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JEE Main 2024 31 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202431 Jan, Evening shift

Physics 23Chemistry 21Mathematics 30

Physics

Q55A nucleus has mass number A₁ and volume V₁. Another nucleus has mass number A₂ and Volume V₂. If relation between mass number is A₂=4 A₁, then V₂/V₁= _ _ _ _ _.Atoms and Nuclei
Q59The magnetic flux φ (in weber) linked with a closed circuit of resistance 8 Ω varies with time (in seconds) as φ=5 t²-36 t+1. The induced current in the…Electromagnetic Induction and Alternating Currents
Q62Light from a point source in air falls on a convex curved surface of radius 20 ~cm and refractive index 1.5. If the source is located at 100 ~cm from the…Optics
Q66Two circular coils P and Q of 100 turns each have same radius of π ~cm. The currents in P and R are 1 A and 2 A respectively. P and Q are placed with their…Magnetic Effects of Current and Magnetism
Q69A body of mass ' m ' is projected with a speed ' u ' making an angle of 45^(°) with the ground. The angular momentum of the body about the point of…Rotational Motion
Q70Two identical spheres each of mass 2 ~kg and radius 50 ~cm are fixed at the ends of a light rod so that the separation between the centers is 150 ~cm. Then…Rotational Motion
Q5924An AC voltage V=20 sin 200 π t is applied to a series LCR circuit which drives a current I=10 sin (200 π t+(π)/3). The average power dissipated is:Electromagnetic Induction and Alternating Currents
Q6138The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:Atoms and Nuclei
Q6440By what percentage will the illumination of the lamp decrease if the current drops by 20%?Current Electricity
Q6493The resistance per centimeter of a meter bridge wire is r, with X Ω resistance in left gap. Balancing length from left end is at 40 ~cm with 25 Ω resistance…Current Electricity
Q6665In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if…Dual Nature of Matter and Radiation
Q6821Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric…Electromagnetic Waves
Q6934Force between two point charges q₁ and q₂ placed in vacuum at ' r ' cm apart is F. Force between them when placed in a medium having dielectric constant K=5…Electrostatics
Q7219The mass of the moon is 1/144 times the mass of a planet and its diameter is 1/16 times the diameter of a planet. If the escape velocity on the planet is v…Gravitation
Q7323A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:Thermodynamics
Q7430The speed of sound in oxygen at S.T.P. will be approximately: (given, R=8.3 ~JK⁻¹, γ=1.4)Thermodynamics
Q7717A uniform magnetic field of 2 × 10⁻³ ~T acts along positive Y -direction. A rectangular loop of sides 20 ~cm and 10 ~cm with current of 5 ~A is in Y-Z plane…Magnetic Effects of Current and Magnetism
Q7920A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity ' v '. Another ball of the same mass but of…Properties of Solids and Liquids
Q8276Consider two physical quantities A and B related to each other as E=(B-x²)/(A t) where E, x and t have dimensions of energy, length and time respectively. The…Units and Measurements
Q8318The measured value of the length of a simple pendulum is 20 ~cm with 2 ~mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second…Units and Measurements
Q8384If two vectors A and B having equal magnitude R are inclined at angle θ, thenKinematics
Q8470When unpolarized light is incident at an angle of 60^(°) on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction…Optics
Q8611A body of mass 2 ~kg begins to move under the action of a time dependent force given by F=(6 t i+6 t² j) N. The power developed by the force at the time t is…Work, Energy and Power

Chemistry

Q1Number of isomeric products formed by monochlorination of 2-methylbutane in presence of sunlight is _ _ _ _.Some Basic Principles of Organic Chemistry
Q2From the vitamins A, B₁, ~B₆, ~B₁₂, C, D, E and K, the number of vitamins that can be stored in our body is _ _ _ _ _.Biomolecules
Q3A diatomic molecule has a dipole moment of 1.2 ~D. If the bond distance is 1 ~A^(°), then fractional charge on each atom is _ _ _ _ _ × 10⁻¹ esu. (Given 1…Chemical Bonding and Molecular Structure
Q6r=k[A] for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is _ _ _ _ m inutes.Chemical Kinetics
Q8A compound (x) with molar mass 108 ~g ~mol⁻¹ undergoes acetylation to give product with molar mass 192 ~g ~mol⁻¹. The number of amino groups in the compound…Organic Compounds Containing Nitrogen
Q12The values of conductivity of some materials at 298.15 ~K⁻¹ ~in ~Sm⁻¹ are 2.1 × 10³, 1.0 × 10⁻¹⁶, 1.2 × 10,3.91,1.5 × 10⁻², 1 × 10⁻⁷, 1.0 × 10³. The number of…Redox Reactions and Electrochemistry
Q17Number of moles of H⁺ ions required by 1 ~mole of MnO₄⁻ to oxidise oxalate ion to CO₂ is _ _ _ _ _.Redox Reactions and Electrochemistry
Q18In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is (+) _ _ _ _ _.Redox Reactions and Electrochemistry
Q19The molarity of 1 ~L orthophosphoric acid (H₃ PO₄) having 70% purity by weight (specific gravity 1.54 ~g ~cm⁻³) is _ _ _ _ _ M. (Molar mass of H₃ PO₄=98 ~g…Some Basic Concepts in Chemistry
Q22If 5 moles of an ideal gas expands from 10 ~L to a volume of 100 ~L at 300 ~K under isothermal and reversible condition then work, w, is -x ~J. The value of x…Chemical Thermodynamics
Q345Which of the following is least ionic?Chemical Bonding and Molecular Structure
Q423A (g) B (g) +C/2(g) The correct relationship between K P, α and equilibrium pressure P isEquilibrium
Q653Select the option with correct property -Coordination Compounds
Q654Match List I with List II List - I (Complex ion) List - II (Electronic Configuration) (A) [Cr(H₂O)₆]³⁺ (I) t 2 g ² e g ⁰ (B) [Fe(H₂ O)₆]³⁺ (II) t 2 g ³ e g ⁰…Coordination Compounds
Q790Choose the correct statements from the following A. Mn₂ O₇ is an oil at room temperature B. V₂ O₄ reacts with acid to give VO₂ ²⁺ C. CrO is a basic oxide D…d- and f-Block Elements
Q1461Given below are two statements: Statement I: Group 13 trivalent halides get easily hydrolyzed by water due to their covalent nature. Statement II: AlCl₃ upon…p-Block Elements
Q1518Given below are two statements: Statement I: S₈ solid undergoes disproportionation reaction under alkaline conditions to form S²⁻ and S₂ O₃ ²⁻. Statement II…p-Block Elements
Q1519Choose the correct statements from the following A. All group 16 elements form oxides of general formula EO₂ and EO₃, where E=S, Se, Te and Po. Both the types…p-Block Elements
Q1735The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room…Principles Related to Practical Chemistry
Q2083A sample of CaCO₃ and MgCO₃ weighed 2.21 ~g is ignited to constant weight of 1.152 ~g. The composition of mixture is: (Given molar mass in g ~mol⁻¹ CaCO₃…Some Basic Concepts in Chemistry
Q2213The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) areAtomic Structure

Mathematics

Q25A line passes through A(4,-6,-2) and B(16,-2,4). The point P(a, b, c), where a, b, c are non-negative integers, on the line A B lies at a distance of 21…Three Dimensional Geometry
Q29Let the coefficient of x^(r) in the expansion of (x+3)ⁿ⁻¹+(x+3)ⁿ⁻²(x+2)+(x+3)ⁿ⁻³(x+2)²+.+(x+2)ⁿ⁻¹ be α r. If Σ r=0 ⁿ α r =βⁿ-γⁿ, β, γ N, then the value of…Binomial Theorem and Its Simple Applications
Q33|120/(π³) ∫₀^π (x² sin x cos x)/(sin ⁴ x+ cos ⁴ x) d x| is equal to _ _ _ _.Integral Calculus
Q35Let y=y(x) be the solution of the differential equation sec ² x d x+(e^(2 y) tan ² x+ tan x) d y=0,0< x<(π)/2, y(π / 4)=0. If y(π / 6)=α, then e^(8 α) is…Differential Equations
Q39If lim x → 0 (a x² eˣ-b log e (1+x)+c x e⁻ˣ)/(x² sin x)=1, then 16(a²+b²+c²) is equal to _ _ _ _.Limit, Continuity and Differentiability
Q40Let A be a 3 × 3 matrix and det(A)=2. If n=det(adj(adj(..(adj A)) 2024- times)), then the remainder when n is divided by 9 is equal to _ _ _ _ _.Matrices and Determinants
Q45Let a, b, c be the lengths of three sides of a triangle satistying the condition (a²+b²) x²-2 b(a+c) x+(b²+c²)=0. If the set of all possible values of x is…Complex Numbers and Quadratic Equations
Q47Let A=\1,2,3,, 100. Let R be a relation on A defined by (x, y) R if and only if 2 x=3 y. Let R₁ be a symmetric relation on A such that R R₁ and the number of…Sets, Relations and Functions
Q50Let A(-2,-1), B(1,0), C(α, β) and D(γ, δ) be the vertices of a parallelogram A B C D. If the point C lies on 2 x-y=5 and the point D lies on 3 x-2 y=6, then…Coordinate Geometry
Q52Let a=3 i+2 j+k, b=2 i-j+3 k and c be a vector such that (a+b) × c=2(a × b)+24 j-6 k and (a-b+i) · c=-3. Then |c|² is equal to _ _ _ _.Vector Algebra
Q2527Let (α, β, γ) be the mirror image of the point (2,3,5) in the line (x-1)/2=(y-2)/3=(z-3)/4. Then, 2 α+3 β+4 γ is equal toThree Dimensional Geometry
Q2528The shortest distance, between lines L₁ and L₂, where L₁: (x-1)/2=(y+1)/(-3)=(z+4)/2 and L₂ is the line, passing through the points A(-4,4,3), B(-1,6,3) and…Three Dimensional Geometry
Q2731Let f: → R →(0, ∞) be strictly increasing function such that lim x → ∞ (f(7 x))/(f(x))=1. Then, the value of lim x → ∞ [(f(5 x))/(f(x))-1] is equal toLimit, Continuity and Differentiability
Q2732If the function f:(-∞,-1] →(a, b] defined by f(x)=e^(x³-3 x+1) is one - one and onto, then the distance of the point P(2 b+4, a+2) from the line x+e⁻³ y=4 is:Limit, Continuity and Differentiability
Q2866The area of the region enclosed by the parabolas y=4 x-x² and 3 y=(x-4)² is equal to:Integral Calculus
Q3087Let a variable line passing through the centre of the circle x²+y²-16 x-4 y=0, meet the positive co-ordinate axes at the points A and B. Then the minimum…Coordinate Geometry
Q3166Let z₁ and z₂ be two complex numbers such that z₁+z₂=5 and z₁³+z₂³=20+15 i Then, |z₁⁴+z₂⁴| equals -Complex Numbers and Quadratic Equations
Q3473Let f, g:(0, ∞) → R be two functions defined by f(x)=∫ -x ˣ(|t|-t²) e^(-t²) d t and g(x)=∫₀^(x²) t^(1 / 2) e^(-t) d t. Then, the value of 9(f(√(log e…Integral Calculus
Q3564The temperature T(t) of a body at time t=0 is 160^(°) F and it decreases continuously as per the differential equation (d T)/(d t)=-K(T-80), where K is a…Differential Equations
Q3768Let P be a parabola with vertex (2,3) and directrix 2 x+y=6. Let an ellipse E: (x²)/(a²)+(y²)/(b²)=1, a>b, of eccentricity 1/(√(2)) pass through the focus of…Coordinate Geometry
Q4081If a= sin ⁻¹(sin (5)) and b= cos ⁻¹(cos (5)), then a²+b² is equal toTrigonometry
Q4218Consider the function f:(0, ∞) → R defined by f(x)=e^(-| log e x|). If m and n be respectively the number of points at which f is not continuous and f is not…Limit, Continuity and Differentiability
Q4633Let A be a 3 × 3 real matrix such that A(l 1 0 1)=2(l 1 0 1), A(l -1 0 1)=4(l -1 0 1), A(l 0 1 0)=2(l 0 1 0). Then, the system (A-3 I)(lx y z)=(l1 2 3) has:Matrices and Determinants
Q4782The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isPermutations and Combinations
Q4808If for some m, n; ⁶ C m +2(⁶ C m+1)+ ⁶ C m+2 > ⁸ C₃ and ⁿ⁻¹ P₃: ⁿ P₄=1: 8, then ⁿ P m+1 + ⁿ⁺¹ C m is equal toPermutations and Combinations
Q4992A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head isStatistics and Probability
Q5270Let 2^(nd), 8^(th) and 44^(th) terms of a non-constant A. P. be respectively the 1^(st), 2^(nd) and 3^(rd) terms of a G. P. If the first term of the A. P. is…Sequence and Series
Q5492Let the mean and the variance of 6 observations a, b, 68,44,48,60 be 55 and 194, respectively. If a>b, then a+3 b isStatistics and Probability
Q5555Let A(a, b), B(3,4) and C(-6,-8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2 a+3,7 b+5)…Coordinate Geometry
Q5641The number of solutions, of the equation e^(sin x)-2 e^(- sin x)=2, is:Trigonometry