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JEE Main 2026 6 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20266 Apr, Evening shift

Physics 20Chemistry 23Mathematics 25

Physics

Q26The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is _ _ _.Units and Measurements
Q27Match List - I with List - II. List - I: A. Boltzmann constant; B. Stefan's constant; C. Planck's constant; D. Gravitational constant. List - II: I. […Units and Measurements
Q28A solid sphere (A) of mass 5m and a spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is…Rotational Motion
Q30A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both…Thermodynamics
Q31For an electromagnetic wave propagating through vacuum, k, E and ω represent propagation vector, electric field and angular frequency, respectively. The…Electromagnetic Waves
Q32Two identical bodies A and B of equal masses have initial velocities v₁=4 i m/s and v₂=4 j m/s respectively. The body A has acceleration a₁=6 i+6 j m/s ²…Kinematics
Q34A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm ³ (dm: decimeter) The vessel is placed on a solid block of…Properties of Solids and Liquids
Q35If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture…Kinetic Theory of Gases
Q36A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The…Oscillations and Waves
Q37The electric potential as a function of x, y is given by V=5(x²-y²) V. The electric field at a point (2, 3) m is _ _ _ V/m.Electrostatics
Q38A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the…Magnetic Effects of Current and Magnetism
Q39A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B=0.4 sin (300t) Tesla. The normal to the plane of loop makes an angle…Electromagnetic Induction and Alternating Currents
Q40A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere…Electrostatics
Q41The energy released if hydrogen atoms are combined to form ⁴₂He is _ _ _ MeV. (Take binding energies per nucleon of ²₁H and ⁴₂He as 1.1 MeV and 7.2 MeV…Atoms and Nuclei
Q42Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is _ _ _.Optics
Q46A block takes t time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time t/2 to slide…Laws of Motion
Q47The de Broglie wavelength for an electron accelerated through the potential difference of V₁ volt is λ₁. When the potential difference is changed to V₂ volt…Dual Nature of Matter and Radiation
Q48A moving coil of galvanometer when shunted with 2 Ω resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 Ω is connected…Current Electricity
Q49Two cells of emfs 1 V and 2 V and internal resistance 2 Ω and 1 Ω, respectively connected in parallel, gave a current of 1 A through an external resistance…Current Electricity
Q50A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance…Optics

Chemistry

Q51Which of the following contain the same number of atoms ? (Given: Molar mass in g mol ⁻¹ of H, He, O and S are 1, 4, 16 and 32 respectively) A. 2 g of O₂ gas…Some Basic Concepts in Chemistry
Q52The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state (n) are respectively (Given: Hydrogen atom Bohr radius is 52.9 pm)Atomic Structure
Q53Given below are two statements: Statement I: The number of compounds among SO₂, SO₃, SF₄, SF₆ and H₂S in which sulphur does not obey the Octet rule is 3…Chemical Bonding and Molecular Structure
Q54Match List - I with List - II. Given V₁ and V₂ are initial and final volumes respectively. List - I (Isothermal process): A. Reversible expansion; B. Free…Chemical Thermodynamics
Q55Given below are two statements: [Chamber 1: 18 g glucose in 100 mL aqueous solution | semi-permeable membrane | Chamber 2: 30 g glucose in 250 mL aqueous…Solutions
Q56Given is a concentrated solution of a weak electrolyte A x B y of concentration 'c' and dissociation constant 'K'. The degree of dissociation is given by:Equilibrium
Q58In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble…Classification of Elements and Periodicity in Properties
Q59Given below are two statements: Statement I: F₂O<H₂O<Cl₂O is the correct trend in terms of bond angle. Statement II: SiF₄, SnF₄ and PbF₄ are ionic in nature…Chemical Bonding and Molecular Structure
Q60The correct order of first (Δ i H₁) and second (Δ i H₂) ionisation enthalpy values of Cr and Mn are: A. Δ i H₁: Cr > Mn B. Δ i H₂: Cr > Mn C. Δ i H₁: Mn > Cr…d- and f-Block Elements
Q61Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ? A. [NiCl₄]²⁻ – sp³…Coordination Compounds
Q62Given below are two statements: Statement I: A mixture of C₁₂H₂₂O₁₁ (sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential…Purification and Characterisation of Organic Compounds
Q63Shown below is the structure of methyl acetate with three different α, β and γ carbon - oxygen bonds: H₃C - C(=O) α - β O - γ CH₃, where α is the C=O bond, β…Some Basic Principles of Organic Chemistry
Q64'x' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. 'y' is the…Organic Compounds Containing Oxygen
Q65An optically active alkyl bromide C₄H₉Br, reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B]…Hydrocarbons
Q66Consider the following reaction. C₆H₅-O - CH₂-C₆H₅ +HI→ Product. Statement I: In the above reaction, product formed will be a mixture of benzyl alcohol and…Organic Compounds Containing Oxygen
Q67Consider the following organic reaction sequence. Choose the final product (X) from the following (consider the major product in all intermediate reactions)…Organic Compounds Containing Nitrogen
Q69Consider the following reactions. Total number of electrons in the π bonds and lone pair of electrons in the product (X) is: CHO - (CHOH)₄-CH₂OH (i) HI, Δ…Biomolecules
Q70Treatment of a gas 'X' with a freshly prepared ferrous sulphate solution gives a compound 'Y' as a brown ring. The compounds X and Y are.p-Block Elements
Q71An excess of AgNO₃ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number of moles of AgCl precipitated will be _ _…Coordination Compounds
Q72An alkane (Y) requires 8 moles of oxygen for complete combustion and on chlorination with Cl₂/hν, (Y) gives only one monochlorinated product (Z). The total…Hydrocarbons
Q73500 mL of 0.2 M MnO₄^(- s)olution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This…Redox Reactions and Electrochemistry
Q74In a closed flask at 600 K, one mole of X₂Y₄(g) attains equilibrium as given below: X₂Y₄(g) 2XY₂(g). At equilibrium, 75% X₂Y₄(g) was dissociated and the total…Equilibrium
Q75Decomposition of a hydrocarbon follows the equation k=(5.5×10¹¹ s⁻¹) e^(-28000 K/T). The activation energy of reaction is _ _ _ kJ mol ⁻¹. (Nearest Integer)…Chemical Kinetics

Mathematics

Q1Let f: R → R be defined as f(x) = (2x² - 3x + 2)/(3x² + x + 3). Then f is:Sets, Relations and Functions
Q2Consider the quadratic equation (n²-2n+2)x²-3x+(n²-2n+2)²=0, n R. Let α be the minimum value of the product of its roots and β be the maximum value of the sum…Sequence and Series
Q3Let S= C: z²+√(6) iz-3=0. Then Σ z S z⁸ is equal to:Complex Numbers and Quadratic Equations
Q4The sum of all possible values of θ [0, 2π], for which the system of equations: x cos 3θ-8y-12z=0, x cos 2θ+3y+3z=0, x+y+3z=0 has a non-trivial solution, is…Matrices and Determinants
Q5Let A= 1 0 0 3 1 0 9 3 1 and B=[b ij ], 1≤ i,j≤ 3. If B=A⁹⁹-I, then the value of (b₃₁-b₂₁)/(b₃₂) is:Matrices and Determinants
Q6The sum 1+1/2(1²+2²)+1/3(1²+2²+3²)+ upto 10 terms is equal to:Sequence and Series
Q7A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10^(th) floor. The number of ways…Permutations and Combinations
Q8Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14, α<β, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α+2 and…Statistics and Probability
Q9A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of…Statistics and Probability
Q10Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of…Coordinate Geometry
Q11The eccentricity of an ellipse E with centre at the origin O is (3)/2 and its directrices are x=±(4 6)/3. Let H: (x²)/(a²)-(y²)/(b²)=1 be a hyperbola whose…Coordinate Geometry
Q12Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P (α, 0), α>0, be a focus of E and AB be a chord passing…Coordinate Geometry
Q13If sin (tan ⁻¹(x 2))= cot (sin ⁻¹√(1-x²)), x (0,1), then the value of x is:Trigonometry
Q14The shortest distance between the lines (x-4)/1=(y-3)/2=(z-2)/(-3) and (x+2)/2=(y-6)/4=(z-5)/(-5) is:Three Dimensional Geometry
Q15Let a=2 i+3 j+3 k and b=6 i+3 j+3 k. Then the square of the area of the triangle with adjacent sides determined by the vectors (2 a+3 b) and (a- b) is:Vector Algebra
Q16Let lim x→2 ((tan (x-2))(rx²+(p-2)x-2p))/((x-2)²)=5 for some r, p. If the set of all possible values of q, such that the roots of the equation rx²-px+q=0 lie…Limit, Continuity and Differentiability
Q17Let A= 1 3 -1 2 1 α 0 1 -1 be a singular matrix. Let f(x)=∫₀ˣ(t²+2t+3) dt, x [1,α]. If M and m are respectively the maximum and the minimum values of f in…Integral Calculus
Q18Let f:R be such that f(xy)=f(x)f(y), for all x,y and f(0)≠0. Let g:[1,∞) be a differentiable function such that x²g(x)=∫₁ˣ(t²f(t)-tg(t))dt. Then g(2) is equal…Differential Equations
Q19The area of the region \(x,y): x²-8x≤ y≤ -x is:Integral Calculus
Q20The value of the integral ∫₋₁¹((x³+|x|+1)/(x²+2|x|+1))dx is equal to:Integral Calculus
Q21Let R=\(x,y): log e (x+y)≤ 2. Then the minimum number of elements, required to be added in R to make it a transitive relation, is _ _ _.Sets, Relations and Functions
Q22If (1-x³)¹⁰=Σ r=0 ¹⁰a r x^(r)(1-x)^(30-2r), then 9a₉/(a₁₀) is equal to _ _ _.Binomial Theorem and Its Simple Applications
Q23Let the line x-y=4 intersect the circle C: (x-4)²+(y+3)²=9 at the points Q and R. If P (α,β) is a point on C such that PQ = PR, then (6α+8β)² is equal to _ _ _.Coordinate Geometry
Q24Let the image of the point P (0,-5,0) in the line (x-1)/2=y/1=(z+1)/(-2) be the point R and the image of the point Q (0,(-1)/2,0) in the line…Three Dimensional Geometry
Q25Let f(x)= x³+8; x<0, x²-4; x≥0, and g(x)= (x-8)^(1/3); x<0, (x+4)^(1/2); x≥0. Then the number of points, where the function gof is discontinuous, is _ _ _.Limit, Continuity and Differentiability