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JEE Main 2023 13 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202313 Apr, Evening shift

Physics 25Chemistry 23Mathematics 30

Physics

Q59An atom absorbs a photon of wavelength 500 ~nm and emits another photon of wavelength 600 ~nm. The net energy absorbed by the atom in this process is n × 10⁻⁴…Dual Nature of Matter and Radiation
Q60An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24 ~cm². The two ends of the wire are connected…Electromagnetic Induction and Alternating Currents
Q63A bi convex lens of focal length 10 ~cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _…Optics
Q67Two plates A and B have thermal conductivities 84 ~Wm⁻¹ ~K⁻¹ and 126 ~Wm⁻¹ ~K⁻¹ respectively. They have same surface area and same thickness. They are placed…Thermodynamics
Q73A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the…Rotational Motion
Q77In an experiment with sonometer when a mass of 180 ~g is attached to the string, it vibrates with fundamental frequency of 30 ~Hz. When a mass m is attached…Oscillations and Waves
Q78A car accelerates from rest to u ~m / s. The energy spent in this process is E J. The energy required to accelerate the car from u ~m / s to 2 u m / s is…Work, Energy and Power
Q5918Given below are two statements: Statement I: An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II: An…Electromagnetic Induction and Alternating Currents
Q6134Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The binding energy per nucleon is…Atoms and Nuclei
Q6286A vehicle of mass 200 ~kg is moving along a levelled curved road of radius 70 ~m with angular velocity of 0.2 ~rad / s. The centripetal force acting on the…Kinematics
Q6328To radiate EM signal of wavelength λ with high efficiency, the antennas should have a minimum size equal to:Communication Systems
Q6659Given below are two statements: Statement I: Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission…Dual Nature of Matter and Radiation
Q6810In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative z -axis and magnetic field is along the…Electromagnetic Waves
Q6933A 10 ~μ C charge is divided into two parts and placed at 1 ~cm distance so that the repulsive force between them is maximum. The charges of the two parts are:Electrostatics
Q7162Two planets A and B of radii R and 1.5 R have densities ρ and ρ / 2 respectively. The ratio of acceleration due to gravity at the surface of B to A is:Gravitation
Q7207Given below are two statements: Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet…Gravitation
Q7317The mean free path of molecules of a certain gas at STP is 1500 ~d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the…Kinetic Theory of Gases
Q7418The initial pressure and volume of an ideal gas are P ₀ and V ₀. The final pressure of the gas when the gas is suddenly compressed to volume V₀/4 will be…Thermodynamics
Q7715An electron is moving along the positive x -axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will…Magnetic Effects of Current and Magnetism
Q7829The distance travelled by an object in time t is given by s=(2.5) t². The instantaneous speed of the object at t=5 ~s will be:Kinematics
Q7877A passenger sitting in a train A moving at 90 ~km / h observes another train B moving in the opposite direction for 8 ~s. If the velocity of the train B is 54…Kinematics
Q7917Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A spherical body of radius (5 ± 0.1) mm…Properties of Solids and Liquids
Q8172A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is:Oscillations and Waves
Q8271In the equation [X+a/(Y²)][Y-b]=R T, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the…Units and Measurements
Q8450In a Young's double slits experiment, the ratio of amplitude of light coming from slits is 2: 1. The ratio of the maximum to minimum intensity in the…Optics

Chemistry

Q4A(g) → 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The…Chemical Kinetics
Q8At 298 ~K, the standard reduction potential for Cu²⁺ / Cu electrode is 0.34 ~V. Given: K sp Cu(OH)₂=1 × 10⁻²⁰ Take (2.303 RT)/F=0.059 ~V The reduction…Redox Reactions and Electrochemistry
Q1120 mL of 0.1 ~M ~NaOH is added to 50 ~mL of 0.1 ~M acetic acid solution. The pH of the resulting solution is _ _ _ _ _ _ × 10⁻² (Nearest integer) Given…Equilibrium
Q150.400 ~g of an organic compound (X) gave 0.376 ~g of AgBr in Carius method for estimation of bromine.% of bromine in the compound (X) is _ _ _ _ _ _. (Given…Principles Related to Practical Chemistry
Q17See the following chemical reaction: Cr₂ O₇²⁻+XH⁺+6 ~F e ²⁺ → YCr³⁺+6 ~F e ³⁺+Z H₂ O The sum of X, Y and Z is _ _ _ _ _ _Redox Reactions and Electrochemistry
Q19Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4~ A^(o). The radius of sodium atom is _ _ _ _ _ × ~10⁻¹ A^(o)…Solid State
Q20Sea water contains 29.25% ~NaCl and 19% ~MgCl₂ by weight of solution. The normal boiling point of the sea water is _ _ _ _ _ _ ^(°) C (Nearest integer) Assume…Solutions
Q211 ~g of a carbonate (M₂ CO₃) on treatment with excess HCl produces 0.01 ~mol of CO₂. The molar mass of M₂ CO₃ is _ _ _ _ _ g ~mol⁻¹. (Nearest integer)Some Basic Concepts in Chemistry
Q22The orbital angular momentum of an electron in 3 ~s orbital is (x h)/(2 π). The value of x is _ _ _ _ _ _ (nearest integer)Atomic Structure
Q78Given below are two statements: Statement I: Tropolone is an aromatic compound and has 8 π electrons. Statement II: π electrons of > C=O group in tropolone is…Some Basic Principles of Organic Chemistry
Q243The naturally occurring amino acid that contains only one basic functional group in its chemical structure isBiomolecules
Q257Given below are two statements: Statement I: SO₂ and H₂ O both possess V-shaped structure. Statement II: The bond angle of SO₂ is less than that of H₂ O. In…Chemical Bonding and Molecular Structure
Q552Match List I with List II 1 - Bromopropane is reacted with reagents in List I to give product in List II LIST I - Reagent LIST II - Product A. KOH (alc) I…Organic Compounds Containing Nitrogen
Q692The total number of stereoisomers for the complex [Cr(o x)₂ ClBr]³⁻ (where o x= oxalate) is:Coordination Compounds
Q745Which of the following complexes will exhibit maximum attraction to an applied magnetic field?Coordination Compounds
Q1047Which of the following are the Green house gases? A. Water vapour B. Ozone C. I ₂ D. Molecular hydrogen Choose the most appropriate answer from the options…Environmental Chemistry
Q1261Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Isotopes of hydrogen have almost same…Hydrogen
Q1373Given below are two statements related to Ellingham diagram: Statement I: Ellingham diagrams can be constructed for formation of oxides, sulfides and halides…Isolation of Elements
Q1457The covalency and oxidation state respectively of boron in [BF₄]⁻, are:p-Block Elements
Q1707Match List I with List II LIST I LIST II A. Weak intermolecular forces of attraction I. Hexamethylenediamine + adipic acid B. Hydrogen bonding II. AlEt₃+TiCl₄…Polymers
Q1780In the wet tests for detection of various cations by precipitation, Ba²⁺ cations are detected by obtaining precipitate ofPrinciples Related to Practical Chemistry
Q1837Identify the correct order of standard enthalpy of formation of sodium halides:S Block Elements
Q2281Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The diameter of colloidal particles in…Surface Chemistry

Mathematics

Q28The remainder, when 7¹⁰³ is divided by 17, is _ _ _ _ _Binomial Theorem and Its Simple Applications
Q33Let f n =∫₀^((π)/2)(Σ k=1 ⁿ sin ^(k-1) x)(Σ k=1 ⁿ(2 k-1) sin ^(k-1) x) cos x d x, n N. Then f₂₁-f₂₀ is equal to _ _ _ _ _Integral Calculus
Q34If y=y(x) is the solution of the differential equation (d y)/(d x)+(4 x)/((x²-1)) y=(x+2)/((x²-1)^(5/2)), x > 1 such that y(2)=2/9 log e (2+√(3)) and…Differential Equations
Q35Let f(x)=Σ k=1 ¹⁰ k x^(k), x R. If 2 f(2)+f^()(2)=119(2)ⁿ+1 then n is equal to _ _ _ _ _ _Limit, Continuity and Differentiability
Q37The foci of a hyperbola are (± 2,0) and its eccentricity is 3/2. A tangent, perpendicular to the line 2 x+3 y=6, is drawn at a point in the first quadrant on…Coordinate Geometry
Q38For x (-1,1], the number of solutions of the equation sin ⁻¹ x=2 tan ⁻¹ x is equal to _ _ _ _ _.Trigonometry
Q43Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1,2,3,4,5 with repetition, is _ _ _ _ _.Permutations and Combinations
Q46Let [α] denote the greatest integer ≤ α. Then [√(1)]+[√(2)]+[√(3)]+ +[√(120)] is equal to _ _ _ _ _Complex Numbers and Quadratic Equations
Q49Let A=\-4,-3,-2,0,1,3,4 and R=\(a, b) A × A: b=|a|. or.b²=a+1 be a relation on A. Then the minimum number of elements, that must be added to the relation R so…Sets, Relations and Functions
Q50The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were…Statistics and Probability
Q2465The plane, passing through the points (0,-1,2) and (-1,2,1) and parallel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point:Three Dimensional Geometry
Q2516The line, that is coplanar to the line (x+3)/(-3)=(y-1)/1=(z-5)/5, is:Three Dimensional Geometry
Q2607Let N be the foot of perpendicular from the point P(1,-2,3) on the line passing through the points (4,5,8) and (1,-7,5). Then the distance of N from the plane…Three Dimensional Geometry
Q2859The area of the region \(x, y): x² ≤ y ≤|x²-4|, y ≥ 1 isIntegral Calculus
Q2940The coefficient of x⁵ in the expansion of (2 x³-1/(3 x²))⁵ is:Binomial Theorem and Its Simple Applications
Q3140Let the centre of a circle C be (α, β) and its radius r < 8. Let 3 x+4 y=24 and 3 x-4 y=32 be two tangents and 4 x+3 y=1 be a normal to C. Then (α-β+r) is…Coordinate Geometry
Q3228Let S= C: z=i(z²+Re(z)). Then Σ z S |z|² is equal to:Complex Numbers and Quadratic Equations
Q3460The value of (e^(- (π)/4) + ∫₀^((π)/4) e⁻ˣ tan ⁵⁰xdx)/(∫₀^((π)/4) e⁻ˣ(tan ⁴⁹x + tan ⁵¹x)dx) isIntegral Calculus
Q3884The range of f(x)=4 sin ⁻¹((x²)/(x²+1)) isSets, Relations and Functions
Q4298If lim x → 0 (e^(a x)- cos (b x)-(cx e^(-c x))/2)/(1- cos (2 x))=17, then 5 a²+b² is equal toLimit, Continuity and Differentiability
Q4389The statement (p (q)) ((p) q) ((p) (q)) is equivalent to _ _ _ _ _.Mathematical Reasoning
Q4544Let for A = [ 1 2 3 α 3 1 1 1 2 ],|A| = 2. If |2 adj (2 adj (2A))| = 32ⁿ, then 3n + α is equal toMatrices and Determinants
Q4624If the system of equations 2 x+y-z=5 2 x-5 y+λ z=μ x+2 y-5 z=7 has infinitely many solutions, then (λ+μ)²+(λ-μ)² is equal toMatrices and Determinants
Q4851All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The…Permutations and Combinations
Q4896The random variable X follows binomial distribution B(n, p), for which the difference of the mean and the variance is 1. If 2 P(X=2)=3 P(X=1), then n² P(X>1)…Statistics and Probability
Q5162Let α, β be the roots of the equation x²-√(2) x+2=0. Then α¹⁴+β¹⁴ is equal toComplex Numbers and Quadratic Equations
Q5268Let a ₁, a ₂, a ₃,.... be a G.P. of increasing positive numbers. Let the sum of its 6^(t)h and 8^(t)h terms be 2 and the product of its 3^(r)d and 5^(t)h…Sequence and Series
Q5545Let (α, β) be the centroid of the triangle formed by the lines 15 x-y=82,6 x-5 y=-4 and 9 x+4 y=17. Then α+2 β and 2 α-β are the roots of the equation:Coordinate Geometry
Q5836Let |a|=2,|b|=3 and the angle between the vectors a and b be (π)/4. Then |(a+2 b) ×(2 a-3 b)|² is equal to:Vector Algebra
Q5837Let for a triangle ABC, AB=-2 i+j+3 k CB=α i+β j+γ k CA=4 i+3 j+δ k If δ > 0 and the area of the triangle ABC is 5 √(6), then C B · C A is equal toVector Algebra