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JEE Main 2023 24 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202324 Jan, Morning shift

Physics 23Chemistry 17Mathematics 30

Physics

Q50Assume 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~ A^(1/3) m. The approximate ratio of…Atoms and Nuclei
Q51A 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…Current Electricity
Q57A stream of a positively charged particles having q/m = 2 × 10¹¹C/kg and velocity v ₀ = 3 × 10⁷ i m/s is deflected by an electric field 1.8 j kV/m. The…Electrostatics
Q61A 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…Thermodynamics
Q68Vectors a i + b j + k and 2 i - 3 j + 4 k are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x is _ _ _ _ _ _.Kinematics
Q71A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5^(th) second. The force acted on the body is _ _ _ _ N.Work, Energy and Power
Q6132Consider the following radioactive decay process ₈₄²¹⁸A α A₁ β ^ - A₂ γ A₃ α A₄ β ⁺ A₅ γ A₆ The mass number and the atomic number of A ₆ are given by:Atoms and Nuclei
Q6658From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the…Dual Nature of Matter and Radiation
Q6711A 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…Electromagnetic Induction and Alternating Currents
Q6809In E and K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: (ω - angular frequency):Electromagnetic Waves
Q6886Given 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…Electronic Devices
Q6932If two charges q ₁ and q ₂ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between…Electrostatics
Q7161The 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 R…Gravitation
Q7416Given 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…Kinetic Theory of Gases
Q74971 g of a liquid is converted to vapour at 3 × 10 ⁵ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm ³ during this phase…Thermodynamics
Q7595Given 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…Laws of Motion
Q7694A 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…Magnetic Effects of Current and Magnetism
Q7714Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by…Magnetic Effects of Current and Magnetism
Q7800The 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:Kinematics
Q7959A 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…Properties of Solids and Liquids
Q8269Match List I with List II List-I List-II A. Planck's constant (h) I. [M¹ L² T⁻²] B. Stopping potential (Vs) II. [M¹ L¹ T⁻¹] C. Work function (φ) III. [M¹ L²…Units and Measurements
Q8468Given below are two statements: Statement I: If the Brewster's angle for the light propagating from air to glass is θ B, then the Brewster's angle for the…Optics
Q8510A travelling wave is described by the equation y(x,t) = [0.05 sin (8x - 4t)] m The velocity of the wave is: [all the quantities are in SI unit]Oscillations and Waves

Chemistry

Q3The 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…Chemical Kinetics
Q5The d-electronic configuration of [CoCl₄]²⁻ in tetrahedral crystal field in e^(m)t₂ⁿ. Sum of "m" and "number of unpaired electrons" is _ _ _ _ _ _Coordination Compounds
Q7At 298 K, a 1 litre solution containing 10 mmol of C r₂ O₇²⁻ and 100 mmol of Cr³⁺ shows a pH of 3.0. Given: C r₂ O₇²⁻ → C r³⁺; E° = 1.330 V and (2.303 RT)/F =…Redox Reactions and Electrochemistry
Q10The dissociation constant of acetic acid is x×10⁻⁵. When 25 mL of 0.2 M~CH₃COONa solution is mixed with 25 mL of 0.02 M~CH₃COOH solution, the pH of the…Equilibrium
Q135 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…Some Basic Concepts in Chemistry
Q14When Fe 0.93 O is heated in presence of oxygen, it converts to Fe₂O₃. The number of correct statement/s from the following is _ _ _ _ A. The equivalent weight…Some Basic Concepts in Chemistry
Q15If 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 _ _ _ _ n m…Atomic Structure
Q18For independent process at 300 K Process | Δ H/kJ~mol⁻¹ | Δ S/J~K⁻¹ A | -25 | -80 B | -22 | 40 C | 25 | -50 D | 22 | 20 The number of non-spontaneous process…Chemical Thermodynamics
Q264Order of Covalent bond; A.~KF > KI; LiF > KF B.~KF < KI; LiF > KF C.~SnCl₄ > SnCl₂; CuCl > NaCl D.~LiF > KF; CuCl < NaCl E.~KF < KI; CuCl > NaCl Choose the…Chemical Bonding and Molecular Structure
Q336Decreasing 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…Chemical Bonding and Molecular Structure
Q598The primary and secondary valencies of cobalt respectively in [Co(NH₃)₅Cl]Cl₂ are:Coordination Compounds
Q1045Which of the following is true about freons?Environmental Chemistry
Q1149Assertion 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…Organic Compounds Containing Halogens
Q1406Match List I with List II List-I List-II A. Reverberatory furnace I. Pig Iron B. Electrolytic cell II. Aluminium C. Blast furnace III. Silicon D. Zone…Isolation of Elements
Q1982In 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…Solutions
Q2212The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion isAtomic Structure
Q2280Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same…Surface Chemistry

Mathematics

Q20The shortest distance between the lines (x - 2)/3 = (y + 1)/2 = (z - 6)/2 and (x - 6)/3 = (1 - y)/2 = (z + 8)/0 is equal to _ _ _ _Three Dimensional Geometry
Q24Suppose Σ r = 0 ²⁰²³ r²~²⁰²³C r = 2023 × α × 2²⁰²². Then the value of α is _ _ _ _ _ _Binomial Theorem and Its Simple Applications
Q26The value of 12∫₀³ | x² - 3x + 2 |dx is _ _ _ _ _ _Integral Calculus
Q27The value of 8/(π)∫₀^((π)/2) ((cos x)²⁰²³)/((sin x)²⁰²³ + (cos x)²⁰²³)dx is _ _ _ _ _ _Integral Calculus
Q29Let C be the largest circle centred at (2, 0) and inscribed in the ellipse (x²)/36 + (y²)/16 = 1. If (1, α) lies on C, then 10 α² is equal to _ _ _ _ _ _Coordinate Geometry
Q30Let 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 _ _ _ _Coordinate Geometry
Q38A 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…Permutations and Combinations
Q39The 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 _ _ _ _ _ _…Permutations and Combinations
Q43Let 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 _ _ _Complex Numbers and Quadratic Equations
Q45The 4 ^(t)h term of GP is 500 and its common ratio is 1/m,m. Let S n denote the sum of the first n terms of this GP. If S₆ > S₅ + 1 and S₇ < S₆ + 1/2, then…Sequence and Series
Q2464The distance of the point (-1,9,-16) from the plane 2x+3y-z=5 measured parallel to the line (x + 4)/3 = (2 - y)/4 = (z - 3)/12 is:Three Dimensional Geometry
Q2604The 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:Three Dimensional Geometry
Q2858The area enclosed by the curves y² + 4x = 4 and y - 2x = 2 is:Integral Calculus
Q3007The value of Σ r = 0 ²² ²²C r ²³C r isBinomial Theorem and Its Simple Applications
Q3246Let p,q and (1 - 3 i)²⁰⁰ = 2¹⁹⁹(p + iq),i = √(- 1) then p+q+q² and p-q+q² are roots of the equation.Complex Numbers and Quadratic Equations
Q3558Let 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 toDifferential Equations
Q4079tan ⁻¹((1 + 3)/(3 + 3)) + sec ⁻¹(√((8 + 4 3)/(6 + 3 3))) is equal to:Trigonometry
Q4212Let f(x) = \ x² sin (1/x), x ≠ 0 0, x = 0. Then at x=0Limit, Continuity and Differentiability
Q4257lim t → 0 (1^(1/(sin ²t)) + 2^(1/(sin ²t)) +... + n^(1/(sin ²t)))^(sin ²t) is equal toLimit, Continuity and Differentiability
Q4387The compound statement ((P Q)) ((P) Q) ⇒ ((P) (Q)) is equivalent toMathematical Reasoning
Q4509If A and B are two non-zero n × n matrices such that A²+B=A²B, then:Matrices and Determinants
Q4542Let 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 [ α ² α 1 1 1 1 a b c ] is…Matrices and Determinants
Q4757Let 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:Coordinate Geometry
Q4925Let 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 =…Statistics and Probability
Q4926Let Ω be the sample space and A Ω be an event. Given below are two statements: (S1): If P(A) = 0, then A = φ (S2): If P(A) = 1, then A = Ω Then:Statistics and Probability
Q5063The equation x² - 4x + [x] + 3 = x[x], where [x] denotes the greatest integer function, has:Complex Numbers and Quadratic Equations
Q5228For three positive integers p, q, r, x^ p q² = y^(qr) = z^(p²r) and r = pq + 1 such that 3, 3 log y x, 3 log z y, 7 log x z are in A.P. with common difference…Sequence and Series
Q5390The relation R = (a,b): gcd (a,b) = 1,2a ≠ b,a,b Z\ is:Sets, Relations and Functions
Q5697Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that QA/AR = RB/BP = PC/CQ = 1/2. Then (Area(Δ PQR))/(Area(Δ…Vector Algebra
Q5746Let u = i - j - 2 k, v = 2 i + j - k, v. w = 2 and v × w = u + λ v. Then u. w is equal to:Vector Algebra