**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.

(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. 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:-

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

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^{−34}Js)

(1) D

(2) B

(3) C

(4) A

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

5. The distance travelled by a particle is related to time t as x = 4t^{2}. 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}

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

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

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

(C) Smaller in size then object

(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

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:-

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

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.

(C) The Centripetal force acting on the planet is directed away from 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

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 cm^{2}) is :

(1) 1.0

(2) 2.0

(3) 1.5

(4) 0.5

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

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

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

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

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

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

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

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)

**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)

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 _______.

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:-

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.

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}.

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 :

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 _____.

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

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

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.

**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

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

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 CO_{2}.CO is neutral whereas CO_{2} is acidic in nature

Reason 𝐑: CO_{2} 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

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

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

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

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

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

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

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

41. What is the mass ratio of ethylene glycol (C_{2}H_{6}O_{2}, 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

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

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

44. The isomeric deuterated bromide with molecular formula C_{4}H_{8}DBr 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

45. A chloride salt solution acidified with dil. HNO_{3} gives a curdy white precipitate, [A], on addition of AgNO_{3}⋅[A] on treatment with NH_{4}OH gives a clear solution, B. A and B are respectively

(1) AgCl & (NH_{4})[Ag(OH)_{2}]

(2) AgCl & [Ag(NH_{3})_{2}]Cl

(3) H[AgCl_{3}] & (NH_{4})[Ag(OH)_{2}]

(4) H[AgCl_{3}] & [Ag(NH_{3})_{2}]Cl

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

47. ꞌA’ in the given reaction is

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

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

(C) Polychlorinated biphenyls act as cleansing solvents.

(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

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

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

(1) Li

(2) K

(3) Rb

(4) Na

**Section B**

51. Total number of moles of AgCl precipitated on addition of excess of AgNO_{3} to one mole each of the following complexes [Co(NH_{3})_{4}Cl_{2}]Cl,[Ni(H_{2}O)_{6}]Cl_{2},[Pt(NH_{3})_{2}Cl_{2}] and [Pd(NH_{3})_{4}]Cl_{2} is ____

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.

(C) As the adsorption proceeds, ΔH becomes more and more negative.

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

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})

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

55. 28.0 L of CO_{2} 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}(CH_{4}) = −900 kJ mol^{−}^{1}

∆H_{c}(C_{2}H_{4}) = −1400 kJ mol^{−}^{1}

56. Pt(s) |H_{2}(g) (1bar)| |H + (aq) (1M)| |M^{3+}(aq), M^{+}(aq)|Pt(s)

The E_{ cell} for the given cell is 0.1115 V at 298 K when

The value of a is

Given : E^{θ}M^{3+}/M^{+} = 0.2 V

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 C_{2}H_{5}OH (aq) and 0.25 M KBr (aq)

(B) 0.100 M K4[Fe(CN)_{6}] (aq) and 0.100 M FeSO_{4}(NH_{4})_{2}SO_{4} (aq)

(C) 0.05 M K_{4}[Fe(CN)_{6}] (aq) and 0.25 M NaCl (aq)

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

(E) 0.02 M KCl⋅MgCl_{2}⋅6H_{2}O(aq) and 0.05 M KCl(aq)

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.

(C) The time required for 10% completion is 25 times the time required for 90% completion.

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

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

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.

(C) The molecule in the bulk can never come to the liquid surface.

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

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

**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

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

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?

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 y^{2} = 6x. The locus of its circumcentre is:

(1) 4y^{2} – 18y – 3x – 18 = 0

(2) 4y^{2} – 18y – 3x + 18 = 0

(3) 4y^{2} – 18y + 3x + 18 = 0

(4) 4y^{2} + 18y + 3x + 18 = 0

65. Let f(x) = 2X^{n} + 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

66. is equal to

(1) ^{51}C_{4} – ^{45}C_{4}

(2) ^{52}C_{3} – ^{45}C_{3}

(3) ^{52}C_{4} – ^{45}C_{4}

(4) ^{51}C_{3} – ^{45}C_{3}

67. Let the function f(x) = 2x^{3} + (2p − 7) x^{2} + 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, ∞)

68. Let and where i = √−1.

If M = A^{T}BA, then the inverse of the matrix AM^{2023} A^{T} is

69. Let and Then is equal to

70. The integral is equal to

71. Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x^{2} − y^{2} + 64x + 4y + 44 = 0.Then the area of the region above the parabola x^{2} = y + 4, below the transverse axis T and on the right of the conjugate axis C is:

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

73. If the function is continuous at x = π/2, then 9λ + 6log_{e}μ + μ^{6} – e^{6}^{λ} is equal to

(1) 10

(2) 2e^{4} + 8

(3) 11

(4) 8

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

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

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)

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) A^{13} B^{26} − B^{26} A^{13} is symmetric

(S2)A^{26}C^{13} − C^{13} A^{26} 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

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

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

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

**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.

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

83. Let a ∈ ℝ and let α, β be the roots of the equation x^{2} + 60^{1/4}x + a = 0. If α^{4} + β^{4} = −30, then the product of all possible values of a is

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

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

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

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

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

89. If where m and n are coprime natural numbers, then m^{2} + n^{2} − 5 is equal to

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