**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.

(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. 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

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^{a}ρ^{b}s^{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)

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

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 _______ (μ_{0} = 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

5. The electric potential at the centre of two concentric half rings of radii R_{1} and R_{2}, having same linear charge density 𝜆 is :

(1) λ/2ε_{0}

(2) λ/4ε_{0}

(3) 2λ/ε_{0}

(4) λ/ε_{0}

6. If the distance of the earth from Sun is 1.5 × 10^{6} Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :

(1) 6 × 10^{6} km

(2) 3 × 10^{6} km

(3) 3 × 10^{7} km

(4) 6 × 10^{7} km

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

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

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

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

E_{x} = E_{0}sin(kz − ωt)

B_{y} = B_{0}sin(kz − ωt)

Then the correct relation between E_{o} and B_{o} is given by

(1) E_{o }B_{o} = ωk

(2) E_{o} = kB_{o}

(3) kE_{o} = ωB_{o}

(4) ωE_{o} = kB_{o}

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

(1) NAND

(2) OR

(3) AND

(4) NOR

12. Let γ_{1} be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and γ_{2} be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, γ_{1}/ γ_{2} is :

(1) 25/21

(2) 35/27

(3) 21/25

(4) 27/35

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

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:

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}

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

17. In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T_{3} > T_{2} > T_{1} as:

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

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

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

**SECTION-B**

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

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)

23. The energy released per fission of nucleus of ^{240}X is 200MeV. The energy released if all the atoms in 120 g of pure ^{240}X undergo fission is ______ × 10^{25}MeV (Given NA = 6 × 10^{23})

24. A uniform solid cylinder with radius R and length L has moment of inertia I_{1}, 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 I_{2} is the moment of inertia of the carved out portion of the cylinder then I_{1}/I_{2} = ________ (Both I_{1} and I_{2} are about the axis of the cylinder)

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 _______

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 ______

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.

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

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.

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/s^{2} and π = 22/7)

**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.

(C) Lithium carbonate is highly stable to heat.

(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

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

33. A student has studied the decomposition of a gas AB_{3} at 25∘ He obtained the following data.

The order of the reaction is

(1) 0(zero)

(2) 0.5

(3) 1

(4) 2

34. K_{2}Cr_{2}O_{7} paper acidified with dilute H2SO4 turns green when exposed to

(1) Carbon dioxide

(2) Sulphur trioxide

(3) Sulphur dioxide

(4) Hydrogen sulphide

35. Which will undergo deprotonation most readily in basic medium?

(1) c only

(2) a only

(3) Both a and c

(4) b only

36. The hybridization and magnetic behaviour of cobalt ion in [Co(NH_{3})_{6}]^{3+} complex, respectively is

(1) d^{2}sp^{3} and paramagnetic

(2) sp^{3}d^{2} and diamagnetic

(3) d^{2}sp^{3} and diamagnetic

(4) sp^{3}d^{2} and paramagnetic

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

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

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

40. Which one amongst the following are good oxidizing agents?

(A) Sm^{2+ } (B) Ce^{2+} (C) Ce^{4+} (D) Tb^{4+}

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

41. Which one amongst the following are good oxidizing agents?

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

43. Find out the major products from the following reaction

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

45. In which of the following reactions the hydrogen peroxide acts as a reducing agent?

(1) PbS + 4H_{2}O_{2} → PbSO_{4} + 4H_{2}O

(2) Mn^{2+} + H_{2}O_{2} → Mn^{4+} + 2OH^{−}

(3) HOCl + H_{2}O_{2} → H_{3}O^{+} + Cl^{−} + O_{2}

(4) 2Fe2+ + H2O2 → 2Fe3+ + 2OH^{−}

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

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

48. What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : N_{2}; N_{2}^{+} ; O_{2}; O_{2}^{+}?

(1) 2, 1, 0, 1

(2) 0, 1, 0, 1

(3) 0, 1, 0, 1

(4) 2, 1, 2, 1

49. The metal which is extracted by oxidation and subsequent reduction from its ore is:

(1) Ag

(2) Fe

(3) Cu

(4) Al

50. Choose the correct colour of the product for the following reaction.

(1) White

(2) Red

(3) Blue

(4) Yellow

**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) T_{4} > T_{3} > T_{2} > T_{1}

(B) The black body consists of particles performing simple harmonic motion.

(C) The peak of the spectrum shifts to shorter wavelength as temperature increases.

(E) The given spectrum could be explained using quantisation of energy.

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

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

(C) It decreases with increase in temperature

(D) It results into unimolecular layer

(E) No activation energy is needed

54. Sum of π – bonds present in peroxodisulphuric acid and pyrosulphuric acid is:

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)

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.

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)

(C) Liquid and gaseous carbon dioxide coexist between points (b) and (c)

(D) As the volume decreases from (b) to (c), the amount of liquid decreases

58. Maximum number of isomeric monochloro derivatives which can be obtained from 2, 2, 5, 5 tetramethylhexane by chlorination is ______

59. Total number of tripeptides possible by mixing of valine and proline is ________

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)

**Mathematics**

**SECTION-A**

61. If, f(x) = x^{3} – x^{2}f 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)

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)

63. If, then then

(1) 1011

(2) 2010

(3) 1010

(4) 2011

64. Let Let be parallel to be perpendicular to then the value of is

(1) 7

(2) 9

(3) 6

(4) 11

65. Let y = y(x) be the solution of the differential equation (x^{2} − 3y^{2})dx + 3xydy = 0, y(1) = 1. Then 6y^{2}(e) is equal to

(1) 2e^{2}

(2) 3e^{2}

(3) e^{2}

(4)

66. The locus of the mid points of the chords of the circle C_{1} : (x − 4)^{2} + (y − 5)^{2} = 4 which subtend an angle θ_{1} at the centre of the circle C_{1}, is a circle of radius r_{i}. If and then θ_{2} is equal to

(1) π/4

(2) π/2

(3) π/6

(4) 3π/4

67. The number of real solutions of the equation is

(1) 0

(2) 3

(3) 4

(4) 2

68. Let A be a 3×3 matrix such that |adj(adj(adjA))|=12^{4} Then |A^{−1}adjA| is equal to

(1) √6

(2) 2√3

(3) 12

(4) 1

69. is equal to

(1) 2π

(2) π/6

(3) π/3

(4) π/2

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

71. If (^{30}C_{1})^{2} + 2(^{30}C_{2})^{2} + 3(^{30}C_{3})^{2} + … + 30(^{30}C_{30})^{2} then α is equal to :

(1) 30

(2) 10

(3) 60

(4) 15

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

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

74. Let the six numbers a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, be in A.P. and a_{1} + a_{3} = 10. If the mean of these six numbers is 19/2 and their variance is σ^{2}, then 8σ^{2} is equal to :

(1) 210

(2) 220

(3) 200

(4) 105

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 y^{2} = 6x in the first quadrant is :

(1) 4

(2) 2

(3) √6

(4) 2√2

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)

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)

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

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

80. The value of is

**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

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 y^{2} = λx with one vertex at the vertex of the parabola, is

83. Let S ={θ ∈ [0, 2π):tan(π cosθ) + tan(π sin θ) = 0}.

Then is equal to

84. If then value of n is

85. Let the sum of the coefficients of the first three terms in the expansion of be 376. Then the coefficient of x^{4} is

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

87. Let is equal to

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

89. If the area of the region bounded by the curves y^{2} − 2y = −x, x + y = 0 is A, then 8 A is equal to

90. Let f be a differentiable function defined on [0, π/2] such that f(x) > 0 and is equal to