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

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JEE Main 20265 Apr, Evening shift

Physics 22Chemistry 22Mathematics 25

Physics

Q27In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The…Units and Measurements
Q28A mass of 1 kg is kept on a inclined plane with 30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved…Work, Energy and Power
Q30A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle θ₁ and in the next 2 s…Rotational Motion
Q31An object of uniform density rolls up the curved path with the initial velocity v₀ as shown in the figure. If the maximum height attained by an object is…Rotational Motion
Q32A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth (R e). The increase in potential energy will be _ _ _. (g…Gravitation
Q33Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is _ _ _. (S is the surface tension of…Properties of Solids and Liquids
Q34An ideal gas at pressure P and temperature T is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is _ _ _.Thermodynamics
Q35Match List - I with List - II. List - I: A. sin ²ω t; B. sin ³(2ω t); C. sin (ω t)+ cos (πω t); D. cos ω t+ cos 2ω t. List - II: I. Periodic with time period…Oscillations and Waves
Q36A metal rod of length L rotates about one end at origin with a uniform angular velocity ω. The magnetic field radially falls off as B(r)=B₀e^(-λ r); λ being a…Electromagnetic Induction and Alternating Currents
Q38A particle of charge q and mass m is projected from origin with an initial velocity v=(v₀/(2) x+v₀/(2) y). There exists a uniform magnetic field B=B₀ z and a…Magnetic Effects of Current and Magnetism
Q39Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The electromagnetic wave exerts…Electromagnetic Waves
Q40A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two…Optics
Q41An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal…Optics
Q42The maximum intensity in a Young's double slit experiment is I₀. Distance between the slits (d) is 5λ, where λ is the wavelength of light used. The intensity…Optics
Q43An electron is travelling with a velocity v in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron…Dual Nature of Matter and Radiation
Q44Assuming the experimental mass of ¹²₆C as 12 u, the mass defect of ¹²₆C atom is _ _ _ MeV/ c². (Mass of proton = 1.00727 u. mass of neutron = 1.00866 u, 1 u =…Atoms and Nuclei
Q45In a semiconductor p-n diode, the doping concentrations on p-side and n-side are 10¹⁵ atoms/cm ³ and 10¹⁸ atoms/cm ³, respectively. Which one of the following…Electronic Devices
Q46A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600×10⁻⁶ m³. The elastic potential energy stored in…Properties of Solids and Liquids
Q47The heat extracted out of x gram of water initially at 50°C to cool it down to 0°C is sufficient to evaporate (1000-x) gram of water also initially at 50°C…Properties of Solids and Liquids
Q48A series LCR circuit with R=20 Ω, L=1.6 H and C=40 is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _ _ _ Ω.Electromagnetic Induction and Alternating Currents
Q49When an external resistance of 5 Ω is connected across terminals of a cell, a current of 0.25 A flows through it. When the 5 Ω resistor is replaced by a 2 Ω…Current Electricity
Q50A circular loop of radius 20 cm and resistance 2 Ω is placed in a time varying magnetic field B=(2t²+2t+3) T. At t=0, for the plane of the loop being…Electromagnetic Induction and Alternating Currents

Chemistry

Q51What volume of hydrogen gas at STP would be liberated by action of 50 mL of H₂SO₄ of 50% purity (density = 1.3 g mL ⁻¹) on 20 g of zinc ? Given: Molar mass of…Some Basic Concepts in Chemistry
Q52Which of the following statement(s) is/are true ? A. If two orbitals have the same value of (n+l), the orbital with lower value of n will have lower energy…Atomic Structure
Q54Consider the following data for the reaction X₂(g)+Y₂(g) 2XY(g) at 600 K. The Δ r G^ (in kJ mol ⁻¹) for the reaction is: [Table — XY(g): Δ f H^ 600 K =42 kJ…Chemical Thermodynamics
Q55The correct order of molar heat capacities measured at 298 K and 1 bar is:Chemical Thermodynamics
Q56The reaction A(g) B(g)+C(g) was initiated with the amount 'a' of A(g). At equilibrium it is found that the amount of A(g) remaining is (a-x) at a total…Equilibrium
Q57One half cell in a voltaic cell is constructed by dipping silver rod in AgNO₃ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar…Redox Reactions and Electrochemistry
Q58Given below are two statements: Statement I: The number of pairs among [Al₂O₃, Cr₂O₃], [Cl₂O₇, Mn₂O₇], [Na₂O, V₂O₃] and [CO, N₂O] that contain oxides of same…Classification of Elements and Periodicity in Properties
Q59Given below are two statements: Statement I: Aluminium upon reaction with NaOH forms [Al(OH)₆]³⁻ ion. Statement II: The geometry of ICl₄^-, ClO₃^(- a)nd…p-Block Elements
Q60Given below are two statements: Statement I: Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their…Coordination Compounds
Q61Identify the correct statements from the following A. [Fe(C₂O₄)₃]³⁻ is the most stable complex among [Fe(OH)₆]³⁻, [Fe(C₂O₄)₃]³⁻ and [Fe(SCN)₆]³⁻ B. The…Coordination Compounds
Q62Match List - I with List - II. List - I (Purification technique): A. Simple distillation; B. Fractional distillation; C. Steam distillation; D. Distillation…Purification and Characterisation of Organic Compounds
Q63IUPAC name of the some alkenes are given below. Find out the correct stability order. A. 2-Methylbut-2-ene B. cis-But-2-ene C. 2, 3-Dimethylbut-2-ene D…Hydrocarbons
Q64Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass 72 g mol ⁻¹.Some Basic Principles of Organic Chemistry
Q65Complete the following reaction sequence and give the name of major product 'P'. CH₃CH₂C N (i) OH^-/H₂O/Δ (ii) H₃O⁺ (iii) Cl₂/Red P (iv) H₂O P (Major product)Organic Compounds Containing Oxygen
Q66Given below are two statements: Statement I: The condensation reaction between CH₃-CH=O and H₂N-NH-C(=O)-NH₂ under optimum pH will produce…Organic Compounds Containing Oxygen
Q67Given below are two statements: Statement I: Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will give benzylamine. Statement II…Organic Compounds Containing Nitrogen
Q68Identify the incorrect statement about tertiary structure of proteins.Biomolecules
Q70A paper dipped in a dil. H₂SO₄ solution of 'X' upon treatment with SO₂ gas turns into green. The compound 'X' is:Principles Related to Practical Chemistry
Q71The total number of unpaired electrons present in the d³, d⁴ (low spin) d⁵ (high spin), d⁶ (high spin) and d⁷ (low spin) octahedral complex systems is _ _ _.Coordination Compounds
Q72RMgI when treated with ice cold water liberated a gas which occupied 1.4 dm ³ /g at STP. The gas produced is further reacted with iodine in presence of HIO₃…Organic Compounds Containing Halogens
Q7320 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a…Solutions
Q74At 298 K, the molar conductivity of x% (w/w) MX solution (aqueous) is 123.5 S cm ² mol ⁻¹. The conductance of same solution is 1.9×10⁻³ S. The value of x is _…Redox Reactions and Electrochemistry

Mathematics

Q1Let α, β be the roots of the equation x²-x+p=0 and γ, δ be the roots the equation x²-4x+q=0; p, q Z. If α, β, γ, δ are in G.P., then |p+q| equals:Complex Numbers and Quadratic Equations
Q2Let z₁, z₂ C be the distinct solutions of the equation z²+4z-(1+12i)=0. Then |z₁|²+|z₂|² is equal to:Complex Numbers and Quadratic Equations
Q3If f:N is defined by f(n)= n -1 -5 -2n² 3(2k+1) 2k+1 -3n³ 3k(2k+1) 3k(k+2)+1, k, and Σ n=1 ^(k) f(n)=98, then k is equal to:Matrices and Determinants
Q4Let M be a 3×3 matrix such that M 1 0 0 = 1 2 3, M 0 1 0 = 0 1 2 and M 0 0 1 = -1 1 1. If M x y z = 1 7 11, then x+y+z equals:Matrices and Determinants
Q5If the sum of the first 10 terms of the series 1/(1+1⁴×4)+2/(1+2⁴×4)+3/(1+3⁴×4)+4/(1+4⁴×4)+ is m/n, gcd (m,n)=1, then m+n is equal to:Sequence and Series
Q6Let A₁, A₂, A₃,, A₃₉ be 39 arithmetic means between the numbers 59 and 159. Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ is equal to:Sequence and Series
Q7The coefficient of x² in the expansion of (2x²+1/x)¹⁰, x≠0, is:Binomial Theorem and Its Simple Applications
Q8The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is selected the captain…Statistics and Probability
Q9A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is:Permutations and Combinations
Q10A variable X takes values 0, 0, 2, 6, 12, 20,, n(n-1) with frequencies ⁿC₀, ⁿC₁, ⁿC₂, ⁿC₃, ⁿC₄, ⁿC₅,, ⁿC n, respectively. If the mean of this data is 60, then…Statistics and Probability
Q11Let the point P be the vertex of the parabola y=x²-6x+12. If a line passing through the point P intersects the circle x²+y²-2x-4y+3=0 at the points R and S…Coordinate Geometry
Q12Let the directrix of the parabola P: y²=8x, cut x -axis at the point A. Let B(α,β), α>1, be a point on P such that the slope of AB is 3/5. If BC is a focal…Coordinate Geometry
Q13Let the eccentricity e of a hyperbola satisfy the equation 6e²-11e+3=0. If the foci of the hyperbola are (3,5) and (3,-4), then the length of its latus rectum…Coordinate Geometry
Q14Let a triangle PQR be such that P and Q lie on the line (x+3)/8=(y-4)/2=(z+1)/2 and are at a distance of 6 units from R(1,2,3). If (α,β,γ) is the centroid of…Three Dimensional Geometry
Q15If the distance of the point (a,2,5) from the image of the point (1,2,7) in the line x/1=(y-1)/1=(z-2)/2 is 4, then the sum of all possible values of a is…Three Dimensional Geometry
Q16Let O be the origin, OP= a and OQ= b. If R is the point on OP such that OP=5OR, and M is the point such that OQ=5RM, then PM is equal to:Vector Algebra
Q17Let f(x)= lim y→0 ((1- cos (xy)) tan (xy))/(y³). Then the number of solutions of the equation f(x)= sin x, x is:Limit, Continuity and Differentiability
Q18Let (2^(1-a)+2^(1+a)), f(a), (3^(a)+3^(-a)) be in A.P. and α be the minimum value of f(a). Then the value of the integral ∫ log e (α-1) ^(log e…Integral Calculus
Q19Let f:[1,∞) be a differentiable function defined as f(x)=∫₁ˣ f(t) dt+(1-x)(log e x-1)+e. Then the value of f(f(1)) is:Differential Equations
Q20Let f(x) and g(x) be twice differentiable functions satisfying f''(x)=g''(x) for all x, f'(1)=2g'(1)=4 and g(2)=3f(2)=9. Then f(25)-g(25) is equal to:Differential Equations
Q21Let A=\1,4,7 and B=\2,3,8. Then the number of elements, in the relation R=\((a₁,b₁),(a₂,b₂)) ((A× B)×(A× B)): a₁+b₂ divides a₂+b₁ is _ _ _.Sets, Relations and Functions
Q22From the point (-1,-1), two rays are sent making angles of 45° with the line x+y=0. These rays get reflected from the mirror x+2y=1. If the equations of the…Coordinate Geometry
Q23If S=\θ [-π,π]: cos θ cos (5θ)/2= cos 7θ cos (7θ)/2, then n(S) is equal to _ _ _.Trigonometry
Q24Let f:R be a function such that f(x)+3f((π)/2-x)= sin x, x. Let the maximum value of f on R be α. If the area of the region bounded by the curves g(x)=x² and…Integral Calculus
Q25Let y=y(x) be the solution of the differential equation (tan x)^(1/2)dy=(sec ³x-(tan x)^(3/2)y)dx, 0<x<(π)/2, y((π)/4)=(6 2)/5. If y((π)/3)=4/5α, then α⁴…Differential Equations