JEE MAIN 24th 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. A circular loop of radius 𝑟 is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance 𝑟 from the center of the loop on its axis is:
(1) 2√2 : 1
(2) 1 : 3√2
(3) 1 : √2
(4) 3√2 : 2
2. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth Re = 6400 km ):
(1) 8 N
(2) 4.9 N
(3) 9.8 N
(4) 19.6 N
3. Two long straight wires P and Q carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F1 – If distance between wires is halved and currents on them are doubled, force F2 on 10 cm length of wire P will be:
(1) F1/8
(2) 8F1
(3) 10F1
(4) F1/10
4. Given below are two statements :
Statement I : The temperature of a gas is −73°C. When the gas is heated to 527°C, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. 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
5. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:
(1) 272 m
(2) 68 m
(3) 192 m
(4) 136 m
6. Given below are two statements :
Statement I : If the Brewster’s angle for the light propagating from air to glass is 𝜃B, then the Brewster’s angle for the light propagating from glass to air is
Statement II : The Brewster’s angle for the light propagating from glass to air is tan−1(μg) where μg is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:
(1) Both Statement I and Statement II are false
(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 true
7. A 100 m long wire having cross-sectional area 6.25 × 10−4 m2 and Young’s modulus is 1010 Nm−2 is subjected to a load of 250 N, then the elongation in the wire will be:
(1) 4 × 10−3 m
(2) 6.25 × 10−3 m
(3) 6.25 × 10−6 m
(4) 4 × 10−4 m
8. If two charges q1 and q2 are separated with distance ‘d’ and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
(1) 2d√k
(2) 1.5d√k
(3) d√k
(4) k√k
9. Consider the following radioactive decay process
The mass number and the atomic number of A6 are given by:
(1) 210 and 84
(2) 210 and 82
(3) 211 and 80
(4) 210 and 80
10. From the photoelectric effect experiment, following observations are made. Identify which of these are correct.
(A) The stopping potential depends only on the work function of the metal.
(B) The saturation current increases as the intensity of incident light increases.
(C) The maximum kinetic energy of a photo electron depends on the intensity of the incident light.
(D) Photoelectric effect can be explained using wave theory of light.
Choose the correct answer from the options given below:
(1) A, C, D only
(2) B, C only
(3) B only
(4) A, B, D only
11. Given below are two statements:
Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.
In the light of the above statements, choose the correct answer from the options given below:
(1) Both Statement I and Statement II are true
(2) Statement I is false but Statement II is true
(3) Statement I is true but Statement II is false
(4) Both Statement I and Statement II are false
12. 1 g of a liquid is converted to vapour at 3 × 105 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm3 during this phase change, then the increase in internal energy in the process will be:
(1) 432000 J
(2) 4320 J
(3) 4800 J
(4) 4.32 × 108 J
13. As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3Ω. The currents through the resistors R4 and R5 are I4 and I5 The values of I4 and I5 are:
14. A modulating signal is a square wave, as shown in the figure.
If the carrier wave is given as c(t) = 2sin(8πt) volts, the modulation index is:
(1) 1/4
(2) 1/2
(3) 1
(4) 1/3
15. A conducting circular loop of radius 10/√π cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:
(1) emf = 1mV
(2) emf = 5mV
(3) emf = 100mV
(4) emf = 10mV
16. In represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :
(ω – angular frequency):
17. 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-III, B-I, C-II, D-IV
(3) A-II, B-IV, C-III, D-I
(4) A-III, B-IV, C-I, D-II
18. A travelling wave is described by the equation
y(x, t) = [0.05sin (8x – 4t)]m
The velocity of the wave is : [all the quantities are in SI unit]
(1) 8 ms−1
(2) 4 ms−1
(3) 0.5 ms−1
(4) 2 ms−1
19. As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g =10 m/s2 )
(1) (4√3 + 1)N
(2) 4(√3 + 1)N
(3) (4√3 – 1)N
(4) 4(√3 – 1)N
20. Given below are two statements: one is labelled as Assertion 𝐀 and the other is labelled as Reason 𝐑
Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement.
Reason : The current in the forward bias is more than the current in the reverse bias for a p − n junction diode.
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
SECTION-B
21. Vectors are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x is
22. Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6×10−27 kg and radius of nucleus is 1.5 × 10−15 A1/3 The approximate ratio of the nuclear density and water density is n × 1013. The value of n is
23. A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n × 10−3Ω. If the resistivity of the material is 2.4 × 10−8 Ωm. The value of n is
24. A stream of a positively charged particles having and velocity
is deflected by an electric field
The electric field exists in a region of 10 cm along x direction. Due to the electric field, the deflection of the charge particles in the 𝑦 direction is _____ mm
25. As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance = ____cm, from concave lens.
26. Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x is ______
27. A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is π/√x in SI unit. The value of x is ________
28. A hole is drilled in a metal sheet. At 27°C, the diameter of hole is 5 cm. When the sheet is heated to 177°C, the change in the diameter of hole is d × 10−3 The value of d will be ________ if coefficient of linear expansion of the metal is 1.6 × 10−5/°C.
29. In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ S.
30. A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is ______ N.
Chemistry
SECTION-A
31. ‘A’ and ‘ B ‘ formed in the following set of reactions are:
32. Decreasing order of the hydrogen bonding in following forms of water is correctly represented by
(A) Liquid water
(B) Ice
(C) Impure water
Choose the correct answer from the options given below:
(1) B > A > C
(2) A > B > C
(3) A = B > C
(4) C > B > A
33. Increasing order of stability of the resonance structures is:
Choose the correct answer from the options given below:
(1) D, C, A, B
(2) D, C, B, A
(3) C, D, A, B
(4) C, D, B, A
34. ꞌRꞌ formed in the following sequence of reactions is:
35. The primary and secondary valencies of cobalt respectively in [Co(NH3)5ClClCl2 are:
(1) 3 and 6
(2) 2 and 6
(3) 3 and 5
(4) 2 and 8
36. An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is:
(1) Co2+
(2) Ni2+
(3) Fe2+
(4) Cu2+
37. Reaction of BeO with ammonia and hydrogen fluoride gives A which on thermal decomposition gives BeF2 and NH4 What is ‘A’ ?
(1) (NH4)2BeF4
(2) H3NBeF3
(3) (NH4)Be2F5
(4) (NH4)BeF3
38. 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-I, B-III, C-II, D-IV
(3) A-III, B-IV, C-I, D-II
(4) A-I, B-IV, C-II, D-III
39. 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-III, B-I, C-II, D-IV
(3) A-II, B-III, C-IV, D-I
(4) A-III, B-IV, C-I, D-II
40. In the following given reaction, ‘ A ‘ is
41. It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power “n” i.e. vn of X-rays emitted is plotted against atomic number “Z”, following graph is obtained.
The value of ꞌꞌnꞌꞌ is
(1) 3
(2) 2
(3) 1
(4) 1/2
42. Given below are two statements:
Statement I : Noradrenaline is a neurotransmitter.
Statement II : Low level of noradrenaline is not the cause of depression in human.
In the light of the above statements, choose the correct 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) Both Statement I and Statement II are incorrect
(4) Statement I is incorrect but Statement II is correct
43. Which of the Phosphorus oxoacid can create silver mirror from AgNO3 solution?
(1) (HPO3)n
(2) H4P2O6
(3) H4P2O5
(4) H4P2O7
44. Compound (X) undergoes following sequence of reactions to give the Lactone (Y).
Compound (X) is
45. Order of Covalent bond:
(A) KF > KI; LiF > KF
(B) KF < KI; LiF > KF
(C) SnCl4 > SnCl; CuCl > NaCl
(D) LiF > KF; CuCl < NaCl
(E) KF < KI; CuCl > NaCl
Choose the correct answer from the options given below:
(1) C, E only
(2) B, C, E only
(3) A, B only
(4) B, C only
46. Which of the following is true about freons?
(1) These are radicals of chlorine and chlorine monoxide
(2) These are chemicals causing skin cancer
(3) These are chlorofluorocarbon compounds
(4) All radicals are called freons
47. In the depression of freezing point experiment
(A) Vapour pressure of the solution is less than that of pure solvent
(B) Vapour pressure of the solution is more than that of pure solvent
(C) Only solute molecules solidify at the freezing point
(D) Only solvent molecules solidify at the freezing point
Choose the most appropriate answer from the options given below:
(1) A and C only
(2) A only
(3) A and D only
(4) B and C only
48. Statement I : For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration.
Statement II : For colloidal particles, the potential difference between the fixed layer and the diffused layer of same charges is called the electrokinetic potential or zeta potential.
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
49. Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases.
Reason R : I− is a good nucleophile as well as a good leaving group.
In the light of the above statements, choose the correct answer from the options given below
(1) 𝐀 is false but 𝐑 is true
(2) 𝐀 is true but 𝐑 is false
(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
50. The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is
(1) Cr2+
(2) Ti2+
(3) V2+
(4) Mn2+
SECTION-B
51. When Fe93O is heated in presence of oxygen, it converts to Fe2O3. The number of correct statement/s from the following is
(A) The equivalent weight of Fe0.93O is
(B) The number of moles of Fe2+ and Fe3+ in 1 mole of Fe0.93O is 0.79 and 0.14 respectively
(C) Fe0.93O is metal deficient with lattice comprising of cubic closed packed arrangement of O2− ions
(D) The % composition of Fe2+ and Fe3+ in Fe0.93O is 85% and 15% respectively
52. The number of correct statement/s from the following is
(A) Larger the activation energy, smaller is the value of the rate constant.
(B) The higher is the activation energy, higher is the value of the temperature coefficient.
(C) At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature
(D) A plot of is a straight line with slope equal to –Ea/R
53. For independent processes at 300 K
The number of non-spontaneous processes from the following is
54. 5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL ) of this solution would be required to prepare 500 mL of 0.1M solution? Given: Molar Mass of Na,O and H is 23,16 and 1 g mol−1 respectively
55. If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is nm. (Nearest integer)
56. Uracil is a base present in RNA with the following structure. % of N in uracil is
57. The dissociation constant of acetic acid is x × 10−5. When 25 mL of 0.2MCH3COONa solution is mixed with 25 mL of 0.02MCH3COOH solution, the pH of the resultant solution is found to be equal to 5 . The value of 𝑥 is
58. Number of moles of AgCl formed in the following reaction is _______
59. The d-electronic configuration of [CoCl4]2− in tetrahedral crystal field is emt2n. Sum of ꞌꞌmꞌꞌ and ꞌꞌnumber of unpaired electronsꞌꞌ is
60. At 298 K, a 1 litre solution containing 10mmol of Cr2O72− and 100 mmol of Cr3+ shows a pH of 3.0.
Given : Cr2O72− → Cr3+; E° = 1.330 V and
The potential for the half cell reaction is x × 10−3 V. The value of x is
Mathematics
SECTION-A
61. Let
Then
is equal to
(1) 2
(2) 3/2
(3) 1
(4) −2/3
62. is equal to
(1) n2
(2)
(3) n
(4) n2 + n
63. Let α be a root of the equation (a – c)x2 + (b – a)x + (c – b) = 0 where a, b, c are distinct real numbers such that the matrix is singular. Then, the value of
is
(1) 12
(2) 9
(3) 3
(4) 6
64. The area enclosed by the curves y2 + 4x = 4 and y – 2x = 2 is
(1) 9
(2) 22/3
(3) 23/3
(4) 25/3
65. Let p, q ∈ ℝ and (1 – √3i)200 = 2199(p + iq), i = √−1 Then p + q + q2 and p – q + q2 are roots of the equation
(1) x2 – 4x – 1 = 0
(2) x2 – 4x + 1 =0
(3) x2 + 4x – 1 =0
(4) x2 + 4x + 1 =0
66. Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
x + y + z = 1
2x + Ny + 2z = 2
3x + 3y + Nz = 3
has unique solution is k/6, then the sum of value of k and all possible values of N is
(1) 21
(2) 18
(3) 20
(4) 19
67. For three positive integers and r = pq + 1 such that 3, 3logyx, 3logzy, 7logxz are in A.P. with common difference 1/2. Then r – p – q is equal to
(1) −6
(2) 12
(3) 6
(4) 2
68. The relation R = {(a, b): gcd(a, b) = 1, 2a ≠ b, a, b ∈Z} is :
(1) reflexive but not symmetric
(2) transitive but not reflexive
(3) symmetric but not transitive
(4) neither symmetric nor transitive
69. Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that Then
is equal to
(1) 4
(2) 3
(3) 1
(4) 2
70. Let y = y(x) be the solution of the differential equation x3dy + (xy – 1)dx = 0, x > 0, y(1/2) = 3 – e. Then y(1) is equal to
(1) 1
(2) e
(3) 3
(4) 2 – e
71. If A and B are two non-zero n×n matrics such that A2 + B = A2 B, then
(1) A2 = I or B – I
(2) A2B = I
(3) AB = I
(4) A2B = BA2
72. The equation x2 – 4x + [x] + 3 = x[x], where [x] denotes the greatest integer function, has :
(1) a unique solution in (−∞,1)
(2) no solution
(3) exactly two solutions in (−∞,∞)
(4) a unique solution in (−∞,∞)
73. Let a tangent to the curve y2 = 24x meet the curve xy = 2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the
(1) Length of latus rectum 3/2
(2) directrix 4x = −3
(3) length of latus rectum 2
(4) directrix 4x = 3
74. Let Ω be the sample space and A ⊆ Ω be an event.
Given below are two statements:
(S1) : If P(A) = 0, then A = ∅
(S2) : If P(A) = 1, then A = Ω
Then
(1) both (S1) and (S2) are true
(2) only (S1) is true
(3) only (S2) is true
(4) both (S1) and (S2) are false
75. The value of is
(1) 44C23
(2) 45C23
(3) 44C22
(4) 45C24
76. The distance of the point (−1, 9, −16) from the plane 2x + 3y – z = 5 measured parallel to the line is
(1) 31
(2) 13√2
(3) 20√2
(4) 26
77. is equal to:
(1) π/3
(2) π/4
(3) π/6
(4) π/2
78. Let
Then at x = 0
(1) f is continuous but not differentiable
(2) f and fꞌ both are continuous
(3) fꞌ is continuous but not differentiable
(4) f is continuous but fꞌ is not continuous
79. The compound statement (∼(P ∧ Q)) ∨ ((∼P) ∧ Q) ⇒ ((∼P) ∧ (∼Q)) is equivalent to
(1) (~Q) ∨ P
(2) ((~P) ∨ Q) ∧ (~Q)
(3) (~P) ∨ Q
(4) ((~P) ∨ Q) ∧ ((~Q) ∨ P)
80. The distance of the point (7,−3,−4) from the plane passing through the points (2,−3,1),(−1,1,−2) and (3,−4,2) is :
(1) 5
(2) 4
(3) 5√2
(4) 4√2
SECTION-B
81. Let λ ∈ ℝ and let the equation E be |x|2 − 2|x| + |λ − 3| = 0. Then the largest element in the set S= {x + λ : x is an integer solution of E} is
82. Let a tangent to the curve 9x2 + 16y2 = 144 intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is
83. The shortest distance between the lines and
is equal to
84. Suppose Then the value of α is
85. The value of is
86. The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is
87. A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
88. The 4th term of GP is 500 and its common ratio is 1/m. m ∈ Let Sn denote the sum of the first n terms of this GP. If S6 > S5 + 1 and S7 < S6 + 1/2, then the number of possible values of m is
89. Let C be the largest circle centred at (2,0) and inscribed in the ellipse If (1, α) lies on C, then 10 α2 is equal to
90. The value of is