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JEE Main 2026 28 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202628 Jan, Evening shift

Physics 16Chemistry 20Mathematics 25

Physics

Q26A plane electromagnetic wave is moving in free space with velocity c = 3 × 10⁸ m/s and its electric field is given as E = 54 sin (kz - ω t)j V/m, where j is…Electromagnetic Waves
Q27When the position vector r = xi + yj + zk changes sign as -r, which one of the following vector will not flip under sign change ?Rotational Motion
Q28A nucleus has mass number α and radius R_α. Another nucleus has mass number β and radius R_β. If β = 8α then R_α / R_β is:Atoms and Nuclei
Q32As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring…Oscillations and Waves
Q33Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is _ _ _ _. (Given: h = 6.63 × 10⁻³⁴ J.s and c = 3 × 10⁸ m/s)Dual Nature of Matter and Radiation
Q34A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t³ - 3t. A. The particle returns to its original position (origin) 0.866 units…Kinematics
Q35Identify the correct statements: A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the…Electrostatics
Q36The time period of a simple harmonic oscillator is T = 2π√(k/m). Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50…Units and Measurements
Q37In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording…Units and Measurements
Q38A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this…Magnetic Effects of Current and Magnetism
Q39Match List - I with List - II. List - I: A. Coefficient of viscosity B. Surface tension C. Pressure D. Surface energy. List - II: I. [ML⁻¹T⁻²] II. [ML²T⁻²]…Units and Measurements
Q40The mean free path of a molecule of diameter 5 × 10⁻¹⁰ m at the temperature 41°C and pressure 1.38 × 10⁵ Pa, is given as _ _ _ _ m. (Given k B = 1.38 × 10⁻²³…Kinetic Theory of Gases
Q41The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%…Oscillations and Waves
Q45For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.Optics
Q49A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes…Optics
Q50Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s…Oscillations and Waves

Chemistry

Q51The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is 10¹⁶ s⁻¹. The wave number of photon 'C' is 10⁴ cm⁻¹. The correct order of energy of…Atomic Structure
Q52Consider the elements N, P, O, S, Cl and F. The number of valence electrons present in the elements with most and least metallic character from the above list…Classification of Elements and Periodicity in Properties
Q53Given below are two statements: Statement I: The increasing order of boiling point of hydrogen halides is HCl < HBr < HI < HF. Statement II: The increasing…p-Block Elements
Q55A student performed analysis of aliphatic organic compound 'X' which on analysis gave C = 61.01%, H = 15.25%, N = 23.74%. This compound, on treatment with…Organic Compounds Containing Nitrogen
Q56Identify the correct statements: The presence of -NO₂ group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring…Organic Compounds Containing Nitrogen
Q57A student has been given 0.314 g of an organic compound and asked to estimate Sulphur. During the experiment, the student has obtained 0.4813 g of barium…Purification and Characterisation of Organic Compounds
Q58Match List - I with List - II according to shape. List - I: A. XeO₃ B. XeF₂ C. XeO₂F₂ D. XeOF₄. List - II: I. BrF₅ II. NH₃ III. [I₃]^(- I)V. SF₄. Choose the…Chemical Bonding and Molecular Structure
Q60Total number of alkali insoluble solid sulphonamides obtained by reaction of given amines with Hinsberg's reagent is _ _ _ _. Aniline, N-Methylaniline…Organic Compounds Containing Nitrogen
Q61For the given reaction; CaCO₃ + 2HCl CaCl₂ + H₂O + CO₂. If 90 g CaCO₃ is added to 300 mL of HCl which contains 38.55% HCl by mass and has density 1.13 g mL⁻¹…Some Basic Concepts in Chemistry
Q62Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in 250 mL of solution. III. 9.0 g Urea in 500 mL…Solutions
Q63The correct order of acidic strength of the major products formed in the given reactions, is: A. PhNH₂ (1) NaNO₂ + HCl (<5°C) (2) CuCN (3) H₃O⁺/Δ [A] B…Organic Compounds Containing Oxygen
Q64The plot of log ₁₀K vs 1/T gives a straight line. The intercept and slope respectively are (where K is equilibrium constant).Chemical Thermodynamics
Q66The correct increasing order of spin-only magnetic moment values of the complex ions [MnBr₄]²⁻ (A), [Cu(H₂O)₆]²⁺ (B), [Ni(CN)₄]²⁻ (C) and [Ni(H₂O)₆]²⁺ (D) is:Coordination Compounds
Q67Observe the following equilibrium in a 1 L flask. A(g) B(g). At T(K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles…Equilibrium
Q68Consider the following statements about manganate and permanganate ions. Identify the correct statements. A. The geometry of both manganate and permanganate…d- and f-Block Elements
Q69Consider the following reactions Na₂B₄O₇ Δ 2X + Y; CuSO₄ + Y Non-Luminous flame Z + SO₃; 2Z + 2X + Carbon Luminous flame 2Q + Na₂B₄O₇ + CO. The oxidation…p-Block Elements
Q70The reactions which produce alcohol as the product are: A. CH₄ + O₂ Mo₂O₃, Δ B. 2CH₃CH₃ + 3O₂ (CH₃COO)₂Mn, Δ C. (CH₃)₃CH KMnO₄ D. 2CH₄ + O₂ Cu/523 K/100 atm…Hydrocarbons
Q71A B (first reaction) C D (second reaction). Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same…Chemical Kinetics
Q74For strong electrolyte Λ m increases slowly with dilution and can be represented by the equation Λ m = Λ m° - Ac^(1/2). Molar conductivity values of the…Redox Reactions and Electrochemistry
Q75The number of isoelectronic species among Sc³⁺, Cr²⁺, Mn³⁺, Co³⁺ and Fe³⁺ is 'n'. If 'n' moles of AgCl is formed during the reaction of complex with formula…Coordination Compounds

Mathematics

Q1Let the arithmetic mean of 1/a and 1/b be 5/16, a > 2. If α is such that a, 4, α, b are in A.P., then the equation α x² - ax + 2(α - 2b) = 0 has:Sequence and Series
Q2Given below are two statements: Statement I: The function f: R → R defined by f(x) = x/(1+|x|) is one-one. Statement II: The function f: R → R defined by f(x)…Sets, Relations and Functions
Q3Let A = C: |z-2| ≤ 4 and B = C: |z-2| + |z+2| = 5. Then the max \|z₁ - z₂|: z₁ A and z₂ B is:Complex Numbers and Quadratic Equations
Q4Given below are two statements: Statement I: 25¹³+20¹³+8¹³+3¹³ is divisible by 7. Statement II: The integral part of (7+4√(3))²⁵ is an odd number. In the…Binomial Theorem and Its Simple Applications
Q5An ellipse has its center at (1, -2), one focus at (3, -2) and one vertex at (5, -2). Then the length of its latus rectum is:Coordinate Geometry
Q6Let A be the focus of the parabola y² = 8x. Let the line y = mx + c intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC…Coordinate Geometry
Q7Considering the principal values of inverse trigonometric functions, the value of the expression tan (2 sin ⁻¹(2/(√(13))) - 2 cos ⁻¹(3/(√(10)))) is equal to:Trigonometry
Q8The sum of all the elements in the range of f(x) = Sgn(sin x) + Sgn(cos x) + Sgn(tan x) + Sgn(cot x), x ≠ (nπ)/2, n Z, where Sgn(t) = 1, if t > 0 -1, if t <…Trigonometry
Q9Let y = y(x) be the solution of the differential equation xdy/dx - y = x² cot x, x (0, π). If y((π)/2) = (π)/2, then 6y((π)/6) - 8y((π)/4) is equal to:Differential Equations
Q10Let [·] denote the greatest integer function. Then ∫ -π/2 ^(π/2) ((12(3+[x]))/(3+[ sin x]+[ cos x])) dx is equal to:Integral Calculus
Q11Let f(x) = ∫ dx/(x^(2/3) + 2x^(1/2)) be such that f(0) = -26 + 24 log e (2). If f(1) = a + b log e (3), where a, b Z, then a + b is equal to:Integral Calculus
Q12Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line (x-1)/1 = y/2 = (z-1)/1. Then the distance of Q from the line (x-9)/3 = (y-9)/2 = (z-5)/(-2) isThree Dimensional Geometry
Q13The sum of the coefficients of x⁴⁹⁹ and x⁵⁰⁰ in (1+x)¹⁰⁰⁰ + x(1+x)⁹⁹⁹ + x²(1+x)⁹⁹⁸ + + x¹⁰⁰⁰ is:Binomial Theorem and Its Simple Applications
Q14Let the ellipse E: (x²)/144 + (y²)/169 = 1 and the hyperbola H: (x²)/16 - (y²)/(λ²) = -1 have the same foci. If e and L respectively denote the eccentricity…Coordinate Geometry
Q15Let the circle x² + y² = 4 intersect x-axis at the points A(a, 0), a > 0 and B(b, 0). Let P(2 cos α, 2 sin α), 0 < α < (π)/2 and Q(2 cos β, 2 sin β) be two…Coordinate Geometry
Q16The probability distribution of a random variable X is given below: X: 4k, 30/7k, 32/7k, 34/7k, 36/7k, 38/7k, 40/7k, 6k; P(X): 2/15, 1/15, 2/15, 1/5, 1/15…Statistics and Probability
Q176/(3²⁶) + (10·1)/(3²⁵) + (10·2)/(3²⁴) + (10·2²)/(3²³) + + (10·2²⁴)/3 is equal to:Sequence and Series
Q18Let P₁: y = 4x² and P₂: y = x² + 27 be two parabolas. If the area of the bounded region enclosed between P₁ and P₂ is six times the area of the bounded region…Integral Calculus
Q19Let P be a point in the plane of the vectors AB = 3i + j - k and AC = i - j + 3k such that P is equidistant from the lines AB and AC. If |AP| = (√(5))/2, then…Vector Algebra
Q20Let f(x) = lim θ → 0 ((cos π x - x^((2/θ)) sin (x-1))/(1 + x^((2/θ))(x-1))), x R. Consider the following two statements: (I) f(x) is discontinous at x = 1…Limit, Continuity and Differentiability
Q21If the distance of the point P(43, α, β), β < 0, from the line r = 4i - k + μ(2i + 3k), μ R along a line with direction ratios 3, -1, 0 is 13√(10), then α² +…Three Dimensional Geometry
Q22Three persons enter in a lift at the ground floor. The lift will go upto 10^(th) floor. The number of ways, in which the three persons can exit the lift at…Permutations and Combinations
Q23If Σ r=1 ²⁵ (r/(r⁴ + r² + 1)) = p/q, where p and q are positive integers such that gcd (p, q) = 1, then p + q is equal to _ _ _ _.Sequence and Series
Q24Let f be a differentiable function satisfying f(x) = 1 - 2x + ∫₀ˣ e^((x-t)) f(t) dt, x R and let g(x) = ∫₀ˣ (f(t) + 2)¹⁵ (t-4)⁶ (t+12)¹⁷ dt, x R. If p and q…Differential Equations
Q25Let A = 3 -4 1 -1 and B be two matrices such that A¹⁰⁰ = 100B + I. Then the sum of all the elements of B¹⁰⁰ is _ _ _ _Matrices and Determinants