

(2) Δ = V,∇ = Λ

(3) Δ = Λ, ∇ = V

(4) Δ = Λ, ∇ = Λ

Answer: (1)

62. If the four points, whose position vectors are and are coplanar, then α is equal to

(1) 73/17

(2) 107/17

(3) −73/17

(4) −107/17

Answer: (1)

63. The foot of perpendicular of the point (2, 0, 5) on the line is (α, β, γ). Then, which of the following is NOT correct?

Answer: (1)

64. The equations of two sides of a variable triangle are x = 0 and y = 3, and its third side is a tangent to parabola y² = 6x. The locus of its circumcentre is:

(1) 4y² – 18y – 3x – 18 = 0

(2) 4y² – 18y – 3x + 18 = 0

(3) 4y² – 18y + 3x + 18 = 0

(4) 4y² + 18y + 3x + 18 = 0

Answer: (3)

65. Let f(x) = 2Xⁿ + λ, λ ∈ ℝ, n ∈ ℕ, and f(4) = 133, f(5) 255. Then the sum of all the positive integer divisors of (f(3) – f(2)) is

(1) 60

(2) 59

(3) 61

(4) 58

Answer: (1)

66. is equal to

(1) ⁵¹C₄ – ⁴⁵C₄

(2) ⁵²C₃ – ⁴⁵C₃

(3) ⁵²C₄ – ⁴⁵C₄

(4) ⁵¹C₃ – ⁴⁵C₃

Answer: (3)

67. Let the function f(x) = 2x³ + (2p − 7) x² + 3(2p − 9) x − 6 have a maxima for some value of x < 0 and a minima for some value of x > 0.Then,the set of all values of p is

(1) (0, 9/2)

(2) (−∞, 9/2)

(3) (−9/2, 9/2)

(4) (9/2, ∞)

Answer: (2)

68. Let and where i = √−1.

If M = A^TBA, then the inverse of the matrix AM²⁰²³ A^T is

Answer: (4)

69. Let and Then is equal to

Answer: (3)

70. The integral is equal to

Answer: (2)

71. Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x² − y² + 64x + 4y + 44 = 0.Then the area of the region above the parabola x² = y + 4, below the transverse axis T and on the right of the conjugate axis C is:

Answer: ()

72. Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N−2,√3N, N+2 are in geometric progression be k/48. Then the value of k is

(1) 8

(2) 16

(3) 2

(4) 4

Answer: (4)

73. If the function is continuous at x = π/2, then 9λ + 6log_eμ + μ⁶ – e⁶^λ is equal to

(1) 10

(2) 2e⁴ + 8

(3) 11

(4) 8

Answer: (*)

74. The number of functions f:{1, 2, 3, 4} → {a∈ : ℤ|a| ≤ 8} satisfying ∀ n ∈ {1, 2, 3) is

(1) 1

(2) 4

(3) 2

(4) 3

Answer: (2)

75. Let y = y(t) be a solution of the differential equation where, α > 0, β > 0 and γ > 0. Then

(1) is −1

(2) is 1

(3) does not exist

(4) is 0

Answer: (4)

76. Let z be a complex number such that z ≠ − Then z lies on the circle of radius 2 and centre

(1) (2, 0)

(2) (0, 2)

(3) (0, −2)

(4) (0, 0)

Answer: (3)

77. Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements

(S1) A¹³ B²⁶ − B²⁶ A¹³ is symmetric

(S2)A²⁶C¹³ − C¹³ A²⁶ is symmetric

Then,

(1) Only S2 is true

(2) Both S1 and S2 are false

(3) Only S1 is true

(4) Both S1 and S2 are true

Answer: (1)

78. The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

(1) 12

(2) 120

(3) 72

(4) 6

Answer: (3)

79. Let f : ℝ → ℝ be a function defined by

f(x) = log_√_m{√2(sin x – cos x) + m – 2}, for some m, such that the range of f is [0, 2]. Then the value of m is

(1) 5

(2) 4

(3) 3

(4) 2

Answer: (1)

80. The shortest distance between the lines x + 1 = 2y = −12z and x = y + 2 = 6z − 6 is

(1) 3/2

(2) 2

(3) 5/2

(4) 3

Answer: (2)

SECTION-B

81. 25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is k/10. Then the value of k is.

Answer: (9)

82. The remainder when (2023)²⁰²³ is divided by 35 is

Answer: (7)

83. Let a ∈ ℝ and let α, β be the roots of the equation x² + 60^1/4x + a = 0. If α⁴ + β⁴ = −30, then the product of all possible values of a is

Answer: (45)

84. For the two positive numbers a, b is a, b and 1/18 are in a geometric progression, while 1/a, 10 and 1/b are in an arithmetic progression, then 16a + b is equal to

Answer: (3)

85. If m and n respectively are the numbers of positive and negative values of q in the interval [–p, p] that satisfy the equation then mn is equal to

Answer: (25)

86. If the shortest distance between the line joining the points (1,2,3) and (2,3,4),and the line then 28a² is equal to

Answer: (18)

87. Points P(–3,2),Q(9,10) and (a,4) lie on a circle C with PR as its diameter, The tangents to C at the points Q and R intersect at the point S. If S lies on the line 2x – ky = 1, then k is equal to

Answer: (3)

88. Suppose Anil’s mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil’s mother can offer 5 fruits to Anil is

Answer: (6860)

89. If where m and n are coprime natural numbers, then m² + n² − 5 is equal to

Answer: (20)

90. A triangle is formed by X- axis, Y-axis and the line 3x + 4y = 4y = 60. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is

Answer: (31)

JEE Main Session 2 24th January 2023 Shift 2 Question Paper and Answer Key

May 10, 2023May 9, 2023 by suresh84

JEE MAIN 24^th January 2023 Shift 2

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: A pendulum clock when taken to Mount Everest becomes fast.

Reason : The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.

In the light of the above statements, choose the most appropriate answer from the options given below

(1) Both 𝐀 and 𝐑 are correct but 𝐑 is NOT the correct explanation of 𝐀

(2) A is correct but 𝐑 is not correct

(3) Both 𝐀 and 𝐑 are correct and 𝐑 is the correct explanation of 𝐀

(4) 𝐀 is not correct but 𝐑 is correct

Answer: (4)

2. The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v = r^aρ^bs^c. The values of a, b and c respectively are

(1) (−3/2, 1/2, 1/2)

(2) (3/2, −1/2, 1/2)

(3) (−3/2, −1/2, 1/2)

(4) (3/2, 1/2, −1/2)

Answer: (3)

3. Given below are two statements:

Statement I : Acceleration due to earth’s gravity decreases as you go ‘up’ or ‘down’ from earth’s surface.

Statement II : Acceleration due to earth’s gravity is same at a height ‘h’ and depth ‘d’ from earth’s surface, if h = d.

In the light of above statements, choose the most appropriate answer form the options given below

(1) Both Statement I and Statement II are incorrect

(2) Statement I is incorrect but statement II is correct

(3) Both Statement I and II are correct

(4) Statement I is correct but statement II is incorrect

Answer: (4)

4. A long solenoid is formed by winding 70 turns cm^–1. If 2.0 A current flows, then the magnetic field produced inside the solenoid is _______ (μ₀ = 4π × 10⁻⁷ TmA⁻¹)

(1) 88 × 10⁻⁴ T

(2) 352 × 10⁻⁴ T

(3) 176 × 10⁻⁴ T

(4) 1232 × 10⁻⁴ T

Answer: (3)

5. The electric potential at the centre of two concentric half rings of radii R₁ and R₂, having same linear charge density 𝜆 is :

(1) λ/2ε₀

(2) λ/4ε₀

(3) 2λ/ε₀

(4) λ/ε₀

Answer: (1)

6. If the distance of the earth from Sun is 1.5 × 10⁶ Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :

(1) 6 × 10⁶ km

(2) 3 × 10⁶ km

(3) 3 × 10⁷ km

(4) 6 × 10⁷ km

Answer: (2)

7. A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 × 10⁻¹⁵ eVs ) :

(1) 99.3 nm

(2) 941 nm

(3) 974 nm

(4) 94.1 nm

Answer: (4)

8. A cell of emf 90 V is connected across series combination of two resistors each of 100Ω resistance. A voltmeter of resistance 400Ω is used to measure the potential difference across each resistor. The reading of the voltmeter will be:

(1) 90 V

(2) 45 V

(3) 80 V

(4) 40 V

Answer: (2)

9. If two vectors and are perpendicular to each other. Then, the value of m will be:

(1) −1

(2) 3

(3) 2

(4) 1

Answer: (3)

10. The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by

E_x = E₀sin(kz − ωt)

B_y = B₀sin(kz − ωt)

Then the correct relation between E_o and B_o is given by

(1) E_oB_o = ωk

(2) E_o = kB_o

(3) kE_o = ωB_o

(4) ωE_o = kB_o

Answer: (3)

11. The logic gate equivalent to the given circuit diagram is :

(1) NAND

(2) OR

(3) AND

(4) NOR

Answer: (1)

12. Let γ₁ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and γ₂ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, γ₁/ γ₂ is :

(1) 25/21

(2) 35/27

(3) 21/25

(4) 27/35

Answer: (1)

13. When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

(1) Spherical aberration

(2) Polarisation

(3) Chromatic aberration

(4) Scattering

Answer: (*)

14. A metallic rod of length ‘L’ is rotated with an angular speed of ‘ω’ normal to a uniform magnetic field ‘B’ about an axis passing through one end of rod as shown in figure. The induced emf will be:

Answer: (4)

15. An a-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

(1) λ_α < λ_p < λ_e

(2) λ_α = λ_p = λ_e

(3) λ_α > λ_p > λ_e

(4) λ_α > λ_p < λ_e

Answer: (1)

16. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason

Assertion A : Steel is used in the construction of buildings and bridges.

Reason R : Steel is more elastic and its elastic limit is high.

In the light of above statements, choose the most appropriate answer from the options given below

(1) Both 𝐀 and 𝐑 are correct and 𝐑 is the correct explanation of 𝐀

(2) Both 𝐀 and 𝐑 are correct but 𝐑 is NOT the correct explanation of 𝐀

(3) A is correct but 𝐑 is not correct

(4) A is not correct but 𝐑 is correct

Answer: (1)

17. In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T₃ > T₂ > T₁ as:

Answer: (3)

18. Match List I with List II

Choose the correct answer from the options given below:

(1) A-II, B-I, C-IV, D-III

(2) A-I, B-III, C-II, D-IV

(3) A-IV, B-III, C-I, D-II

(4) A-II, B-III, C-I, D-IV

Answer: (1)

19. A body of mass 200 g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5rad/s. Then the ratio of extension in the spring to its natural length will be :

(1) 2 : 5

(2) 1 : 1

(3) 2 : 3

(4) 1 : 2

Answer: (3)

20. The velocity time graph of a body moving in a straight line is shown in figure.

The ratio of displacement to distance travelled by the body in time 0 to 10 s is :

(1) 1 : 1

(2) 1 : 2

(3) 1 : 3

(4) 1 : 4

Answer: (3)

SECTION-B

21. A body of mass 1 kg begins to move under the action of a time dependent force

Answer: (100)

22. A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ________ cm

(Given refractive index of water = 4/3)

Answer: (54)

23. The energy released per fission of nucleus of ⁡²⁴⁰X is 200MeV. The energy released if all the atoms in 120 g of pure ⁡²⁴⁰X undergo fission is ______ × 10²⁵MeV (Given NA = 6 × 10²³)

Answer: (6)

24. A uniform solid cylinder with radius R and length L has moment of inertia I₁, about the axis of the cylinder. A concentric solid cylinder of radius Rꞌ = R/2 and Length Lꞌ = L/2 is carved out of the original cylinder. If I₂ is the moment of inertia of the carved out portion of the cylinder then I₁/I₂ = ________ (Both I₁ and I₂ are about the axis of the cylinder)

Answer: (32)

25. A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes x/4pF. The value of x is _______

Answer: (105)

26. A single turn current loop in the shape of a right angle triangle with sides 5 cm,12 cm,13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be x/130 N. The value of x is ______

Answer: (9)

27. A mass m attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is _____ kg.

Answer: (1)

28. If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _________ %

Answer: (44)

29. Three identical resistors with resistance R = 12 Ω and two identical inductors with self inductance L = 5mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _______ A.

Answer: (3)

30. A Spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is 3696 × 10⁻^x The value of x is (Given, g = 9.8 m/s² and π = 22/7)

Answer: (7)

Chemistry

SECTION-A

31. Identify the correct statements about alkali metals.

(A) The order of standard reduction potential (M + ∣M) for alkali metal ions is Na>Rb>Li.

(B) CsI is highly soluble in water.

(D) Potassium dissolved in concentrated liquid ammonia is blue in colour and paramagnetic.

(E) All the alkali metal hydrides are ionic solids.

Choose the correct answer from the options given below:

(1) C and E only

(2) A, B and E only

(3) A, B, D only

(4) A and E only

Answer: (4)

32. Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: Beryllium has less negative value of reduction potential compared to the other alkaline earth metals.

Reason : Beryllium has large hydration energy due to small size of Be2+ but relatively large value of atomization enthalpy

In the light of the above statements, choose the most appropriate answer from the options given below

(1) A is not correct but R is correct

(2) A is correct but 𝑅 is not correct

(3) Both A and R are correct and R is the correct explanation of A

(4) Both A and R are correct but R is NOT the correct explanation of A

Answer: (3)

33. A student has studied the decomposition of a gas AB₃ at 25∘ He obtained the following data.

The order of the reaction is

(1) 0(zero)

(2) 0.5

(3) 1

(4) 2

Answer: (2)

34. K₂Cr₂O₇ paper acidified with dilute H2SO4 turns green when exposed to

(1) Carbon dioxide

(2) Sulphur trioxide

(3) Sulphur dioxide

(4) Hydrogen sulphide

Answer: (3)

35. Which will undergo deprotonation most readily in basic medium?

(1) c only

(2) a only

(3) Both a and c

(4) b only

Answer: (2)

36. The hybridization and magnetic behaviour of cobalt ion in [Co(NH₃)₆]³⁺ complex, respectively is

(1) d²sp³ and paramagnetic

(2) sp³d² and diamagnetic

(3) d²sp³ and diamagnetic

(4) sp³d² and paramagnetic

Answer: (3)

37. Given below are two statements:

In the light of the above statements, choose the correct answer from the options given below :

(1) Statement I is false but Statement II is true

(2) Statement I is true but Statement II is false

(3) Both Statement I and Statement II are true

(4) Both Statement I and Statement II are false

Answer: (2)

38. Which of the following cannot be explained by crystal field theory?

(1) The order of spectrochemical series

(2) Stability of metal complexes

(3) Magnetic properties of transition metal complexes

(4) Colour of metal complexes

Answer: (1)

39. The number of s-electrons present in an ion with 55 protons in its unipositive state is

(1) 8

(2) 10

(3) 9

(4) 12

Answer: (2)

40. Which one amongst the following are good oxidizing agents?

(A) Sm²⁺ (B) Ce²⁺ (C) Ce⁴⁺ (D) Tb⁴⁺

Choose the most appropriate answer from the options given below:

(1) D only

(2) C only

(3) C and D only

(4) A and B only

Answer: (3)

41. Which one amongst the following are good oxidizing agents?

Answer: (1)

42. Match List I with List II

Choose the correct answer from the options given below:

(1) A-I, B-III, C-II, D-IV

(2) A-IV, B-III, C-II, D-I

(3) A-I, B-II, C-III, D-IV

(4)A-II, B-I, C-III, D-IV

Answer: (3)

43. Find out the major products from the following reaction

Answer: (2)

44. Given below are two statements, one is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑

Assertion : Benzene is more stable than hypothetical cyclohexatriene

Reason : The delocalized π electron cloud is attracted more strongly by nuclei of carbon atoms.

In the light of the above statements, choose the correct answer from the options given below:

(1) Both A and R are correct and R is the correct explanation of A

(2) Both A and R are correct but R is NOT the correct explanation of A

(3) A is false but R is true

(4) A is true but 𝑅 is false

Answer: (1)

45. In which of the following reactions the hydrogen peroxide acts as a reducing agent?

(1) PbS + 4H₂O₂ → PbSO₄ + 4H₂O

(2) Mn²⁺ + H₂O₂ → Mn⁴⁺ + 2OH⁻

(3) HOCl + H₂O₂ → H₃O⁺ + Cl⁻ + O₂

(4) 2Fe2+ + H2O2 → 2Fe3+ + 2OH⁻

Answer: (3)

46. Given below are two statements:

Statement I : Pure Aniline and other arylamines are usually colourless.

Statement II : Arylamines get coloured on storage due to atmospheric reduction

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Both Statement I and Statement II are incorrect

(2) Statement I is incorrect but Statement II is correct

(3) Statement I is correct but Statement II is incorrect

(4) Both Statement I and Statement II are correct

Answer: (3)

47. Correct statement is:

(1) An average human being consumes nearly 15 times more air than food

(2) An average human being consumes 100 times more air than food

(3) An average human being consumes equal amount of food and air

(4) An average human being consumes more food than air

Answer: (1)

48. What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : N₂; N₂⁺ ; O₂; O₂⁺?

(1) 2, 1, 0, 1

(2) 0, 1, 0, 1

(3) 0, 1, 0, 1

(4) 2, 1, 2, 1

Answer: (2)

49. The metal which is extracted by oxidation and subsequent reduction from its ore is:

(1) Ag

(2) Fe

(3) Cu

(4) Al

Answer: (1)

50. Choose the correct colour of the product for the following reaction.

(1) White

(2) Red

(3) Blue

(4) Yellow

Answer: (2)

SECTION-B

51. Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is ____________.

(A) T₄ > T₃ > T₂ > T₁

(B) The black body consists of particles performing simple harmonic motion.

(E) The given spectrum could be explained using quantisation of energy.

Answer: (2)

52. The number of units, which are used to express concentration of solutions from the following is______ Mass percent, Mole, Mole fraction, Molarity, ppm, Molality

Answer: (5)

53. The number of statement/s which are the characteristics of physisorption is______________

(A) It is highly specific in nature

(B) Enthalpy of adsorption is high

(D) It results into unimolecular layer

(E) No activation energy is needed

Answer: (2)

54. Sum of π – bonds present in peroxodisulphuric acid and pyrosulphuric acid is:

Answer: (8)

55. If the pKa of lactic acid is 5, then the pH of 0.005M calcium lactate solution at 25°C is _________ × 10^–1 (Nearest integer)

Answer: (85)

56. The total pressure observed by mixing two liquids A and B is 350 mmHg when their mole fractions are 0.7 and 0.3 respectively. The total pressure become 410 mmHg if the mole fractions are changed to 0.2 and 0.8 respectively for A and B. The vapour pressure of pure A is________ mm Hg. (Nearest integer) Consider the liquids and solutions behave ideally.

Answer: (314)

57. The number of statement/s, which are correct with respect to the compression of carbon dioxide from point (a) in the Andrews isotherm from the following is _________

(A) Carbon dioxide remains as a gas upto point (b)

(B) Liquid carbon dioxide appears at point (c)

(D) As the volume decreases from (b) to (c), the amount of liquid decreases

Answer: (4)

58. Maximum number of isomeric monochloro derivatives which can be obtained from 2, 2, 5, 5 tetramethylhexane by chlorination is ______

Answer: (3)

59. Total number of tripeptides possible by mixing of valine and proline is ________

Answer: (8)

60. One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is _______ J (nearest integer)

Answer: (6)

Mathematics

SECTION-A

61. If, f(x) = x³ – x²f ꞌ (1) + xf ꞌꞌ(2) – f ꞌꞌ(3), x ∈ ℝ then

(1) f(1) + f(2) + f(3) = f(0)

(2) 2f(0) − f(1) + f(3) = f(2)

(3) 3f(1) + f(2) = f(3)

(4) f(3) − f(2)= f(1)

Answer: (2)

62. If the system of equations

X + 2y + 3z = 3

4x + 3y – 4z = 4

8x + 4y – λz = 9 + μ

has infinitely many solutions, then the ordered pair (λ, μ) is equal to :

(1) (−72/5, 21/5)

(2) (−72/5, −21/5)

(3) (72/5, −21/5)

(4) (72/5, 21/5)

Answer: (3)

63. If, then then

(1) 1011

(2) 2010

(3) 1010

(4) 2011

Answer: (1)

64. Let Let be parallel to be perpendicular to then the value of is

(1) 7

(2) 9

(3) 6

(4) 11

Answer: (1)

65. Let y = y(x) be the solution of the differential equation (x² − 3y²)dx + 3xydy = 0, y(1) = 1. Then 6y²(e) is equal to

(1) 2e²

(2) 3e²

(3) e²

(4)

Answer: (1)

66. The locus of the mid points of the chords of the circle C₁ : (x − 4)² + (y − 5)² = 4 which subtend an angle θ₁ at the centre of the circle C₁, is a circle of radius r_i. If and then θ₂ is equal to

(1) π/4

(2) π/2

(3) π/6

(4) 3π/4

Answer: (2)

67. The number of real solutions of the equation is

(1) 0

(2) 3

(3) 4

(4) 2

Answer: (1)

68. Let A be a 3×3 matrix such that |adj⁡(adj⁡(adj⁡A))|=12⁴ Then |A⁻¹adj⁡A| is equal to

(1) √6

(2) 2√3

(3) 12

(4) 1

Answer: (2)

69. is equal to

(1) 2π

(2) π/6

(3) π/3

(4) π/2

Answer: (1)

70. The number of square matrices of order 5 with entries form the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is

(1) 125

(2) 225

(3) 150

(4) 120

Answer: (4)

71. If (³⁰C₁)² + 2(³⁰C₂)² + 3(³⁰C₃)² + … + 30(³⁰C₃₀)² then α is equal to :

(1) 30

(2) 10

(3) 60

(4) 15

Answer: (4)

72. Let the plane containing the line of intersection of the planes P1: x + (λ + 4)y + z = 1 and P2: 2x + y+ z = 2 pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of the point (2λ, λ ,−λ) from the plane P2 is

(1) 4√6

(2) 3√6

(3) 5√6

(4) 2√6

Answer: (2)

73. Let f(x) be a function such that and f(x + y) = f(x) ∙ f(y) for all x, y ∈ If f(1) = 3 and then the value of n is

(1) 9

(2) 6

(3) 8

(4) 7

Answer: (4)

74. Let the six numbers a₁, a₂, a₃, a₄, a₅, a₆, be in A.P. and a₁ + a₃ = 10. If the mean of these six numbers is 19/2 and their variance is σ², then 8σ² is equal to :

(1) 210

(2) 220

(3) 200

(4) 105

Answer: (1)

75. The equations of the sides AB and AC of a triangle ABC are (λ + 1) x + λy = 4 and λx + (1 − λ) y + λ = 0 respectively. Its vertex A is on the y – axis and its orthocentre is (1,2). The length of the tangent from the point C to the part of the parabola y² = 6x in the first quadrant is :

(1) 4

(2) 2

(3) √6

(4) 2√2

Answer: (4)

76. Let p and q be two statements. Then ∼(p ∧ (p ⇒ ∼q)) is equivalent to

(1) p ∨ (p ∧ q)

(2) p ∨ (p ∧ (∼q))

(3) (∼p) ∨ q

(4) p ∨ ((∼p) ∧ q)

Answer: (3)

77. The set of all values of a for which lim_x_→_a([x – 5] – [2x + 2]) = 0, where [∝] denotes the greatest integer less than or equal to α is equal to

(1) [−7.5, −6.5)

(2) [−7.5, −6.5]

(3) (−7.5, −6.5]

(4) (−7.5, −6.5)

Answer: (4)

78. If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to the planes x + 2y + z = 0 and 3y – z = 3 is (α, β, γ), then α + β + γ is equal to

(1) 3

(2) 1

(3) −1

(4) 5

Answer: (4)

79. The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition, is

(1) 168

(2) 220

(3) 120

(4) 48

Answer: (1)

80. The value of is

Answer: (1)

SECTION-B

81. If the shortest distance between the lines and is 6, then the square of sum of all possible values of λ is

Answer: (384)

82. Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y² = λx with one vertex at the vertex of the parabola, is

Answer: (432)

83. Let S ={θ ∈ [0, 2π):tan⁡(π cos⁡θ) + tan⁡(π sin θ) = 0}.

Then is equal to

Answer: (2)

84. If then value of n is

Answer: (5)

85. Let the sum of the coefficients of the first three terms in the expansion of be 376. Then the coefficient of x⁴ is

Answer: (405)

86. The equations of the sides AB, BC and CA of a triangle ABC are : 2x + y = 0, x + py = 21a, (a ≠ 0) and x – y = 3 respectively. Let P(2, a) be the centroid of △ Then (BC)² is equal to

Answer: (122)

87. Let is equal to

Answer: (8)

88. The minimum number of elements that must be added to the relation R={(a, b),(b, c),(b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is

Answer: (13)

89. If the area of the region bounded by the curves y² − 2y = −x, x + y = 0 is A, then 8 A is equal to

Answer: (36)

90. Let f be a differentiable function defined on [0, π/2] such that f(x) > 0 and is equal to

Answer: (27)

JEE Main Session 1 1st February 2023 Shift 1 Question Paper and Answer Key

May 10, 2023May 9, 2023 by suresh84

JEE MAIN 1st February 2023 Shift 1

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 ms⁻¹. Neglecting the air resistance, the speed with which the stone hits the ground will be __ ms⁻¹ (given, g = 10 ms⁻²).

(1) 15

(2) 20

(3) 30

(4) 25

Answer: (1)

2. Let σ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region E_I, E_II and E_III are:

Answer: (3)

3. A mercury drop of radius 10⁻³ m is broken into 125 equal size droplets. Surface tension of mercury is 0.45 Nm⁻¹. The gain in surface energy is:

(1) 28 × 10⁻⁵ J

(2) 17.5 × 10⁻⁵ J

(3) 5 × 10⁻⁵ J

(4) 2.26 × 10⁻⁵ J

Answer: (4)

4. If earth has a mass nine times and radius twice to that of a planet P. Then will be the minimum velocity required by a rocket to pull out of gravitational force of P, where υ_e is escape velocity on earth. The value of x is

(1) 1

(2) 3

(3) 18

(4) 2

Answer: (4)

5. A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, γ = 3/2) :

(1)

(2) W = RT[2 − √2]

(3) W = TR[√2 – 2]

(4)

Answer: (2)

6. represents the equation of state of some gases. Where P is the pressure, 𝑉 is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of b²/a, will be:

(1) Compressibility

(2) Energy density

(3) Modulus of rigidity

(4) Bulk modulus

Answer: (1)

7. The equivalent resistance between A and B of the network shown in figure:

(1)

(2) 21R

(3) 14R

(4)

Answer: (1)

8. Match List I with List II:

Choose the correct answer from the options given below:

(1) A-IV, B-III, C-I, D-II

(2) A-IV, B-II, C-I, D-III

(3) A-II, B-IV, C-I, D-III

(4) A-II, B-I, C-III, D-IV

Answer: (3)

9. An object moves with speed 𝑣₁, 𝑣₂ and 𝑣₃ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

Answer: (3)

10. ʹn’ polarizing sheets are arranged such that each makes an angle 45° with the preceding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be I/64. The value of n will be:

(1) 4

(2) 3

(3) 5

(4) 6

Answer: (4)

11. Match List I with List II:

Choose the correct answer from the options given below:

(1) A-I, B-III, C-IV, D-II

(2) A-IV, B-I, C-II, D-III

(3) A-IV, B-III, C-II, D-I

(4) A-I, B-II, C-III, D-IV

Answer: (2)

12. A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of 𝜆. An alpha particle having certain kinetic energy has the same de-Brogle wavelength 𝜆. The ratio of kinetic energy of proton and that of alpha particle is:

(1) 2 : 1

(2) 1 : 2

(3) 1 : 4

(4) 4 : 1

Answer: (3)

13. A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, g = 10 ms⁻²):

(1) 0.60

(2) 0.25

(3) 0.75

(4) 0.50

Answer: (4)

14. Given below are two statements:

Statement I: Acceleration due to gravity is different at different places on the surface of earth.

Statement II: Acceleration due to gravity increases as we go down below the earth’s surface.

In the light of the above statements, choose the correct answer from the options given below

(1) Statement I is false but Statement II is true

(2) Statement I is true but Statement II is false

(3) Both Statement I and Statement II are false

(4) Both Statement I and Statement II are true

Answer: (2)

15. Which of the following frequencies does not belong to FM broadcast.

(1) 64MHz

(2) 89MHz

(3) 99MHz

(4) 106MHz

Answer: (1)

16. The mass of proton, neutron and helium nucleus are respectively 1.0073u, 1.0087u and 4.0015u. The binding energy of helium nucleus is:

(1) 28.4MeV

(2) 56.8 MeV

(3) 14.2 MeV

(4) 7.1 MeV

Answer: (1)

17. A steel wire with mass per unit length 7.0 × 10⁻³ kg m⁻¹ is under tension of 70 N. The speed of transverse waves in the wire will be:

(1) 100 m/s

(2) 10 m/s

(3) 50 m/s

(4) 200 πm/s

Answer: (1)

18. Match List I with List II:

Choose the correct answer from the options given below:

(1) A-II, B-III, C-I, D-IV

(2) A-I, B-II, C-III, D-IV

(3) A-II, B-I, C-III, D-IV

(4) A-III, B-I, C-II, D-IV

Answer: (1)

19. Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

Answer: (2)

20. The average kinetic energy of a molecule of the gas is

(1) proportional to absolute temperature

(2) proportional to pressure

(3) proportional to volume

(4) dependent on the nature of the gas

Answer: (1)

SECTION-B

21. A small particle moves to position from its initial position under the action of force The value of work done will be ______ J.

Answer: (40)

22. A certain pressure ‘P’ is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is 3/x.

The value of x is _______.

Answer: (1)

23. A light of energy 12.75eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is The value of x is _______ (use h = 4.14 × 10⁻¹⁵ eVs, c = 3 × 10⁸ ms⁻¹).

Answer: (828)

24. A charge particle of 2μC accelerated by a potential difference of 100 V enters a region of uniform magnetic field of magnitude 4mT at right angle to the direction of field. The charge particle completes semicircle of radius 3 cm inside magnetic field. The mass of the charge particle is ______ × 10⁻¹⁸

Answer: (144)

25. The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ________ cm.

Answer: (2)

26. In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5 V is found to be 60 cm. If this cell is replaced by another cell of emf E, the length-of null point increases by 40 cm. The value of E is The value of x is ________.

Answer: (25)

27. A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be x/3 cm. The value of x is ______.

Answer: (32)

28. A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ms⁻¹.

(Given g=10 ms⁻² )

Answer: (2)

29. A series LCR circuit is connected to an ac source of 220 V,50 Hz. The circuit contain a resistance R = 100Ω and an inductor of inductive reactance X_L= 79.6 Ω. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ________ μ

Answer: (40)

30. Two equal positive point charges are separated by a distance 2a. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge q₀ becomes maximum is a/√ The value of x is ________.

Answer: (2)

Chemistry

SECTION-A

31. A solution of FeCl₃ when treated with K₄[Fe(CN)₆] gives a prussian blue precipitate due to the formation of

(1) K[Fe₂(CN)₆]

(2) Fe₄[Fe(CN)₆]₃

(3) Fe[Fe(CN)₆]

(4) Fe₃[Fe(CN)₆]₂

Answer: (2)

32. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: Hydrogen is an environment friendly fuel.

Reason R: Atomic number of hydrogen is 1 and it is a very light element.

In the light of the above statements, choose the correct answer from the options given below

(1) A is true but 𝐑 is false

(2) 𝐀 is false but 𝐑 is true

(3) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(4) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

Answer: (4)

33. Resonance in carbonate ion (CO₃²⁻) is

Which of the following is true?

(1) All these structures are in dynamic equilibrium with each other.

(2) It is possible to identify each structure individually by some physical or chemical method.

(3) Each structure exists for equal amount of time.

(4) CO₃²⁻ has a single structure i.e., resonance hybrid of the above three structures.

Answer: (4)

34. Match List I with List II

Choose the correct answer from the options given below:

(1) (A) −IV,(B)−II,(C)−I,(D)−III

(2) (A) −II,(B)−I,(C)−III,(D) –IV

(3) (A) – III, (B) – I, (C) – II, (D) – IV

(4) (A) – II, (B) −IV,(C)−I,(D) −III

Answer: (3)

35. Identify the incorrect option from the following:

Answer: (4)

36. But-2-yne is reacted separately with one mole of Hydrogen as shown below:

(A) A is more soluble than

(B) B. The boiling point & melting point of A are higher and lower than B respectively.

(D) Br₂ adds easily to B than A.

Identify the incorrect statements from the options given below:

Answer: (2)

37. In the following reaction, ‘ A ‘ is

Answer: (3)

38. Highest oxidation state of Mn is exhibited in Mn₂O₇. The correct statements about Mn₂O₇ are

(A) Mn is tetrahedrally surrounded by oxygen atoms.

(B) Mn is octahedrally surrounded by oxygen atoms.

(D) Contains Mn-Mn bond.

Choose the correct answer from the options given below:

(1) A and C only

(2) A and D only

(3) B and C only

(4) B and D only

Answer: (1)

39. Match List I with List II

Choose the correct answer from the options given below:

(1) (A) – III, (B) – IV, (C) – II, (D) – I

(2) (A) – III, (B) – II, (C) – IV, (D) – I

(3) (A) – I, (B) – IV, (C) – II, (D) – III

(4) (A) −II,(B) −IV, (C) – I, (D) – III

Answer: (4)

40. The correct representation in six membered pyranose form for the following sugar [X] is

Answer: (2)

41. Which of the following complex will show largest splitting of d-orbitals ?

(1) [F_eF₆]³⁻

(2) [Fe(C₂O₄)₃]³⁻

(3) [Fe(CN)₆]³⁻

(4) [Fe(NH₃)₆]³⁺

Answer: (3)

42. Which of the following are the example of double salt?

(A) FeSO₄ ⋅ (NH₄)₂SO₄ ⋅ 6H₂O

(B) CuSO₄, 4NH₃H₂O

(D) Fe(CN)₂ . 4KCN

Choose the correct answer

(1) B and D only

(2) A and C only

(3) A and B only

(4) A, B and D only

Answer: (1)

43. Decreasing order of dehydration of the following alcohols is

(1) b > a > d > c

(2) a > d > b > c

(3) d > b > c > a

(4) b > d > c >a

Answer: (4)

44. Given below are two statements:

Statement I: Chlorine can easily combine with oxygen to form oxides; and the product has a tendency to explode.

Statement II: Chemical reactivity of an element can be determined by its reaction with oxygen and halogens.

In the light of the above statements, choose the correct answer from the options given below

(1) Both the Statements I and II are true

(2) Both the Statements I and II are false

(3) Statement I is false but Statement II is true

(4) Statement I is true but Statement II is false

Answer: (1)

45. Choose the correct statement(s):

(A) Beryllium oxide is purely acidic in nature.

(B) Beryllium carbonate is kept in the atmosphere of CO₂.

(D) Beryllium shows anomalous behavior. Choose the correct answer from the options given below:

(1) B, C and D only

(2) A only

(3) A, B and C only

(4) A and B only

Answer: (1)

46. Which of the following represents the lattice structure of A₉₅O containing A²⁺, A³⁺ and O²⁻ ions? ⊙ A²⁺ ⊙ A³⁺ ⊙ O²⁻

(1) A only

(2) B and C only

(3) A and B only

(4) B only

Answer: (1)

47. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: In an Ellingham diagram, the oxidation of carbon to carbon monoxide shows a negative slope with respect to temperature.

Reason R: CO tends to get decomposed at higher temperature.

In the light of the above statements, choose the correct answer from the options given below

(1) Both 𝐀 and 𝐑 are correct but 𝐑 is NOT the correct explanation of 𝐀

(2) Both 𝐀 and 𝐑 are correct and 𝐑 is the correct explanation of 𝐀

(3) A is correct but 𝐑 is not correct

(4) A is not correct but 𝐑 is correct

Answer: (3)

48. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: Amongst He, Ne, Ar and Kr; 1 g of activated charcoal adsorbs more of Kr.

Reason R: The critical volume V_c ( cm³ mol⁻¹) and critical pressure P_c (atm) is highest for Krypton but the compressibility factor at critical point Z_c is lowest for Krypton.

In the light of the above statements, choose the correct answer from the options given below

(1) 𝐀 is true but 𝐑 is false

(2) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(3) A is false but 𝐑 is true

(4) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

Answer: (1)

49. Match List I with List II

Choose the correct answer from the options given below:

(1) (A) − III,(B) − IV,(C) − I,(D) − II

(2) (A) −II,(B) −I,(C) −III, (D) – IV

(3) (A) −III,(B)−IV,(C)−II,(D)−I

(4) (A) −I,(B) −II,(C) −III,(D) −IV

Answer: (2)

50. How can photochemical smog be controlled?

(1) By using catalytic convertors in the automobiles/industry.

(2) By complete combustion of fuel.

(3) By using tall chimneys.

(4) By using catalyst.

Answer: (1)

SECTION-B

51. (i) X(g) ⇌ Y(g) + Z(g) K_p1 = 3

(ii) A(g) ⇌ 2B(g) K_p2 = 1

If the degree of dissociation and initial concentration of both the reactants X(g) and A(g) are equal, then the ratio of the total pressure at equilibrium (p₁/p₂) is equal to x : 1. The value of x is ______ (Nearest integer)

Answer: (12)

52. Electrons in a cathode ray tube have been emitted with a velocity of 1000 ms⁻¹. The number of following statements which is/are true about the emitted radiation is

Given : h = 6 × 10⁻³⁴ Js, m_e = 9 × 10⁻³¹ kg.

(A) The deBroglie wavelength of the electron emitted is 666.67 nm.

(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube.

(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

Answer: (2)

53. A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of both of them to be same? _____ min.

Answer: (15)

54. Sum of oxidation states of bromine in bromic acid and perbromic acid is

Answer: (12)

55. 25 mL of an aqueous solution of KCl was found to require 20 mL of 1M AgNO₃ solution when titrated using K₂CrO₄ as an indicator. What is the depression in freezing point of KCl solutions of the given concentration? ______ (Nearest integer).

(Given : K_f = 2.0 K kg mol⁻¹)

Assume (1) 100% ionization and

(2) density of the aqueous solution as 1 g mL⁻¹

Answer: (3)

56. At 25∘C, the enthalpy of the following processes are given:

What would be the value of X for the following reaction? (Nearest integer)

H₂O(g) → H(g) + OH(g)∆H° = XkJmol⁻¹

Answer: (499)

57. At what pH, given half cell MnO₄⁻(0.1M) ∣ Mn²⁺(0.001M) will have electrode potential of 1.282 V ? (Nearest Integer)

Answer: (3)

58. The density of 3M solution of NaCl is 1.0 g mL⁻¹. Molality of the solution is ____ × 10⁻² (Nearest integer).

Given: Molar mass of Na and Cl is 23 and 35.5 g mol⁻¹ respectively.

Answer: (364)

59. Number of isomeric compounds with molecular formula C₉H₁₀O which (i) do not dissolve in NaOH (ii)do not dissolve in HCl.(iii) do not give orange precipitate with 2,4DNP (iv) on hydrogenation give identical compound with molecular formula C₉H₁₂O is

Answer: (2)

60. The total number of chiral compound/s from the following is

Answer: (2)

Mathematics

SECTION-A

61. f y = y(x) is the solution curve of the differential equation y(0) = 1, then y(π/6) is equal to

Answer: (2)

62. Let R be a relation on ℝ, given by R = {(a, b) : 3a – 3b + √7 is an irrational number}.

Then R is

(1) an equivalence relation

(2) reflexive and symmetric but not transitive

(3) reflexive but neither symmetric nor transitive

(4) reflexive and transitive but not symmetric

Answer: (3)

63. For a triangle ABC, the value of cos⁡2A + cos⁡2B + cos 2C is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?

(1) perimeter of ∆ ABC is 18√3

(2) sin 2A + sin 2B + sin 2C = sin A + sin B + sin C

(3)

(4) area of ∆ ABC is 27√3/2

Answer: (4)

64. Let S be the set of all solutions of the equation Then is equal to

(1) π – 2sin⁻¹ (√3/4)

(2) π – sin⁻¹ (√3/4)

(3) −2π/3

(4) 0

Answer: (*)

65. Let S denote the set of all real values of 𝜆 such that the system of equations

λx + y + z = 1

x + λy + z = 1

x + y + λz = 1

is inconsistent, then is equal to

(1) 4

(2) 12

(3) 6

(4) 2

Answer: (3)

66. In a binomial distribution B(n, p), the sum and the product of the mean and the variance are 5 and 6 respectively, then 6(n + p – q) is equal to

(1) 52

(2) 50

(3) 51

(4) 53

Answer: (1)

67. The combined equation of the two lines ax + by + c = 0 and aʹx + bʹy + cʹ = 0 can be written as (ax + by + c) (aʹx + bʹy + cʹ) = 0.

The equation of the angle bisectors of the lines represented by the equation 2x² + xy – 3y² = 0 is

(1) x² – y² – 10xy = 0

(2) x² – y² + 10xy = 0

(3) 3x² + 5xy + 2y² = 0

(4) 3x² + xy – 2y² = 0

Answer: (1)

68. The area enclosed by the closed curve C given by the differential equation y(1) = 0 is 4π.

Let P and Q be the points of intersection of the curve C and the 𝑦-axis. If normals at 𝑃 and Q on the curve C intersect 𝑥-axis at points R and S respectively, then the length of the line segment RS is

(1) 2

(2) 4√3/3

(3) 2√3

(4) 2√3/3

Answer: (2)

69. The value of is :

(1) 2⁵⁰/51!

(2) 2⁵¹/50!

(3) 2⁵⁰/50!

(4) 2⁵¹/51!

Answer: (1)

70. The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5 then the sum of cubes of the remaining two observations is

(1) 1216

(2) 1072

(3) 1456

(4) 1792

Answer: (2)

71. The sum to 10 terms of the series is

(1) 55/111

(2) 56/111

(3) 58/111

(4) 59/111

Answer: (1)

72. The shortest distance between the lines and is

(1) 5√3

(2) 7√3

(3) 6√3

(4) 4√3

Answer: (3)

73. is equal to

(1) log_e 2

(2) log_e (3/2)

(3) log_e (2/3)

(4) 0

Answer: (1)

74. Let the image of the point P(2, −1, 3) in the plane x + 2y – z = 0 be Q. Then the distance of the plane 3x + 2y + z + 29 = 0 from the point Q is

(1) 24√2/7

(2) 2√14

(3) 3√14

(4) 22√2/7

Answer: (3)

75. Let f(x) = 2x + tan⁻¹ x and Then

(1) min fʹ(x) = 1 + maxgʹ(x)

(2) max f(x) > max g(x)

(3) there exist 0 < x₁ < x₂ < 3 such that f(x) < g(x), ∀x ∈ (x₁, x₂)

(4) there exists

Answer: (2)

76. If the orthocentre of the triangle, whose vertices are (1, 2) (2, 3) and (3, 1) is (α, β), then the quadratic equation whose roots are α + 4β and 4α + β, is

(1) x² – 20x + 99 = 0

(2) x² – 19x + 90 = 0

(3) x² – 22x + 120 = 0

(4) x² – 18x + 80 = 0

Answer: (1)

77. Let S = {x: x ∈ ℝ and

Then n(S) is equal to

(1) 4

(2) 0

(3) 6

(4) 2

Answer: (1)

78. If the center and radius of the circle are respectively (α, β) and γ. Then 3(α + β + γ) is equal to

(1) 11

(2) 12

(3) 9

(4) 10

Answer: (2)

79. Let If α and β respectively are the maximum and the minimum values of f, then

(1) α² + β² = 9/2

(2) β² − 2√α = 19/4

(3) α² – β² = 4√3

(4) β² + 2√α = 19/4

Answer: (2)

80. The negation of the expression q ∨ ((∼q) ∧ p) is equivalent to

(1) (~p) ∨ (~q)

(2) p ∧ (~q)

(3) (~p) ∨ q

(4) (~p) ∧ (~q)

Answer: (4)

SECTION B

81. Let and be a vector such that If the minimum value of the scalar triple product and where m and n are coprime natural numbers, then m + n is equal to

Answer: (3501)

82. The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is

Answer: (50400)

83. The remainder, when 19²⁰⁰ + 23²⁰⁰ is divided by 49 is _____

Answer: (29)

84. The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is

Answer: (514)

85. Let f : ℝ → ℝ be a differentiable function such that If f(0) = e⁻², then 2f(0) – f(2) is equal to

Answer: (1)

86. If f(x) = x² + gʹ(1)x + gʺ(2) and g(x) = f(1)x² + xfʹ(x) + fʺ(x), then the value of f(4) – g(4) is equal to

Answer: (14)

87. Let A be the area bounded by the curve y = x|x − 3|, the x-axis and the ordinates x = −1 and x = 2. Then 12A is equal to

Answer: (62)

88. If where l, m, n ∈ ℕ, m and n are coprime then l + m + n is equal to

Answer: (63)

89. Let a₁ = 8, a₂, a₃, …, a_n be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170, then the product of its middle two terms is

Answer: (754)

90. A(2, 6, 2), B(−4, 0, λ), C(2, 3, −1) and D(4, 5, 0), |λ| ≤ 5 are the vertices of a quadrilateral ABCD. If its area is 18 square units, then 5 − 6λ is equal to

Answer: (11)

JEE Main Session 1 31st January 2023 Shift 1 Question Paper and Answer Key

May 10, 2023May 9, 2023 by suresh84

JEE MAIN 31^th January 2023 Shift 1

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A/2, the kinetic energy of the block is :

(1) 18.75 J

(2) 9.75 J

(3) 37.5 J

(4) 12.5 J

Answer: (1)

2. The drift velocity of electrons for a conductor connected in an electrical circuit is V_d. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

(1) V_d

(2) V_d/4

(3) 2V_d

(4) V_d/2

Answer: (1)

3. The initial speed of a projectile fired from ground is u. At the highest point during its motion, the speed of projectile is The time of flight of the projectile is :

(1) 2u/g

(2) u/2g

(3) √3u/g

(4) u/g

Answer: (4)

4. The correct relation between γ = c_p/c_v and temperature T is :

(1) γαT⁰

(2) γαT

(3)

(4)

Answer: (1)

5. The effect of increase in temperature on the number of electrons in conduction band (n_e) and resistance of a semiconductor will be as:

(1) Both n_e and resistance increase

(2) Both n_e and resistance decrease

(3) n_e decreases, resistance increases

(4) n_e increases, resistance decreases

Answer: (4)

6. The amplitude of 15sin⁡(1000πt) is modulated by 10sin⁡(4πt) signal. The amplitude modulated signal contains frequency (ies) of

(A) 500 Hz (B) 2 Hz (C) 250 Hz (D) 498 Hz (E) 502 Hz

Choose the correct answer from the options given below:

(1) A only

(2) B only

(3) A and B only

(4) A, D and E only

Answer: (4)

7. Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarized light is I₀ then intensity of transmitted light after passing through polaroid B will be:

(1) I₀/4

(2) I₀/2

(3) Zero

(4) I₀/8

Answer: (4)

8. As shown in figure, a 70 kg garden roller is pushed with a force of at an angle of 30° with horizontal. The normal reaction on the roller is

(Given g = 10 ms⁻²)

(1) 800√2 N

(2) 200√3 N

(3) 600 N

(4) 800 N

Answer: (4)

9. If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop. In the process the released surface energy is- (Take π = 22/7)

(1) 8.8 × 10⁻⁵ J

(2) 7.92 × 10⁻⁴ J

(3) 7.92 × 10⁻⁶ J

(4) 9.68 × 10⁻⁴ J

Answer: (2)

10. The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

(1) −4.5 J

(2) zero

(3) 4.5 J

(4) 6 J

Answer: (C)

11. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason 𝐑

Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction.

Reason R: Davisson Germer Experimentally verified the wave nature of electrons.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Both A and R are correct and R is the correct explanation of A

(2) A is not correct but R is correct

(3) A is correct but R is not correct

(4) Both A and R are correct but R is Not the correct explanation of A

Answer: (1)

12. A free neutron decays into a proton but a free proton does not decay into neutron. This is because

(1) proton is a charged particle

(2) neutron is an uncharged particle

(3) neutron is a composite particle made of a proton and an electron

(4) neutron has larger rest mass than proton

Answer: (4)

13. Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following Assume negligible air friction}

(1) Insulating ball will reach the earth’s surface earlier than the metal ball

(2) Metal ball will reach the earth’s surface earlier than the insulating ball

(3) Both will reach the earth’s surface simultaneously.

(4) Time taken by them to reach the earth’s surface will be independent of the properties of their materials

Answer: (1)

14. If R, X_L, and X_C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

(1) R/X_LX_C

(2)

(3)

(4) RX_LX_C

Answer: (2)

15. 100 balls each of mass m moving with speed ν simultaneously strike a wall normally and reflected back with same speed, in time t sec. The total force exerted by the balls on the wall is

(1) 100mν/t

(2) 200mνt

(3) mν/100t

(4) 200mν/t

Answer: (4)

16. If a source of electromagnetic radiation having power 15 kW produces 10¹⁶ photons per second, the radiation belongs to a part of spectrum is.

(Take Planck constant h=6 × 10⁻³⁴Js )

(1) Micro waves

(2) Ultraviolet rays

(3) Gamma rays

(4) Radio waves

Answer: (3)

17. Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

Answer: (1)

18. A bar magnet with a magnetic moment 5.0 Am² is placed in parallel position relative to a magnetic field of 0.4 T. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _______.

(1) 1 J

(2) 4 J

(3) 2 J

(4) zero

Answer: (2)

19. At a certain depth “d ” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400 km ). The depth d is equal to

(1) 4800 km

(2) 2560 km

(3) 640 km

(4) 5260 km

Answer: (A)

20. A rod with circular cross-section area 2 cm² and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is 4π × 10⁻⁶ The relative permeability of the rod is (Given : Permeability of vacuum μ₀ = 4π × 10⁻⁷NA⁻²)

(1) 5/16

(2) 12.5

(3) 125

(4) 32/5

Answer: (3)

SECTION-B

21. In a medium the speed of light wave decreases to 0.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is x : 1. The value of x is (Given speed of light in free space =3 × 10⁸ ms⁻¹ and for the given medium μ_r = 1)

Answer: (5)

22. A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10⁻³ The speed of the centre of mass of the sphere is _________ cms⁻¹

Answer: (10)

23. A lift of mass M = 500 kg is descending with speed of 2 ms⁻¹. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2 ms⁻². The kinetic energy of the lift at the end of fall through to a distance of 6 m will be _______ kJ.

Answer: (7)

24. In the figure given below, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant (K = 2 N m⁻¹). If the block is horizontally displaced through ‘X’ m then the number of complete oscillations it will make in 14π seconds will be ________.

Answer: (20)

25. An inductor of 0.5mH, a capacitor of 20𝜇F and resistance of 20Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is √x The value of x is-

Answer: (242)

26. The speed of a swimmer is 4 kmh⁻¹ in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km, he reaches a point 750 m down the stream on the opposite bank. The speed of the river water is _______ kmh⁻¹.

Answer: (3)

27. For hydrogen atom, 𝜆₁ and 𝜆₂ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of 𝜆₁ and 𝜆₂ is x/32. The value of x is

Answer: (27)

28. Two identical cells, when connected either in parallel or in series gives same current in an external resistance 5Ω. The internal resistance of each cell will be ______ Ω.

Answer: (5)

29. Expression for an electric field is given by The electric flux through the cube of side 20 cm when placed in electric field (as shown in the figure) is _____ Vcm.

Answer: (640)

30. A thin rod having a length of 1 m and area of cross-section 3 × 10⁻⁶ m² is suspended vertically from one end. The rod is cooled from 210°C to 160° After cooling, a mass M is attached at the lower end of the rod such that the length of rod again becomes 1 m. Young’s modulus and coefficient of linear expansion of the rod are 2 × 10¹¹ Nm⁻² and 2 × 10⁻⁵ K⁻¹, respectively. The value of M is _____ kg. (Take g = 10 ms⁻²)

Answer: (60)

Chemistry

SECTION-A

31. Match items of column I and II

Correct match is

(1) A-(ii), B-(iii), C-(iv), D-(i)

(2) A-(i), B-(iii), C-(ii), D-(iv)

(3) A-(ii), B-(iv), C-(i), D-(iii)

(4) A-(iii), B-(iv), C-(ii), D-(i)

Answer: (1)

32.

Consider the above reaction and identify the product B. Options

Answer: (1)

33. An organic compound ‘A’ with emperical formula C₆H₆O gives sooty flame on burning. Its reaction with bromine solution in low polarity solvent results in high yield of B.B is

Answer: (3)

34. When Cu²⁺ ion is treated with KI, a white precipitate, X appears in solution. The solution is titrated with sodium thiosulphate, the compound Y is formed. X and Y respectively are

(1) X=CuI₂ Y=Na₂ S₄O₆

(2) X=CuI₂ Y=Na₂ S₂O₃

(3) X=Cu₂I₂ Y=Na₂ S₄O₅

(4) X=Cu₂I₂ Y=Na₂ S₄O₆

Answer: (4)

35. Choose the correct set of reagents for the following conversion. trans⁡(Ph – CH = CH − CH₃) → cis⁡(Ph – CH = CH − CH₃)

(1) Br₂, aq ⋅ KOH, NaNH₂, Na(LiqNH₃)

(2) Br₂, alc ⋅ KOH, NaNH₂, H₂ Lindlar Catalyst

(3) Br₂, aq⋅KOH, NaNH₂, H₂ Lindlar Catalyst

(4) Br₂, alc ⋅ KOH, NaNH₂, Na(LiqNH₃)

Answer: (2)

36. Consider the following reaction

The correct statement for product B is. It is

(1) optically active alcohol and is neutral

(2) racemic mixture and gives a gas with saturated NaHCO₃ solution

(3) optically active and adds one mole of bromine

(4) racemic mixture and is neutral

Answer: (2)

37. The methods NOT involved in concentration of ore are

(A) Liquation

(B) Leaching

(D) Hydraulic washing

(E) Froth floatation

Choose the correct answer from the options given below :

(1) C, D and E only

(2) B, D and C only

(3) B, D and C only

(4) B, D and C only

Answer: (3)

38. A protein ‘X’ with molecular weight of 70,000 u, on hydrolysis gives amino acids. One of these amino acid is

Answer: (4)

39. Nd²⁺ =

(1) 4f³

(2) 4f⁴6 s²

(3) 4f⁴

(4) 4f²6 s²

Answer: (3)

40. Match List I with List II

Choose the correct answer from the options given below:

(1) A-IV, B-III, C-II, D-I

(2) A-IV, B-I, C-II, D-III

(3) A-II, B-I, C-III, D-IV

(4) A-II, B-I, C-IV, D-III

Answer: (4)

41. Identify X,Y and Z in the following reaction. (Equation not balanced)

(1) X = ClONO₂, Y = HOCl, Z = HNO₃

(2) X = ClONO₂, Y = HOCl, Z = NO₂

(3) X = ClNO₂, Y = HCl, Z = HNO₃

(4) X = ClNO₃, Y = Cl₂, Z = NO₂

Answer: (1)

42. The correct increasing order of the ionic radii is

(1) S²⁻ < Cl⁻ < Ca²⁺ < K⁺

(2) K⁺ < S²⁻ < Ca²⁺ < Cl⁻

(3) Ca²⁺ < K⁺ < Cl⁻ < S²⁻

(4) Cl⁻ < Ca²⁺ < K⁺ < S²⁻

Answer: (3)

43. Cobalt chloride when dissolved in water forms pink colored complex X which has octahedral geometry. This solution on treating with conc HCl forms deep blue complex, Y which has a Z X, Y and Z, respectively, are

(1) X = [Co(H₂O)₆]²⁺, Y = [CoCl₄]²⁻, Z = Tetrahedral

(2) X = [Co(H₂O)₆]²⁺, Y = [CoCl₆]³⁻, Z = Octahedral

(3) X = [Co(H₂O)₄Cl₂]⁺, Y = [CoCl₄]²⁻, Z = Tetrahedral

(4) X = [Co(H₂O)₆]³⁺, Y = [CoCl₆]³⁻, Z= Octahedral

Answer: (1)

44. H₂O₂ acts as a reducing agent in

(1) 2NaOCl + H₂O₂ → 2NaCl + H₂O + O₂

(2) Na₂S + 4H₂O₂ → Na₂SO₄ + 4H₂O

(3) 2Fe²⁺ + 2H⁺ + H₂O₂ → 2Fe³⁺ + 2H₂O

(4) Mn²⁺ + 2H₂O₂ → MnO₂ + 2H₂O

Answer: (1)

45. Adding surfactants in non polar solvent, the micelles structure will look like

(1) a

(2) d

(3) b

(4) c

Answer: (1)

46. The correct order of melting points of dichlorobenzenes is

Answer: (2)

47. The correct order of basicity of oxides of vanadium is

(1) V₂O₅ > V₂O₄ > V₂O₃

(2) V₂O₄ > V₂O₃ > V₂O₅

(3) V₂O₃ > V₂O₅ > V₂O₄

(4) V₂O₃ > V₂O₄ > V₂O₅

Answer: (4)

48. Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar ?

(1) Sucralose

(2) Aspartame

(3) Alitame

(4) Saccharin

Answer: (3)

49. Which one of the following statements is correct for electrolysis of brine solution?

(1) Cl₂ is formed at cathode

(2) O₂ is formed at cathode

(3) H₂ is formed at anode

(4) OH⁻ is formed at cathode

Answer: (4)

50. Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from n = 4 to n = 2 of He⁺ spectrum

(1) n = 2 to n = 1

(2) n = 1 to n = 2

(3) n = 3 to n = 4

(4) n = 1 to n = 3

Answer: (1)

SECTION B

51. The oxidation state of phosphorus in hypophosphoric acid is +

Answer: (4)

52. The enthalpy change for the conversion of is (−) kJmol⁻¹ (Nearest integer)

Given :

Answer: (610)

53. The logarithm of equilibrium constant for the reaction Pd²⁺ + 4Cl⁻ ⇌ PdCl₄²⁻ is (Nearest integer)

Answer: (6)

54. On complete combustion, 0.492 g of an organic compound gave 0.792 g of CO₂. The % of carbon in the organic compound is _____ (Nearest integer)

Answer: (44)

55. Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of 11.5 g of zinc with excess HCl is L (Nearest integer) (Given : Molar mass of Zn is 65.4 g mol⁻¹ and Molar volume of H₂ at STP = 22.7 L )

Answer: (4)

56. A → B

The rate constants of the above reaction at 200 K and 300 K are 0.03 min⁻¹ and 0.05 min⁻¹ respectively. The activation energy for the reaction is J⁡(Nearest integer) (Given : ln⁡10 = 2.3 R = 8.3 J K⁻¹ mol⁻¹

log 5 = 0.70

log 3 = 0.48

log 2 = 0.30)

Answer: (2520)

57. For reaction :

K_p = 2 × 10¹² at 27°C and 1 atm pressure. The K_c for the same reaction is × 10¹³. (Nearest integer) (Given R=0.082 L atm K⁻¹ mol⁻¹)

Answer: (1)

58. The total pressure of a mixture of non-reacting gases X(0.6 g) and Y(0.45 g) in a vessel is 740 mm of Hg. The partial pressure of the gas X is _____ mm of Hg. (Nearest Integer)

(Given : molar mass X = 20 and Y = 45 g mol⁻¹ )

Answer: (555)

59. How many of the transformations given below would result in aromatic amines ?

Answer: (3)

60. At 27∘C, a solution containing 2.5 g of solute in 250.0 mL of solution exerts an osmotic pressure of 400 Pa. The molar mass of the solute is _____ gmol⁻¹ (Nearest integer)

(Given : R=0.083 L_bar K⁻¹ mol⁻¹)

Answer: (62250)

Mathematics

SECTION-A

61. If the maximum distance of normal to the ellipse from the origin is 1, then the eccentricity of the ellipse is :

(1) 1/2

(2) √3/4

(3) √3/2

(4) 1/√2

Answer: (3)

62. Let a differentiable function f satisfy Then 12f(8) is equal to :

(1) 34

(2) 1

(3) 17

(4) 19

Answer: (3)

63. For all z ∈ C on the curve C₁ : |z| = 4, let the locus of the point be the curve C₂. Then :

(1) the curve C₁ lies inside C₂

(2) the curve C₂ lies inside C₁

(3) the curves C₁ and C₂ intersect 4 points

(4) the curves C₁ and C₂ intersect at 2 points

Answer: (3)

64. Then, at x = 1,

(1) √2yʹ − 3π²y = 0

(2) yʹ + 3π²y = 0

(3) 2yʹ + 3π²y = 0

(4) 2yʹ + √3π²y = 0

Answer: (3)

65. A wire of length 20 m is to be cut into two pieces. A piece of length 𝑙₁ is bent to make a square of area 𝐴1 and the other piece of length 𝑙₂ is made into a circle of area A₂. If 2A₁+ 3A₂ is minimum then (π𝑙₁) : 𝑙₂ is equal to :

(1) 1 : 6

(2) 6 : 1

(3) 3 : 1

(4) 4 : 1

Answer: (2)

66. Let a circle C₁ be obtained on rolling the circle x² + y² – 4x – 6y + 11 = 0 upwards 4 units on the tangent 𝑇 to it at the point (3, 2). Let C₂ be the image of C₁ in T. Let A and B be the centers of circles C₁ and C₂ respectively, and 𝑀 and N be respectively the feet of perpendiculars drawn from A and B on the x-axis. Then the area of the trapezium AMNB is :

(1) 4(1 + √2)

(2) 3 + 2√2

(3) 2(1 + √2)

(4) 2(2 + √2)

Answer: (1)

67. A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

(1) 3/7

(2) 5/7

(3) 5/6

(4) 2/7

Answer: (2)

68. Let y = f(x) represent a parabola with focus (−1/2, 0) and directrix y = −1/2. Then

(1) contains exactly two elements

(2) contains exactly one element

(3) is an empty set

(4) is an infinite set

Answer: (1)

69. Let be two nonzero vectors such that and Consider the following two statements:

Then

(1) both (A) and (B) are correct

(2) only (A) is correct

(3) neither (A) nor (B) is correct

(4) only (B) is correct

Answer: (2)

70. The value of is equal to

Answer: (4)

71. Let the shortest distance between the lines and L₁ : x + 1 = y – 1 = 4 – z be 2√ If (α, β, γ) lies on L, then which of the following is NOT possible ?

(1) α − 2γ = 19

(2) 2α + γ = 7

(3) 2α – γ = 9

(4) α + 2γ = 24

Answer: (4)

72. For the system of linear equations

x + y + z = 6 αx + βy + 7z = 3 x + 2y + 3z = 14 which of the following is NOT true ?

(1) If α = β and α ≠ 7, then the system has a unique solution

(2) If α = β = 7, then the system has no solution

(3) For every point (α, β) ≠ (7, 7) on the line x – 2y + 7 = 0, the system has infinitely many solutions

(4) There is a unique point (α, β) on the line x + 2y + 18 = 0 for which the system has infinitely many solutions

Answer: (3)

73. If the domain of the function where [x] is greatest integer ≤ x, is [2, 6), then its range is

Answer: (3)

74. Let R be a relation on N × N defined by (a, b) R (c, d) if and only if ad(b − c) = bc(a − d). Then R is

(1) transitive but neither reflexive nor symmetric

(2) symmetric but neither reflexive nor transitive

(3) symmetric and transitive but not reflexive

(4) reflexive and symmetric but not transitive

Answer: (2)

75. (S1) (p ⇒ q) ∨ (p ∧ (∼q)) is a tautology (S2) ((∼p) ⇒ (∼q)) ∧ ((∼p) ∨ q) is a contradiction.

Then

(1) both (S1) and (S2) are correct

(2) only ( S1) is correct

(3) only (S2) is correct

(4) both (S1) and (S2) are wrong

Answer: (2)

76. If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

(1) 7

(2) 3

(3) 9/2

(4) 14

Answer: (1)

77. Let Then the sum of the diagonal elements of the matrix (A + I)¹¹ is equal to

(1) 6144

(2) 2050

(3) 4097

(4) 4094

Answer: (3)

78. The number of real roots of the equation is :

(1) 3

(2) 1

(3) 2

(4) 0

Answer: (2)

79. If 0 < α < 13, then sin⁻¹(sin α) + cos⁻¹(cos α) is equal to

(1) 16

(2) 0

(3) π

(4) 16 – 5π

Answer: (3)

80. Let α ∈ (0, 1) and β = log_e(1 – α). Let x ∈ (0, 1). Then the integral is equal to

(1) β + P₅₀(α)

(2) P₅₀(α) – β

(3) β – P₅₀(α)

(4) −(β + P₅₀(α))

Answer: (4)

SECTION B

81. Let α > 0, be the smallest number such that the expansion of has a term βx^−α, β ∈ ℕ. Then α is equal to

Answer: (2)

82. Let for x ∈ ℝ

Then area bounded by the curve y = (f ° g) (x) and the lines y = 0, 2y – x = 15 is equal to

Answer: (72)

83. Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

Answer: (710)

84. If the variance of the frequency distribution

is 3, then α is equal to

Answer: (5)

85. Let θ be the angle between the planes and Let L be the line that meets P₂ at the point (4, −2, 5) and makes an angle θ with the normal of P₂. If α is the angle between L and P₂, then (tan² θ) (cot² α) is equal to

Answer: (9)

86. Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is

Answer: (2997)

87. Let be two vectors such that and Then is equal to

Answer: (36)

88. Let the line intersect the plane 2x + y + 3z = 16 at the point P. Let the point Q be the foot of perpendicular from the point R(1, −1, −3) on the line L. If α is the area of triangle PQR, then α² is equal to

Answer: (180)

89. Let a₁, a₂, …, a_n be in A.P. If a₅ = 2a₇ and a₁₁= 18, then is equal to

Answer: (8)

90. The remainder on dividing 5⁹⁹ by 11 is :

Answer: (9)

JEE Main Session 1 29th January 2023 Shift 1 Question Paper and Answer Key

May 10, 2023May 9, 2023 by suresh84

JEE MAIN 29^th January 2023 Shift 1

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ‘R′ is placed inside a large square loop of wire of side (L >> R). The loops are coplanar and their centers coincide :

Answer: (4)

2. The threshold wavelength for photoelectric emission from a material is 5500A. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a

(A) 75 W infra –red lamp

(B) 10 W infra-red lamp

(D) 10 W ultra-violet lamp

Choose the correct answer from the options given below:

(1) B and C only

(2) A and D only

(3) C only

(4) C and D only

Answer: (4)

3. Match List I with List II:

Choose the correct answer from the options given below:

(1) A-II, B – III, C-I, D-IV

(2) A-II, B – III, C-IV, D-I

(3) A-III, B – II, C-IV, D-I

(4) A-III, B – II, C-I, D-IV

Answer: (3)

4. In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface ‘ S ‘ having area of 4L². The flux through the opposite surface to ‘ S ‘ is given by

(1) q/12ε₀

(2) q/6ε₀

(3) q/3ε₀

(4) q/2ε₀

Answer: (2)

5. A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of 30 m/s.If both trains emit sounds with frequency 300 Hz,(Speed of sound: 330m/s) approximate difference of frequencies heard by the person will be:

(1) 55 Hz

(2) 80 Hz

(3) 33 Hz

(4) 10 Hz

Answer: (1)

6. A block of mass m slides down the plane inclined at angle 30° with an acceleration g/4. The value of coefficient of kinetic friction will be:

Answer: (1)

7. A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the tyre when the temperature increases to 36° C is

(1) 270 kPa

(2) 262 kPa

(3) 360 kPa

(4) 278 kPa

Answer: (4)

8. A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve z direction and lying in xy plane is shown in figure. The plot of component of magnetic field (By) at a distance ꞌaꞌ (less than radius of the coil) and on yz plane vs z coordinate looks like

Answer: (1)

9. Surface tension of a soap bubble is 2.0 × 10^–2 Nm^–1. Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be:

Take [π = 22/7]

(1) 9.24 × 10⁻⁴ J

(2) 5.76 × 10⁻⁴ J

(3) 0.72 × 10⁻⁴ J

(4) 18.48 × 10⁻⁴ J

Answer: (4)

10. Given below are two statements: One is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑.

Assertion A: If dQ and dW represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics dQ = dU – dW

Reason R: First law of thermodynamics is based on law of conservation of energy.

In the light of the above statements, choose the correct answer from the options given below:.

(1) Both A and R are correct and R is the correct explanation of A

(2) A is not correct but R is correct

(3) A is correct but R is not correct

(4) Both A and R are correct but R is not the correct explanation of A

Answer: (1)

11. If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be

(1) 1/8

(2) 1/2

(3) 1/4

(4) 1/16

Answer: (1)

12. Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

Answer: (2)

13. If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be: Given: Earth’s radius = 6.4 × 10⁶ m

(1) 28 km

(2) 36 km

(3) 32 km

(4) 64 km

Answer: (4)

14. A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34.[take g = 10 ms⁻²]

(1) 17 ms⁻¹

(2) 13 ms⁻¹

(3) 22.4 ms⁻¹

(4) 3.4 ms⁻¹

Answer: (2)

15. Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

(1) 1 : 27

(2) 1 : 1

(3) 1 : 3

(4) 3 : 1

Answer: (4)

16. A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be

(1) 1 : 2

(2) 1 : 4

(3) 4 : 1

(4) 4 : 3

Answer: (4)

17. Which of the following are true?

(A) Speed of light in vacuum is dependent on the direction of propagation.

(B) Speed of light in a medium is independent of the wavelength of light.

(D) The speed of light in a medium is independent of intensity.

Choose the correct answer from the options given below:

(1) C and D only

(2) B and C only

(3) A and C only

(4) B and D only

Answer: (1)

18. In a Young’s double slit experiment, two slits are illuminated with a light of wavelength 800 nm. The line joining A₁P is perpendicular to A1A₂ as shown in the figure. If the first minimum is detected at P, the value of slits separation ‘a’ will be:

The distance of screen from slits D = 5 cm

(1) 0.5 mm

(2) 0.1 mm

(3) 0.4 mm

(4) 0.2 mm

Answer: (4)

19. Which one of the following statement is not correct in the case of light emitting diodes?

(A) It is a heavily doped p-n junction.

(B) It emits light only when it is forward biased.

(D) The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used.

Choose the correct answer from the options given below:

(1) A

(2) C and D

(3) C

(4) B

Answer: (3)

20. The magnitude of magnetic induction at mid point O due to current arrangement as shown in Fig will be

(1) μ₀I/πa

(2) μ₀I/2πa

(3) 0

(4) μ₀I/4πa

Answer: (1)

SECTION-B

21. As shown in the figure, three identical polaroids P₁, P₂ and P₃ are placed one after another. The pass axis of P₂ and P₃ are inclined at angle of 60∘ and 90∘ with respect to axis of P₁. The source S has an intensity of The intensity of light at point O is –W/m².

Answer: (24)

22. A 0.4 kg mass takes 8 s to reach ground when dropped from a certain height ꞌP’ above surface of earth. The loss of potential energy in the last second of fall is ______ J.

(Take g = 10 m/s²)

Answer: (300)

23. Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _______degree.

Answer: (120)

24. A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2 s. The average acceleration during contact is _____ ms⁻² (Given g=10 ms⁻² )

Answer: (120)

25. A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B= 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2cms⁻¹. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ____ mV. (Given g = 10 ms^–2)

Answer: (10)

26. A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ ms⁻¹

Answer: (40)

27. A body cools from 60°C to 40°C in 6 minutes. If, temperature of surroundings is 10° Then, after the next 6 minutes, its temperature will be ______ °C.

Answer: (28)

28. In a metre bridge experiment the balance point is obtained if the gaps are closed by 2Ω and 3Ω. A shunt of X Ω is added to 3Ω resistor to shift the balancing point by 22.5 cm. The value of X is ____

Answer: (2)

29. A point charge q₁ = 4q₀ is placed at origin. Another point charge q₂ = −q₀ is placed at = 12 cm. Charge of proton is q₀ .The proton is placed on 𝑥xaxis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.

Answer: (24)

30. A radioactive element emits two α-articles, one electron and two positrons. The product nucleus is represented by The value of P is

Answer: (87)

Chemistry

SECTION-A

31. “A” obtained by Ostwald’s method involving air oxidation of NH3, upon further air oxidation produces “B”. “B” on hydration forms an oxoacid of Nitrogen along with evolution of “A”. The oxoacid also produces “A” and gives positive brown ring test. Identify A and B, respectively.

(1) N₂O₃, NO₂

(2) NO₂, N₂O₄

(3) NO₂, N₂O₅

(4) NO, NO₂

Answer: (4)

32. Correct statement about smog is:

(1) Classical smog also has high concentration of oxidizing agents

(2) Both NO₂ and SO₂ are present in classical smog

(3) NO₂ is present in classical smog

(4) Photochemical smog has high concentration of oxidizing agents

Answer: (4)

33. The standard electrode potential (M³⁺/M²⁺) for V, Cr, Mn & Co are −0.26 V, −0.41 V,+1.57 V and +1.97 V, respectively. The metal ions which can liberate H₂ from a dilute acid are

(1) Mn²⁺ and Co²⁺

(2) Cr²⁺ and Co²⁺

(3) V²⁺ and Cr²⁺

(4) V²⁺ and Mn²⁺

Answer: (3)

34. The shortest wavelength of hydrogen atom in Lyman series is 𝜆. The longest wavelength in Balmer series of He⁺ is

(1) 36λ/5

(2) 9λ/5

(3) 5/9λ

(4) 5λ/9

Answer: (2)

35. The bond dissociation energy is highest for

(1) F₂

(2) Br₂

(3) I₂

(4) Cl₂

Answer: (4)

36. The increasing order of pK_a for the following phenols is

(A) 2, 4-Dinitrophenol

(B) 4-Nitrophenol

(D) Phenol

(E) 3-Chlorophenol

Choose the correct answer from the option given below:

(1) (A),(B),(E),(D),(C)

(2) (C), (D), (E), (B), (A)

(3) (A), (E), (B), (D), (C)

(4) (C), (E), (D), (B), (A)

Answer: (1)

37. For 1 mol of gas, the plot of pV p is shown below. p is the pressure and V is the volume of the gas

What is the value of compressibility factor at point?

Answer: (2)

38. Match List I with List II.

Choose the correct answer from the options given below:

(1) (A)−II, (B)−I, (C)−IV, (D)−III

(2) (A) −I, (B)−II, (C)−IV, (D)−III

(3) (A)−II, (B)−I, (C)−IV, (D)−II

(4) (A) −III, (B)−I, (C)−II, (D)−IV

Answer: (4)

39. During the borax bead test with CuSO₄, a blue green colour of the bead was observed in oxidising flame due to the formation of

(1) CuO

(2) Cu(BO₂)₂

(3) Cu₃B₂

(4) Cu

Answer: (2)

40. Which of the following salt solution would coagulate the colloid solution formed when FeCl₃ is added to NaOH solution, at the fastest rate?

(1) 10 mL of 0.1 mol dm^–3 Na₂SO₄

(2) 10 mL of 0.2 mol dm^–3 AlCl₃

(3) 10 mL of 0.1 mol dm^–3 Ca₃(PO₄)₂

(4) 10 mL of 0.15 mol dm–3 CaCl2

Answer: (2)

41. Number of cyclic tripeptides formed with 2 amino acids A and B is:

(1) 5

(2) 2

(3) 4

(4) 3

Answer: (3)

42. The correct order of hydration enthalpies is

(A) K⁺ (B) Rb⁺ (C) Mg²⁺

(D) Cs⁺ (E) Ca²⁺

Choose the correct answer from the options given below:

(1) E > C > A > B > D

(2) C > A > E > B > D

(3) C > E > A > D > B

(4) C > E > A > B > D

Answer: (4)

43. Chiral complex from the following is:

Here en = ethylene diamine

(1) cis −[PtCl₂(en)₂]²⁺

(2) trans−[PtCl₂(en)₂]²⁺

(3) cis−[PtCl₂(NH₃)₂]

(4) trans−[Co(NH₃)₄Cl₂]⁺

Answer: (1)

44. Identify the correct order for the given property for following compounds.

Choose the correct answer from the option given below:

(1) (B), (C) and (D) only

(2) (A), (C) and (D) only

(3) (A), (B) and (E) only

(4) (A), (C) and (E) only

Answer: (4)

45. The magnetic behavior of Li₂O, Na₂O₂ and KO₂, respectively, are

(1) Paramagnetic, paramagnetic and diamagnetic

(2) diamagnetic, paramagnetic and diamagnetic

(3) paramagnetic, diamagnetic and paramagnetic

(4) diamagnetic, diamagnetic and paramagnetic

Answer: (4)

46. The reaction representing the Mond process for metal refining is__________

Answer: (4)

47. Which of the given compounds can enhance the efficiency of hydrogen storage tank?

(1) Di-isobutylaluminium hydride

(2) NaNi_…….

(3) Li/P₄

(4) SiH₄

Answer: (2)

48. Match List I with List II.

Choose the correct answer from the options given below:

(1) (A) −III, (B) −IV, (C)−I, (D) –II

(2) (A) – II, (B) −I, (C) – III, (D) – IV

(3) (A) −III, (B) −IV, (C)−II, (D) –I

(4) (A) −II, (B)−IV, (C)−I, (D)−III

Answer: (1)

49. The major product ‘P’ for the following sequence of reactions is:

Answer: (4)

50. Compound that will give positive Lassaigne’s test for both nitrogen and halogen is:

(1) NH₂OH.HCl

(2) CH₃NH₂.HCl

(3) NH₄Cl

(4) N₂H₄.HCl

Answer: (2)

SECTION-B

51. Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is x × 10⁻¹. The value of x is_______ (Nearest integer). Assume complete dissociation.

Answer: (5)

52. Water decomposes at 2300 K

The percent of water decomposing at 2300 K and 1 bar is_______ (Nearest integer). Equilibrium constant for the reaction is 2 × 10⁻³ at 2300 K.

Answer: (2)

53. The sum of bridging carbonyls in W(CO)₆ and Mn₂(CO)₁₀ is_______

Answer: (0)

54. Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15°C. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at −0.80C. The solubility product of PbCl₂ formed is_____×10⁻⁶ at 298 K. (Nearest integer)

(Given : Kb=0.5 K kg mol^–1 and K_f

=1.8 K kg mol⁻¹. Assume molality to be equal to molarity in all cases.)

Answer: (13)

55. 17 mg of a hydrocarbon (M.F. C₁₀H₁₆ ) takes up 8.40 mL of the H₂ gas measured at 0°C and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields

The number of double bond/s present in the hydrocarbon is_______

Answer: (3)

56. Consider the following reaction approaching equilibrium at 27°C and 1 atm pressure

The standard Gibb’s energy change (∆_rG^θ) at 27°C is (−) _______ KJ mol⁻¹ (Nearest integer).

(Given : R = 8.3 J K⁻¹ mol⁻¹ and ln 10 = 2.3)

Answer: (6)

57. The number of molecules or ions from the following, which do not have odd number of electrons are______

(A) NO₂

(B) ICl₄⁻

(D) ClO₂

(E) NO₂⁺

(F) NO

Answer: (3)

58. Following chromatogram was developed by adsorption of compound ‘A’ on a 6 cm TLC glass plate. Retardation factor of the compound ‘A’ is ______ × 10⁻¹

Answer: (6)

59. For certain chemical reaction X→Y, the rate of formation of product is plotted against the time as shown in the figure. The number of correct statement/s from the following is_____

(A) Over all order of this reaction is one

(B) Order of this reaction can’t be determined

(D) In region-II, the reaction is of first order

(E) In region-II, the order of reaction is in the range of 0.1 to 0.9.

Answer: (2)

60. Following figure shows dependence of molar conductance of two electrolytes on concentration. is the limiting molar conductivity.

The number of incorrect statement(s) from the following is________

(A) for electrolyte A is obtained by extrapolation

(B) For electrolyte B, Λm vs √c graph is a straight line with intercept equal to

(D) for any electrolyte A or B can be calculated using λ° for individual ions

Answer: (2)

Mathematics

SECTION-A

61. Let α and β be real numbers. Consider a 3 × 3 matrix A such that A²= 3A + αI. If A⁴ = 21A + βI, then

(1) β = −8

(2) β = 8

(3) α = 4

(4) α = 1

Answer: (1)

62. Let x = 2 be a root of the equation x² + px + q = 0 and

where [·] denotes greatest integer function, is

(1) 0

(2) −1

(3) 2

(4) 1

Answer: (1)

63. Let B and C be the two points on the line y + x = 0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y – 2x = 2 such that △ABC is an equilateral triangle. Then, the area of the △ABC is

(1) 10/√3

(2) 3√3

(3) 2√3

(4) 8/√3

Answer: (4)

64. Consider the following system of equations

αx + 2y + z = 1

2αx + 3y + z = 1

3x + αy + 2z = β

for some α, β ∈ ℝ. Then which of the following is NOT correct.

(1) It has a solution if α = −1 and β ≠ 2

(2) It has a solution for all α ≠ −1 and β = 2

(3) It has no solution for α =3 and β ≠ 2

(4) It has no solution for α = −1 and β ∈ ℝ

Answer: (4)

65. Let y = f(x) be the solution of the differential equation y(x + 1)dx − x²dy = 0, y(1) = e. Then is equal to

(1) 1/e²

(2) e²

(3) 0

(4) 1/e

Answer: (3)

66. The domain of is

(1) ℝ − {3}

(2) (−1, ∞) −{3}

(3) (2, ∞) −{3}

(4) ℝ −{−1,3}

Answer: (3)

67. Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

(1) 5/24

(2) 1/6

(3) 5/36

(4) 2/15

Answer: (2)

68. Let [x] denote the greatest integer ≤ Consider the function f(x) = max{x², 1 + [x]}. Then the value of the integral is

Answer: (1)

69. For two non-zero complex numbers z₁ and z₂, if Re⁡(z₁z₂)=0 and Re⁡(z₁ + z₂) = 0, then which of the following are possible?

(A) Im (z₁) > 0 and Im(z₂) > 0

(B) Im (z₁) < 0 and Im (z₂) > 0

(D) Im(z₁) < 0 and Im (z₂) < 0

Choose the correct answer from the options given below:

(1) B and D

(2) A and B

(3) B and C

(4) A and C

Answer: (3)

70. If the vectors and are coplanar and the projection of is √54 units, then the sum of all possible values of λ + μ is equal to

(1) 0

(2) 24

(3) 6

(4) 18

Answer: (2)

71. Let − 2((1 – sin² 2θ) and If then f(β) is equal to

(1) 5/4

(2) 3/2

(3) 9/8

(4) 11/8

Answer: (2)

72. If p, q and r three propositions, then which of the following combination of truth values of p, q and r makes the logical expression {(p ∨ q) ∧ ((~p) ∨ r)}→((~q) ∨ r) false?

(1) p = T, q = T, r = F

(2) p = T, q = F, r = T

(3) p = F, q = T, r = F

(4) p = T, q = F, r = F

Answer: (3)

73. Let Δ be the area of the region {(x, y) ∈ ℝ² : x² + y² ≤ 21, y² ≤ 4x, x ≥ 1}. Then is equal to

Answer: (2)

74. A light ray emits from the origin making an angle 30∘ with the positive x-axis. After getting reflected by the line x + y = 1, if this ray intersects x-axis at Q, then the abscissa of Q is

Answer: (2)

75. Let A = {(x, y) ∈ ℝ² : y ≥ 0, and B = {(x, y) ∈ ℝ × ℝ: 0 ≤ y ≤ min Then the ratio of the area of A to the area of B is

Answer: (3)

76. Let λ ≠ 0 be a real number. Let α, β be the roots of the equation 14x² – 31x + 3λ = 0 and α, γ be the roots of the equation 35x² – 53x + 4λ = 0. Then 3α/β and 4α/γ are the roots of the equation

(1) 49x² – 245x + 250 = 0

(2) 7x² + 245x – 250 = 0

(3) 7x² – 245x + 250 = 0

(4) 49x² + 245x + 250 = 0

Answer: (1)

77. Let the tangents at the points A(4,−11) and B(8,−5) on the circle x² + y² – 3x + 10y −15 = 0, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

(1) 2√13

(2) √13

(3) 3√3/4

(4) 2√13/3

Answer: (4)

78. Let x ∈ ℝ be a function which satisfies Then (a + b) is equal to

(1) −2π(π – 2)

(2) −2π(π + 2)

(3) −π(π – 2)

(4) −π(π + 2)

Answer: (2)

79. Let f : R → R be a function such that Then

(1) f(x) is one-one in [1, ∞) but not in (−∞, ∞)

(2) f(x) is one-one in (−∞, ∞)

(3) f(x) is many-one in ((−∞, −1)

(4) f(x) is many-one in (1, ∞)

Answer: (1)

80. Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable 𝑋 denote the number of rotten apples. If μ and σ² represent mean and variance of 𝑋, respectively, then 10(μ² + σ²) is equal to

(1) 250

(2) 25

(3) 30

(4) 20

Answer: (4)

Section B

81. Let the co-ordinates of one vertex of △ ABC be A(0, 2, α) and the other two vertices lie on the line For α ∈ ℤ if the area of △ABC is 21 sq. units and the line segment BC has length 2√21 units, then α² is equal to

Answer: (9)

82. Let f : ℝ → ℝ be a differentiable function that satisfies the relation f(x + y) = f(x) + f(y) – 1, ∀x, y ∈ ℝ. If fꞌ(0) = 2, then |f(−2)| is equal to

Answer: (3)

83. Suppose f is a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈ ℕ and f(1) = 1/5. If then m is equal to

Answer: (10)

84. Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)ⁿ be in the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is

Answer: (1120)

85. Let a₁, a₂, a₃, … be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a₁a₉ + a₂a₄a₉ + a₅ + a₇ is equal to

Answer: (60)

86. Let the equation of the plane P containing the line be ax + by + 3z = 2(a + b) and the distance of the plane P from the point (1, 27, 7) be c. Then a² + b² + c² is equal to

Answer: (355)

87. If the co-efficient of x⁹ in and the co-efficient of x⁻⁹ in are equal, then (αβ)² is equal to

Answer: (1)

88. Let be three non-zero non-coplanar vectors. Le the position vectors of four points, A, B, C and D be If are coplanar, then λ is equal to

Answer: (2)

89. Five digit numbers are formed using the digits 1, 2, 3,5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1 . Then the serial number of 35337 is

Answer: (1436)

90. If all the six digit numbers x₁x₂x₃x₄x₅x₆ with 0 < x₁ < x₂ < x₃ < x₄ < x₅ < x₆ are arranged in the increasing order, then the sum of the digits in the 72th number is

Answer: (32)

JEE Main Session 1 25th January 2023 Shift 1 Question Paper and Answer Key

May 10, 2023May 6, 2023 by suresh84

JEE MAIN 25^th January 2023 Shift 1

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. Match List I with List II

Choose the correct answer from the options given below:

(1) A-II , B-I , C-III , D-IV

(2) A-IV, B-III , C-I , D-II

(3) A-III , B-IV, C-I , D-II

(4) A-IV , B-III , C-II , D-I

Answer: (2)

2. The ratio of the density of oxygen nucleus (₈¹⁶O) and helium nucleus (₂⁴He) is

(1) 4:1

(2) 2:1

(3) 1:1

(4) 8:1

Answer: (3)

3. The root mean square velocity of molecules of gas is

(1) Inversely proportional to square root of temperature

(2) Proportional to square of temperature (T²)

(3) Proportional to temperature (T)

(4) Proportional to square root of temperature (√T)

Answer: (4)

4. Match List I with List II

Choose the correct answer from the options given below :

(1) A-III, B-I, C-IV, D-II

(2) A-I, B-III, C-IV, D-II

(3) A-III, B-IV, C-I, D-II

(4) A-II, B-I, C-IV, D-III

Answer: (1)

5. A message signal of frequency 5kHz is used to modulate a carrier signal of frequency 2MHz. The bandwidth for amplitude modulation is:

(1) 20 kHz

(2) 5 kHz

(3) 10 kHz

(4) 2.5 kHz

Answer: (3)

6. An object of mass 8 kg hanging from one end of a uniform rod CD of mass 2 kg and length 1m pivoted at its end C on a vertical walls as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is: (Take g = 10 m/s²)

(1) 90 N

(2) 30 N

(3) 300 N

(4) 240 N

Answer: (3)

7. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity.

Reason R: For a p-n junction diode, at applied voltage

V the current in the forward bias is more than the current in the reverse bias for |V₂| > ± V ≥ |V₀| where V₀ is the threshold voltage and V_z is the breakdown voltage.

In the light of the above statements, choose the correct answer from the options given below

(1) Both A and R are true and R is correct explanation A

(2) A is false but R is true

(3) Both A and R are true but R is NOT the correct explanation A

(4) A is true but R is false

Answer: (2)

8. In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ω₀.The value of x is:

(1) 4

(2) 1/16

(3) 16

(4) 1/4

Answer: (4)

9. A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform metallic wires is 8.92 × 10^–3 kg density is 8.92 × 103 kg/m3 and resistivity is 1.7 × 10^–8 Ω – m. The length of wire is:

(1) l = 10 m

(2) l = 100 m

(3) l = 5 m

(4) l = 6.8 m

Answer: (1)

10. A car travels a distance of ‘x′ with speed ν₁ and then same distance ′x′ with speed ν₂ in the same direction. The average speed of the car is:

Answer: (1)

11. A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take g = 10 m/s²)

(1) π/3

(2) π/2

(3) π/4

(4) π/6

Answer: (3)

12. A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long it will take to cool from 75°C to 69°C?

(1) 1 minute

(2) 1.4 minutes

(3) 0.5 minute

(4) 2 minutes

Answer: (2)

13. A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2m long and 0.2m in diameter. The magnetic intensity at the center of the solenoid when a current of 2A flows through it is?

(1) 2.4 × 10³ Am⁻¹

(2) 1.2 × 10³ Am⁻¹

(3) 2.4 × 10⁻³ Am⁻¹

(4) 1 Am⁻¹

Answer: (2)

14. In Young’s double slits experiment, the position of 5th bright fringe from the central maximum is 5cm. The distance between slits and screen is 1m and wavelength of used monochromatic light is 600 nm. The separation between the slits is:

(1) 48 μm

(2) 36 μm

(3) 12 μm

(4) 60 μm

Answer: (4)

15. An electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at the point and instant?

(1) Negative direction of y

(2) Positive direction of z

(3) Positive direction of x

(4) Negative direction of x

Answer: (3)

16. A parallel plate capacitor has plate area 40 cm² and plates separation 2mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is:

(1) 24ε₀ F

(2)

(3)

(4) 10ε₀ F

Answer: (2)

17. Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately)

(Take g = 10 ms⁻²,radius of earth = 6400 km )

(1) 12 hours

(2) 1 hour 40 minutes

(3) 24 hours

(4) 1 hour 24 minutes

Answer: (4)

18. Electron beam used in an electron microscope, when accelerated by a voltage of 20kV,has a de−Broglie wavelength of 𝜆₀.If the voltage is increased to 40kV, then the de-Broglie wavelength associated with the electron beam would be:

(1) 3λ₀

(2) λ₀/2

(3) λ₀/√2

(4) 9λ₀

Answer: (3)

19. A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

(1) 300 K

(2) 900 K

(3) 1000 K

(4) 360 K

Answer: (3)

20. T is the time period of simple pendulum on the earth’s surface. Its time Period becomes x T when taken to a height R (equal to earth’s radius) above the earth’s surface. Then, the value of x will be:

(1) 4

(2) 2

(3) 1/4

(4) 1/2

Answer: (2)

SECTION-B

21. A uniform electric field of 10 N/C is created between two parallel charged pates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5eV. The length of each pate is 10 cm. The angle (θ) of deviation of the path of electron as it comes out of the field is ______ (in degree).

Answer: (45)

22. The wavelength of the radiation emitted is 𝜆₀ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be . The value of x is _____.

Answer: (27)

23. As shown in the figure, in an experiment to determine Young’s modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of wire is 62.8cm and its diameter is 4 mm. The Young’s modulus is found to be x × 10⁴ Nm^–2. The value of x is __________

Answer: (5)

24. I_CM is the moment of inertia of a circular disc about an axis (CM)passing through its center and perpendicular. To the plane of disc. I_AB is it′s moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance 2/3R from center.

Where R is the radius of the disc. The ratio of I_AB and I_CM is x : 9.

The value of x is ______

Answer: ()

25. An object of mass ‘m’ initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx, where k is constant and x is the distance covered by the object from the initial position. The expression of kinetic energy of the object will be

Answer: (2)

26. An LCR series circuit of capacitance 62.5nF and resistance of 50Ω, is connected to an A.C. source of frequency 2.0kHz. For maximum value of amplitude of current in circuit, the value of inductance is _______ mH. Take π² = 10)

Answer: (100)

27. The distance between two consecutive points with phase difference of 60∘ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is ___________ km/s

Answer: (18)

28. In the given circuit, the equivalent resistance between the terminal A and B is Ω.

Answer: (10)

29. If and then, The unit vector in the direction of The value of x is

Answer: (4)

30. A ray of light is incident from air on a glass plate having thickness √3 cm and refractive index √2. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is _______ × 10^–2 cm. (given sin 15° = 0.26)

Answer: (52)

Chemistry

SECTION-A

31. In the cumene to phenol preparation in presence of air, the intermediate is

Answer: (3)

32. The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH⁻ is

Answer: (3)

33. Match List I with List II

Choose the correct answer from the options given below:

(1) A-II, B-I, C-III, D-IV

(2) A-II, B-I, C-IV, D-III

(3) A-IV, B-III, C-II, D-I

(4) A-II, B-IV, C-I, D-III

Answer: (2)

34. Which of the following conformations will be the most stable ?

Answer: (2)

35. The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph

Answer: (4)

36. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason 𝐑 :

Assertion A : Acetal / Ketal is stable in basic medium.

Reason R : The high leaving tendency of alkoxide ion gives the stability to acetal/ ketal in basic medium.

In the light of the above statements, choose the correct answer from the options given below :

(1) A is true but R is false

(2) A is false but R is true

(3) Both A and R are true but R is NOT the correct explanation of A

(4) Both A and R are true and R is the correct explanation of A

Answer: (1)

37. A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at 1/3^rd of the total faces. The empirical formula of the compound is

(1) XY_2.5

(2) X₂Y_1.5

(3) X_2.5Y

(4) X_1.5Y₂

Answer: (4)

38. Match the List-I with List-II

Correct match is-

(1) A → iii, B → i, C → iv, D → ii

(2) A → i, B → iii, C → ii, D → iv

(3) A → iv, B → ii, C → iii, D → i

(4) A → i, B → iii, C → iv, D → ii

Answer: (4)

39. Which of the following statements is incorrect for antibiotics?

(1) An antibiotic must be a product of metabolism.

(2) An antibiotic should promote the growth or survival of microorganisms.

(3) An antibiotic is a synthetic substance produced as a structural analogue of naturally occurring antibiotic.

(4) An antibiotic should be effective in low concentrations.

Answer: (2)

40. The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

(1) Me₃ N > Me₂NH > MeNH₂ > NH₃

(2) Me₂NH > MeNH₂ > Me₃ N > NH₃

(3) Me₂NH > Me₃ N > MeNH₂ > NH₃

(4) NH₃ > Me₃ N > MeNH₂ > Me₂NH

Answer: (2)

41. ’25 volume’ hydrogen peroxide means

(1) 1 L marketed solution contains 25 g of H₂O₂.

(2) 1 L marketed solution contains 75 g of H₂O₂.

(3) 1 L marketed solution contains 250 g of H₂O₂.

(4) 100 mL marketed solution contains 25 g of H₂O₂.

Answer: (2)

42. The radius of the 2nd orbit of Li²⁺ is x. The expected radius of the 3rd orbit of Be³⁺ is

Answer: (1)

43. Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A] and [B] are respectively

(1) P₄O₆ and H₃PO₃

(2) PCl₅ and H₃PO₄

(3) POCl₃ and H₃PO₄

(4) PCl₃ and H₃PO₃

Answer: (4)

44. Inert gases have positive electron gain enthalpy. Its correct order is

(1) He < Kr < Xe <Ne

(2) He < Xe < Kr < Ne

(3) He < Ne < Kr < Xe

(4) Xe < Kr < Ne < He

Answer: (2)

45. Identify the product formed ( and E)

Answer: (3)

46. Match items of Row I with those of Row II.

Answer: (4)

47. Which one of the following reactions does not occur during extraction of copper ?

(1) 2Cu₂ S + 3O₂ → 2Cu₂O + 2SO₂

(2) FeO + SiO₂ → FeSiO₃

(3) 2FeS + 3O₂→ 2FeO+2SO₂

(4) CaO + SiO₂→ CaSiO₃

Answer: (4)

48. Some reactions of NO₂ relevant to photochemical smog formation are

Identify A, B, X and Y

(1) Y = NO₂, A = O₃, B = O₂

(2) X = [O], Y = NO, A = O₂, B = O₃

(3) X = N₂O, Y = [O], A = O₃, B = NO

(4) X = NO, Y = [O], A = O₂, B = N₂O₃

Answer: (2)

49.

The correct sequence of reagents for the preparation of Q and R is :

(1) (i) CrO₂Cl₂,H₃O⁺; (ii) Cr₂O₃,770 K, 20 atm; (iii) NaOH; (iv) H₃O⁺

(2) (i) KMnO₄,OH⁻; (ii) Mo₂O₃,Δ; (iii) NaOH; (iv) H₃O⁺

(3) (i) Cr₂O₃,770 K, 20 atm; (ii) CrO₂Cl₂,H₃O⁺; (iii) NaOH; (iv) H₃O⁺

(4) (i) Mo₂O₃, Δ; (ii) CrO₂Cl₂, H₃O⁺; (iii) NaOH; (iv) H₃O⁺

Answer: (3)

50. Compound A reacts with NH₄Cl and forms a compound B. Compound B reacts with H₂O and excess of CO₂ to form compound C which on passing through or reaction with saturated NaCl solution forms sodium hydrogen carbonate. Compound A, B and C, are respectively.

(1) CaCl₂, NH₃, NH₄HCO₃

(2) Ca(OH)₂, NH₄^⨁, (NH₄)₂CO₃

(3) CaCl₂, NH₄^⨁, (NH₄)₂CO₃

(4) Ca(OH)₂, NH₃, NH₄HCO₃

Answer: (4)

SECTION-B

51. For the first order reaction A→B, the half life is 30 min. The time taken for 75% completion of the reaction is ____ min. (Nearest integer)

Given : log 2 = 0.3010

log 3 = 0.4771

log 5 = 0.6989

Answer: (60)

52. How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? (Given: Atomic number : V, 23; Cr, 24; Fe, 26; Ni, 28) V³⁺, Cr³⁺, Fe²⁺, Ni³⁺

Answer: (2)

53. In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in the compound is______ (Nearest Integer)

(Given: Atomic mass Ba: 137u, S:32 u, O: 16u )

Answer: (42)

54. The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph. The molar mass of PVC is ____ gmol⁻¹ (Nearest integer)

(Given : R = 0.083 L atm K⁻¹ mol⁻¹)

Answer: (41500)

55. The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume of its solution required for the complete neutralization of 25 mL of 0.24MNaOH is ___ × 10⁻² mL (Nearest integer)

Answer: (12)

56. An athlete is given 100 g of glucose (C₆H₁₂O₆) for energy. This is equivalent to 1800 kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is____ g (Nearest integer) Assume that there is no other way of consuming stored energy.

Given : The enthalpy of evaporation of water is 45 kJ mol⁻¹

Molar mass of C, H & O are 12, 1 and 16 g mol⁻¹

Answer: (360)

57. The number of paramagnetic species from the following is

[Ni(CN)₄]²⁻, [Ni(CO)₄], [NiCl₄]²⁻

[Fe(CN)₆]⁴⁻, [Cu(NH₃)₄]²⁺

[Fe(CN)₆]³⁻ and [Fe(H₂O)₆]²⁺

Answer: (4)

58. Consider the cell

Pt(s) | H₂(g) (1 atm) | H⁺] = 1) || Fe³⁺ (aq), Fe²⁺ (aq) | Pt(s)

Given and T = 298 K

If the potential of the cell is 0.712 V, the ratio of concentration of Fe²⁺ to Fe³⁺ is (Nearest integer)

Answer: (10)

59. The total number of lone pairs of electrons on oxygen atoms of ozone is

Answer: (6)

60. A litre of buffer solution contains 0.1 mole of each of NH₃ and NH₄ On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be____×10⁻³ (Nearest integer)

[Given : pK_b(NH₃) = 4.745

log 2 = 0.301

Log 3 = 0.477

T = 298 K]

Answer: (9)

Mathematics

SECTION-A

61. The points of intersection of the line ax + by = 0, (a ≠ b) and the circle x² + y² – 2x = 0 are A(α, 0) and B(1, β). The image of the circle with AB as a diameter in the line x + y + 2 = 0 is :

(1) x² + y² + 3x + 3y + 4 = 0

(2) x² + y² + 3x + 5y + 8 = 0

(3) x² + y² − 5x − 5y + 12 = 0

(4) x² + y² + 5x + 5y + 12 = 0

Answer: (4)

62. The distance of the point (6, −2√2) from the common tangent y = mx + c, m > 0, of the curves x = 2y² and x = 1 + y² is :

(1) 14/3

(2) 5√3

(3) 1/3

(4) 5

Answer: (4)

63. Let be three non zero vectors such that If be a vector such that then is equal to

(1) −1/4

(2) 1/4

(3) 3/4

(4) 1/2

Answer: (2)

64. The vector is rotated through a right angle, passing through the y-axis in its way and the resulting vector is Then the projection of is :

(1) 2√3

(2) 1

(3) 3√2

(4) √6

Answer: (3)

65. Let z₁= 2 + 3i and z₂ = 3 + 4i. The set S ={z ∈ C : |z − z₁|² − |z − z₂|² = |z₁ − z₂|²} represents a

(1) hyperbola with the length of the transverse axis 7

(2) hyperbola with eccentricity 2

(3) straight line with the sum of its intercepts on the coordinate axes equals −18

(4) straight line with the sum of its intercepts on the coordinate axes equals 14

Answer: (4)

66. The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is 10.2, then their new variance is equal to :

(1) 3.96

(2) 4.08

(3) 4.04

(4) 3.92

Answer: (1)

67. Let S₁ and S₂ be respectively the sets of all a ∈ ℝ − {0} for which the system of linear equations

ax + 2ay – 3az = 1

(2a + 1)x + (2a + 3)y + (a + 1)z = 2

(3a + 5)x + (a + 5)y + (a + 2)z = 3

has unique solution and infinitely many solutions. Then

(1) S₁ is an infinite set and n(S₂) = 2

(2) S₁ = Φ and S₂ = ℝ − {0}

(3) n(S₁) = 2 and S₂ is an infinite set

(4) S₁ = ℝ − {0} and S₂ = Φ

Answer: (4)

68. The value of is :

Answer: (1)

69. The statement (p ∧ (∼q)) ⇒ (p ⇒ (∼q)) is

(1) a tautology

(2) a contradiction

(3) equivalent to p ∨ q

(4) equivalent to (∼p) ∨ (∼q)

Answer: (1)

70. Consider the lines L₁ and L₂ given by

A line L₃ having direction ratios 1, −1, −2, intersects L₁ and L₂ at the points P and Q respectively. Then the length of line segment PQ is

(1) 3√2

(2) 4√3

(3) 4

(4) 2√6

Answer: (4)

71. Let If then f(4) is equal to

(1) log_e 19 – log_e 20

(2) log_e 17 – log_e 18

(3)

(4)

Answer: (4)

72. The minimum value of the function is :

(1) e(e – 1)

(2) 2(e – 1)

(3) 2

(4) 2e – 1

Answer: ()

73. Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space and the event A = {x ∈ S : x is a multiple of 3}. Then P(A) is equal to

(1) 7/22

(2) 1/5

(3) 15/44

(4) 1/3

Answer: (4)

74. Let x = 2 be a local minima of the function f(x) = 2x⁴ – 18x² + 8x + 12, x ∈ (−4, 4). If M is local maximum value of the function f in (−4, 4), then M=

Answer: (3)

75. Let f: (0, 1) → ℝ be a function defined by and g(x) = (f(−x) – f(x)). Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0,1)

Then,

(1) Both (I) and (II) are true

(2) Neither (I) nor (II) is true

(3) Only (I) is true

(4) Only (II) is true

Answer: (1)

76. Let y(x) = (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 + x¹⁶). Then yꞌ − yꞌꞌ at x = −1 is equal to:

(1) 976

(2) 944

(3) 464

(4) 496

Answer: (4)

77. The distance of the point P(4, 6, −2) from the line passing through the point (−3, 2, 3) and parallel to a line with direction ratios 3, 3, −1 is equal to :

(1) √14

(2) 3

(3) √6

(4) 2√3

Answer: (1)

78. Let x, y, z > 1 and Then |adj(adj A²)| is equal to

(1) 2⁸

(2) 4⁸

(3) 6⁴

(4) 2⁴

Answer: (1)

79. If a_r is the coefficient of x^{10− r} in the Binomial expansion of (1 + x)¹⁰, then is equal to

(1) 5445

(2) 3025

(3) 4895

(4) 1210

Answer: (4)

80. Let y = y(𝑥) be the solution curve of the differential equation x > 0, y(1) = 3. Then is equal to :

Answer: (4)

SECTION-B

81. The constant term in the expansion of

Answer: (1080)

82. For some a, b, c ∈ ℕ, let f(x) = ax – 3 and g(x) = x^b + c, x ∈ ℝ. If then (f ° g) (ac) + (g ° f) (b) is equal to

Answer: (2039)

83. Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of 𝑆 that have the sum of all elements a multiple of 3, is

Answer: (43)

84. Let the equation of the plane passing through the line x – 2y – z – 5 = 0 = x + y + 3z – 5 and parallel to the line x + y + 2z – 7 = 0 = 2x + 3y + z – 2 be ax + by + cz = 65. Then the distance of the point (a, b, c) from the plane 2x + 2y – z + 16 = 0 is

Answer: (9)

85. If the sum of all the solutions of −1 < x < 1, x ≠ 0, is then α is equal to

Answer: (2)

86. The vertices of a hyperbola H are (±6, 0) and its eccentricity is √5/2. Let N be the normal to H at a point in the first quadrant and parallel to the line √2x + y = 2√

If ds the length of the line segment of N between H and the y-axis then d² is equal to

Answer: (216)

87. Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 , is

Answer: (120)

88. Let Then the maximum value of β for which the equation has real roots, is

Answer: (25)

89. It the area enclosed by the parabolas P₁ : 2y = 5x² and P₂ : x² – y + 6 = 0 is equal to the area enclosed by 𝑃1 and y = αx, α > 0, then α³ is equal to

Answer: (600)

90. Let A₁, A₂, A₃ be the three A.P. with the same common difference d and having their first terms as A, A +1, A+2, respectively. Let a, b, c be the 7th , 9th ,17th terms of A₁, A₂, A₃, respectively such that

If a = 29, then the sum of first 20 terms of an AP whose first term is c – a − b and common difference is d/12, is equal to

Answer: (495)

JEE Main Session 1 24th January 2023 Shift 1 Question Paper and Answer Key

May 10, 2023May 6, 2023 by suresh84

JEE MAIN 24^th January 2023 Shift 1

Physics

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

1. A circular loop of radius 𝑟 is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance 𝑟 from the center of the loop on its axis is:

(1) 2√2 : 1

(2) 1 : 3√2

(3) 1 : √2

(4) 3√2 : 2

Answer: (1)

2. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth R_e = 6400 km ):

(1) 8 N

(2) 4.9 N

(3) 9.8 N

(4) 19.6 N

Answer: (1)

3. Two long straight wires P and Q carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F₁ – If distance between wires is halved and currents on them are doubled, force F₂ on 10 cm length of wire P will be:

(1) F₁/8

(2) 8F₁

(3) 10F₁

(4) F₁/10

Answer: (2)

4. Given below are two statements :

Statement I : The temperature of a gas is −73°C. When the gas is heated to 527°C, the root mean square speed of the molecules is doubled.

Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:

(1) Statement I is false but Statement II is true

(2) Both Statement I and Statement II are false

(3) Statement I is true but Statement II is false

(4) Both Statement I and Statement II are true

Answer: (3)

5. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:

(1) 272 m

(2) 68 m

(3) 192 m

(4) 136 m

Answer: (1)

6. Given below are two statements :

Statement I : If the Brewster’s angle for the light propagating from air to glass is 𝜃B, then the Brewster’s angle for the light propagating from glass to air is

Statement II : The Brewster’s angle for the light propagating from glass to air is tan⁻¹(μg) where μg is the refractive index of glass.

In the light of the above statements, choose the correct answer from the options given below:

(1) Both Statement I and Statement II are false

(2) Statement I is true but Statement II is false

(3) Statement I is false but Statement II is true

(4) Both Statement I and Statement II are true

Answer: (2)

7. A 100 m long wire having cross-sectional area 6.25 × 10⁻⁴ m² and Young’s modulus is 10¹⁰ Nm⁻² is subjected to a load of 250 N, then the elongation in the wire will be:

(1) 4 × 10⁻³ m

(2) 6.25 × 10⁻³ m

(3) 6.25 × 10⁻⁶ m

(4) 4 × 10⁻⁴ m

Answer: (1)

8. If two charges q₁ and q₂ are separated with distance ‘d’ and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

(1) 2d√k

(2) 1.5d√k

(3) d√k

(4) k√k

Answer: (3)

9. Consider the following radioactive decay process

The mass number and the atomic number of A₆ are given by:

(1) 210 and 84

(2) 210 and 82

(3) 211 and 80

(4) 210 and 80

Answer: (4)

10. From the photoelectric effect experiment, following observations are made. Identify which of these are correct.

(A) The stopping potential depends only on the work function of the metal.

(B) The saturation current increases as the intensity of incident light increases.

(D) Photoelectric effect can be explained using wave theory of light.

Choose the correct answer from the options given below:

(1) A, C, D only

(2) B, C only

(3) B only

(4) A, B, D only

Answer: (3)

11. Given below are two statements:

Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.

Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.

In the light of the above statements, choose the correct answer from the options given below:

(1) Both Statement I and Statement II are true

(2) Statement I is false but Statement II is true

(3) Statement I is true but Statement II is false

(4) Both Statement I and Statement II are false

Answer: (3)

12. 1 g of a liquid is converted to vapour at 3 × 10⁵ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm³ during this phase change, then the increase in internal energy in the process will be:

(1) 432000 J

(2) 4320 J

(3) 4800 J

(4) 4.32 × 10⁸ J

Answer: (2)

13. As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3Ω. The currents through the resistors R₄ and R₅ are I₄ and I₅ The values of I₄ and I₅ are:

Answer: (1)

14. A modulating signal is a square wave, as shown in the figure.

If the carrier wave is given as c(t) = 2sin(8πt) volts, the modulation index is:

(1) 1/4

(2) 1/2

(3) 1

(4) 1/3

Answer: (2)

15. A conducting circular loop of radius 10/√π cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

(1) emf = 1mV

(2) emf = 5mV

(3) emf = 100mV

(4) emf = 10mV

Answer: (4)

16. In represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :

(ω – angular frequency):

Answer: (4)

17. Match List I with List II:

Choose the correct answer from the options given below:

(1) A-I, B-III, C-IV, D-II

(2) A-III, B-I, C-II, D-IV

(3) A-II, B-IV, C-III, D-I

(4) A-III, B-IV, C-I, D-II

Answer: (4)

18. A travelling wave is described by the equation

y(x, t) = [0.05sin (8x – 4t)]m

The velocity of the wave is : [all the quantities are in SI unit]

(1) 8 ms⁻¹

(2) 4 ms⁻¹

(3) 0.5 ms⁻¹

(4) 2 ms⁻¹

Answer: (3)

19. As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g =10 m/s² )

(1) (4√3 + 1)N

(2) 4(√3 + 1)N

(3) (4√3 – 1)N

(4) 4(√3 – 1)N

Answer: (2)

20. Given below are two statements: one is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑

Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement.

Reason : The current in the forward bias is more than the current in the reverse bias for a p − n junction diode.

In the light of the above statements, choose the correct answer from the options given below:

(1) A is true but 𝐑 is false

(2) 𝐀 is false but 𝐑 is true

(3) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(4) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

Answer: (4)

SECTION-B

21. Vectors are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x is

Answer: (1)

22. Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6×10⁻²⁷ kg and radius of nucleus is 1.5 × 10⁻¹⁵ A^1/3 The approximate ratio of the nuclear density and water density is n × 10¹³. The value of n is

Answer: (11)

23. A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n × 10⁻³Ω. If the resistivity of the material is 2.4 × 10⁻⁸ Ωm. The value of n is

Answer: (2)

24. A stream of a positively charged particles having and velocity is deflected by an electric field The electric field exists in a region of 10 cm along x direction. Due to the electric field, the deflection of the charge particles in the 𝑦 direction is _____ mm

Answer: (2)

25. As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance = ____cm, from concave lens.

Answer: (120)

26. Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x is ______

Answer: (110)

27. A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is π/√x in SI unit. The value of x is ________

Answer: (5)

28. A hole is drilled in a metal sheet. At 27°C, the diameter of hole is 5 cm. When the sheet is heated to 177°C, the change in the diameter of hole is d × 10⁻³ The value of d will be ________ if coefficient of linear expansion of the metal is 1.6 × 10⁻⁵/°C.

Answer: (12)

29. In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ S.

Answer: (10)

30. A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is ______ N.

Answer: (40)

Chemistry

SECTION-A

31. ‘A’ and ‘ B ‘ formed in the following set of reactions are:

Answer: (2)

32. Decreasing order of the hydrogen bonding in following forms of water is correctly represented by

(A) Liquid water

(B) Ice

Choose the correct answer from the options given below:

(1) B > A > C

(2) A > B > C

(3) A = B > C

(4) C > B > A

Answer: (1)

33. Increasing order of stability of the resonance structures is:

Choose the correct answer from the options given below:

(1) D, C, A, B

(2) D, C, B, A

(3) C, D, A, B

(4) C, D, B, A

Answer: (BONUS)

34. ꞌRꞌ formed in the following sequence of reactions is:

Answer: (2)

35. The primary and secondary valencies of cobalt respectively in [Co(NH₃)₅Cl^ClCl₂ are:

(1) 3 and 6

(2) 2 and 6

(3) 3 and 5

(4) 2 and 8

Answer: (1)

36. An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is:

(1) Co²⁺

(2) Ni²⁺

(3) Fe²⁺

(4) Cu²⁺

Answer: (2)

37. Reaction of BeO with ammonia and hydrogen fluoride gives A which on thermal decomposition gives BeF₂ and NH₄ What is ‘A’ ?

(1) (NH₄)₂BeF₄

(2) H₃NBeF₃

(3) (NH₄)Be₂F₅

(4) (NH₄)BeF₃

Answer: (1)

38. Match List I with List II

Choose the correct answer from the options given below:

(1) A-IV, B-II, C-I, D-III

(2) A-I, B-III, C-II, D-IV

(3) A-III, B-IV, C-I, D-II

(4) A-I, B-IV, C-II, D-III

Answer: (1)

39. Match List I with List II

Choose the correct answer from the options given below:

(1) A-II, B-I, C-III, D-IV

(2) A-III, B-I, C-II, D-IV

(3) A-II, B-III, C-IV, D-I

(4) A-III, B-IV, C-I, D-II

Answer: (2)

40. In the following given reaction, ‘ A ‘ is

Answer: (3)

41. It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power “n” i.e. vⁿ of X-rays emitted is plotted against atomic number “Z”, following graph is obtained.

The value of ꞌꞌnꞌꞌ is

(1) 3

(2) 2

(3) 1

(4) 1/2

Answer: (4)

42. Given below are two statements:

Statement I : Noradrenaline is a neurotransmitter.

Statement II : Low level of noradrenaline is not the cause of depression in human.

In the light of the above statements, choose the correct answer from the options given below

(1) Statement I is correct but Statement II is incorrect

(2) Both Statement I and Statement II are correct

(3) Both Statement I and Statement II are incorrect

(4) Statement I is incorrect but Statement II is correct

Answer: (1)

43. Which of the Phosphorus oxoacid can create silver mirror from AgNO₃ solution?

(1) (HPO₃)_n

(2) H₄P₂O₆

(3) H₄P₂O₅

(4) H₄P₂O₇

Answer: (3)

44. Compound (X) undergoes following sequence of reactions to give the Lactone (Y).

Compound (X) is

Answer: (4)

45. Order of Covalent bond:

(A) KF > KI; LiF > KF

(B) KF < KI; LiF > KF

(D) LiF > KF; CuCl < NaCl

(E) KF < KI; CuCl > NaCl

Choose the correct answer from the options given below:

(1) C, E only

(2) B, C, E only

(3) A, B only

(4) B, C only

Answer:

46. Which of the following is true about freons?

(1) These are radicals of chlorine and chlorine monoxide

(2) These are chemicals causing skin cancer

(3) These are chlorofluorocarbon compounds

(4) All radicals are called freons

Answer: (3)

47. In the depression of freezing point experiment

(A) Vapour pressure of the solution is less than that of pure solvent

(B) Vapour pressure of the solution is more than that of pure solvent

(D) Only solvent molecules solidify at the freezing point

Choose the most appropriate answer from the options given below:

(1) A and C only

(2) A only

(3) A and D only

(4) B and C only

Answer: (3)

48. Statement I : For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration.

Statement II : For colloidal particles, the potential difference between the fixed layer and the diffused layer of same charges is called the electrokinetic potential or zeta potential.

In the light of the above statements, choose the correct answer from the options given below

(1) Statement I is false but Statement II is true

(2) Statement I is true but Statement II is false

(3) Both Statement I and Statement II are true

(4) Both Statement I and Statement II are false

Answer: (2)

49. Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases.

Reason R : I⁻ is a good nucleophile as well as a good leaving group.

In the light of the above statements, choose the correct answer from the options given below

(1) 𝐀 is false but 𝐑 is true

(2) 𝐀 is true but 𝐑 is false

(3) Both 𝐀 and 𝐑 are true but 𝐑 is NOT the correct explanation of 𝐀

(4) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

Answer: (3)

50. The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

(1) Cr²⁺

(2) Ti²⁺

(3) V²⁺

(4) Mn²⁺

Answer: (3)

SECTION-B

51. When Fe₉₃O is heated in presence of oxygen, it converts to Fe₂O₃. The number of correct statement/s from the following is

(A) The equivalent weight of Fe_0.93O is

(B) The number of moles of Fe²⁺ and Fe³⁺ in 1 mole of Fe_0.93O is 0.79 and 0.14 respectively

(D) The % composition of Fe²⁺ and Fe³⁺ in Fe_0.93O is 85% and 15% respectively

Answer: (4)

52. The number of correct statement/s from the following is

(A) Larger the activation energy, smaller is the value of the rate constant.

(B) The higher is the activation energy, higher is the value of the temperature coefficient.

(D) A plot of is a straight line with slope equal to –E_a/R

Answer: (4)

53. For independent processes at 300 K

The number of non-spontaneous processes from the following is

Answer: (2)

54. 5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL ) of this solution would be required to prepare 500 mL of 0.1M solution? Given: Molar Mass of Na,O and H is 23,16 and 1 g mol⁻¹ respectively

Answer: (180)

55. If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is nm. (Nearest integer)

Answer: (492)

56. Uracil is a base present in RNA with the following structure. % of N in uracil is

Answer: (25)

57. The dissociation constant of acetic acid is x × 10⁻⁵. When 25 mL of 0.2MCH₃COONa solution is mixed with 25 mL of 0.02MCH₃COOH solution, the pH of the resultant solution is found to be equal to 5 . The value of 𝑥 is

Answer: (10)

58. Number of moles of AgCl formed in the following reaction is _______

Answer: (2)

59. The d-electronic configuration of [CoCl₄]²⁻ in tetrahedral crystal field is e^mt₂ⁿ. Sum of ꞌꞌmꞌꞌ and ꞌꞌnumber of unpaired electronsꞌꞌ is

Answer: (*)

60. At 298 K, a 1 litre solution containing 10mmol of Cr₂O₇²⁻ and 100 mmol of Cr³⁺ shows a pH of 3.0.

Given : Cr₂O₇²⁻ → Cr³⁺; E° = 1.330 V and

The potential for the half cell reaction is x × 10⁻³ V. The value of x is

Answer: (917)

Mathematics

SECTION-A

61. Let Then is equal to

(1) 2

(2) 3/2

(3) 1

(4) −2/3

Answer: (3)

62. is equal to

(1) n²

(2)

(3) n

(4) n² + n

Answer: (3)

63. Let α be a root of the equation (a – c)x² + (b – a)x + (c – b) = 0 where a, b, c are distinct real numbers such that the matrix is singular. Then, the value of is

(1) 12

(2) 9

(3) 3

(4) 6

Answer: (3)

64. The area enclosed by the curves y² + 4x = 4 and y – 2x = 2 is

(1) 9

(2) 22/3

(3) 23/3

(4) 25/3

Answer: (1)

65. Let p, q ∈ ℝ and (1 – √3i)²⁰⁰ = 2¹⁹⁹(p + iq), i = √−1 Then p + q + q² and p – q + q² are roots of the equation

(1) x² – 4x – 1 = 0

(2) x² – 4x + 1 =0

(3) x² + 4x – 1 =0

(4) x² + 4x + 1 =0

Answer: (2)

66. Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

x + y + z = 1

2x + Ny + 2z = 2

3x + 3y + Nz = 3

has unique solution is k/6, then the sum of value of k and all possible values of N is

(1) 21

(2) 18

(3) 20

(4) 19

Answer: (3)

67. For three positive integers and r = pq + 1 such that 3, 3log_yx, 3log_zy, 7log_xz are in A.P. with common difference 1/2. Then r – p – q is equal to

(1) −6

(2) 12

(3) 6

(4) 2

Answer: (4)

68. The relation R = {(a, b): gcd(a, b) = 1, 2a ≠ b, a, b ∈Z} is :

(1) reflexive but not symmetric

(2) transitive but not reflexive

(3) symmetric but not transitive

(4) neither symmetric nor transitive

Answer: (4)

69. Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that Then is equal to

(1) 4

(2) 3

(3) 1

(4) 2

Answer: (2)

70. Let y = y(x) be the solution of the differential equation x³dy + (xy – 1)dx = 0, x > 0, y(1/2) = 3 – e. Then y(1) is equal to

(1) 1

(2) e

(3) 3

(4) 2 – e

Answer: (1)

71. If A and B are two non-zero n×n matrics such that A² + B = A² B, then

(1) A² = I or B – I

(2) A²B = I

(3) AB = I

(4) A²B = BA²

Answer: (4)

72. The equation x²– 4x + [x] + 3 = x[x], where [x] denotes the greatest integer function, has :

(1) a unique solution in (−∞,1)

(2) no solution

(3) exactly two solutions in (−∞,∞)

(4) a unique solution in (−∞,∞)

Answer: (4)

73. Let a tangent to the curve y² = 24x meet the curve xy = 2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the

(1) Length of latus rectum 3/2

(2) directrix 4x = −3

(3) length of latus rectum 2

(4) directrix 4x = 3

Answer: (4)

74. Let Ω be the sample space and A ⊆ Ω be an event.

Given below are two statements:

(S1) : If P(A) = 0, then A = ∅

(S2) : If P(A) = 1, then A = Ω

Then

(1) both (S1) and (S2) are true

(2) only (S1) is true

(3) only (S2) is true

(4) both (S1) and (S2) are false

Answer: (4)

75. The value of is

(1) ⁴⁴C₂₃

(2) ⁴⁵C₂₃

(3) ⁴⁴C₂₂

(4) ⁴⁵C₂₄

Answer: (2)

76. The distance of the point (−1, 9, −16) from the plane 2x + 3y – z = 5 measured parallel to the line is

(1) 31

(2) 13√2

(3) 20√2

(4) 26

Answer: (4)

77. is equal to:

(1) π/3

(2) π/4

(3) π/6

(4) π/2

Answer: (1)

78. Let

Then at x = 0

(1) f is continuous but not differentiable

(2) f and fꞌ both are continuous

(3) fꞌ is continuous but not differentiable

(4) f is continuous but fꞌ is not continuous

Answer: (4)

79. The compound statement (∼(P ∧ Q)) ∨ ((∼P) ∧ Q) ⇒ ((∼P) ∧ (∼Q)) is equivalent to

(1) (~Q) ∨ P

(2) ((~P) ∨ Q) ∧ (~Q)

(3) (~P) ∨ Q

(4) ((~P) ∨ Q) ∧ ((~Q) ∨ P)

Answer: (4)

80. The distance of the point (7,−3,−4) from the plane passing through the points (2,−3,1),(−1,1,−2) and (3,−4,2) is :

(1) 5

(2) 4

(3) 5√2

(4) 4√2

Answer: (3)

SECTION-B

81. Let λ ∈ ℝ and let the equation E be |x|² − 2|x| + |λ − 3| = 0. Then the largest element in the set S= {x + λ : x is an integer solution of E} is

Answer: (5)

82. Let a tangent to the curve 9x² + 16y²= 144 intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is

Answer: (7)

83. The shortest distance between the lines and is equal to

Answer: (14)

84. Suppose Then the value of α is

Answer: (1012)

85. The value of is

Answer: (2)

86. The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Answer: (60)

87. A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

Answer: (546)

88. The 4^th term of GP is 500 and its common ratio is 1/m. m ∈ Let S_n denote the sum of the first n terms of this GP. If S₆ > S₅ + 1 and S₇ < S₆ + 1/2, then the number of possible values of m is

Answer: (12)

89. Let C be the largest circle centred at (2,0) and inscribed in the ellipse If (1, α) lies on C, then 10 α² is equal to

Answer: (118)

90. The value of is

Answer: (22)

JEE MAIN 2023 Eligibility Criteria

December 27, 2022December 27, 2022 by suresh84

Eligibility Criteria

Age Criteria

For appearing in the JEE (Main) – 2023, there is no age limit for the candidates. The candidates who have passed the class 12/equivalent examination in 2021, 2022, or appearing in 2023 irrespective of their age can appear in JEE (Main) – 2023 examination. However, the candidates may be required to fulfill the age criteria of the Institute(s) to which they are desirous of taking admission.

List of Qualifying Examinations (QE)

The final examination of the 10+2 system, conducted by any recognized Central/ State Board, such as the Central Board of Secondary Education, New Delhi; Council for the Indian School Certificate Examinations, New Delhi; etc.
Intermediate or two-year Pre-University examination conducted by a recognized Board/ University.
Final examination of the two-year course of the Joint Services Wing of the National Defence Academy.
Senior Secondary School Examination conducted by the National Institute of Open Schooling with a minimum of five subjects.
Any Public School/ Board/ University examination in India or any foreign country is recognized as equivalent to the 10+2 system by the Association of Indian Universities (AIU).
Higher Secondary Certificate Vocational Examination.
A Diploma recognized by AICTE or a State board of technical education of at least 3 years duration.
General Certificate Education (GCE) examination (London/Cambridge/Sri Lanka) at the Advanced (A) level.
High School Certificate Examination of the Cambridge University or International Baccalaureate Diploma of the International Baccalaureate Office, Geneva.
Candidates who have completed the Class 12 (or equivalent) examination outside India or from a Board not specified above should produce a certificate from the Association of Indian Universities (AIU) to the effect that the examination they have passed is equivalent to the Class 12 Examination.
In case the Class 12 Examination is not a public examination, the candidate must have passed at least one public (Board or Pre-University) examination earlier.

Year of Appearance in Qualifying Examination

Only those candidates who have passed the Class 12/equivalent examination in 2021, 2022, or those who are appearing in Class 12/equivalent examination in 2023, are eligible to appear in JEE (Main) – 2023.
Candidates who passed the Class 12/equivalent examination in 2020 or before as well as those who will appear in such examination in 2024 or later are not eligible to appear in JEE (Main) – 2023.

State of Eligibility

State code of eligibility means the code of the State from where the candidate has passed Class 12 (or equivalent) qualifying examination by virtue of which the candidate becomes eligible to appear in JEE (Main) – 2023. It is important to note that the State code of eligibility does NOT depend upon the native place or the place of residence of the candidate. For example, if a candidate appears for the Class 12 (or equivalent) qualifying examination from an Institution situated in New Delhi and is a resident of Noida, Uttar Pradesh, then the candidate’s State code of eligibility will be that of Delhi and NOT that of Uttar Pradesh.

If a candidate has passed the Class 12 (or equivalent) qualifying examination from one State but appeared for improvement from another State, the candidate’s State code of eligibility will be from where the candidate first passed the Class 12 (or equivalent) examination and NOT the State from where the candidate has appeared for improvement.

Candidate passed/appearing for Class 12 from NIOS should select the State of Eligibility according to the State in which the study Centre is located.

For Indian nationals passing the Class 12 (or equivalent) examination from Nepal/Bhutan, the State code of eligibility will be determined based on a permanent address in India as given in the passport of the candidate.

The State code of eligibility of OCI passing Class 12 (or equivalent) examination in India is at par with Indian nationals. However, OCI passing the Class 12 (or equivalent) examination from an institution abroad are eligible for Other State quota seats or All India quota seats (but NOT for Home State quota seats) in all NITs, IIITs and Other-CFTIs.

Please Visit More Details

JEE MAIN Information Bulletin

https://jeemain.nta.nic.in/

JEE MAIN 2023 Information Bulletin

December 27, 2022December 27, 2022 by suresh84

JEE Main Session 2 29th July 2022 Shift 2 Question Paper and Answer Key

December 19, 2022 by suresh84

JEE Main Session 2 29^th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be

(A) 3F/2

(B) 3F/4

(D) 2F

Answer: (B)

2. Match List I with List II.

Choose the correct answer from the options given below:

(A) A-III, B-II, C-I, D-IV

(B) A-III, B-IV, C-II, D-I

(D) A-II, B-III, C-I, D-IV

Answer: (B)

3. Two identical thin metal plates has charge q₁ and q₂ respectively such that q₁> q₂. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is

Answer: (C)

4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan andmanganing are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(D) A is false but R is true.

Answer: (A)

5. A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

(A) 1:4

(B) 1:2

(D) 2:1

Answer: (B)

6. A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is

(A) 1.2 × 10^–5 N directed towards wire X

(B) 1.2 × 10^–4 N directed away from wire X

(D) 2.4 × 10^–5 N directed towards wire X

Answer: (A)

7. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

(A) g/2n

(B) g/n

(D) g/2n²

Answer: (D)

8. A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by π/2. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?

(A) 10/√2

(B) 5/√2

(D) 5/2

Answer: (D)

9. An unpolarised light beam of intensity 2I₀ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

(A) I₀/4

(B) I₀/2

(D) 3I₀/2

Answer: (C)

10. An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

(A) √2 : 1

(B) 2√2 : 1

(D) 8 : 1

Answer: (B)

11. Read the following statements:

(A) Volume of the nucleus is directly proportional to the mass number.

(B) Volume of the nucleus is independent of mass number.

(D) Density of the nucleus is directly proportional to the cube root of the mass number.

(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options

(A) (A) and (D) only

(B) (A) and (E) only

(D) (A) and (C) only

Answer: (B)

12. An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be

[If, g = 10 ms^–2 and radius of earth = 6400 km]

(A) 48 MJ

(B) 24MJ

(D) 12MJ

Answer: (A)

13. A ball is released from a height h. If t₁ and t₂ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t₁ and t₂.

(A) t₁ = (√2)t₂

(B) t₁ = (√2 – 1)t₂

(D) t₂ = (√2 – 1)t₁

Answer: (D)

14. Two bodies of masses m₁ = 5 kg and m₂ = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m1 will be

[Take g = 10 ms^–2]

(A) 30 N

(B) 40 N

(D) 60 N

Answer: (B)

15. If momentum of a body is increased by 20%, then its kinetic energy increases by

(A) 36%

(B) 40%

(D) 48%

Answer: (C)

16. The torque of a force about the origin is τ. If the force acts on a particle whose position vector is then the value of τ will be

Answer: (C)

17. A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

(A) −450 J

(B) 450 J

(D) 1350 J

Answer: (B)

18. The vertical component of the earth’s magnetic field is 6 × 10^–5 T at any place where the angle of dip is 37°. The earth’s resultant magnetic field at that place will be (Given tan 37° = 3/4)

(A) 8 × 10⁻⁵ T

(B) 6 × 10⁻⁵ T

(D) 1 × 10⁻⁴ T

Answer: (D)

19. The root mean square speed of smoke particles of mass 5 × 10⁻¹⁷ in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 10⁻²³ JK⁻¹]

(A) 60 mm s⁻¹

(B) 12mm s⁻¹

(D) 36mm s⁻¹

Answer: (C)

20. Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is

(A) 1.732

(B) 1.333

(D) 2.732

Answer: (C)

SECTION-B

21. A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√F rad s⁻¹.

Answer: (4)

22. Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is a × 10^–2m². The value of ‘a’ will be _____.

Answer: (84)

23. A metal wire of length 0.5 m and cross-sectional area 10^–4 m² has breaking stress 5 × 10⁸ Nm^–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms^–1.

Answer: (50)

24. The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10^–4 The value of x is _______. [use g = 10 m/s²]

Answer: (25)

25. A modulating signal 2sin (6.28 × 10⁶) t is added to the carrier signal 4sin(12.56 × 10⁹) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.

Answer: (2)

26. The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms^–1. The area of cross-section of the wire is 2.0 mm² and its Young’s modulus is 1.2 × 10¹¹ Nm^–2. The extension of the wire over its natural length due to its tension will be x × 10^–5 The value of x is _____.

Answer: (15)

27. The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5√x s. The value of x will be _____.

Answer: (5)

28. A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be ____ Ω.

Answer: (480)

29. Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be ‘e’ after a time 1/aλ. The value of a is _____.

Answer: (9)

30. A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in the LC circuit will be ______A.

Answer: (10)

CHEMISTRY

SECTION-A

1. Consider the reaction

4HNO₃(l) + 3KCl(s) → Cl₂(g) + NOCl(g) + 2H₂O(g) + 3KNO₃(s)

The amount of HNO₃ required to produce 110.0 g of KNO₃is :

(Given : Atomic masses of H, O, N and K are 1, 16, 14 and 39, respectively.)

(A) 32.2 g

(B) 69.4 g

(D) 162.5 g

Answer: (C)

2. Given below are the quantum numbers for 4 electrons.

(A)n = 3, l = 2, m₁ = 1, ms = +1/2

(B)n = 4, l = 1, m₁ = 0, ms = +1/2

(C)n = 4, l = 2, m₁ = –2, ms = –1/2

(D)n = 3, l = 1, m₁ = –1, ms = +1/2

The correct order of increasing energy is :

(A) D < B < A < C

(B) D < A < B < C

(D) B < D < C < A

Answer: (B)

3. C(s) + O₂(g) → CO₂(g) + 400 kJ

When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into ‘CO’ and the remaining is converted into ‘CO₂‘.

The heat generated when 0.6 kg of coal is burnt is ______.

(A) 1600 kJ

(B) 3200 kJ

(D) 6600 kJ

Answer: (D)

4. 200 mL of 0.01 M HCl is mixed with 400 mL of 0.01M H₂SO₄. The pH of the mixture is ____.

(A) 1.14

(B) 1.78

(D) 3.02

Answer: (B)

5. Given below are the critical temperatures of some of the gases :

The gas showing least adsorption on a definite amount of charcoal is :

(A) He

(B) CH₄

(D) NH₃

Answer: (A)

6. In liquation process used for tin (Sn), the metal :

(A) is reacted with acid

(B) is dissolved in water

(D) is fused with NaOH.

Answer: (C)

7. Given below are two statements.

Statement I:Stannane is an example of a molecular hydride.

Statement II:Stannane is a planar molecule. In the light of the above statement, choose the most appropriate answer from the options given below :

(A) Both Statement I and Statement II are true.

(B) Both Statement I and Statement II are false.

(D) Statement I is false but Statement II is true.

Answer: (C)

8. Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?

(A)

(B) CaSO₄.2H₂O

(D) CaCO₃

Answer: (B)

9. When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to :

(A) B₂O₃

(B) Co(BO₂)₂

(D) Co[B₄O₅(OH)₄]

Answer: (B)

10. Which of the following 3d-metal ion will give the lowest enthalpy of hydration (∆_hydH) when dissolved in water ?

(A) Cr²⁺

(B) Mn²⁺

(D) Co²⁺

Answer: (B)

11. Octahedral complexes of copper (II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion ?

(en–ethylenediamine; H₂N-CH₂-CH₂-NH₂)

(A) [Cu(H₂O)₆]SO₄

(B) [Cu(en)(H₂O)₄]SO₄

(D) trans-[Cu(en)₂Cl₂]

Answer: (A)

12. Dinitrogen is a robust compound, but reacts at high altitude to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is :

(A) NO

(B) NO₃⁻

(D) NO₂⁻

Answer: (C)

13. Correct structure of γ-methylcyclohexanecarbaldehyde is :

Answer: (A)

14. Compound ‘A’ undergoes following sequence of reactions to give compound ‘B’. The correct structure and chirality of compound ‘B’ is:

[where Et is –C₂H₅]

Answer: (C)

15. Given below are two statements.

Statement I: The compound is optically active.

Statement II: is mirror image of above compound A.

In the light of the above statement, choose the most appropriate answer from the options given below.

(A) Both Statement I and Statement II are correct

(B) Both Statement I and Statement II are incorrect.

(D) Statement I is incorrect but Statement II is correct.

Answer: (C)

16. When enthanol is heated with conc. H₂SO₄, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is :

(A) Formaldehyde

(B) Formic acid

(C)Glycol

(D) Ethanoic acid

Answer: (C)

17. The Hinsberg reagent is :

Answer: (A)

18. Which of the following is NOT a natural polymer?

(A) Protein

(B) Starch

(D) Rayon

Answer: (D)

19. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Amylose is insoluble in water.

Reason R : Amylose is a long linear molecule with more than 200 glucose units.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both A and R are correct and R is the correct explanation of A.

(B) Both A and R are correct and R is NOT the correct explanation of A.

(D) A is not correct but R is correct.

Answer: (D)

20. A compound ‘X’ is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with CH₃ Compound ‘X’ exists in ionized form in basic medium. The compound ‘X’ is :

(A) methyl orange

(B) methyl red

(D) erichrome Black T

Answer: (C)

SECTION-B

21. ‘x’ g of molecular oxygen (O₂) is mixed with 200 g of neon (Ne). The total pressure of the nonreactive mixture of O₂ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of ‘x’ is_____. [Given: Molar mass of O₂ = 32 g mol^–1. Molar mass of Ne = 20 g mol^–1]

Answer: (80)

22. Consider, PF₅, BrF₅, PCl₃, SF₆, [ICl₄]^–, ClF₃ and IF₅.

Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having sp³d² hybridisation is____.

Answer: (4)

23. 1.80 g of solute A was dissolved in 62.5 cm³ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is _______ g mol^–1.

[Given: Freezing point of ethanol is 156.0 K. Density of ethanol is 0.80 g cm^–3.

Freezing point depression constant of ethanol is 2.00 K kg mol^–1]

Answer: (80)

24. For a cell, Cu(s) |Cu²⁺(0.001M| |Ag⁺(0.01M)| Ag(s) the cell potential is found to be 0.43 V at 298 K. The magnitude of standard electrode potential for Cu²⁺/Cu is _______ × 10^–2 V.

Answer: (34)

25. Assuming 1μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is______ × 10^–1μ

[Given :ln 10 = 2.303; log2 = 0.30]

Answer: (1)

26. Sum of oxidation state (magnitude) and coordination number of cobalt in Na[Co(bpy)Cl₄] is_______.

Answer: (9)

27. Consider the following sulphure based oxoacids. H₂SO₃, H₂SO₄, H₂S₂O₈ and H₂S₂O₇.

Amongst these oxoacids, the number of those with peroxo(O-O) bond is______.

Answer: (1)

28. A 1.84 mg sample of polyhydric alcoholic compound ‘X’ of molar mass 92.0 g/mol gave 1.344 mL of H₂ gas at STP. The number of alcoholic hydrogens present in compound ‘X’ is____.

Answer: (3)

29. The number of stereoisomers formed in a reaction of (±) Ph(C=O) C(OH)(CN)Ph with HCN is_____.

Answer: (3)

30. The number of chlorine atoms in bithionol is____.

Answer: (4)

MATHEMATICS

SECTION-A

1. If z ≠ 0 be a complex number such that then the maximum value of |z| is

(A) √2

(B) 1

(D) √2 + 1

Answer: (D)

2. Which of the following matrices can NOT be obtained from the matrix by a single elementary row operation?

Answer: (C)

3. If the system of equations

x + y + z = 6

2x + 5y + αz = β

x + 2y + 3z = 14

has infinitely many solutions, then α + β is equal to

(A) 8

(B) 36

(D) 48

Answer: (C)

4. Let the function be continuous at x = 0.

The α is equal to :

(A) 10

(B) −10

(D) −5

Answer: (D)

5. If [t] denotes the greatest integer ≤ t, then the value of is

Answer: (A)

6. Let be a sequence such that a₀ = a₁ = 0 and a_n+2 = 3a_n+1 – 2a_n + 1, ∀ n ≥

Then a₂₅ a₂₃ – 2 a₂₅ a₂₂ – 2 a₂₃ a₂₄ + 4 a₂₂ a₂₄ is equal to:

(A) 483

(B) 528

(D) 624

Answer: (B)

7. is equal to:

(A) 22! – 21!

(B) 22! – 2(21!)

(D) 21! – 20!

Answer: (B)

8. For then

Answer: (A)

9. If the solution curve of the differential equation passes through the points (2, 1) and (k + 1, 2), k > 0, then

Answer: (A)

10. Let y = y(x) be the solution curve of the differential equation x >−1 which passes through the point (0, 1). Then y(1) is equal to

(A) 1/2

(B) 3/2

(D) 7/2

Answer: (B)

11. Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that If one vertex of the square is (10 (cos α – sin α), 10(sin α + cos α)), where α ∈ (0, π/2) and the equation of one diagonal is (cosα – sin α)x + (sin α + cosα) y = 10, then 72(sin⁴α + cos⁴α) + a² – 3a + 13 is equal to

(A) 119

(B) 128

(D) 155

Answer: (B)

12. The number of elements in the set

(A) 1

(B) 3

(D) infinite

Answer: (A)

13. Let A(α, −2), B(α, 6) and C(α/4, −2) be vertices of a ΔABC. If (5, α/4) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?

(A) Area is 24

(B) Perimeter is 25

(D) Inradius is 2

Answer: (B)

14. Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane such that ∠PRQ = 60°, then the area of ΔPQR is equal to :

(A) √3/2

(B) √3

(D) 3

Answer: (B)

15. If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

(A) 21/2

(B) 59/8

(D) 95/8

Answer: (D)

16. Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

(A) 4/9

(B) 5/18

(D) 3/10

Answer: (B)

17. S = {z = x + iy: |z – 1 + i| ≥ |z|, |z| < 2, |z + i| = |z – 1|}.Then the set of all values of x, for which w = 2x + iy∈ S for some y ∈ R is

Answer: (B)

18. Let be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and then is equal to :

(A) 10

(B) 14

(D) 18

Answer: (C)

19. The domain of the function is:

(A) [1, ∞)

(B) [−1, 2]

(D) (−∞, 2]

Answer: (C)

20. The statement (p ⇒ q) ∨ (p ⇒ r) is NOT equivalent to

(A) (p∧ (~r)) ⇒ q

(B) (~q) ⇒ ((~r) ∨ p)

(D) (p∧ (~q)) ⇒ r

Answer: (B)

SECTION-B

21. The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _______.

Answer: (96)

22. Let α, β(α > β) be the roots of the quadratic equation x² – x – 4 = 0. If P_n = αⁿ – βⁿ, n ∈ℕ then is equal to ______.

Answer: (16)

23. Let For k∈ N, if X’A^kX = 33, then k is equal to _______.

Answer: (10)

24. The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is _______.

Answer: (6)

25. If then L is equal to _____.

Answer: (221)

26. If [t] denotes the greatest integer ≤ t, then the number of points, at which the function is not differentiable in the open interval (–20, 20), is ________.

Answer: (79)

27. If the tangent to the curve y = x³ – x² + x at the point (a, b) is also tangent to the curve y = 5x² + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to ________.

Answer: (195)

28. Let AB be a chord of length 12 of the circle If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to _______.

Answer: (72)

29. Let be two vectors such that and Then is equal to _______.

Answer: (14)

30. Let

S = {(x, y) ∈ℕ×ℕ : 9(x – 3)² + 16(y – 4)²≤ 144}

and

T = {(x, y)∈ℝ×ℝ : (x – 7)² + (y – 4)²≤ 36}.

Then n(S ⋂ T) is equal to ______.

Answer: (27)

JEE Main Session 2 28th July 2022 Shift 2 Question Paper and Answer Key

December 19, 2022 by suresh84

JEE Main Session 2 28^th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Consider the efficiency of Carnot engine is given by where α and β are constants. If T is temperature, k is Boltzmann constant, θ is angular displacement, and x has the dimensions of length. Then, choose the incorrect option

(A) Dimensions of βis same as that of force.

(B) Dimensions of α^–1 x is same as that of energy.

(D) Dimensions of α is same as that of β

Answer: (D)

2. At time t = 0 a particle starts travelling from a height in a plane keeping z coordinate constant. At any instant of time it’s position along the directions are defined at 3t and 5t³ At t = 1 s acceleration of the particle will be

Answer: (B)

3. A pressure-pump has a horizontal tube of cross sectional area 10 cm² for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is

[given: density of water = 1000 kg/m³]

(A) 300 N

(B) 500 N

(D) 400 N

Answer: (D)

4. A uniform metal chain of mass m and length ‘L’ passes over a massless and frictionless pully. It is released from rest with a part of its length ‘l’ is hanging on one side and rest of its length ‘L – l’ is hanging on the other side of the pully. At a certain point of time, when l = L/x, the acceleration of the chain is g/2. The value of x is ______.

(A) 6

(B) 2

(D) 4

Answer: (D)

5. A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it’s kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

(A) 45 m

(B) 90 m

(D) 25 m

Answer: (A)

6. Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4s and 6s respectively. Then the value of h is –

(consider radius of earth R_E = 6400 km and g on earth 10 m/s²)

(A) 1200 km

(B) 1600km

(D) 4800km

Answer: (C)

7. Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 10⁵ N is applied an the top surface of water using a piston. The speed of efflux from the hole will be:

(given atmospheric pressure P_A = 1.01 × 10⁵ Pa, density of water ρ_w = 1000 kg/m³ and gravitational acceleration g = 10 m/s²)

(A) 11.6 m/s

(B) 10.8m/s

(D) 14.4m/s

Answer: (C)

8. A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J mol^–1k^–1)

(A) 2229 J

(B) 5616 J

(D) 13,104 J

Answer: (C)

9. A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :

(Given C_o = capacitance of capacitor with air as medium between plates.)

Answer: (A)

10. A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be_______.

(A) tan⁻¹ (4)

(B) tan⁻¹ (2)

(D) tan⁻¹ (3)

Answer: (B)

11. Given below are two statements :

Statement I : A uniform wire of resistance 80Ω is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5Ω.

Statement II : Two resistance 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3 : 2.

In the light of the above statements, choose the most appropriate answer from the options given below

(A) Both statement I and statement II are correct

(B) Both statement I and statement II are incorrect

(D) Statement I is incorrect but statement II is correct

Answer: (C)

12. A triangular shaped wire carrying 10 A current is placed in a uniform magnetic field of 0.5 T, as shown in figure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm).

(A) 0.126 N

(B) 0.312 N

(D) 0.245 N

Answer: (C)

13. The magnetic field at the center of current carrying circular loop is B₁. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B₂. The value of B₁/B₂ will be

(A) 9 : 4

(B)12 : √5

(D) 5 :√3

Answer: (C)

14. A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

(A) 800 Ω and 1.06 Ω

(B) 10 Ω and 500 Ω

(D) 1.0 Ω and 500 Ω

Answer: (C)

15. Sun light falls normally on a surface of area 36 cm2 and exerts an average force of 7.2 × 10^–9 N within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

(A) 25.92 × 10² W/cm²

(B) 8.64 × 10⁻⁶ W/cm²

(D) 0.06 W/cm²

Answer: (D)

16. The power of a lens (biconvex) is 1.25 m–1 in particular medium. Refractive index of the lens is 1.5, and the radii of curvature are 20 cm and 40 cm, respectively. The refractive index of surrounding medium

(A) 1.0

(B) 9/7

(D) 4/3

Answer: (B)

17. Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

(A) 1 : 2

(B) 1 : 3

(D) 3 : 2

Answer: (C)

18. A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample is

(A) 5 min

(B) 7.5min

(D) 30min

Answer: (A)

19. An npn transistor with current gain β = 100 in common emitter configuration is shown in the figure. The output voltage of the amplifier will be

(A) 0.1 V

(B) 1.0 V

(D) 100 V

Answer: (B)

20. A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is

(A) 220 kHz

(B) 180kHz

(D) 440kHz

Answer: (D)

SECTION-B

21. A ball is thrown vertically upwards with a velocity of 19.6 ms^–1 from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be (k/5) m. The value of k is ______ (use g = 9.8 m/s²)

Answer: (392)

22. The distance of centre of mass from end A of a one dimensional rod (AB) having mass density and length L (in meter) is The value of α is ______. (where x is the distance from end A)

Answer: (8)

23. A string of area of cross-section 4mm² and length 0.5 m is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ______×10^–5.

(use young’s modulus 10¹¹ N/m² and g = 10 m/s²)

Answer: (30)

24. At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

Answer: (750)

25. The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4 (1–cos 4x) J. The time period of the particle for small oscillation (sin θ≃θ) is The value of K is __________

Answer: (2)

26. An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ____________ W.

Answer: (14)

27. For the given circuit the current through battery of 6 V just after closing the switch ‘S’ will be __________ A.

Answer: (1)

28. An object ‘o’ is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10s will be at _______ cm.

Answer: (400)

29. In an experiment with a convex lens, the plot of the image distance (ν′) against the object distance (μ′) measured from the focus gives a curve ν′μ′ = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is _______ cm.

Answer: (15)

30. In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is _________.

Answer: (5)

CHEMISTRY

SECTION-A

1. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Zero orbital overlap is an out of phase overlap.

Reason : It results due to different orientation/ direction of approach of orbitals.

In the light of the above statements. Choose the correct answer from the options given below

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (A)

2. The correct decreasing order for metallic character is

(A) Na > Mg > Be > Si > P

(B) P > Si > Be > Mg > Na

(D) Be > Na > Mg > Si > P

Answer: (A)

3. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The reduction of a metal oxide is easier if the metal formed is in liquid state than solid state.

Reason R : The value of ∆G^⊝becomes more on negative side as entropy is higher in liquid state than solid state.

In the light of the above statements. Choose the most appropriate answer from the options given below

(A) Both A and R are correct and R is the correct explanation of A

(B) Both A and R are correct but R is NOT the correct explanation of A

(D) A is not correct but R is correct

Answer: (A)

4. The products obtained during treatment of hard water using Clark’s method are:

(A) CaCO₃ and MgCO₃

(B) Ca(OH)₂ and Mg(OH)₂

(D) Ca(OH)₂ and MgCO₃

Answer: (C)

5. Statement I: An alloy of lithium and magnesium is used to make aircraft plates.

Statement II: The magnesium ions are important for cell-membrane integrity.

In the light the above statements, choose the correct answer from the options given below

(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(D) Statement I is false but Statement II is true

Answer: (B)

6. White phosphorus reacts with thionyl chloride to give

(A) PCl₅, SO₂ and S₂Cl₂

(B) PCl₃, SO₂ and S₂Cl₂

(D) PCl₅, SO₂ and Cl₂

Answer: (B)

7. Concentrated HNO₃ reacts with Iodine to give

(A) HI, NO₂ and H₂O

(B) HIO₂, N₂O and H₂O

(D) HIO₄, N₂O and H₂O

Answer: (C)

8. Which of the following pair is not isoelectronic species?

(At. no.Sm, 62; Er, 68: Yb, 70: Lu, 71; Eu, 63: Tb, 65; Tm, 69)

(A) Sm²⁺ and Er³⁺

(B) Yb²⁺ and Lu³⁺

(D) Tb²⁺ and Tm⁴⁺

Answer: (D)

9. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Permanganate titrations are not performed in presence of hydrochloric acid.

Reason R: Chlorine is formed as a consequence of oxidation of hydrochloric acid.

In the light of the above statements, choose the correct answer from the options given below

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (A)

10. Match List I with List II

Choose the correct answer from the options given below:

(A) A-IV, B-I, C-III, D-II

(B) A-I. B-IV, C-III, D-II

(D) A-IV, B-I, C-II. D-III

Answer: (B)

11. Dinitrogen and dioxygen. the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because

(A) N₂ is unreactive in the condition of atmosphere.

(B) Oxides of nitrogen are unstable.

(D) The reaction is endothermic and require very high temperature.

Answer: (D)

12. The major product in the given reaction is

Answer: ()

13. Arrange the following in increasing order of reactivity towards nitration

(A) p-xylene (B) bromobenzene

(C)mesitylene (D) nitrobenzene

(E)benzene

Choose the correct answer from the options given below

(A) C < D < E < A < B

(B) D < B < E < A < C

(D) C < D < E < B < A

Answer: (B)

14. Compound I is heated with Conc. HI to give a hydroxy compound A which is further heated with Zn dust to give compound B. Identify A and B.

Answer: (D)

15. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Aniline on nitration yields ortho, meta&para nitro derivatives of aniline.

Reason R: Nitrating mixture is a strong acidic mixture.

In the light of the above statements, choose the correct answer from the options given below

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (A)

16. Match List I with List II

Choose the correct answer from the options given below:

(A) A-II, B-III, C-IV, D-I

(B) A-III, B-II, C-IV, D-I

(D) A-I. B-III, C-IV, D-II

Answer: (B)

17. Two statements in respect of drug-enzyme interaction are given below

Statement I: Action of an enzyme can be blocked only when an inhibitor blocks the active site of the enzyme.

Statement II: An inhibitor can form a strong covalent bond with the enzyme.

In the light of the above statements. Choose the correct answer from the options given below

(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(D) Statement I is false but Statement II is true

Answer: (D)

18. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Thin layer chromatography is an adsorption chromatography.

Reason: A thin layer of silica gel is spread over a glass plate of suitable size in thin layer chromatography which acts as an adsorbent.

In the light of the above statements, choose the correct answer from the options given below

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (A)

19. The formulas of A and B for the following reaction sequence are

(A) A = C₇H₁₄O₈, B = C₆H₁₄

(B) A = C₇H₁₃O₇, B = C₇H₁₄O

(D) A = C₇H₁₄O₈, B = C₆H₁₄O₆

Answer: (A)

20.

Find out the major product for the above reaction.

Answer: (C)

SECTION-B

21. 2L of 0.2 M H₂SO₄ is reacted with 2L of 0.1 M NaOH solution, the molarity of the resulting product Na₂SO₄ in the solution is ____ millimolar. (Nearest integer).

Answer: (25)

22. Metal M crystallizes into a FCC lattice with the edge length of 4.0×10⁻⁸ The atomic mass of the metal is ______ g/mol.

(Nearest integer). (Use : NA = 6.02×10²³ mol⁻¹, density of metal, M = 9.03 g cm⁻³)

Answer: (87)

23. If the wavelength for an electron emitted from Hatom is 3.3×10⁻¹⁰ m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is _____times. (Nearest integer).

[Given : h = 6.626 ×10⁻³⁴Js, Mass of electron = 9.1×10⁻¹]

Answer: (2)

24. A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is _______ atm. (Nearest integer)

Answer: (2)

25. At 600K, 2 mol of NO are mixed with 1 mol of O₂.

2NO_(g) + O₂(g) ⇄ 2NO₂(g)

The reaction occurring as above comes to equilibrium under a total pressure of 1 atom. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is _______. (Nearest integer).

Answer: (2)

26. A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280K and 759 mm Hg. The percentage of nitrogen in the given organic compound is ____. (Nearest integer).

(a) The vapour pressure of water at 280 K is 14.2 mm Hg

(b) R = 0.082 L atm K^–1mol^–1

Answer: (22)

27. On reaction with stronger oxidizing agent like KIO₄, hydrogen peroxide oxidizes with the evolution of O₂. The oxidation number of I in KIO₄changes to ______.

Answer: (5)

28. For a reaction, given below is the graph of ln k vs 1/T. The activation energy for the reaction is equal to ________ cal mol⁻¹. (Nearest integer).

(Given : R = 2 cal K⁻¹ mol⁻¹)

Answer: (8)

29. Among the following the number of curves not in accordance with Freundlich adsorption isotherm is ______.

Answer: (3)

30. Among the following the number of state variable is ______.

Internal energy (U)

Volume (V)

Heat (q)

Enthalpy (H)

Answer: (3)

MATHEMATICS

SECTION-A

1. Let and T = {x ∈Z : x² – 7|x| + 9 ≤ 0}. Then the number of elements in S ∩ T is

(A) 7

(B) 5

(D) 3

Answer: (D)

2. Let α, β be the roots of the equation x² – √2x + √6 = 0 and be the roots of the equation x² + ax + b = 0 . Then the roots of the equation x² – (a + b – 2)x + (a + b + 2) = 0 are

(A) Non-real complex number

(B) Real and both negative

(D) Real and exactly one of them is positive

Answer: (B)

3. Let A and B be any two 3 × 3 symmetric and skew symmetric matrices, respectively. Then which of the following is NOT true?

(A) A⁴ – B⁴ is a symmetric matrix

(B) AB – BA is a symmetric matrix

(D) AB + BA is a skew-symmetric matrix

Answer: (C)

4. Let f(x) = ax² + bx + c be such that f(1) = 3, f(-2) = λ and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then λ is equal to

(A) −4

(B) 13/2

(D) 4

Answer: (D)

5. The function f: ℝ → ℝ defined by is continuous for all x in

(A) ℝ − {−1}

(B) ℝ − {−1, 1}

(D) ℝ − {0}

Answer: (B)

6. The function f(x) = xe^x(1⁻^x), x ∈ ℝ is

(A) Increasing in (−1/2, 1)

(B) Decreasing in (1/2, 2)

(D) Decreasing in (−1/2, 1/2)

Answer: (A)

7. The sum of the absolute maximum and absolute minimum values of the function f(x) = tan⁻¹ (sin x – cos x) in the interval [0, π] is

(A) 0

(B)

(C)

(D) –π/12

Answer: (C)

8. Let and Then is equal to

(A) −2√2/3

(B) 2/3

(D) −2/3

Answer: (D)

9. Let n = 1, 2, 3, ….. Then

(A) 50I₆ – 9I₅ = xI′₅

(B) 50I₆ – 11I₅ = xI′₅

(D) 50I₆ – 11I₅= I′₅

Answer: (A)

10. The area enclosed by the curves y = log_e (x + e²), and x = log_e2, above the line y = 1 is

(A) 2 + e – log_e 2

(B) 1 + e – log_e 2

(D) 1 + log_e 2

Answer: (B)

11. Let y = y(x) be the solution curve of the differential equation passing through the point Then √7 (8) is equal to

(A) 11 + 6log_e 3

(B) 19

(D) 19 – 6log_e 3

Answer: (D)

12. The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is

Answer: (A)

13. Let the tangents at two points A and B on the circle x² + y² – 4x + 3 = 0 meet at origin O(0, 0). Then the area of the triangle OAB is

(A) 3√3/2

(B) 3√3/4

(D) 3/4√3

Answer: (B)

14. Let the hyperbola pass through the point (2√2, −2√2). A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?

(A) (2√3, 3√2)

(B) (3√3, −6√2)

(D) (3√6, 6√2)

Answer: (B)

15. Let the lines and be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

(A) (0, −2, −2)

(B) (−5, 0, −1)

(D) (0, 4, 5)

Answer: (D)

16. A plane P is parallel to two lines whose direction rations are –2, 1, –3 and –1, 2, –2 and it contains the point (2, 2, –2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α, β, γ. If V is the volume of the tetrahedron OABC, where O is the origin and p = α + β + γ, then the ordered pair (V, p) is equal to :

(A) (48, –13)

(B) (24, –13)

(D) (24, –5)

Answer: (B)

17. Let S be the set of all a∈ R for which the angle between the vectors and is acute. Then S is equal to

(A) (−∞, −4/3)

(B) Φ

(D) (12/7, ∞)

Answer: (C)

18. A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that ∠PAO = ∠PBO = 15° and ∠PCO = 45°, where C is the midpoint of AB. Then (OP)² is equal to

Answer: (B)

19. Let A and B be two events such that and Consider

(S1) P(A′ ∪ B) = 5/6,

(S2) P(A′ ∩ B′) = 1/18. Then

(A) Both (S1) and (S2) are true

(B) Both (S1) and (S2) are false

(D) Only (S2) is true

Answer: (A)

20. Let

p : Ramesh listens to music.

q :Ramesh is out of his village.

r : It is Sunday.

s : It is Saturday.

Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as

(A) ((~q) ∧ (r ∨ s)) ⇒ P

(B) (q∧ (r ∨ s)) ⇒ P

(D) p⇒ ((~q)∧ (r ∨ s))

Answer: (D)

SECTION-B

21. Let the coefficients of the middle terms in the expansion of and respectively form the first three terms of an A.P. If d is the common difference of this A.P., then is equal to _______

Answer: (57)

22. A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g is equal to ______.

Answer: (17)

23. Let the tangents at the points P and Q on the ellipse meet at the point R(√2, 2√2 – 2). If S is the focus of the ellipse on its negative major axis, then SP² + SQ²is equal to ________.

Answer: (13)

24. If 1 + (2 + ⁴⁹C₁ + ⁴⁹C₂ + … ⁴⁹C₄₉) (⁵⁰C₂ + ⁵⁰C₄ + … ⁵⁰C₅₀) is equal to 2ⁿ. m, where m is odd, then n + m is equal to ______.

Answer: (99)

25. Two tangent lines l₁ and l₂ are drawn from the point (2, 0) to the parabola 2y² = – x. If the lines l₁ and l₂ are also tangent to the circle (x – 5)² + y² = r, then 17r is equal to _________.

Answer: (9)

26. If where m is odd, then m.n is equal to ______

Answer: (12)

27. Let Then the number of elements in the set

A = {θ∈S : tan θ(1 + √5 tan(2θ)) = √5 – tan(2θ)} is ______

Answer: (5)

28. Let z = a + ib, b≠ 0 be complex numbers satisfying Then the least value of n ∈ N, such that zⁿ = (z + 1)ⁿ, is equal to _____.

Answer: (6)

29. A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ² is the variance of X, then 100 σ² is equal to ____.

Answer: (56)

30. The value of the integral is equal to _______

Answer: (104)

JEE Main Session 2 27th July 2022 Shift 2 Question Paper and Answer Key

December 15, 2022 by suresh84

JEE Main Session 2 27^th July 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. An expression of energy density is given by where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be

(A) [ML²T⁻²θ⁻¹]

(B) [M⁰L²T⁻²]

(D) [M⁰L²T⁰]

Answer: (D)

2. A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T/√2, is

[Take g = 10 m/s²]

Answer: (D)

3. A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be :

(A) Mg

(B) Mg cosθ

(C)

(D)

Answer: (A)

4. A block ‘A’ takes 2 s to slide down a frictionless incline of 30° and length ‘l’, kept inside a lift going up with uniform velocity ‘v’. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately:

(A) 2.66 s

(B) 0.83 s

(D) 0.70 s

Answer: (C)

5. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:

(A) 2.0

(B) 1.0

(D) 1.5

Answer: (C)

6. A body of mass m is projected with velocity λv_ein vertically upward direction from the surface of the earth into space. It is given that evis escape velocity and λ< 1. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be (R : radius of earth)

Answer: (B)

7. A steel wire of length 3.2 m (Y_s = 2.0 × 10¹¹ Nm⁻²) and a copper wire of length 4.4 m (Y_c = 1.1 × 10¹¹ Nm⁻²), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be:

(Given π = 22/7)

(A) 360

(B) 180

(D) 154

Answer: (D)

8. In 1st case, Carnot engine operates between temperatures 300 K and 100 K. In 2nd case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2nd case) will be:

(A) Same as the 1st case

(B) Always greater than the 1st case

(D) May increase or decrease with respect to the 1st case

Answer: (C)

9. Which statements are correct about degrees of freedom?

(A) A molecule with n degrees of freedom has n² different ways of storing energy.

(B) Each degree of freedom is associated with (1/2)RT average energy per mole.

(C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom.

(D) CH₄ has a total of 6 degrees of freedom.

Choose the correct answer from the option given below:

(A) (B) and (C) only

(B) (B) and (D) only

(D) (C) and (D) only

Answer: (B)

10. A charge of 4 μC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

(A) 1 μC and 3 μC

(B) 2 μC and 2 μC

(D) 1.5 μC and 2.5 μC

Answer: (B)

11. (A) The drift velocity of electrons decreases with the increase in the temperature of conductor.

(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.

(D) The drift velocity of electron is inversely proportional to the length of the conductor.

(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below

(A) (A) and (B) only

(B) (A) and (D) only

(D) (B) and (C) only

Answer: (A)

12. A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (B_Q: B_P) is

(A) √3 : 4

(B) 4 :√3

(D) 2 :√3

Answer: (A)

13. A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of the cyclotron ‘dees’ is 60 cm, the kinetic energy of the accelerated protons in MeV will be

(Use m_p = 1.6 × 10⁻²⁷ kg, e = 1.6 × 10⁻¹⁹ C]

(A) 12

(B) 18

(D) 32

Answer: (B)

14. A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude (V_m) 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately :

(A) 466 mA

(B) 312mA

(D) 196mA

Answer: (C)

15. Identify the correct statements from the following descriptions of various properties of electromagnetic waves.

(A) In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

(B) The energy in electromagnetic wave is divided equally between electric and magnetic fields.

(C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

(D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

(E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

Choose the most appropriate answer from the options given below

(A) (D) only

(B) (B) & (D) only

(D) (A), (B) & (E) only

Answer: (B)

16. Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of is equal to will be:

(A) 1.5

(B) 2

(D) 1

Answer: (B)

17. With reference to the observations in photo-electric effect, identify the correct statements from below:

(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.

(B) The value of saturation current increases on moving the source of light away from the metal surface.

(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (Light emitting diode) source of light.

(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.

(E) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves.

Choose the correct answer from the options given below.

(A) (A) & (B) only

(B) (A) & (E) only

(D) (D) & (E) only

Answer: (B)

18. The activity of a radioactive material is 6.4 × 10⁻⁴ Its half life is 5 days. The activity will become 5 × 10⁻⁶ curie after

(A) 7 days

(B) 15 days

(D) 35 days

Answer: (D)

19. For a constant collector-emitter voltage of 8 V, the collector current of a transistor reached to the value of 6 mA from 4 mA, whereas base current changed from 20 μA to 25 μA value. If transistor is in active state, small signal current gain (current amplification factor) will be

(A) 240

(B) 400

(D) 200

Answer: (B)

20. A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) = 5 sin(8πt) Volt. The modulation index is

(A) 0.2

(B) 0.1

(D) 0.4

Answer: (A)

SECTION-B

21. In an experiment to determine the Young’s modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm2) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young’s modulus of given steel wires is x × 10¹¹ Nm^–2, then the value of x is ______.

Answer: (2)

22. In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be ________ cm.

Answer: (40)

23. A thin prism of angle 6º and refractive index for yellow light (n_Y)1.5 is combined with another prism of angle 5º and n_Y = 1.55. The combination produces no dispersion. The net average deviation (δ) produced by the combination is (1/x)°. The value of x is _______

Answer: (4)

24. A conducting circular loop is placed in X -Y plane in presence of magnetic field in SI unit. If the radius of the loop is 1 m, the induced emf in the loop, at time t = 2 s is nπV. The value of n is ______.

Answer: (12)

25. As show in the figure, in the steady state, the charge stored in the capacitor is _________ × 10^–6 C.

Answer: (10)

26. A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _______ ε₀ (Where ε₀ is the permittivity of free space)

Answer: (240)

27. A wire of length 30 cm, stretched between rigid supports, has it’s nth and (n + 1)^th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, its linear mass density is _____ kg/m.

Answer: (3)

28. A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ________

Answer: (2)

29. A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ________ cm. (Take g = 10 m/s²).

Answer: (120)

30. Two inclined planes are placed as shown in figure. A block is projected from the point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top point B at a height 10 m. After reaching the point B the block sides down on inclined plane BC. Time it takes to reach to the point C from point A is t(√2 + 1) s. The value of t is ______. (Use g = 10 m/s²)

Answer: (2)

CHEMISTRY

SECTION-A

1. The correct decreasing order of energy, for the orbitals having, following set of quantum numbers:

(A) n = 3, l = 0, m = 0

(B) n = 4, l = 0, m = 0

(D) n = 3, l = 2, m = 1

(A) (D) > (B) > (C) > (A)

(B) (B) > (D) > (C) > (A)

(D) (B) > (C) > (D) > (A)

Answer: (A)

2. Match List-I with List-II

(A) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(B) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(D) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Answer: (C)

3. The Plot of pH-metric titration of weak base NH₄OH vs strong acid HCl looks like:

Answer: (A)

4. Given below are two statements:

Statement I: For KI, molar conductivity increases steeply with dilution.

Statement II: For carbonic acid, molar conductivity increases slowly with dilution.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(D) Statement I is false but Statement II is true

Answer: (B)

5. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): Dissolved substances can be removed from a colloidal solution by diffusion through a parchment paper. Reason (R): Particles in a true solution cannot pass through parchment paper but the collodial particles can pass through the parchment paper. In the light of the above statements, choose the correct answer from the options given below:

(A) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(B) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(D) (A) is not correct but (R) is correct

Answer: (C)

6. Outermost electronic configurations of four elements A, B, C, D are given below:

(A) 3s² (B) 3s²3p¹ (C) 3s²3p³ (D) 3s²3p⁴ The correct order of first ionization enthalpy for them is:

(A) (A) < (B) < (C) < (D)

(B) (B) < (A) < (D) < (C)

(D) (B) < (A) < (C) < (D)

Answer: (B)

7. An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is:

(A) Mg

(B) Be

(D) Sr

Answer: (A)

8. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): Boron is unable to form BF₆³⁻

Reason (R): Size of B is very small.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both (A) and (R) are true and (R) is the correct explanation of (A)

(B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

(D) (A) is false but (R) is true

Answer: (B)

9. In neutral or alkaline solution, MnO₄⁻ oxidises thiosulphate to:

(A) S₂O₇²⁻

(B) S₂O₈²⁻

(D) SO₄²⁻

Answer: (D)

10. Low oxidation state of metals in their complexes are common when ligands:

(A) have good π-accepting character

(B) have good σ-donor character

(D) arehavind poor σ-donating ability

Answer: (A)

11. Given below are two statements:

Statement I: The non bio-degradable fly ash and slag from steel industry can be used by cement industry.

Statement II: The fuel obtained from plastic waste is lead free.

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) Both Statement I and Statement II are correct

(B) Both Statement I and Statement II are incorrect

(D) Statement I is incorrect but Statement II is correct

Answer: (A)

12. The structure of A in the given reaction is:

Answer: (C)

13. Major product ‘B’ of the following reaction sequence is:

Answer: (B)

14. Match List-I with List-II.

List-II

(I) Gatterman Koch reaction

(II) Etard reaction

(III) Stephen reaction

(IV) Rosenmundreaction Choose the correct answer from the options given below:

(A) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(B) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(D) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Answer: (A)

15. Match List-I with List-II.

Choose the correct answer from the option given below:

(A) (A)-(II), (B)-(III), (C)-(I), (D-(IV)

(B) (A)-(II), (B)-(I), (C)-(III), (D-(IV)

(D) (A)-(I), (B)-( II), (C)-(III), (D-(IV)

Answer: (A)

16. An organic compound ‘A’ contains nitrogen and chlorine. It dissolves readily in water to give a solution that turns litmus red. Titration of compound ‘A’ with standard base indicates that the molecular weight of ‘A’ is 131± When a sample of ‘A’ is treated with aq. NaOH, a liquid separates which contains N but not Cl. Treatment of the obtained liquid with nitrous acid followed by phenol gives orange precipitate. The compound ‘A’ is :

Answer: (D)

17. Match List-I with List-II

List-I

(A) Glucose + HI

(B) Glucose + Br₂ water

(D) Glucose + HNO₃

List-II

(I) Gluconic acid

(II) Glucose pentacetate

(III) Saccharic acid

(IV) Hexane

Choose the correct answer from the options given below:

(A) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(B) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(D) (A)-(I), (B)-(III), (C)-(IV), (D)-(II)

Answer: (A)

18. Which of the following enhances the lathering property of soap?

(A) Sodium stearate

(B) Sodium carbonate

(D) Trisodium phosphate

Answer: (C)

19. Match List-I with List-II

List-I (Mixture)

(A) Chloroform& Aniline

(B) Benzoic acid &Napthalene

(D) Napthalene& Sodium chloride

List-II (Purification Process)

(I) Steam distillation

(II) Sublimation

(III) Distillation

(IV) Crystallisation

(A) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(B) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

(D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Answer: (D)

20. Fe³⁺cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of:

(A) [Fe(H₂O)₆]₂ [Fe(CN)₆]

(B) Fe₂[Fe(CN)₆]₂

(D) Fe₄[Fe(CN)₆]₃

Answer: (D)

SECTION-B

21. The normality of H₂SO₄ in the solution obtained on mixing 100 mL of 0.1 M H₂SO₄ with 50 mL of 0.1 M NaOH is_______×10^–1 (Nearest Integer)

Answer: (1)

22. For a real gas at 25°C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal’s constant ‘b’ should be_________×10^–2 L mol^–1 (Nearest integer) (Given R = 0.083 L bar K^–1mol^–1)

Answer: (25)

23. A gas (Molar mass = 280 g mol^–1) was burnt in excess O2 in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ K^–1 and enthalpy of combustion of gas is 9 kJ mol^–1 then amount of gas burnt is _______ g. (Nearest Integer)

Answer: (35)

24. When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of solute A added is________. (Nearest Integer)

Answer: (3)

25.

If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half of its initial concentration. Then the rate constant of the reaction is x × 10⁻⁶ s⁻¹. The value of x is______.

(Nearest Integer)

Answer: (165)

26. Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of principal ores if (of) iron is_______.

Answer: (4)

27. The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic medium is ______.

Answer: (4)

28. The number of molecule(s) or ion(s) from the following having non-planar structure is______.

Answer: (6)

29. The spin only magnetic moment of the complex present in Fehling’s reagent is______ B.M. (Nearest integer).

Answer: (2)

30.

In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is ______×10⁻² g. (Nearest integer)

Answer: (530)

MATHEMATICS

SECTION-A

1. The domain of the function f(x) = sin⁻¹[2x² – 3] + log₂(log_1/2(x² – 5x + 5)), where [t] is the greatest integer function, is:

Answer: (C)

2. Let S be the set of (α, β), π < α, β < 2π, for which the complex number is purely imaginary and is purely real. Let Z_αβ = sin 2α + icos 2β, (α, β) ∈

Then is equal to:

(A) 3

(B) 3i

(D) 2 – i

Answer: (C)

3. If α, β are the roots of the equation then the equation, whose roots are is

(A) 3x² – 20x – 12 = 0

(B) 3x² – 10x – 4 = 0

(D) 3x² – 20x + 16 = 0

Answer: (B)

4. Let If A² + γA + 18I = 0, then det (A) is equal to ______.

(A) −18

(B) 18

(D) 50

Answer: (B)

5. If for p ≠ q ≠ 0, the function is continuous at x = 0, then:

(A) 7pq f(0) – 1 = 0

(B) 63q f(0) – p² = 0

(D) 7pq f(0) – 9 = 0

Answer: (B)

6. Let f(x) = 2 + |x| – |x – 1| + |x + 1|, x ∈ Consider

Then,

(A) Both (S1) and (S2) are correct

(B) Both (S1) and (S2) are wrong

(D) Only (S2) is correct

Answer: (D)

7. Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the first 21 terms of an AP, whose first term is 10ar, nth term is a_n and the common difference is 10ar², is equal to

(A) 21a₁₁

(B) 22a₁₁

(D) 14a₁₆

Answer: (A)

8. The area of the region enclosed by y ≤ 4x², x²≤ 9y and y ≤ 4, is equal to

(A) 40/3

(B) 56/3

(D) 80/3

Answer: (D)

9. where [t] is the greatest integer function, is equal to

(A) 7/6

(B) 19/12

(D) 3/2

Answer: (B)

10. Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A₁ is twice the area A₂. Then the normal to the curve perpendicular to the line 2x – 12y = 15 does NOT pass through the point.

(A) (6, 21)

(B) (8, 9)

(D) (12, −15)

Answer: (C)

11. The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?

(A) (AC)² =9p

(B) (AC)² + p² = 136

(D) 34 < area (∆ABC) < 38

Answer: (D)

12. A circle C₁ passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C₁. Let C₂ be the circle with OA as a diameter. If the tangent to C₂ at the point A meets the x-axis at P and y-axis at Q, then QA : AP is equal to

(A) 1 : 4

(B) 1 : 5

(D) 1 : 3

Answer: (A)

13. If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then |a| is equal to :

(A) 2√2

(B) 2√3

(D) 4

Answer: (C)

14. If the length of the perpendicular drawn from the point P(a, 4, 2), a> 0 on the line is 2√6 units and Q(α₁, α₂, α₃) is the image of the point P in this line, then is equal to :

(A) 7

(B) 8

(D) 14

Answer: (B)

15. If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a> 0 makes an angle 30° with the plane y – z + 2 = 0, then the direction cosines of the line are :

Answer: (B)

16. Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If then k is equal to

(A) 528

(B) 529

(D) 630

Answer: (B)

17. A six faced die is biased such that3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

(A) 3/11

(B) 5/11

(D) 8/11

Answer: (D)

18. The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45°, Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is 60°. If ∠BAQ = 30°, AB = d and the area of the trapezium PQRB is α, then the ordered pair (d, α) is :

Answer: (A)

19. Let Then

(A) S = {π/12}

(B) S = {2π/3}

(C)

(D)

Answer: (C)

20. If the truth value of the statement

(P ∧ (~R)) → ((~R) ∧ Q)

is F, then the truth value of which of the following is F?

(A) P ∨ Q → ~R

(B) R ∨ Q → ~ P

(D) ~ (R ∨ Q) → ~ P

Answer: (D)

SECTION-B

21. Consider a matrix where α, β, γ are three distinct natural numbers. If then the number of such 3 – tuples (α, β, γ) is ________.

Answer: (42)

22. The number of functions f, from the set A = {x ∈N : x² – 10x + 9 ≤ 0} to the set B = {n² : n ∈ N} such that f(x) ≤ (x – 3)² + 1, for every x ∈ A, is ___________.

Answer: (1440)

23. Let for the 9th term in the binomial expansion of (3 + 6x)ⁿ, in the increasing powers of 6x, to be the greatest for x = 3/2, the least value of n is n0. If k is the ratio of the coefficient of x⁶ to the coefficient of x³, then k + n₀ is equal to :

Answer: (24)

24. is equal to _________.

Answer: (120)

25. A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is __________.

Answer: (5)

26. For the curve C : (x² + y² – 3) + (x² – y² – 1)⁵ = 0, the value of 3y’ – y³y”, at the point (α, α), α> 0, on C, is equal to __________.

Answer: (16)

27. Let f(x) = min{[x – 1], [x – 2], …, [x – 10]} where [t] denotes the greatest integer ≤ Then is equal to _______.

Answer: (385)

28. Let f be a differential function satisfying and f(1) = √ If y = f(x) passes through the point (α, 6), then α is equal to _______.

Answer: (12)

29. A common tangent T to the curves does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂ at (x₂, y₂), then |2x₁ + x₂| is equal to ______.

Answer: (20)

30. Let be three non-coplanar vectors such that and If then α is equal to __________.

Answer: (36)

JEE Main Session 2 26th July 2022 Shift 2 Question Paper and Answer Key

December 15, 2022 by suresh84

JEE Main Session 2 26^th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal, respectively. The ratio of their respective ranges will be

(A) 1 :√2

(B) √2 : 1

(D) √3 : 2

Answer: (C)

2. In aVernierCalipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Verniercalipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

(A) 3.02 cm

(B) 3.06cm

(D) 3.20cm

Answer: (C)

3. A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms^–1 and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.

(A) 0.018 s

(B) 0.036s

(D) 0.072s

Answer: (B)

4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

(A) 1 : 1

(B) 2 : 1

(D) 4 : 1

Answer: (B)

5. Two uniformly charged spherical conductors, A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at surface of the spheres A and B will be

(A) 1 : 2

(B) 2 : 1

(D) 1 : 4

Answer: (B)

6. The oscillating magnetic field in a plane electromagnetic wave is given by By = 5 × 10^–6 sin1000π (5x – 4 × 10⁸t)T. The amplitude of electric field will be:

(A) 15 × 10²Vm^–1

(B) 5 × 10^–6Vm^–1

(D) 4 × 10²Vm^–1

Answer: (D)

7. Light travels in two media M₁ and M₂ with speeds 1.5 × 10⁸ms–1 and 2.0 × 10⁸ms^–1, respectively. The critical angle between them is:

(A) tan⁻¹(3/√7)

(B) tan⁻¹(2/3)

(D) sin⁻¹(2/3)

Answer: (A)

8. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:

(Take radius of earth = 6400 km and g = 10 ms^–2)

(A) 800 km

(B) 1600 km

(D) 4800 km

Answer: (A)

9. The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V, respectively. The percentage modulation index will be:

(A) 0.5%

(B) 50%

(D) 30%

Answer: (B)

10. A nucleus of mass M at rest splits into two parts having masses The ratio of de Broglie wavelength of two parts will be:

(A) 1 : 2

(B) 2 : 1

(D) 2 : 3

Answer: (C)

11. An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately.

(Latent heat of fusion of ice is 3.4 × 105 J kg–1 and thermal conducting of insulation wall is 0.05 Wm^–1°C^–1)

(A) 61 × 10⁻³ kgs⁻¹

(B) 61 × 10⁻⁵ kgs⁻¹

(D) 30 × 10⁻⁵ kgs⁻¹

Answer: (B)

12. A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

Answer: (A)

13. A transverse wave is represented by y = 2sin(ωt – kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be

(A) 4π

(B) 2π

(D) 2

Answer: (A)

14. A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is

(A) 1A

(B) 2A

(C)

(D)

Answer: (A)

15. A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key ‘K’ is closed, the total energy stored across the combination is E₁. Now key ‘K’ is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E₂. The ratio E₁/E₂ will be

(A) 1/10

(B) 2/5

(D) 5/26

Answer: (C)

16. Two concentric circular loops of radii r₁ = 30 cm and r₂ = 50 cm are placed in X–Y plane as shown in the figure. A current I = 7 A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately

Answer: (B)

17. A velocity selector consists of electric field and magnetic field with B = 12 mT. The value of E required for an electron of energy 728 eV moving along the positive x-axis to pass undeflected is

(Given, mass of electron = 9.1 × 10^–31 kg)

(A) 192 kVm⁻¹

(B) 192 mVm⁻¹

(D) 16kVm⁻¹

Answer: (A)

18. Two masses M₁ and M₂ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M₂ is twice that of M₁, the acceleration of the system is a1. When the mass M₂ is thrice that of M₁, the acceleration of the system is a2. The ratio a₁/a₂ will be

(A) 1/3

(B) 2/3

(D) 1/2

Answer: (B)

19. Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of

(A) 4 : 3

(B) (3/4)^1/3

(D) (4/3)^1/3

Answer: (C)

20. The area of cross section of the rope used to lift a load by a crane is 2.5 × 10^–4 m². The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, The required area of cross section of the rope should be

(take g = 10 ms^–2)

(A) 6.25 × 10^–4 m²

(B) 10 × 10^–4 m²

(D) 1.67 × 10^–4 m²

Answer: (A)

SECTION-B

21. If The magnitude of component of vector will be _________ m.

Answer: (2)

22. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _________m.

Given the length of the rod is 10√3 m.

Answer: (5)

23. In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘. For incident angle 60° at the side AC the refracted light beam just grazes along face AC. The refractive index of the liquid The value of x is _______.

(Given refractive index of glass = 1.5)

Answer: (27)

24. Two lighter nuclei combine to from a comparatively heavier nucleus by the relation given below:

The binding energies per nucleon for are 1.1 MeV and 7.6 MeV respectively. The energy released in the process is ______ MeV.

Answer: (26)

25. A uniform heavy rod of mass 20 kg, cross sectional area 0.4 m² and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x × 10^–9 The value of x is ________

(Given Young’s modulus Y = 2 × 10¹¹ Nm^–2 andg = 10 ms^–2)

Answer: (25)

26. The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of 2 kΩ is connected in the collector branch of the circuit used. The input resistance of the transistor is 0.50 kΩ. The voltage gain of the transistor is ________.

Answer: (200)

27. Three point charges of magnitude 5 μC, 0.16μC and 0.3μC are located at the vertices, B, C of a right angled triangle whose sides are AB = 3 cm, BC = 3√2 cm and CA = 3 cm and point A is the right angle corner. Charge at point A, experiences ______N of electrostatic force due to the other two charges.

Answer: (17)

28. In a coil of resistance 8Ω, the magnetic flux due to an external magnetic field varies with time as . The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

Answer: (2)

29. A potentiometer wire of length 300 cm is connected in series with a resistance 780 Ω and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf20 mV is found to be 60 cm. The resistance of the potentiometer wire is _____ Ω.

Answer: (20)

30. As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a)is 3s, then the period of oscillation in figure (b) will be √x s. The value of x is _______

Answer: (2)

CHEMISTRY

SECTION-A

1. Hemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is : (Given : Atomic mass of Fe is 56 u, NA in 6.022 × 10²³mol^–1)

(A) 1.21 × 10⁵

(B) 12.0 × 10¹⁶

(D) 3.4 × 10²²

Answer: (C)

2. Arrange the following in increasing order of their covalent character.

(A) CaF₂ (B) CaCl₂ (C) CaBr₂ (D) CaI₂ Choose the correct answer from the options given below.

(A) B < A < C < D

(B) A < B < C < D

(D) A < C < B < D

Answer: (B)

3. Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is (Given pK_b (NH₃) = 4.74; Molar mass of NH₃ = 17 g mol⁻¹; Molar mass of NH₄Cl = 53.5 g mol^–1)

(A) 53.5 g

(B) 72.3 g

(D) 126.0 g

Answer: (C)

4. At 30°C, the half life for the decomposition of AB₂ is 200 s and is independent of the initial concentration of AB₂. The time required for 80% of the AB2 to decompose is (Given: log 2 = 0.30; log 3 = 0.48)

(A) 200 s

(B) 323 s

(D) 532 s

Answer: (C)

5. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold.

Assertion R : The colour of the colloidal solution depends on the wavelength of light scattered by the dispersed particles.

In the light of the above statements, choose the most appropriate answer from the options given below;

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (A)

6. The metal that has very low melting point and its periodic position is closer to a metalloid is :

(A) Al

(B) Ga

(D) In

Answer: (B)

7. The metal that is not extracted from its sulphide ore is :

(A) Aluminium

(B) Iron

(D) Zinc

Answer: (A)

8. The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

(A) Mn⁴⁺, H₂O only

(B) Mn²⁺, H₂O only

(D) Mn²⁺, H₂O, O₂ only

Answer: (D)

9. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A :LiF is sparingly soluble in water.

Reason R : The ionic radius of Li⁺ ion is smallest among its group members, hence has least hydration enthalpy.

In the light of the above statements, choose the most appropriate answer from the options given below .

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (C)

10. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Boric acid is a weak acid

Reason R : Boric acid is not able to release H+ ion on its own. It receives OH^– ion from water and releases H⁺ ion.

In the light of the above statements, choose the most appropriate answer from the options given below.

(A) Both A and R are correct and R is the correct explanation of A

(B) Both A and R are correct but R is NOT the correct explanation of A

(D) A is not correct but R is correct

Answer: (A)

11. The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

(A) K₃[Cu(CN)₄]

(B) K₂[Cu(CN)₄]

(D) K₄[FeCl₆]

Answer: (A)

12. Match List I with List II.

Choose the correct answer from the options given below :

(A) A-II, B-III, C-IV, D-I

(B) A-II, B-I, C-IV, D-III

(D) A-I, B-IV, C-III, D-II

Answer: (A)

13. The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is :

Answer: (B)

14. Which of the following is not an example of benzenoidcompound ?

Answer: (B)

15. Hydrolysis of which compound will give carbolic acid ?

(A) Cumene

(B) Benzenediazonium chloride

(D) Ethylene glycol ketal

Answer: (B)

16.

Consider the above reaction and predict the major product.

Answer: (A)

17. The correct sequential order of the reagents for the given reaction is :

(A) HNO₂, Fe/H⁺, HNO₂, KI, H₂O/H⁺

(B) HNO₂, KI, Fe/H⁺, HNO₂, H₂O/warm

(D) HNO₂, Fe/H⁺, KI, HNO₂, H₂O/warm

Answer: (B)

18. Vulcanization of rubber is carried out by heating a mixture of :

(A) isoprene and styrene

(B) neoprene and sulphur

(D) neoprene and styrene

Answer: (C)

19. Animal starch is the other name of :

(A) amylose

(B) maltose

(D) amylopectin

Answer: (C)

20. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A :Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium

Reason R : Phenolphthalein is a weak acid. It doesn’t dissociate in basic medium.

In the light of the above statements, choose the most appropriate answer from the options given below :

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A.

(D) A is false but R is true

Answer: (C)

SECTION-B

21. A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m³ at 6 bar and 27°C. The mass of helium in the mixture is _______ g. (nearest integer) Given : R = 8.3 JK^–1mol^–1 (Atomic masses of H and He are 1u and 4u, respectively)

Answer: (8)

22. Consider an imaginary ion The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of ‘a’ is ______. [nearest integer]

Answer: (4)

23. For the reaction

H₂F₂(g) → H₂(g) + F₂(g)

∆U = –59.6 kJ mol^–1 at 27°C.

The enthalpy change for the above reaction is (–) ______ kJ mol^–1 [nearest integer] Given : R = 8.314 JK^–1mol^–1.

Answer: (57)

24. The elevation in boiling point for 1 molal solution of non-volatile solute A is 3K. The depression in freezing point for 2 molalsolution of A in the same solvent is 6 K. The ratio of K_b and K_fe., K_b/K_f is 1 : X. The value of X is [nearest integer]

Answer: (1)

25. 20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of Cu²⁺ is found to be _____ × 10⁻² M [nearest integer]

Given : 2Cu2+ + 4I⁻→ Cu₂I₂ + I₂I2 + 2S₂O₃²⁻→ 2I⁻ + S₄O₆²⁻

Answer: (4)

26. The number of non-ionisable protons present in the product B obtained from the following reaction is _____. C₂H₅OH + PCl₃→ C₂H₅Cl + A

A + PCl₃→ B

Answer: (2)

27. The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF₄, MnF₃ and MnF₂ is ______ B.M. [nearest integer]

Answer: (5)

28. Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is ________.

Answer: (12)

29. A 100 mL solution of CH₃CH₂MgBr on treatment with methanol produces 2.24 mL of a gas at STP. The weight of gas produced is _______ mg. [nearest integer]

Answer: (3)

30. How many of the following drugs is/are example(s) of broad spectrum antibiotic ?Ofloxacin, Penicillin G, Terpineol, Salvarsan

Answer: (1)

MATHEMATICS

SECTION-A

1. The minimum value of the sum of the squares of the roots of x² + (3 – a)x + 1 = 2a is:

(A) 4

(B) 5

(D) 8

Answer: (C)

2. If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

(A) x + 2y – 4 = 0

(B) x² + y – 4 = 0

(D) x² – y + 3 = 0

Answer: (C)

3. Let then the value of A’BA is

(A) 1224

(B) 1042

(D) 539

Answer: (D)

4. is equal to

(A) 2²ⁿ – ²ⁿC_n

(B) 2^{2n – 1}–^{2n – 1}C_{n – 1}

(C)

(D) 2^{n – 1} +^{2n – 1}C_n

Answer: (B)

5. Let P and Q be any points on the curves (x – 1)² + (y + 1)² = 1 and y = x², respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

(A) (0, 1/4)

(B) (1/2, 3/4)

(D) (3/4, 1)

Answer: (C)

6. If the maximum value of a, for which the functionf_a(x) = tan⁻¹2x – 3ax + 7 is non-decreasing in is equal to

Answer: (A)

7. Let for some α ∈ ℝ. Then the value of α + β is :

(A) 14/5

(B) 3/25

(D) 7/2

Answer: (C)

8. The value of is

(A) −2√2

(B) 2√2

(D) 4

Answer: (D)

9. is equal to :-

(A) 10(π + 4)

(B) 10(π + 2)

(D) 20(π + 2)

Answer: (D)

10. Let the solution curve y = f(x) of the differential equation pass through the origin. Then

Answer: (B)

11. The acute angle between the pair of tangents drawn to the ellipse 2x² + 3y² = 5 from the point (1, 3) is

Answer: (B)

12. The equation of a common tangent to the parabolas y = x² and y = –(x – 2)² is

(A) y = 4(x – 2)

(B) y = 4(x – 1)

(D) y = 4(x + 2)

Answer: (B)

13. Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is

(A) 12

(B) 13

(D) 16

Answer: (A)

14. If the line x – 1 = 0 is a directrix of the hyperbola kx² – y² = 6, then the hyperbola passes through the point

(A) (−2√5, 6)

(B) (−√5, 3)

(D) (2√5, 3√6)

Answer: (C)

15. A vector is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors The obtuse angle between is

(A) 3π/4

(B) 2π/3

(D) 5π/6

Answer: (A)

16. If then a value of is

Answer: (B)

17. Negation of the Boolean expression p⇔ (q ⇒ p) is

(A) (~ p) ∧q

(B) p∧ (~ q)

(D) (~ p) ∧ (~ q)

Answer: (D)

18. Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X ≤ 2) is equal to

(A) 73/27

(B) 146/27

(D) 126/81

Answer: (B)

19. The integral is equal to

Answer: (A)

20. The area bounded by the curves y = |x² – 1| and y = 1 is

Answer: (D)

SECTION-B

21. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A : C ∩ B ≠ϕ} is ________

Answer: (112)

22. The largest value of a, for which the perpendicular distance of the plane containing the lines and from the point (2, 1, 4) is √3, is _________.

Answer: (20)

23. Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.

Answer: (30)

24. If where m and n are co-prime, them m + n is equal to

Answer: (166)

25. If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Answer: (3)

26. The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ² is equal to ___________.

Answer: (238)

27. The plane passing through the line L :ℓx – y + 3(1 – ℓ) z = 1, x + 2y – z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x – 8y + 7z = 4. If θ is the acute angle between the line L and the y-axis, then 415 cos²θ is equal to ________.

Answer: (125)

28. Suppose y = y(x) be the solution curve to the differential equation such that is finite. If a and bare respectively the x – and y – intercepts of the tangent to the curve at x = 0, then the value of a – 4b is equal to _______.

Answer: (3)

29. Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ________.

Answer: (53)

30. The number of matrices where a, b, c, d ∈ {−1, 0, 1, 2, 3,………..,10}, such that A = A⁻¹, is _______.

Answer: (50)

JEE Main Session 2 25th July 2022 Shift 2 Question Paper and Answer Key

December 15, 2022 by suresh84

JEE Main Session 2 25^th July 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V, respectively. The modulation index is

(A) 100%

(B) 80%

(D) 50%

Answer: (D)

2. The electric current in a circular coil of 2 turns produces a magnetic induction B₁ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B₂ at its centre. The ratio of B₂/B₁ is

(A) 5/2

(B) 25/4

(D) 25/2

Answer: (B)

3. A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5 × 10^–4 N cm^–1. The radius of drop in cm will be (g = 10 ms^–2)

Answer: (A)

4. Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms^–1collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

(A) 100 N

(B) 200 N

(D) 400 N

Answer: (B)

5. For a free body diagram shown in the figure, the four forces are applied in the ‘x’ and ‘y’ directions. What additional force must be applied and at what angle with positive x-axis so that net acceleration of body is zero?

(A) √2 N, 45°

(B) √2 N, 135°

(C)

(D) 2 N, 45°

Answer: (A)

6. Capacitance of an isolated conducting sphere of radius R₁ becomes n times when it is enclosed by a concentric conducting sphere of radius R₂ connected to earth. The ratio of their radii (R₂/R₁) is:

Answer: (A)

7. The ratio of wavelengths of proton and deuteron accelerated by potential V_p and V_d is 1 : √2. Then, the ratio of V_p to V_d will be:

(A) 1 : 1

(B) √2 : 1

(D) 4 : 1

Answer: (D)

8. For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

(A) 0.8 m

(B) 3.2 m

(D) 5.6 m

Answer: (B)

9. Light wave traveling in air along x-direction is given by E_y = 540 sin π × 10⁴ (x – ct)Vm^–1. Then, the peak value of magnetic field of wave will be (Given c = 3 × 10⁸ms^–1)

(A) 18 × 10^–7 T

(B) 54 × 10^–7 T

(D) 18 × 10^–8 T

Answer: (A)

10. When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

(A) Electromagnetic induction

(B) Resonance in ac circuits

(D) Interference of electromagnetic waves

Answer: (B)

11. An electron with energy 0.1 keV moves at right angle to the earth’s magnetic field of 1 × 10^–4Wbm^–2. The frequency of revolution of the electron will be

(Take mass of electron = 9.0 × 10^–31 kg)

(A) 1.6 × 10⁵ Hz

(B) 5.6 × 10⁵ Hz

(D) 1.8 × 10⁶ Hz

Answer: (C)

12. A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be

(A) 50 V

(B) 75 V

(D) 275 V

Answer: (D)

13. The length of a seconds pendulum at a height h = 2R from earth surface will be

(Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = π²ms^–2)

(A) 2/9 m

(B) 4/9 m

(D) 1/9 m

Answer: (D)

14. Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is √2 times the speed of sound, then the value of n will be

(A) 1

(B) 2

(D) 4

Answer: (B)

15. Let η₁ is the efficiency of an engine at T₁ = 447°C and T₂ = 147°C while η₂ is the efficiency at T₁ = 947°C and T₂ = 47°C. The ratio η₁/ η₂ will be

(A) 0.41

(B) 0.56

(D) 0.70

Answer: (B)

16. An object is taken to a height above the surface of earth at a distance (5/4)R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be

(A) 36%

(B) 50%

(D) 25%

Answer: (A)

17. A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms^–1 gets embedded in it, then loss of kinetic energy will be

(A) 4.9 J

(B) 9.8 J

(D) 19.6 J

Answer: (B)

18. A ball is projected from the ground with a speed 15 ms^–1 at an angle θ with horizontal so that its range and maximum height are equal, then ‘tan θ’ will be equal to

(A) 1/4

(B) 1/2

(D) 4

Answer: (D)

19. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be

(A) 2

(B) 4

(D) 8

Answer: (D)

20. Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. The value of principal quantum number ‘n’ of the excited state will be, (R: Rydberg constant)

Answer: (B)

SECTION-B

21. A particle is moving in a straight line such that its velocity is increasing at 5 ms^–1 per meter. The acceleration of the particle is _______ms^–2 at a point where its velocity is 20 ms^–1.

Answer: (100)

22. Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is ________.

Answer: (2)

23. A block of ice of mass 120 g at temperature 0°C is put in 300 g of water at 25°C. The x g of ice melts as the temperature of the water reaches 0°C. The value of x is _______.

[Use specific heat capacity of water = 4200 Jkg^–1K^–1, Latent heat of ice = 3.5 ×10⁵Jkg^–1]

Answer: (90)

24. is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) Third permitted energy level to the second level and

(ii) The highest permitted energy level to the second permitted level.

The value of x will be ______.

Answer: (5)

25. In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be _______ cm.

Answer: (18)

26. Two ideal diodes are connected in the network as shown is figure. The equivalent resistance between A and B is ________ Ω.

Answer: (25)

27. Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is _________ (degree).

Answer: (60)

28. Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ________ V.

Answer: (6)

29. A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _________ cm.

Answer: (10)

30. Magnetic flux (in weber) in a closed circuit of resistance 20 Ω varies with time t(s) as φ = 8t² – 9t + 5. The magnitude of the induced current at t = 0.25 s will be _______ mA.

Answer: (250)

CHEMISTRY

SECTION-A

1. Match List I with List II:

(A) A-II, B-I, C-IV, D-III

(B) A-II, B-IV, C-III, D-I

(D) A-IV, B-II, C-I, D-III

Answer: (A)

2. Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y. respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be 1 : 4. The ratio of molar masses of X and Y is :

(A) 1 : 4

(B) 1 : 0.25

(D) 1 : 5

Answer: (B)

3. are the respective ionization constants for the following reactions (a),(b), and (c).

The relationship between is given as

Answer: (D)

4. The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is Λ_m1 and that of 20 moles another identical cell heaving 80 mL NaCl solution is Λ_m2, The conductivities exhibited by these two cells are same. The relationship between Λ_m2 and Λ_m1 is

(A) Λ_m2 = 2Λ_m1

(B) Λ_m2 = Λ_m1/2

(D) Λ_m2 = 4Λ_m1

Answer: (A)

5. For micelle formation, which of the following statements are correct?

(A) Micelle formation is an exothermic process.

(B) Micelle formation is an endothermic process.

(D)The entropy change is negative.

(A) A and D only

(B) A and C only

(D) B and D only

Answer: (A)

6. The first ionization enthalpies of Be, B, N and O follow the order

(A) O < N < B < Be

(B) Be < B < N < O

(D) B < Be < O < N

Answer: (D)

7. Given below are two statements.

Statement I:Pig iron is obtained by heating cast iron with scrap iron.

Statement II:Pig iron has a relatively lower carbon content than that of cast iron. In the light of the above statements, choose the correct answer from the options given below.

(A) Both Statement I and Statement II are correct.

(B) Both Statement I and Statement II are not correct.

(D) Statement I is not correct but Statement II is correct.

Answer: (B)

8. High purity (>99.95%) dihydrogen is obtained by

(A) reaction of zinc with aqueous alkali.

(B) electrolysis of acidified water using platinum electrodes.

(D) reaction of zinc with dilute acid.

Answer: (C)

9. The correct order of density is

(A) Be > Mg >Ca>Sr

(B) Sr>Ca> Mg > Be

(D) Be >Sr> Mg >Ca

Answer: (C)

10. The total number of acidic oxides from the : NO, N₂O, B₂O₃, N₂O₅ , CO, SO₃ , P₄O₁₀

(A) 3

(B) 4

(D) 6

Answer: (B)

11. The correct order of energy of absorption for the following metal complexes is

A: [Ni(en)₃ ]²⁺, B: [Ni(NH₃)₆ ]²⁺, C: [Ni(H₂ O)₆ ]²⁺

(A) C < B < A

(B) B < C < A

(D) A < C < B

Answer: (A)

12. Match List I with List II.

Choose the correct answer from the options given below:

(A) A-II, B-III. C-IV, D-I

(B) A-IV, B-III, C-II, D-I

(D) A-III, B-II, C-IV, D-I

Answer: (C)

13. Major product of the following reaction is

Answer: (D)

14. What is the major product of the following reaction?

Answer: (B)

15. Arrange the following in decreasing acidic strength.

(A) A > B > C > D

(B) B > A > C > D

(D) D > C > B > A

Answer: (A)

16.

The correct structure of C is

Answer: (A)

17. Match List I with List II:

Choose the correct answer from the options given below:

(A) A–III, B-I, C-IV, D-II

(B) A–III, B-IV, C-I, D-II

(D) A–II, B-IV, C-I, D-III

Answer: (B)

18. Glycosidic linkage between C₁ of a-glucose and C₂ of b-fructose is found in

(A) maltose

(B) sucrose

(D) amylose

Answer: (B)

19. Some drugs bind to a site other than, the active site of an enzyme. This site is known as

(A) non-active site

(B) allosteric site

(D) therapeutic site

Answer: (B)

20. In base vs. Acid titration, at the end point methyl orange is present as

(A) quinonoid form

(B) heterocyclic form

(D) benzenoid form

Answer: (A)

SECTION-B

21. 56.0 L of nitrogen gas is mixed with excess of hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be______ L.

Answer: (46)

22. A sealed flask with a capacity of 2 dm³ contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is _______ °C. [Nearest integer]

(Given: R = 8.3 J K^–1mol^–1. Atomic masses of C and H are 12u and 1u respectively.) (Assume that propane behaves as an ideal gas.)

Answer: (1655)

23. When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are _____

Answer: (10)

24. While performing a thermodynamics experiment, a student made the following observations,

HCl + NaOH→NaCl + H₂O ∆H = –57.3 kJ mol^–1 CH₃COOH + NaOH→ CH₃COONa + H₂O ∆H = –55.3 kJ mol^–1. The enthalpy of ionization of CH3 COOH as calculated by the student is ______ kJ mol^–1. (nearest integer)

Answer: (2)

25. For the decomposition of azomethane. CH₃N₂CH₃(g) → CH₃CH₃(g) + N₂(g) a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is _____ × 10^–5s. [Nearest integer]

Answer: (2)

26. The sum of number of lone pairs of electrons present on the central atoms of XeO₃, XeOF₄ and XeF₆ is ___________

Answer: (3)

27. The spin-only magnetic moment value of M³⁺ ion (in gaseous state) from the pairs Cr³⁺/Cr²⁺, Mn³⁺/Mn², Fe³⁺/Fe²⁺ and Co³⁺/Co²⁺ that has negative standard electrode potential, is B.M. [Nearest integer]

Answer: (4)

28. A sample of 4.5 mg of an unknown monohydric alcohol, R–OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is ____ g/mol. [Nearest integer]

Answer: (33)

29. The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and substance B from the base line are 3.25 cm. 2.08 cm and 1.05 cm. respectively. The ratio of R_f values of A to B is ______

Answer: (2)

30. The total number of monobromo derivatives formed by the alkanes with molecular formula C₅H₁₂ is (excluding stereo isomers) _____

Answer: (8)

MATHEMATICS

SECTION-A

1. z ∈ ℂ if the minimum value of (|z – 3√2| + |z – p√2i|) is 5√2, then a value of p is _________.

(A) 3

(B) 7/2

(D) 9/2

Answer: (C)

2. The number of real values of λ, such that the system of linear equations

2x – 3y + 5z = 9

x + 3y – z = –18

3x – y + (λ² – | λ |)z = 16

has no solutions, is

(A) 0

(B) 1

(D) 4

Answer: (C)

3. The number of bijective functions f : {1, 3, 5, 7, …, 99} → {2, 4, 6, 8, ….., 100} such that f(3) ≥ f(9) ≥ f(15) ≥ f(21) ≥ … ≥ f(99) is _________.

(A) ⁵⁰P₁₇

(B) ⁵⁰P₃₃

(D) 50!/2

Answer: (B)

4. The remainder when (11)¹⁰¹¹ + (1011)¹¹ is divided by 9 is

(A) 1

(B) 4

(D) 8

Answer: (D)

5. The sum is equal to

(A) 7/87

(B) 7/29

(D) 21/29

Answer: (B)

6. is equal to

(A) 14

(B) 7

(D) 7√2

Answer: (A)

7. is equal to

(A) 1/2

(B) 1

(D) −2

Answer: (C)

8. If A and B are two events such that P(A) = 1/3, P(B) = 1/5 and (A ∪ B) = 1/2, then P(A|B’) + P(B|A’|) is equal to

(A) 3/4

(B) 5/8

(D) 7/8

Answer: (B)

9. Let [t] denote the greatest integer less than or equal to t. Then the value of the integral is equal to

(A)

(B) 52/e

(C)

(D) 104/e

Answer: (B)

10. Let the point P(α, β) be at a unit distance from each of the two lines L₁ : 3x – 4y + 12 = 0 and L₂ : 8x + 6y + 11 = 0. If P lies below L₁ and above L₂, then 100(α + β) is equal to

(A) −14

(B) 42

(D) 14

Answer: (D)

11. Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (-y/x). If the curve passes through the points (1, 2) and (8, 1), then |y(1/8)| is equal to

(A) 2 log_e2

(B) 4

(D) 4 log_e2

Answer: (B)

12. If the ellipse meets the line on the x-axis and the line on the y-axis, then the eccentricity of the ellipse is

(A) 5/7

(B) 2√6/7

(D) 2√5/7

Answer: (A)

13. The tangents at the points A(1, 3) and B(1, –1) on the parabola y² – 2x – 2y = 1 meet at the point P. Then the area (in unit2) of the triangle PAB is :

(A) 4

(B) 6

(D) 8

Answer: (D)

14. Let the foci of the ellipse and the hyperbola coincide. Then the length of the latus rectum of the hyperbola is :

(A) 32/9

(B) 18/5

(D) 27/10

Answer: (D)

15. A plane E is perpendicular to the two planes 2x – 2y + z = 0 and x – y + 2z = 4, and passes through the point P(1, –1, 1). If the distance of the plane E from the point Q(a, a, 2) is 3√2, then (PQ)² is equal to

(A) 9

(B) 12

(D) 33

Answer: (C)

16. The shortest distance between the lines is

(A) 2√29

(B) 1

(C)

(D) √29/2

Answer: (A)

17. Let be a vector such that Then the projection of on the vector is :-

Answer: (A)

18. If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the median is

(A) 11.5

(B) 10.5

(D) 11

Answer: (D)

19. is equal to

(A) 3/16

(B) 1/16

(D) 9/32

Answer: (B)

20. Consider the following statements :

P :Ramu is intelligent.

Q :Ramu is rich.

R :Ramu is not honest.

The negation of the statement “Ramu is intelligent and honest if and only if Ramu is not rich” can be expressed as :

(A) ((P ∧ (~ R)) ∧ Q) ∧ ((~ Q) ∧ ((~ P) ∨ R))

(B) ((P ∧ R) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∨ (~ R)))

(D) ((P ∧ (~ R)) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∧ R))

Answer: (D)

SECTION-B

21. Let A = {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆A : either ∉ T or 2 ∈ T} and C = T ⊆ A : T The sum of all the elements of T is prime number}.Then the number of elements in the set B ∪ C is ______.

Answer: (107)

22. Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, p ≠ 0, and f(1) = 1/3 . If the equations f(x) = 0 and fofofo f(x) = 0 have a common real root, then f(–3) is equal to ______.

Answer: (25)

23. Let If for some n ∈ N, then n + a + b is equal to ________

Answer: (24)

24. The sum of the maximum and minimum values of the function f(x) = |5x – 7| + [x² + 2x] in the interval [5/4, 2], where [t] is the greatest integer ≤ t, is ______.

Answer: (15)

25. Let y = y(x) be the solution of the differential equation If for some n ∈ N, y(2) ∈ [n – 1, n), then n is equal to _________.

Answer: (3)

26. Let f be a twice differentiable function on R. If f’(0) = 4 and then (2a + 1)⁵ a² is equal to _________

Answer: (8)

27. Let for n ∈ Then the sum of all the elements of the set {n ∈ N : a_n∈ (2, 30)} is ______

Answer: (5)

28. If the circles x² + y² + 6x + 8y + 16 = 0 and x² + y² + 2(3 – √3)x + x + 2(4 – √6)y = k + 6√3 + 8√6, k > 0, touch internally at the point P(α, β), then (α + √3)² + (β + √6)² is equal to _________

Answer: (25)

29. Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x³ – 3xy² + 6x² – 5xy – 8y² + 9x + 14 = 0 at the point (–2, 3) be A. Then 8A is equal to _______.

Answer: (170)

30. Let x = sin(2tan⁻¹α) and If S = {α∈ R : y² = 1 – x}, then is equal to _______

Answer: (130)

JEE Main Session 2 29th June 2022 Shift 2 Question Paper and Answer Key

December 12, 2022 by suresh84

JEE Main Session 2 29^th June 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s, the distance travelled by the toy in the next t s will be :

(A) 10 m

(B) 20 m

(D) 40 m

Answer: (C)

2. At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).

(Given: coefficient of linear thermal expansion of gold α_L = 1.4 × 10^–5 K^–1)

(A) 125.7°C

(B) 91.7°C

(D) 152.7°C

Answer: (D)

3. Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulombs force is :

(A) x = d

(B) x = d/2

(D) x = d/2√2

Answer: (D)

4. The speed of light in media ‘A’ and ‘B’ are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s respectively. A ray of light enters from the medium B to A at an incident angle ‘θ’. If the ray suffers total internal reflection, then

Answer: (D)

5. In the following nuclear reaction, Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D₄, respectively, will be ________.

(A) 174 and 71

(B) 174 and 69

(D) 172 and 71

Answer: (A)

6. The electric field at a point associated with a light wave is given by

E = 200[sin(6 × 10¹⁵)t + sin(9 × 10¹⁵)t] Vm^–1

Given : h = 4.14 × 10^–15eVs

If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

(A) 1.90 eV

(B) 3.27 eV

(D) 3.42 eV

Answer: (D)

7. A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one eighth of its initial value. The ratio t₁/t₂ will be

(A) 1/2

(B) 1/3

(D) 1/6

Answer: (D)

8. Starting with the same initial conditions, an ideal gas expands from volume V₁ to V₂ in three different ways. The work done by the gas is W₁ if the process is purely isothermal, W₂, if the process is purely adiabatic and W₃ if the process is purely isobaric. Then, choose the correct option.

(A) W₁< W₂< W₃

(B) W₂< W₃< W₁

(D) W₂< W₁< W₃

Answer: (D)

9. Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 30 μT. The equal current flowing in the two conductors is:

(A) 30 A in the same direction

(B) 30 A in the opposite direction

(D) 300 A in the opposite direction

Answer: (B)

10. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

(A) 40 hours

(B) 36 hours

(D) 25 hours

Answer: (B)

11. The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by

(A) 125 m

(B) 250 m

(D) 500 m

Answer: (C)

12. The motion of a simple pendulum executing S.H.M. is represented by the following equation. y = A sin(πt + φ), where time is measured in second. The length of pendulum is

(A) 97.23 cm

(B) 25.3 cm

(D) 406.1 cm

Answer: (C)

13. A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm³ is:

(A) 72 × 10⁵

(B) 32 × 10⁵

(D) 54 × 10⁴

Answer: (C)

14. Given below are two statements:

Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.

Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) Both statement I and statement II are correct

(B) Both statement I and statement II are incorrect

(D) Statement I is incorrect but statement II is correct

Answer: (C)

15. A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.

The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is (Given g = 10 ms^–2.)

(A) 1 ms⁻²

(B) 1/5ms⁻²

(D) 8/11ms⁻²

Answer: (D)

16. In the given figure, the block of mass m is dropped from the point ‘A’. The expression for kinetic energy of block when it reaches point ‘B’ is

(A)

(B)

(D) mgy₀

Answer: (D)

17. A block of mass M placed inside a box descends vertically with acceleration ‘a’. The block exerts a force equal to one-fourth of its weight on the floor of the box.

The value of ‘a’ will be

(A) g/4

(B) g/2

(D) g

Answer: (C)

18. If the electric potential at any point (x, y, z)m in space is given by V = 3x² The electric field at the point (1, 0, 3)m will be

(A) 3 Vm^–1, directed along positive x-axis

(B) 3 Vm^–1, directed along negative x-axis

(D) 6 Vm^–1, directed along negative x-axis

Answer: (D)

19. The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 Ω. The value of internal resistance of each cell is

(A) 2 Ω

(B) 4 Ω

(D) 8 Ω

Answer: (A)

20. A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

(A) 25 m

(B) 50 m

(D) 200 m

Answer: (B)

SECTION-B

21. The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (–0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ________× 10^–2

Answer: (180)

22. A small spherical ball of radius 0.1 mm and density 104 kg m–3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ______ m.

(Given g = 10 ms^–2, viscosity of water = 1.0 × 10^–5 N-sm^–2).

Answer: (20)

23. In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms–1. The third resonance is observed when the air column has a length of ______ cm.

Answer: (104)

24. Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be _____ V.

Answer: (8)

25. A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ms^–1. The speed with which electrons enters the p side will be the value of x is ________.

(Give mass of electron = 9 × 10^–31 kg, charge on electron = 1.6 × 10^–19 C)

Answer: (14)

26. The displacement current of 4.425 μA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs^–1. The area of each plate of the capacitor is 40 cm². The distance between each plate of the capacitor x × 10^–3 The value of x is,

(Permittivity of free space, E₀ = 8.85 × 10^–12 C² N^–1 m^–2)

Answer: (8)

27. The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I₁. The same rod is bent into a ring and its moment of inertia about a diameter is I₂. If then the value of x will be _________.

Answer: (8)

28. The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ________.

Answer: (20)

29. In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10^–2 m towards the slits, the change in fringe width is 3 × 10^–3 If the distance between the slits is 1 mm, then the wavelength of the light will be _______ nm.

Answer: (600)

30. An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 10²

Answer: (5)

CHEMISTRY

SECTION-A

1. Using the rules for significant figures, the correct answer for the expression will be

(A) 0.005613

(B) 0.00561

(D) 0.006

Answer: (B)

2. Which of the following is the correct plot for the probability density ψ²(r) as a function of distance ‘r’ of the electron from the nucleus for 2s orbital?

Answer: (B)

3. Consider the species CH₄, NH₄⁺ and BH₄⁻.

Choose the correct option with respect to these species.

(A) They are isoelectronic and only two have tetrahedral structures

(B) They are isoelectronic and all have tetrahedral structures.

(D) Only two are isoelectronic and only two have tetrahedral structures.

Answer: (B)

4. 4.0 moles of argon and 5.0 moles of PCl₅ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The K_p for the reaction is [Given : R = 0.082 L atm K^–1mol^–1]

(A) 2.25

(B) 6.24

(D) 15.24

Answer: (A)

5. A 42.12% (w, v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol is

[Given : Molar mass : Na = 23.0 g mol^–1; Cl = 35.5 g mol^–1]

(A) 36 mmol L^–1

(B) 36 mol L^–1

(D) 1440 mmol L^–1

Answer: (D)

6. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The first ionization enthalpy for oxygen is lower than that of nitrogen.

Reason R: The four electrons in 2p orbitals of oxygen experience more electron-electron repulsion.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both A and R are correct and Rj is the correct explanation of A

(B) Both A and R are correct but R is NOT the correct explanation of A

(D) A is not correct but R is correct

Answer: (B)

7. Match List-I with List-II

Choose the correct answer from the options given below:

(A) A-I, B-II, C-III, D-IV

(B) A-III, B-IV, C-II, D-I

(D) A-I, B-II, C-IV, D-III

Answer: (A)

8. Given below are two statements.

Statement-I: In CuSO₄.5H₂O, Cu-O bonds are present.

Statement-II: In CuSO₄.5H₂O, ligands coordinating with Cu(II) ion are O-and S-based ligands.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both Statement-I and Statement-II are correct

(B) Both Statement-I and Statement-II are incorrect

(D) Statement-I is incorrect but Statement-II is correct.

Answer: (C)

9. Amongst baking soda, caustic soda and washing soda, carbonate anion is present in

(A) Washing soda only

(B) Washing soda and caustic soda only

(D) Baking soda, caustic soda and washing soda

Answer: (A)

10. Number of lone pair(s) of electrons on central atom and the shape of BrF₃ molecule respectively, are

(A) 0, triangular planar

(B) 1, pyramidal

(D) 1, bent T-shape

Answer: (C)

11. Aqueous solution of which of the following boron compounds will be strongly basic in nature?

(A) NaBH₄

(B) LiBH₄

(D) Na₂B₄O₇

Answer: (D)

12. Sulphur dioxide is one of the components of polluted air. SO₂ is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by SO₂ is

(A) 2SO₂ + O₂ → 2SO₃

(B) SO₂ + O₃ → SO₃ + O₂

(D) 2SO₂ + O₂ + 2H₂O → 2H₂SO₄

Answer: (D)

13. Which of the following carbocations is most stable?

Answer: (D)

14.

The stable carbocation formed in the above reaction is

Answer: (C)

15. Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9 % and Br 42.9% gave benzoic acid and p-bromobenzoic acid, respectively on oxidation with KMnO₄. Isomer ‘A’ is optically active and gives a pale yellow precipitate when warmed with alcoholic AgNO₃. Isomers ‘A’ and ‘B’ are, respectively.

Answer: (C)

16. In Friedel-Crafts alkylation of aniline, one gets

(A) Alkylated product with ortho and para substitution.

(B) Secondary amine after acidic treatment.

(D) Positively charged nitrogen at benzene ring.

Answer: (D)

17. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Dacron is an example of polyester polymer.

Reason R: Dacron is made up of ethylene glycol and terephthalic acid monomers.

In the light of the above statements, choose the most appropriate answer from the options given below.

(A) Both A and R are correct and R is the correct explanation of A.

(B) Both A and R are correct but R is NOT the correct explanation of A.

(D) A is not correct but R is correct.

Answer: (A)

18. The structure of protein that is unaffected by heating is

(A) Secondary Structure

(B) Tertiary Structure

(D) Quaternary Structure

Answer: (C)

19. The mixture of chloroxylenol and terpineol is an example of

(A) Antiseptic

(B) Pesticide

(D) Narcotic analgesic

Answer: (A)

20. A white precipitate was formed when BaCl₂ was added to water extract of an inorganic salt. Further, a gas ‘X’ with characteristic odour was released when the formed white precipitate was dissolved in dilute HCl. The anion present in the inorganic salt is

(A) I⁻

(B) SO₃²⁻

(D) NO₂⁻

Answer: (B)

SECTION-B

21. A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [nearest integer]

(Given : R = 0.082 L atm K^–1mol^–1]

(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

Answer: (29)

22. 2.2 g of nitrous oxide (N₂O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ΔU is ‘–x’ J. The value of ‘x’ is ____. [nearest integer]

(Given : atomic mass of N = 14 g mol^–1 and of O = 16 g mol^–1

Molar heat capacity of N2O is 100 J K^–1mol^–1)

Answer: (195)

23. Elevation in boiling point for 1.5 molalsolution of glucose in water is 4 K. The depression in freezing point for 4.5 molalsolution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (K_b/K_f) is _______.

Answer: (3)

24. The cell potential for the given cell at 298 K

Pt | H₂ (g, 1 bar) | H+ (aq) || Cu²⁺ (aq) | Cu(s)

is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu²⁺ is 10^–x M. The value of x is _________.

(Given: and

Answer: (7)

25. The equation k = (6.5 × 10¹²s^–1)e^–26000K/T is followed for the decomposition of compound A. The activation energy for the reaction is ______ kJ mol^–1. [nearest integer]

(Given : R = 8.314 J K^–1mol^–1]

Answer: (216)

26. Spin only magnetic moment of [MnBr₆]^4– is ________ B.M. [round off to the closest integer]

Answer: (6)

27. For the reaction given below:

CoCl₃∙ xNH₃ + AgNO₃(aq) →

If two equivalents of AgCl precipitate out, then the value of x will be_______.

Answer: (5)

28. The number of chiral alcohol(s) with molecular formula C₄H₁₀O is ________.

Answer: (1)

29. In the given reaction,

the number of sp² hybridised carbon(s) in compound ‘X’ is _____.

Answer: (8)

30. In the given reaction,

The number of π electrons present in the product ‘P’ is_______.

Answer: (4)

MATHEMATICS

SECTION-A

1. Let α be a root of the equation 1 + x² + x⁴ = 0. Then the value of α¹⁰¹¹ + α²⁰²² – α³⁰³³ is equal to

(A) 1

(B) α

(D) 1 + 2α

Answer: (A)

2. Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

(A) exactly at one point

(B) exactly at two points

(D) at infinitely many points

Answer: (C)

3. Let . If B = I – ⁵C₁(adjA) + ⁵C₂(adjA)² – …. – ⁵C₅(adjA)⁵, then the sum of all elements of the matrix B is

(A) –5

(B) –6

(D) –8

Answer: (C)

4. The sum of the infinite series is equal to

(A) 425/216

(B) 429/216

(D) 280/125

Answer: (C)

5. The value of is equal to

(A) π²/6

(B) π²/3

(D) π²

Answer: (D)

6. Let f : R → R be a function defined by;

Then, which of the following is NOT true?

(A) For n₁ = 3, n₂ = 4, there exists α ∈ (3, 5) where f attains local maxima.

(B) For n₁ = 4, n₂ = 3, there exists α ∈ (3, 5) where f attains local minima.

(D) For n₁ = 4, n₂ = 6, there exists α ∈ (3, 5) where f attains local maxima.

Answer: (C)

7. Let f be a real valued continuous function on [0, 1] and . Then, which of the following points (x, y) lies on the curve y = f(x)?

(A) (2, 4)

(B) (1, 2)

(D) (6, 8)

Answer: (D)

8. If

Answer: (C)

9. If y = y (x) is the solution of the differential equation and y(0) = 0, then 6(y'(0) + (y(log_e√3))²) is equal to:

(A) 2

(B) −2

(D) −1

Answer: (C)

10. Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

(A) 8 only

(B) 2 only

(D) any a > 0

Answer: (D)

11. Let a triangle ABC be inscribed in the circle x² – √2(x + y) + y² = 0 such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

Answer: (*)

12. Let lie on the plane px – qy + z = 5, for some p, q ∈ℝ. The shortest distance of the plane from the origin is :

Answer: (B)

13. The distance of the origin from the centroid of the triangle whose two sides have the equations x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :

(A) √2

(B) 2

(D) 4

Answer: (C)

14. Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line Then, which of the following points lies on T?

(A) (2, 1, 0)

(B) (1, 2, 1)

(D) (1, 3, 2)

Answer: (B)

15. Let A, B, C be three points whose position vectors respectively are

If α is the smallest positive integer for which are non collinear, then the length of the median, in ΔABC, through A is:

(A) √82/2

(B) √62/2

(D) √66/2

Answer: (A)

16. The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to

(A) 5/16

(B) 9/16

(D) 13/16

Answer: (A)

17. The number of values of a ∈ℕ such that the variance of 3, 7, 12, a, 43 – a is a natural number is :

(A) 0

(B) 2

(D) Infinite

Answer: (A)

18. From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

(A) 15√3

(B) 20√3

(D) 30

Answer: (D)

19. Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

(A) p∧ (~ q) ∧ r

(B) (~ p) ∧ (~ q) ∧ r

(D) p∧ q ∧ (~ r)

Answer: (C)

20. Let n ≥ 5 be an integer. If 9ⁿ – 8n – 1 = 64α and 6ⁿ – 5n – 1 = 25β, then α – β is equal to

(A) 1 + ⁿC₂(8 – 5) + ⁿC₃(8² – 5²) + … + ⁿC_n(8ⁿ⁻¹ – 5ⁿ⁻¹)

(B) 1 + ⁿC₂(8 – 5) + ⁿC₄(8² – 5²) + … + ⁿC_n(8ⁿ⁻² – 5ⁿ⁻²)

(D) ⁿC₄(8 – 5) + ⁿC₅(8² – 5²)+ … + ⁿC_n(8ⁿ⁻³ – 5ⁿ⁻³)

Answer: (C)

SECTION-B

21. Let be a vector such that Then, the value of is equal to _______.

Answer: (*)

22. Let y = y(x), x > 1, be the solution of the differential equation with then the value of α + β is equal to ________.

Answer: (14)

23. Let 3, 6, 9, 12, …upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _________.

Answer: (2223)

24. The number of solutions of the equation sin x = cos² x in the interval (0, 10) is _____.

Answer: (4)

25. For real number a, b (a > b > 0), let

and

Then the value of (a – b)² is equal to _____.

Answer: (12)

26. Let f and g be twice differentiable even functions on (–2, 2) such that f(1) = 1 and g(1) = 2 Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

Answer: (4)

27. Let the coefficients of x^–1 and x^–3 in the expansion of be m and n respectively. If r is a positive integer such that mn² = ¹⁵C_r∙ 2^r then the value of r is equal to ________.

Answer: (5)

28. The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _______.

Answer: (1086)

29. Let where α is a non-zero real number an If (I – M²)N = −2I, then the positive integral value of α is ________.

Answer: (1)

30. Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x² – 2x and g(f(x)) = 4x² + 6x + 1, then the value of f(2) + g(2) is ____________ .

Answer: (18)

JEE Main Session 2 28th June 2022 Shift 2 Question Paper and Answer Key

December 11, 2022 by suresh84

JEE Main Session 2 28^th June 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as Here m and n are constants. The relations for distance and time in two systems respectively are :

Answer: (A)

2. A ball is spun with angular acceleration α = 6t² – 2t, where t is in second and α is in rads^–2. At t = 0, the ball has angular velocity of 10 rads^–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

Answer: (B)

3. A block of mass 2 kg moving on a horizontal surface with speed of 4 ms^–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm^–1. The speed of the block as it just crosses the rough surface will be :

(A) Zero

(B) 1.5 ms^–1

(D) 2.5 ms^–1

Answer: (C)

4. A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F_f and F_w are the reaction forces of the floor and the wall, then ratio of F_w/F_f will be:

(Use g = 10 m/s²)

(A) 6/√110

(B) 3/√113

(D) 2/√109

Answer: (C)

5. Water falls from a 40 m high dam at the rate of 9 × 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :

(Take g = 10 ms⁻²)

(A) 25

(B) 50

(D) 18

Answer: (B)

6. Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be

vertical-align: middle; margin-bottom: 1px;

Answer: (C)

7. A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10^–5Nsm^–2 and its density is negligible as compared to that of water (10⁶gm^–3). Terminal velocity of the water drop is

(Take acceleration due to gravity = 10 ms^–2)

(A) 145.4 × 10^–6ms^–1

(B) 118.0 × 10^–6ms^–1

(D) 123.4 × 10^–6ms^–1

Answer: (D)

8. A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

(A) 20 J

(B) 30 J

(D) −60 J

Answer: (B)

9. What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

(A) The velocity of atomic oxygen remains same

(B) The velocity of atomic oxygen doubles

(D) The velocity of atomic oxygen becomes four times

Answer: (B)

10. Two point charges A and B of magnitude +8 × 10^–6 C and –8 × 10^–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 10⁴ NC^–1. The distance ‘d’ between the point charges A and B is:

(A) 2.0 m

(B) 3.0 m

(D) 4.0 m

Answer: (B)

11. Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature co-efficient of resistance of the material of the wire is:

(A) 0.033°C^–1

(B) –0.033°C^–1

(D) 0.055°C^–1

Answer: (A)

12. The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10^–5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

(A) 1.2 × 10^–5

(B) 1.2 × 10^–3

(D) 2.4 × 10^–5

Answer: (A)

13. Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10^–6 N, then the value of x is approximately:

(A) 1

(B) 2.4

(D) 2

Answer: (C)

14. A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:

(Assume the coil to be short circuited.)

(A) Halved

(B) Quadrupled

(D) Doubled

Answer: (D)

15. An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm^–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:

Answer: (B)

16. In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

(A) 3

(B) 2

(D) 0.5

Answer: (B)

17. Let K₁ and K₂ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ₁ and λ₂, respectively are incident on a metallic surface. If λ₁ = 3λ₂ then:

(A) K₁> K₂/3

(B) K₁< K₂/3

(D) K₂ = K₁/3

Answer: (B)

18. Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.

(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below:

(A) (A) and (B) only

(B) (B) and (D) only

(D) (C) and (D) only

Answer: (C)

19. In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode (D₁ or D₂) is 0.6 V. Which of the following output voltage (V₀) waveform across the diode is correct?

Answer: (D)

20. Amplitude modulated wave is represented by V_AM = 10[1 + 0.4 cos(2π × 10⁴t] cos(2π × 10⁷t). The total bandwidth of the amplitude modulated wave is:

(A) 10 kHz

(B) 20 MHz

(D) 10 MHz

Answer: (C)

SECTION-B

21. A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is . Then value of x is _______.

Answer: (150)

22. A zener of breakdown voltage V_Z = 8 V and maximum Zener current, I_ZM = 10 mA is subjected to an input voltage V_i = 10 V with series resistance R = 100 Ω. In the given circuit R_L represents the variable load resistance. The ratio of maximum and minimum value of R_L is __________.

Answer: (2)

23. In a Young’s double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1/α. The value of α is _________.

Answer: (4)

24. In the given circuit, the magnitude of V_L and V_C are twice that of V_R. Given that f = 50 Hz, the inductance of the coil is 1/(Kπ) mH. The value of K is ________.

Answer: (0)

25. All resistances in figure are 1 Ω each. The value of current ‘I‘ is (a/5) A. The value of a is _________.

Answer: (8)

26. A capacitor C₁ of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is ____ μC.

Answer: (100)

27. A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ cm.

(Velocity of sound in air is 340 ms^–1)

Answer: (50)

28. A liquid of density 750 kgm^–3 flows smoothly through a horizontal pipe that tapers incross-sectional area from A1 = 1.2 × 10^–2 m² to The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ________ × 10^–3 m³s^–1.

Answer: (24)

29. A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ________ N.

(Take g = 10 ms^–2)

Answer: (10)

30. A car covers AB distance with first one-third at velocity v₁ms^–1, second one-third at v₂ms^–1 and last one-third at v₃ms^–1. If v₃ = 3v₁, v₂ = 2v₁ and v₁ = 11 ms^–1 then the average velocity of the car is ____ ms^–1.

Answer: (18)

CHEMISTRY

SECTION-A

1. Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is,

Given : Atomic masses of C, H and N are 12, 1 and 14 amu, respectively.

The molar mass of the compound A is 162 g mol^–1.

(A) C₄H₆N₂

(B) C₂H₃N

(D) C₁₀H₁₄N₂

Answer: (D)

2. Consider the following statements :

(A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ = 1, 2, 3, ….

(B) The azimuthal quantum number ‘l’ for a given ‘n’ (principal quantum number) can have values as ‘l’ = 0, 1, 2, …n

(D) ±1/2 are the two possible orientations of electron spin.

(E) For l = 5, there will be a total of 9 orbital

Which of the above statements are correct?

(A) (A), (B) and (C)

(B) (A), (C), (D) and (E)

(D) (A), (B), (C) and (D)

Answer: (C)

3. In the structure of SF₄, the lone pair of electrons on S is in.

(A) Equatorial position and there are two lone pair – bond pair repulsions at 90º

(B) Equatorial position and there are three lone pair – bond pair repulsions at 90º

(D) Axial position and there are two lone pair – bond pair repulsion at 90º

Answer: (A)

4. A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of required to make buffer is _____.

Given :Ka(CH₃CH₂COOH) = 1.3 × 10^–5

(A) 0.03

(B) 0.13

(D) 0.33

Answer: (B)

5. Match List-I with List-II.

Choose the correct answer from the options given below:

(A) (A) – (II), (B) – (III), (C) – (IV), (D) – (I)

(B) (A) – (II), (B) – (I), (C) – (III), (D) – (IV)

(D) (A) – (I), (B) – (III), (C) – (II), (D) – (IV)

Answer: (C)

6. Match List-I with List-II:

Choose the correct answer from the options given below:

(A) A-IV, B-III, C-I, D-II

(B) A-IV, B-II, C-I, D-III

(D) A-I, B-II, C-III, D-IV

Answer: (B)

7. In the metallurgical extraction of copper, following reaction is used :

FeO + SiO₂ → FeSiO₃

FeO and FeSiO₃ respectively are.

(A) Gangue and flux

(B) Flux and slag

(D) Gangue and slag

Answer: (D)

8. Hydrogen has three isotopes: protium (¹H), deuterium (²H or D) and tritium (³H or T). They have nearly same chemical properties but different physical properties. They differ in

(A) Number of protons

(B) Atomic number

(D) Atomic mass

Answer: (D)

9. Among the following, basic oxide is:

(A) SO₃

(B) SiO₂

(D) Al₂O₃

Answer: (C)

10. Among the given oxides of nitrogen; N₂O, N₂O₃, N₂O₄ and N₂O₅, the number of compound/(s) having N – N bond is:

(A) 1

(B) 2

(D) 4

Answer: (C)

11. Which of the following oxoacids of sulphur contains ‘‘S’’ in two different oxidation states?

(A) H₂S₂O₃

(B) H₂S₂O₆

(D) H₂S₂O₈

Answer: (A)

12. Correct statement about photo-chemical smog is:

(A) It occurs in humid climate.

(B) It is a mixture of smoke, fog and SO₂.

(D) It results from reaction of unsaturated hydrocarbons.

Answer: (D)

13. The correct IUPAC name of the following compound is:

(A) 4-methyl-2-nitro-5-oxohept-3-enal

(B) 4-methyl-5-oxo-2-nitrohept-3-enal

(D) 6-formyl-4-methyl-2-nitrohex-3-enal

Answer: (C)

14. The major product (P) of the given reaction is (where, Me is –CH₃)

Answer: (C)

15. 4-Bromophenyl acetic acid.

In the above reaction ‘A’ is

Answer: (C)

16. Isobutyraldehyde on reaction with formaldehyde and K₂CO₃ gives compound ‘A’. Compound ‘A’ reacts with KCN and yields compound ‘B’, which on hydrolysis gives a stable compound ‘C’. The compound ‘C’ is

Answer: (C)

17. With respect to the following reaction, consider the given statements:

(A) o-Nitroaniline and p-nitroaniline are the predominant products.

(B) p-Nitroaniline and m-nitroaniline are the predominant products.

(D) H₂SO₄ acts as an acid.

Choose the correct option.

(A) (A) and (C) are correct statements.

(B) (A) and (D) are correct statements.

(D) (B) and (C) are correct statements.

Answer: (C)

18. Given below are two statements, one is Assertion (A) and other is Reason (R).

Assertion (A): Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties.

Reason (R): The cis-polyisoprene molecules consist of various chains held together by strong polar interactions with coiled structure.

In the light of the above statements, choose the correct one from the options given below:

(A) Both (A) and (R) are true and (R) is the correct explanation of (A).

(B) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(D) (A) is false but (R) is true.

Answer: (C)

19. When sugar ‘X’ is boiled with dilute H₂SO₄ in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’ on oxidation with HNO₃ yields saccharic acid whereas ‘B’ is laevorotatory. The compound ‘X’ is :

(A) Maltose

(B) Sucrose

(D) Starch

Answer: (B)

20. The drug tegamet is:

Answer: (C)

SECTION-B

21. 100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ________ g mol^–1. (Nearest integer).

Answer: (4)

22. For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, Δ_CH^Θ = –601.70 kJ mol^–1, the magnitude of change in internal energy for the reaction is ______ kJ. (Nearest integer)

(Given : R = 8.3 J K^–1mol^–1)

Answer: (600)

23. 2.5 g of protein containing only glycine (C₂H₅NO₂) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be 5.03 × 10^–3 bar. The total number of glycine units present in the protein is _______.

(Given : R = 0.083 L bar K^–1mol^–1)

Answer: (330)

24. For the given reactions

Sn²⁺ + 2e– → Sn

Sn⁴⁺ + 4e– → Sn

The electrode potentials are; and The magnitude of standard electrode potential for Sn⁴⁺/Sn²⁺ i.e. is _______ × 10⁻² V. (Nearest integer)

Answer: (16)

25. A radioactive element has a half-life of 200 days. The percentage of original activity remaining after 83 days is ________. (Nearest integer)

(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

Answer: (75)

26. [Fe(CN)₆]^4–

[Fe(CN)₆]^3–

[Ti(CN)₆]^3–

[Ni(CN)₄]^2–

[Co(CN)₆]^3–

Among the given complexes, number of paramagnetic complexes is_______.

Answer: (2)

27. (a) CoCl₃⋅4 NH₃, (b) CoCl₃⋅5NH₃, (c) CoCl₃.6NH₃ and (d) CoCl(NO₃)₂⋅5NH₃. Number of complex(es) which will exist in cis-trans form is/are______.

Answer: (1)

28. The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793 g of CO₂ and 0.442 g of H₂ The percentage of oxygen composition in the organic compound is_____.[nearest integer]

Answer: (46)

29. The major product of the following reaction contains______bromine atom(s).

Answer: (1)

30. 0.01 M KMnO₄solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO₄ solution left in burette after the end point is _____ml. [nearest integer]

Answer: (30)

MATHEMATICS

SECTION-A

1. Let R₁ = {(a, b) ∈ N × N : |a – b| ≤ 13} and R₂ = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

(A) Both R₁ and R₂ are equivalence relations

(B) Neither R₁ nor R₂ is an equivalence relation

(D) R₂ is an equivalence relation but R₁ is not

Answer: (B)

2. Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

(A) 11/3

(B) 7/3

(D) 14/3

Answer: (A)

3. The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives atleast 4 and atmost 7 candies, C₃ receives atleast 2 and atmost 6 candies, is equal to:

(A) 205

(B) 615

(D) 430

Answer: (D)

4. The term independent of x in the expansion of is

(A) 7/40

(B) 33/200

(D) 11/50

Answer: (B)

5. If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

(A) 21

(B) 22

(D) 24

Answer: (C)

6. Let f, g : R → R be functions defined by

Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :

(A) one point

(B) two points

(D) four points

Answer: (B)

7. Let f : R → R be a differentiable function such that and let for is equal to

(A) 2

(B) 3

(D) −3

Answer: (B)

8. Let f :R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If then

(A) I₁ + 2I₂ = 4nk

(B) I₁ + 2I₂ = 2nk

(D) I₁ + nI₂ = 6n²k

Answer: (C)

9. The area of the bounded region enclosed by the curve and the x-axis is

(A) 9/4

(B) 45/16

(D) 63/16

Answer: (C)

10. Let x = x(y) be the solution of the differential equation such that x(1) = 0. Then, x(e) is equal to

(A) elog_e(2)

(B) −elog_e(2)

(D) −e²log_e(2)

Answer: (D)

11. Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 tanx(cosx – y). If the curve passes through the point (π/4, 0) then the value of is equal to

Answer: (B)

12. Let a triangle be bounded by the lines L₁ : 2x + 5y = 10; L₂ : –4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L₂ at A and L₁ at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to

(A) 110/13

(B) 132/13

(D) 151/13

Answer: (B)

13. Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola e′ and ℓ′ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If then the value of 77a + 44b is equal to

(A) 100

(B) 110

(D) 130

Answer: (D)

14. Let α ∈ where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors then the value of is equal to

(A) 10

(B) 7

(D) 14

Answer: (D)

15. If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is :

(A) 2

(B) 8

(D) 16

Answer: (B)

16. Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

(A) 18

(B) 20

(D) 22

Answer: (D)

17. The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :

(A) 1/24

(B) 1/40

(D) 1/20

Answer: (D)

18. The value of is equal to

(A) 1

(B) 2

(D) 6

Answer: (C)

19. Let be a vector which is perpendicular to the vector If the projection of the vector on the vector is

(A) 1/3

(B) 1

(D) 7/3

Answer: (C)

20. If cot α =1 and sec β = −5/3, where then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :

(A) –1/7 and IVth quadrant

(B) 7 and Ist quadrant

(D) 1/7 and Ist quadrant

Answer: (A)

SECTION-B

21. Let the image of the point P(1, 2, 3) in the line be Q. Let R (α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22(α + β + γ) is equal to ________.

Answer: (125)

22. Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is __________.

Answer: (0)

23. If one of the diameters of the circle x² + y² – 2√2x – 6√2y + 14 = 0 is a chord of the circle (x – 2√2)² + (y – 2√2)² = r², then the value of r² is equal to _______.

Answer: (10)

24. If then the value of (a – b) is equal to _______.

Answer: (11)

25. Let for n = 1, 2, …, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is Then the value of is equal to

Answer: (41651)

26. If the system of linear equations

2x – 3y = γ + 5,

αx + 5y = β + 1,

where α, β, γ ∈ R has infinitely many solutions, then the value of |9α + 3β + 5γ| is equal to _______.

Answer: (58)

27. Let Then, the number of elements in the set {n ∈ {1, 2, ……, 100} : Aⁿ = A} is

Answer: (25)

28. Sum of squares of modulus of all the complex numbers z satisfying is equal to

Answer: (2)

29. Let S = {1, 2, 3, 4}. Then the number of elements in the set {f : S × S → S : f is onto and f(a, b) = f(b, a) ≥ a ∀ (a, b) ∈ S × S is ____________.

Answer: (37)

30. The maximum number of compound propositions, out of p ∨ r ∨ s, p ∨ r ∨ ~s, p ∨ ~q ∨ s, ~p ∨ ~r ∨ s, ~p ∨ ~r ∨ ~s, ~p ∨ q ∨ ~s, q ∨ r ∨ ~s, q ∨ ~r ∨ ~s, ~p ∨ ~q ∨ ~s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to ____________ .

Answer: (9)