**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.

(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:

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

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

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

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

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}

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

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%

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

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

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) n^{2} : N^{2}

(3) N^{2} : n^{2}

(4) N : n

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

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

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

14. For a solid rod, the Young’s modulus of elasticity is 3.2 × 10^{11}Nm^{−2} and density is 8 × 10^{3} kg m^{−3}. The velocity of longitudinal wave in the rod will be.

(1) 145.75 × 10^{3} ms^{−}^{1}

(2) 18.96 × 10^{3} ms^{−}^{1}

(3) 3.65 × 10^{3} ms^{−}^{1}

(4) 6.32 × 10^{3} ms^{−}^{1}

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

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

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

18. Under the same load, wire A having length 5.0 m and cross section 2.5 × 10^{−5} m^{2} stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 × 10^{−5} m^{2} 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

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

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.

**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.

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})

23. For the given circuit, in the steady state, |V_{B} – V_{D}| = ________ V.

24. Two parallel plate capacitors C_{1} and C_{2} each having capacitance of 10μF are individually charged by a 100 V D.C. source. Capacitor C_{1} is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor C_{2} is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor C_{1} 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)

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.

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

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 Li^{2+} will be : x × 10^{−1} The value of x is ____.

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).

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 ______.

30. The displacement equations of two interfering waves are given by y_{2} = 5[sin ωt + √3 cos ωt]cm respectively. The amplitude of the resultant wave is ________ cm.

**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.

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

33. Given below are two statements :

**Statement I :** H_{2}O_{2} is used in the synthesis of Cephalosporin

**Statement II :** H_{2}O_{2} 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

34. A hydrocarbon ‘X’ with formula C_{6}H_{8} uses two moles H_{2} 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

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.

(C) Osmosis always takes place from hypertonic to hypotonic solution.

(D) The density of 32% H_{2}SO_{4} 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

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

(1) BI_{3} > BBr_{3} > BCl_{3} > BF_{3}

(2) BBr_{3} > BI_{3} > BCl_{3} > BF_{3}

(3) BCl_{3} > BF_{3} > BBr_{3} > BI_{3}

(4) BF_{3 }> BCl_{3 }> BBr_{3} > BI_{3}

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) C_{5}H_{8}

(2) C_{11}H_{4}

(3) C_{9}H_{8}

(4) C_{11}H_{8}

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

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

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

(C) n = 3, l = 1, 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

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

(1) Li

(2) Mg

(3) Be

(4) Ca

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

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

(A) Chloroxylenol (B) Bithional

(C) Veronal (D) Prontosil

(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

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.

43. An organic compound [A](C_{4}H_{11}N), shows optical activity and gives N_{2} gas on treatment with HNO_{2}. The compound [A] reacts with PhSO_{2}Cl producing a compound which is soluble in KOH.

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

(1) CO_{2} + H_{2}O → H_{2}CO_{3}

(2) 2SO_{2} + O_{2} + 2H_{2}O → 2H_{2}SO_{4}

(3) 4NO_{2} + O_{2} + 2H_{2}O → 4HNO_{3}

(4) N_{2}O_{5} + H_{2}O → 2HNO_{3}

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

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 :

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

48. In Dumas method for the estimation of N_{2}, the sample is heated with copper oxide and the gas evolved is passed over :

(1) Copper oxide

(2) Ni

(3) Pd

(4) Copper gauze

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

50. Compound A, C_{5}H_{10}O_{5}, given a tetraacetate with AC_{2}O and oxidation of A with Br_{2}−H_{2}O gives an acid, C_{5}H_{10}O_{6} .Reduction of A with HI gives isopentane. The possible structure of A is :

**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)

52. Enthalpies of formation of CCl_{4}( g), H_{2}O(g), CO_{2}(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)

CCl_{4}(g) + 2H_{2}O(g) → CO_{2}(g) + 4HCl(g)

53. A sample of a metal oxide has formula M_{83}O_{1.00}. The metal M can exist in two oxidation states + 2 and +3.In the sample of M_{0.83}O_{1.00}, the percentage of metal ions existing in + 2 oxidation state is %. (nearest integer)

54. The resistivity of a 0.8M solution of an electrolyte is 5 × 10^{−3} Ω cm. Its molar conductivity is ______ × 10^{4}Ω^{−1} cm^{2} mol^{−1} (Nearest integer)

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})

56. If the CFSE of [Ti(H_{2}O)_{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 × 10^{8} m/s and Avogadro’s Constant (N_{A}) = 6 × 10^{23}/mol

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 _____

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

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}]

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

**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

62. Among the relations

and T = {(a, b): a, b ∈ ℝ, a^{2} – b^{2} ∈ 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

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

(1) 4

(2) 2√2

(3) √2

(4) 2

64. The complex number is equal to :

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

66.

(1) does not exist

(2) is equal to 27

(3) is equal to 27/2

(4) is equal to 9

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)

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

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

70. The absolute minimum value, of the function f(x) = |x^{2} – x + 1| + [x^{2} – 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

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

72. Let a_{1}, a_{2}, a_{3}, … be an A.P. If a_{7} = 3, the product a_{1}a_{4} 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

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

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

(1) 560

(2) 449

(3) 339

(4) 336

75. Let the plane P : 8x + α_{1}y + α_{2}y + α_{2}z + 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

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

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

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

(1) (0, 4]

(2) (4, ∞)

(3) (2, 12]

(4) (8, ∞)

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

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

**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

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 2^{84}, then n is equal to

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

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 unit^{2}, then is equal to

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

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

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

88. If ^{2n+1}P_{n}_{−}_{1} : ^{2n}^{−}^{1}P_{n} = 11 : 21, then n^{2} + n + 15 is equal to :

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

90. The sum 1^{2} – 2 ∙ 3^{2} + 3 ∙ 5^{2} – 4 ∙ 7^{2} + 5 ∙ 9^{2} − … + 15 ∙ 29^{2} is

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