**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.

(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 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

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:

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

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

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)

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 b^{2}/a, will be:

(1) Compressibility

(2) Energy density

(3) Modulus of rigidity

(4) Bulk modulus

7. The equivalent resistance between A and B of the network shown in figure:

(1)

(2) 21R

(3) 14R

(4)

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

9. An object moves with speed 𝑣_{1}, 𝑣_{2} and 𝑣_{3} 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:

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

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

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

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

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

15. Which of the following frequencies does not belong to FM broadcast.

(1) 64MHz

(2) 89MHz

(3) 99MHz

(4) 106MHz

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

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

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

19. Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

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

**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.

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 _______.

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 × 10^{8} ms^{−}^{1}).

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}

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.

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 ________.

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 ______.

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} )

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

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 q_{0} becomes maximum is a/√ The value of x is ________.

**Chemistry**

**SECTION-A**

31. A solution of FeCl_{3} when treated with K_{4}[Fe(CN)_{6}] gives a prussian blue precipitate due to the formation of

(1) K[Fe_{2}(CN)_{6}]

(2) Fe_{4}[Fe(CN)_{6}]_{3}

(3) Fe[Fe(CN)_{6}]

(4) Fe_{3}[Fe(CN)_{6}]_{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

33. Resonance in carbonate ion (CO_{3}^{2}^{−}) 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) CO_{3}^{2−} has a single structure i.e., resonance hybrid of the above three structures.

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

35. Identify the incorrect option from the following:

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.

(C) A is more polar than B because dipole moment of A is zero.

(D) Br_{2} adds easily to B than A.

Identify the incorrect statements from the options given below:

37. In the following reaction, ‘ A ‘ is

38. Highest oxidation state of Mn is exhibited in Mn_{2}O_{7}. The correct statements about Mn_{2}O_{7} are

(A) Mn is tetrahedrally surrounded by oxygen atoms.

(B) Mn is octahedrally surrounded by oxygen atoms.

(C) Contains Mn-O-Mn bridge.

(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

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

40. The correct representation in six membered pyranose form for the following sugar [X] is

41. Which of the following complex will show largest splitting of d-orbitals ?

(1) [F_{e}F_{6}]^{3}^{−}

(2) [Fe(C_{2}O_{4})_{3}]^{3}^{−}

(3) [Fe(CN)_{6}]^{3}^{−}

(4) [Fe(NH_{3})_{6}]^{3+}

42. Which of the following are the example of double salt?

(A) FeSO_{4} ⋅ (NH_{4})_{2}SO_{4} ⋅ 6H_{2}O

(B) CuSO_{4}, 4NH_{3}H_{2}O

(C) K_{2}SO_{4} ⋅ Al_{2}(SO_{4})_{3} ⋅ 24H_{2}O

(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

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

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

45. Choose the correct statement(s):

(A) Beryllium oxide is purely acidic in nature.

(B) Beryllium carbonate is kept in the atmosphere of CO_{2}.

(C) Beryllium sulphate is readily soluble in water.

(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

46. Which of the following represents the lattice structure of A_{95}O containing A^{2+}, A^{3+} and O^{2−} ions? ⊙ A^{2+} ⊙ A^{3+} ⊙ O^{2−}

(1) A only

(2) B and C only

(3) A and B only

(4) B only

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

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} ( cm^{3} 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

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

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.

**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 (p_{1}/p_{2}) is equal to x : 1. The value of x is ______ (Nearest integer)

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.

(C) The cathode rays start from cathode and move towards anode.

(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

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.

54. Sum of oxidation states of bromine in bromic acid and perbromic acid is

55. 25 mL of an aqueous solution of KCl was found to require 20 mL of 1M AgNO_{3} solution when titrated using K_{2}CrO_{4} 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}

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)

H_{2}O(g) → H(g) + OH(g)∆H° = XkJmol^{−}^{1}

57. At what pH, given half cell MnO_{4}^{−}(0.1M) ∣ Mn^{2+}(0.001M) will have electrode potential of 1.282 V ? (Nearest Integer)

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.

59. Number of isomeric compounds with molecular formula C_{9}H_{10}O 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 C_{9}H_{12}O is

60. The total number of chiral compound/s from the following is

**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

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

63. For a triangle ABC, the value of cos2A + cos2B + 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

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

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

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

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 2x^{2} + xy – 3y^{2} = 0 is

(1) x^{2} – y^{2} – 10xy = 0

(2) x^{2} – y^{2} + 10xy = 0

(3) 3x^{2} + 5xy + 2y^{2} = 0

(4) 3x^{2} + xy – 2y^{2} = 0

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

69. The value of is :

(1) 2^{50}/51!

(2) 2^{51}/50!

(3) 2^{50}/50!

(4) 2^{51}/51!

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

71. The sum to 10 terms of the series is

(1) 55/111

(2) 56/111

(3) 58/111

(4) 59/111

72. The shortest distance between the lines and is

(1) 5√3

(2) 7√3

(3) 6√3

(4) 4√3

73. is equal to

(1) log_{e} 2

(2) log_{e} (3/2)

(3) log_{e} (2/3)

(4) 0

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

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 < x_{1} < x_{2} < 3 such that f(x) < g(x), ∀x ∈ (x_{1}, x_{2})

(4) there exists

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) x^{2} – 20x + 99 = 0

(2) x^{2} – 19x + 90 = 0

(3) x^{2} – 22x + 120 = 0

(4) x^{2} – 18x + 80 = 0

77. Let S = {x: x ∈ ℝ and

Then n(S) is equal to

(1) 4

(2) 0

(3) 6

(4) 2

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

79. Let If α and β respectively are the maximum and the minimum values of f, then

(1) α^{2} + β^{2} = 9/2

(2) β^{2} − 2√α = 19/4

(3) α^{2} – β^{2} = 4√3

(4) β^{2} + 2√α = 19/4

80. The negation of the expression q ∨ ((∼q) ∧ p) is equivalent to

(1) (~p) ∨ (~q)

(2) p ∧ (~q)

(3) (~p) ∨ q

(4) (~p) ∧ (~q)

**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

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

83. The remainder, when 19^{200} + 23^{200} is divided by 49 is _____

84. The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is

85. Let f : ℝ → ℝ be a differentiable function such that If f(0) = e^{−2}, then 2f(0) – f(2) is equal to

86. If f(x) = x^{2} + gʹ(1)x + gʺ(2) and g(x) = f(1)x^{2} + xfʹ(x) + fʺ(x), then the value of f(4) – g(4) is equal to

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

88. If where l, m, n ∈ ℕ, m and n are coprime then l + m + n is equal to

89. Let a_{1} = 8, a_{2}, a_{3}, …, 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

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

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