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JEE Main 2026 5 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20265 Apr, Morning shift

Physics 18Chemistry 24Mathematics 23

Physics

Q26In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7^(th) Vernier…Experimental Skills
Q27L, C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula M L² T⁻⁴ A⁻² corresponds to _ _ _ _ _.Units and Measurements
Q28When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately α%. The value of α is…Gravitation
Q31The Young's modulus of steel wire of radius r and length L is Y. If the radius r and length L of the wire are doubled then the value of YProperties of Solids and Liquids
Q32Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Statement I: Change in internal energy of a system…Thermodynamics
Q33Consider the following statements: A. Zeroth law of thermodynamics gives concept of temperature B. First law of thermodynamics gives concept of internal…Thermodynamics
Q35An electron of mass m is moving in an electric field E = -2E₀i (E₀ = constant > 0), with an initial velocity V = v₀i (v₀ = constant > 0). If λ₀ = h/4mv₀, its…Dual Nature of Matter and Radiation
Q36In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The ratio of the radius of the orbits in given by r i: r…Atoms and Nuclei
Q37A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 μ F capacitor. The rate of change of potential difference across…Electromagnetic Waves
Q39In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is 2.4 μ m. If the experiment is carried out in another…Optics
Q40A ray of light passing through an equilateral prism is having velocity 2.12 × 10⁸ m/s in the prism material, then the minimum angle of deviation is _ _ _ _…Optics
Q41Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the…Dual Nature of Matter and Radiation
Q42A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of…Optics
Q44An a.c. source of angular frequency ω is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the…Electromagnetic Induction and Alternating Currents
Q46A cube has side length 5 cm and modulus of rigidity 10⁵ N/m². The displacement produced by a force of 10 N in the upper face of cube is _ _ m m.Properties of Solids and Liquids
Q47From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of…Kinematics
Q48A transverse wave on a string is described by y = 3 sin (36t + 0.018x + π/4), where x, y are in cm and t in seconds. The least distance between the two…Oscillations and Waves
Q49The charged particle moving in a uniform magnetic field of (3i + 2j) T has an acceleration (4i - x/2j)m/s². The value of x isMagnetic Effects of Current and Magnetism

Chemistry

Q51How many grams of residue is obtained by heating 2.76 g of silver carbonate? (Given: Molar mass of C, O and Ag are 12, 16 and 108 g mol⁻¹ respectively)Some Basic Concepts in Chemistry
Q52Arrange the following atomic orbitals of multi electron atoms in order of increasing energy. A. n = 3, l = 2, m = +1 B. n = 4, l = 0, m = 0 C. n = 6, l = 1, m…Atomic Structure
Q53Identify the correct statements from the following: A. Heisenberg uncertainty principle is applicable to electrons. B. The size of 2p x orbital is less than…Atomic Structure
Q54What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and 14 g mol⁻¹…Solutions
Q55M₃A₂ is a sparingly soluble salt of molar mass y g mol⁻¹ and solubility x g L⁻¹. The ratio of the molar concentration of the anion (A³⁻) to the solubility…Equilibrium
Q56Arrange the following resultant mixtures in increasing order of their pH values A. 10 mL 0.2 M Ca(OH)₂ + 25 mL 0.1 M HCl B. 10 mL 0.01 M H₂SO₄ + 10 mL 0.01 M…Equilibrium
Q57First order gas phase reaction A → B + C; p i = initial pressure of gas A, p t = total pressure of the reaction mixture at time t. Expression of rate constant…Chemical Kinetics
Q58Given below are two statements: Statement I: The correct order of electronegativity of fluorine, oxygen and nitrogen is F > O > N. Statement II: The oxidation…Classification of Elements and Periodicity in Properties
Q59Correct statements from the following are: A. Nitrogen in oxidation states from +1 to +4 disproportionates in acid medium. B. Nitrogen has the ability to form…p-Block Elements
Q60Which of the following is NOT a physical or chemical characteristics of interstitial compounds?d- and f-Block Elements
Q61The correct statements about metal carbonyls are A. The metal-carbon bonds in metal carbonyls possess both σ and π -character. B. Due to synergic bonding…Coordination Compounds
Q62Given below are two statements: Statement I: Each electron in e g orbitals destabilizes the orbitals by +0.6 Δ o and each electron in the t 2g orbitals…Coordination Compounds
Q63Given below are two statements: Statement I: On the basis of inductive effect, the order of stability of alkyl carbanions is CH₃^- > CH₃-CH₂^- > (CH₃)₂CH^- >…Some Basic Principles of Organic Chemistry
Q65For the following Friedel Craft's alkylation reaction, which of the statements are correct? Benzene + 1-chloropropane Anhydrous AlCl₃ Alkylbenzene. A. Major…Hydrocarbons
Q66Benzyl isocyanide can be obtained from A. Benzyl bromide AgCN B. Benzylamine CHCl₃, Aq NaOH C. Bromobenzene AgCN D. Aniline CHCl₃, Aq NaOH E. 2-Phenylethyl…Organic Compounds Containing Nitrogen
Q67Consider compounds A, B and C with following structural formulae A = CH₃-CH₂-CH₂-CH₂-CH₂-OH, B = CH₂=CH-CH₂-CH₂-CH₃, C = HO-CH₂-CH₂-CH(OH)-CH₃. For the…Organic Compounds Containing Oxygen
Q68Identify the incorrect statements. A. Benzylamine is a stronger base than aniline. B. p-Methoxyaniline can be synthesized by Gabriel phthalimide synthesis. C…Organic Compounds Containing Nitrogen
Q69Identify the correct statements. A. Glucose exists in two anomeric forms. B. Anomers of glucose differ in configuration at C-1 in cyclic hemiacetal structure…Biomolecules
Q70Given below are two statements: Statement I: Sodium dichromate and potassium dichromate are classified as primary standards in titrimetric analysis. Statement…Principles Related to Practical Chemistry
Q71Consider the following species: BrF₅, XeF₅^-, BF₄^-, ICl₄^-, XeF₄, SF₄, NH₄⁺, ClF₃, XeF₂, ICl₂^-. Number of species having sp³d hybridized central atom is _ _…Chemical Bonding and Molecular Structure
Q72In an estimation of sulphur by Carius method 0.2 g of the substance gave 0.6 g of BaSO₄. The percentage of sulphur in the substance is _ _ _ _%. (Given molar…Purification and Characterisation of Organic Compounds
Q73One mole of phenol is treated with dilute HNO₃ at 298 K to give a mixture of products. The mixture is separated by steam distillation. The steam volatile…Organic Compounds Containing Oxygen
Q74The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below A(g) B(g) + C(g)…Equilibrium
Q75If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be _ _ _ _ minutes. (Given: log 2…Chemical Kinetics

Mathematics

Q1Let a, b C. Let α, β be the roots of the equation x² + ax + b = 0. If β - α = √(11) and β² - α² = 3i√(11), then (β³ - α³)² is equal to:Complex Numbers and Quadratic Equations
Q2Let the sum of the first n terms of an A.P. be 3n² + 5n. Then the sum of squares of the first 10 terms of the A.P. is:Sequence and Series
Q3Let A be a 3 × 3 matrix such that A^(T) 1 0 1 = 5 2 2, A^(T) 0 0 1 = 3 1 1, A 1 0 1 = 3 4 4 and A 0 0 1 = 1 3 1. If det (A) = 1, then det (adj(A² + A)) is…Matrices and Determinants
Q4Consider the system of linear equations in x, y, z: x + 2y + tz = 0, 6x + y + 5tz = 0, 3x + t²y + f(t)z = 0, where f: R → R is a differentiable function. If…Matrices and Determinants
Q5Σ n=1 ¹⁰(528/(n(n+1)(n+2))) is equal to:Sequence and Series
Q6Let tan A, tan B, where A, B (-(π)/2, (π)/2), be the roots of the quadratic equation x² - 2x - 5 = 0. Then 20 sin ²((A+B)/2) is equal to:Trigonometry
Q7A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability…Statistics and Probability
Q8The mean deviation about the mean for the data x i: 5, 7, 9, 10, 12, 15 with frequencies f i: 8, 6, 2, 2, 2, 6 is equal to:Statistics and Probability
Q9Let a focus of the ellipse E: (x²)/(a²) + (y²)/(b²) = 1 be S(4, 0) and its eccentricity be 4/5. If the point P(3, α) lies on E and O is the origin, then the…Coordinate Geometry
Q10Let P be a moving point on the circle x² + y² - 6x - 8y + 21 = 0. Then, the maximum distance of P from the vertex of the parabola x² + 6x + y + 13 = 0 is…Coordinate Geometry
Q11In an equilateral triangle PQR, let the vertex P be at (3, 5) and the side QR be along the line x + y = 4. If the orthocentre of the triangle PQR is (α, β)…Coordinate Geometry
Q12The sum of all the integral values of p such that the equation 3 sin ² x + 12 cos x - 3 = p, x R, has at least one solution, is:Trigonometry
Q13The square of the distance of the point P(5, 6, 7) from the line (x-2)/2 = (y-5)/3 = (z-2)/4 is equal to:Three Dimensional Geometry
Q14Let a = √(7)i + j - k and b = j + 2k. If r is a vector such that r × a + a × b = 0 and r · a = 0, then |3r|² is equal to:Vector Algebra
Q15The square of the distance of the point of intersection of the lines r = (i + j - k) + λ(ai - j), a ≠ 0 and r = (4i - k) + μ(2i + ak) from the origin is:Three Dimensional Geometry
Q17The product of all possible values of α, for which lim x→0 ((1- cos (α x) cos ((α+1)x) cos ((α+2)x))/(sin ²((α+1)x)))=2, is:Limit, Continuity and Differentiability
Q18The value of the integral ∫₀^∞ (log e (x))/(x²+4) dx is:Integral Calculus
Q19Let f: R → R be a differentiable function such that f((x+y)/3) = (f(x)+f(y))/3 for all x, y R, and f'(0) = 3. Then the minimum value of the function g(x) = 3…Limit, Continuity and Differentiability
Q20The value of the integral ∫ π/6 ^(π/3)((4-cosec² x)/(cos ⁴ x))dx is:Integral Calculus
Q21Let A = \1, 2, 3, 4, 5, 6. The number of one-one functions f: A → A such that f(1) ≥ 3, f(3) ≤ 4 and f(2) + f(3) = 5, is _ _ _.Permutations and Combinations
Q22Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number…Permutations and Combinations
Q23If the sum of the coefficients of x⁷ and x¹⁴ in the expansion of (1/(x³) - x⁴)ⁿ, x ≠ 0, is zero, then the value of n is _ _ _ _.Binomial Theorem and Its Simple Applications
Q24If (π)/4 + Σ p=1 ¹¹ tan ⁻¹((2^(p-1))/(1+2^(2p-1))) = α, then tan α is equal to _ _ _ _ _.Trigonometry