**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.

(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. 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

2. The ratio of the density of oxygen nucleus (_{8}^{16}O) and helium nucleus (_{2}^{4}He) is

(1) 4:1

(2) 2:1

(3) 1:1

(4) 8:1

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 (T^{2})

(3) Proportional to temperature (T)

(4) Proportional to square root of temperature (√T)

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

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

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/s^{2})

(1) 90 N

(2) 30 N

(3) 300 N

(4) 240 N

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 |V_{2}| > ± V ≥ |V_{0}| where V_{0} 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

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 ω_{0}.The value of x is:

(1) 4

(2) 1/16

(3) 16

(4) 1/4

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

10. A car travels a distance of ‘x′ with speed ν_{1} and then same distance ′x′ with speed ν_{2} in the same direction. The average speed of the car is:

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/s^{2})

(1) π/3

(2) π/2

(3) π/4

(4) π/6

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

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 × 10^{3} Am^{−}^{1}

(2) 1.2 × 10^{3} Am^{−}^{1}

(3) 2.4 × 10^{−}^{3} Am^{−}^{1}

(4) 1 Am^{−1}

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

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

16. A parallel plate capacitor has plate area 40 cm^{2} 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) 24ε_{0} F

(2)

(3)

(4) 10ε_{0} F

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

18. Electron beam used in an electron microscope, when accelerated by a voltage of 20kV,has a de−Broglie wavelength of 𝜆_{0}.If the voltage is increased to 40kV, then the de-Broglie wavelength associated with the electron beam would be:

(1) 3λ_{0}

(2) λ_{0}/2

(3) λ_{0}/√2

(4) 9λ_{0}

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

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

**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).

22. The wavelength of the radiation emitted is 𝜆_{0} 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 _____.

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 × 10^{4} Nm^{–2}. The value of x is __________

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 ______

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

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 π^{2} = 10)

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

28. In the given circuit, the equivalent resistance between the terminal A and B is Ω.

29. If and then, The unit vector in the direction of The value of x is

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)

**Chemistry**

**SECTION-A**

31. In the cumene to phenol preparation in presence of air, the intermediate is

32. The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH^{−} is

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

34. Which of the following conformations will be the most stable ?

35. The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph

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

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) X_{2}Y_{1.5}

(3) X_{2.5}Y

(4) X_{1.5}Y_{2}

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

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.

40. The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

(1) Me_{3} N > Me_{2}NH > MeNH_{2} > NH_{3}

(2) Me_{2}NH > MeNH_{2} > Me_{3} N > NH_{3}

(3) Me_{2}NH > Me_{3} N > MeNH_{2} > NH_{3}

(4) NH_{3} > Me_{3} N > MeNH_{2} > Me_{2}NH

41. ’25 volume’ hydrogen peroxide means

(1) 1 L marketed solution contains 25 g of H_{2}O_{2}.

(2) 1 L marketed solution contains 75 g of H_{2}O_{2}.

(3) 1 L marketed solution contains 250 g of H_{2}O_{2}.

(4) 100 mL marketed solution contains 25 g of H_{2}O_{2}.

42. The radius of the 2nd orbit of Li^{2+} is x. The expected radius of the 3rd orbit of Be^{3+} is

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) P_{4}O_{6} and H_{3}PO_{3}

(2) PCl_{5} and H_{3}PO_{4}

(3) POCl_{3} and H_{3}PO_{4}

(4) PCl_{3} and H_{3}PO_{3}

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

45. Identify the product formed ( and E)

46. Match items of Row I with those of Row II.

47. Which one of the following reactions does not occur during extraction of copper ?

(1) 2Cu_{2} S + 3O_{2} → 2Cu_{2}O + 2SO_{2}

(2) FeO + SiO_{2} → FeSiO_{3}

(3) 2FeS + 3O_{2 }→ 2FeO+2SO_{2}

(4) CaO + SiO_{2 }→ CaSiO_{3}

48. Some reactions of NO_{2} relevant to photochemical smog formation are

Identify A, B, X and Y

(1) Y = NO_{2}, A = O_{3}, B = O_{2}

(2) X = [O], Y = NO, A = O_{2}, B = O_{3}

(3) X = N_{2}O, Y = [O], A = O_{3}, B = NO

(4) X = NO, Y = [O], A = O_{2}, B = N_{2}O_{3}

49.

The correct sequence of reagents for the preparation of Q and R is :

(1) (i) CrO_{2}Cl_{2},H_{3}O^{+}; (ii) Cr_{2}O_{3},770 K, 20 atm; (iii) NaOH; (iv) H_{3}O^{+}

(2) (i) KMnO_{4},OH^{−}; (ii) Mo_{2}O_{3},Δ; (iii) NaOH; (iv) H_{3}O^{+}

(3) (i) Cr_{2}O_{3},770 K, 20 atm; (ii) CrO_{2}Cl_{2},H_{3}O^{+}; (iii) NaOH; (iv) H_{3}O^{+}

(4) (i) Mo_{2}O_{3}, Δ; (ii) CrO_{2}Cl_{2}, H_{3}O^{+}; (iii) NaOH; (iv) H_{3}O^{+}

50. Compound A reacts with NH_{4}Cl and forms a compound B. Compound B reacts with H_{2}O and excess of CO_{2} 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) CaCl_{2}, NH_{3}, NH_{4}HCO_{3}

(2) Ca(OH)_{2}, NH_{4}^{⨁}, (NH_{4})_{2}CO_{3}

(3) CaCl_{2}, NH_{4}^{⨁}, (NH_{4})_{2}CO_{3}

(4) Ca(OH)_{2}, NH_{3}, NH_{4}HCO_{3}

**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

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) V^{3+}, Cr^{3+}, Fe^{2+}, Ni^{3+}

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 )

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})

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)

56. An athlete is given 100 g of glucose (C_{6}H_{12}O_{6}) 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}

57. The number of paramagnetic species from the following is

[Ni(CN)_{4}]^{2}^{−}, [Ni(CO)_{4}], [NiCl_{4}]^{2}^{−}

[Fe(CN)_{6}]^{4}^{−}, [Cu(NH_{3})_{4}]^{2+}

[Fe(CN)_{6}]^{3}^{−} and [Fe(H_{2}O)_{6}]^{2+}

58. Consider the cell

Pt(s) | H_{2}(g) (1 atm) | H^{+}] = 1) || Fe^{3+} (aq), Fe^{2+} (aq) | Pt(s)

Given and T = 298 K

If the potential of the cell is 0.712 V, the ratio of concentration of Fe^{2+} to Fe^{3+} is (Nearest integer)

59. The total number of lone pairs of electrons on oxygen atoms of ozone is

60. A litre of buffer solution contains 0.1 mole of each of NH_{3} and NH_{4} 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}(NH_{3}) = 4.745

log 2 = 0.301

Log 3 = 0.477

T = 298 K]

**Mathematics**

**SECTION-A**

61. The points of intersection of the line ax + by = 0, (a ≠ b) and the circle x^{2} + y^{2} – 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) x^{2} + y^{2} + 3x + 3y + 4 = 0

(2) x^{2} + y^{2} + 3x + 5y + 8 = 0

(3) x^{2} + y^{2} − 5x − 5y + 12 = 0

(4) x^{2} + y^{2} + 5x + 5y + 12 = 0

62. The distance of the point (6, −2√2) from the common tangent y = mx + c, m > 0, of the curves x = 2y^{2} and x = 1 + y^{2} is :

(1) 14/3

(2) 5√3

(3) 1/3

(4) 5

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

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

65. Let z_{1 }= 2 + 3i and z_{2} = 3 + 4i. The set S ={z ∈ C : |z − z_{1}|^{2} − |z − z_{2}|^{2} = |z_{1} − z_{2}|^{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

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

67. Let S_{1} and S_{2} 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) S_{1} is an infinite set and n(S_{2}) = 2

(2) S_{1} = Φ and S_{2} = ℝ − {0}

(3) n(S_{1}) = 2 and S_{2} is an infinite set

(4) S_{1} = ℝ − {0} and S_{2} = Φ

68. The value of is :

69. The statement (p ∧ (∼q)) ⇒ (p ⇒ (∼q)) is

(1) a tautology

(2) a contradiction

(3) equivalent to p ∨ q

(4) equivalent to (∼p) ∨ (∼q)

70. Consider the lines L_{1} and L_{2} given by

A line L_{3} having direction ratios 1, −1, −2, intersects L_{1} and L_{2} 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

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)

72. The minimum value of the function is :

(1) e(e – 1)

(2) 2(e – 1)

(3) 2

(4) 2e – 1

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

74. Let x = 2 be a local minima of the function f(x) = 2x^{4} – 18x^{2} + 8x + 12, x ∈ (−4, 4). If M is local maximum value of the function f in (−4, 4), then M=

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

76. Let y(x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 + x^{16}). Then yꞌ − yꞌꞌ at x = −1 is equal to:

(1) 976

(2) 944

(3) 464

(4) 496

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

78. Let x, y, z > 1 and Then |adj(adj A^{2})| is equal to

(1) 2^{8}

(2) 4^{8}

(3) 6^{4}

(4) 2^{4}

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

80. Let y = y(𝑥) be the solution curve of the differential equation x > 0, y(1) = 3. Then is equal to :

**SECTION-B**

81. The constant term in the expansion of

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

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

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

85. If the sum of all the solutions of −1 < x < 1, x ≠ 0, is then α is equal to

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 d^{2} is equal to

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

88. Let Then the maximum value of β for which the equation has real roots, is

89. It the area enclosed by the parabolas P_{1} : 2y = 5x^{2} and P_{2} : x^{2} – y + 6 = 0 is equal to the area enclosed by 𝑃1 and y = αx, α > 0, then α^{3} is equal to

90. Let A_{1}, A_{2}, A_{3} 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 A_{1}, A_{2}, A_{3}, 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