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JEE Main 2026 21 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202621 Jan, Evening shift

Physics 19Chemistry 22Mathematics 25

Physics

Q27The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is _ _…Oscillations and Waves
Q29The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of…Rotational Motion
Q30A battery with EMF E and internal resistance r is connected across a resistance R. The power consumption in R will be maximum when:Current Electricity
Q31Surface tension of two liquids (having same densities), T₁ and T₂, are measured using capillary rise method utilizing two tubes with inner radii of r₁ and r₂…Properties of Solids and Liquids
Q32A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v₀…Units and Measurements
Q33Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is:Units and Measurements
Q34Given below are two statements: Statement I: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away…Optics
Q35A capacitor C is first charged fully with potential difference of V₀ and disconnected from the battery. The charged capacitor is connected across an inductor…Electromagnetic Induction and Alternating Currents
Q36A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by x(t)=α t²+β t+γ m, where α=1 m/s ², β=1 m/s and…Work, Energy and Power
Q38Two cars A and B each of mass 10³ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The…Rotational Motion
Q39The r.m.s. speed of oxygen molecules at 47°C is equal to that of the hydrogen molecules kept at _ _ _°C. (Mass of oxygen molecule/mass of hydrogen molecule =…Kinetic Theory of Gases
Q40A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round…Kinematics
Q42Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are…Electrostatics
Q43A large drum having radius R is spinning around its axis with angular velocity ω, as shown in figure. The minimum value of ω so that a body of mass M remains…Laws of Motion
Q46A particle having electric charge 3×10⁻¹⁹ C and mass 6×10⁻²⁷ kg is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave…Dual Nature of Matter and Radiation
Q47The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having…Properties of Solids and Liquids
Q48A diatomic gas (γ=1.4) does 100 J of work when it is expanded isobarically. Then the heat given to the gas _ _ _ J.Thermodynamics
Q49An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, σ=10 mho/m. The ratio of maximum conduction current density to…Electromagnetic Waves
Q50In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of…Optics

Chemistry

Q52Match List - I with List - II. List - I (Reagents): A. H₂, Pd- BaSO₄ B. SnCl₂, HCl C. CrO₂Cl₂, CS₂ D. CO, HCl, Anhyd. AlCl₃ List - II (Reaction Name…Organic Compounds Containing Oxygen
Q53The correct increasing order of C - H(A), C - O(B), C = O(C) and C N(D) bonds in terms of covalent bond length is:Chemical Bonding and Molecular Structure
Q54By usual analysis, 1.00 g of compound (X) gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is: (nearest integer) (Given…Purification and Characterisation of Organic Compounds
Q55Given below are two statements: Statement I: The correct order in terms of atomic/ionic radii is Al>Mg>Mg²⁺>Al³⁺. Statement II: The correct order in terms of…Classification of Elements and Periodicity in Properties
Q56The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is: CH₃Br+Nu^() CH₃Nu+Br^()Organic Compounds Containing Halogens
Q57Nitrobenzene is subjected to the following sequence: (1) Br₂/FeBr₃/Δ (2) Sn/HCl/Δ (3) pH neutralisation (4) Br₂/H₂O (5) NaNO₂/HBr, 0 - 5°C (6) CuBr/NaBr Major…Organic Compounds Containing Nitrogen
Q59Consider the following spectral lines for atomic hydrogen: A. First line of Paschen series B. Second line of Balmer series C. Third line of Paschen series D…Atomic Structure
Q60Given below are some of the statements about Mn and Mn₂O₇. Identify the correct statements. A. Mn forms the oxide Mn₂O₇, in which Mn is in its highest…d- and f-Block Elements
Q61On heating a mixture of common salt and K₂Cr₂O₇ in equal amount along with concentrated H₂SO₄ in a test tube, a gas is evolved. Formula of the gas evolved and…Principles Related to Practical Chemistry
Q62Match List - I with List - II. List - I (Pair of Compounds): A. 2-Methylpropene and but-1-ene B. Cis-but-2-ene and trans-but-2-ene C. 2-Butanol and diethyl…Some Basic Principles of Organic Chemistry
Q63Consider the following data: Δ f H^ (methane, g) =-X kJ mol ⁻¹ Enthalpy of sublimation of graphite =Y kJ mol ⁻¹ Dissociation enthalpy of H₂=Z kJ mol ⁻¹ The…Chemical Thermodynamics
Q64Given below are two statements: Statement I: The correct order in terms of bond dissociation enthalpy is Cl₂>Br₂>F₂>I₂. Statement II: The correct trend in the…p-Block Elements
Q65Given below are two statements: Statement I: Crystal Field Stabilization Energy (CFSE) of [Cr(H₂O)₆]²⁺ is greater than that of [Mn(H₂O)₆]²⁺. Statement II…Coordination Compounds
Q67The correct statements are: A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed hydrolysis. B. During…Biomolecules
Q68Decomposition of A is a first order reaction at T(K) and is given by A(g) B(g)+C(g). In a closed 1 L vessel, 1 bar A(g) is allowed to decompose at T(K). After…Chemical Kinetics
Q69Aqueous HCl reacts with MnO₂(s) to form MnCl₂(aq), Cl₂(g) and H₂O(l). What is the weight (in g) of Cl₂ liberated when 8.7 g of MnO₂(s) is reacted with excess…Some Basic Concepts in Chemistry
Q70Given below are four compounds: (a) n-propyl choride (b) iso-propyl chloride (c) sec-butyl chloride (d) neo-pentyl chloride Percentage of carbon in the one…Organic Compounds Containing Halogens
Q71Identify the metal ions among Co²⁺, Ni²⁺, Fe²⁺, V³⁺ and Ti²⁺ having a spin-only magnetic moment value more than 3.0 BM. The sum of unpaired electrons present…Coordination Compounds
Q72The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature…Solutions
Q73A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol ⁻¹) led to an elevation of the boiling point by 0.5 K. The relative…Solutions
Q74MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K. MX(s) M⁺(aq)+X^-(aq); K sp =10⁻¹⁰ If the standard reduction potential…Redox Reactions and Electrochemistry
Q75The first and second ionization constants of H₂X are 2.5×10⁻⁸ and 1.0×10⁻¹³ respectively. The concentration of X²⁻ in 0.1 M H₂X solution is _ _ _ ×10⁻¹⁵ M…Equilibrium

Mathematics

Q1For the matrices A= 3 -4 1 -1 and B= -29 49 -13 18, if (A¹⁵+B) x y = 0 0, then among the following which one is true?Matrices and Determinants
Q2Let A=: |x²-10|≤ 6 and B=: |x-2|>1. ThenSets, Relations and Functions
Q3Let one end of a focal chord of the parabola y²=16x be (16, 16). If P(α, β) divides this focal chord internally in the ratio 5:2, then the minimum value of…Coordinate Geometry
Q4Let f(x)=x³+x²f'(1)+2xf''(2)+f'''(3), x. Then the value of f'(5) is:Limit, Continuity and Differentiability
Q5Let y=y(x) be the solution of the differential equation sec xdy/dx-2y=2+3 sin x, x (-(π)/2, (π)/2), y(0)=-7/4. Then y((π)/6) is equal to:Differential Equations
Q6Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L from the point (-2, r, 1) is…Three Dimensional Geometry
Q7If the system of equations 3x+y+4z=3, 2x+α y-z=-3, x+2y+z=4 has no solution, then the value of α is equal to:Matrices and Determinants
Q8Let α and β be the roots of the equation x²+2ax+(3a+10)=0 such that α<1<β. Then the set of all possible values of a is:Complex Numbers and Quadratic Equations
Q9The positive integer n, for which the solutions of the equation x(x+2)+(x+2)(x+4)+ +(x+2n-2)(x+2n)=8n/3 are two consecutive even integers, is:Sequence and Series
Q10A random variable X takes values 0, 1, 2, 3 with probabilities (2a+1)/30, (8a-1)/30, (4a+1)/30, b respectively, where a, b. Let μ and σ respectively be the…Statistics and Probability
Q11Let f:R be a twice differentiable function such that f''(x)>0 for all x and f'(a-1)=0, where a is a real number. Let g(x)=f(tan ²x-2 tan x+a), 0<x<(π)/2…Limit, Continuity and Differentiability
Q12Let y²=12x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that OPA=90°. Then the locus of the…Coordinate Geometry
Q13Let z be the complex number satisfying |z-5|≤ 3 and having maximum positive principal argument. Then 34|(5z-12)/(5iz+16)|² is equal to:Complex Numbers and Quadratic Equations
Q14Let A=\2, 3, 5, 7, 9. Let R be the relation on A defined by xRy if and only if 2x≤ 3y. Let l be the number of elements in R, and m be the minimum number of…Sets, Relations and Functions
Q15For a triangle ABC, let p=BC, q=CA and r=BA. If |p|=2√(3), |q|=2 and cos θ=1/(√(3)), where θ is the angle between p and q, then |p×(q-3r)|²+3|r|² is equal to:Vector Algebra
Q16If the area of the region \(x, y): 1-2x≤ y≤ 4-x², x≥ 0, y≥ 0 is (α)/(β), α, β, gcd (α, β)=1, then the value of (α+β) is:Integral Calculus
Q17If the line α x+4y=√(7), where α, touches the ellipse 3x²+4y²=1 at the point P in the first quadrant, then one of the focal distances of P is:Coordinate Geometry
Q18Let the line L₁ be parallel to the vector -3i+2j+4k and pass through the point (2, 6, 7), and the line L₂ be parallel to the vector 2i+j+3k and pass through…Three Dimensional Geometry
Q19The largest n, for which 7ⁿ divides 101!, is:Binomial Theorem and Its Simple Applications
Q20Let a₁, a₂/2, a₃/(2²),, (a₁₀)/(2⁹) be a G.P. of common ratio 1/(2). If a₁+a₂+ +a₁₀=62, then a₁ is equal to:Sequence and Series
Q21If (1/(¹⁵C₀)+1/(¹⁵C₁))(1/(¹⁵C₁)+1/(¹⁵C₂)) (1/(¹⁵C₁₂)+1/(¹⁵C₁₃))= α¹³ ¹⁴C₀ ¹⁴C₁ ¹⁴C₁₂, then 30α is equal to _ _ _.Binomial Theorem and Its Simple Applications
Q22If P is a point on the circle x²+y²=4, Q is a point on the straight line 5x+y+2=0 and x-y+1=0 is the perpendicular bisector of PQ, then 13 times the sum of…Coordinate Geometry
Q23If ∫₀¹ 4 cot ⁻¹(1-2x+4x²) dx=a tan ⁻¹(2)-b log e (5), where a, b, then (2a+b) is equal to _ _ _.Integral Calculus
Q24Let the maximum value of (sin ⁻¹x)²+(cos ⁻¹x)² for x [-(3)/2, 1/(2)] be m/nπ², where gcd (m, n)=1. Then m+n is equal to _ _ _.Trigonometry
Q25Let [·] denote the greatest integer function and f(x)= lim n→∞ 1/(n³)Σ k=1 ⁿ[(k²)/(3ˣ)]. Then 12Σ j=1 ^(∞)f(j) is equal to _ _ _.Integral Calculus