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JEE Main 2026 2 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20262 Apr, Evening shift

Physics 20Chemistry 23Mathematics 25

Physics

Q26Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are _ _ _.Units and Measurements
Q27A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the…Laws of Motion
Q28Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below…Laws of Motion
Q29A particle having charge 10⁻⁹ C moving in x - y plane in fields of 0.4 j N/C and 4×10⁻³ k T experiences a force of (4 i+2 j)×10⁻¹⁰ N. The velocity of the…Magnetic Effects of Current and Magnetism
Q31If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and…Gravitation
Q32In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100…Experimental Skills
Q33The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is απ×10⁻⁴ J. The value of α is _ _ _…Properties of Solids and Liquids
Q34A mixture of carbon dioxide and oxygen has volume 8310 cm ³, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and…Kinetic Theory of Gases
Q35If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m ³ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is…Properties of Solids and Liquids
Q36A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the…Work, Energy and Power
Q37An electromagnetic wave travels in free space along the x -direction. At a particular point in space and time, B=2×10⁻⁷ j T is associated with this wave. The…Electromagnetic Waves
Q38Two resistors of 200 Ω and 400 Ω are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 Ω resistance. The…Current Electricity
Q39Two metal plates (A, B) are kept horizontally with separation of (12/(π)) cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm ³)…Electrostatics
Q40Two point charges 8 μ C and -2 μ C are located at x=2 cm and x=4 cm, respectively on the x -axis. The ratio of electric flux due to these charges through two…Electrostatics
Q43A circular current loop of radius R is placed inside square loop of side length L (L R) such that they are co-planar and their centers coincide. The…Electromagnetic Induction and Alternating Currents
Q44The binding energy per nucleon of ²⁰⁹₈₃Bi is _ _ _ MeV. [Take m(²⁰⁹₈₃Bi)=208.980388 u, m p =1.007825 u, m n =1.008665 u, 1 u = 931 MeV/c ² ]Atoms and Nuclei
Q45The equation of motion of a particle is given by x=a sin (50t+π/3) cm. The particle will come to rest at time t₁ and it will have zero acceleration at time…Oscillations and Waves
Q46In a Young's double slit experiment, the intensity at some point on the screen is found to be 3/4 times of the maximum of the interference pattern. The path…Optics
Q47Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _ _ _.Atoms and Nuclei
Q485 moles of unknown gas is heated at constant volume from 10° C to 20° C. The molar specific heat of this gas at constant pressure c p =8 cal/mol.° C and…Thermodynamics

Chemistry

Q51The ratio of mass percentage (w/w) of C: H in a hydrocarbon is 12: 1. It has two carbon atoms. The weight (in g) of CO₂(g) formed when 3.38 g of this…Some Basic Concepts in Chemistry
Q52The first and second ionization constants of a weak dibasic acid H₂A are 8.1×10⁻⁸ and 1.0×10⁻¹³ respectively. 0.1 mol of H₂A was dissolved in 1L of 0.1 M HCl…Equilibrium
Q53SF₄ is isostructural with: A. BrF₄^() B. CH₄ C. IF₄^() D. XeF₄ E. XeO₂F₂ Choose the correct answer from the options given below:Chemical Bonding and Molecular Structure
Q54Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is…Chemical Thermodynamics
Q55Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol ⁻¹) in 0.5 L of water at 300 K. Its osmotic pressure is x bar. Solution B is…Solutions
Q56At 25° C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not…Equilibrium
Q57Consider the reaction aX→ bY, for which the rate constant at 30° C is 1×10⁻³ mol ⁻¹ L s ⁻¹. Which of the following statements are true ? A. When concentration…Chemical Kinetics
Q58The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is:p-Block Elements
Q59Given below are two statements: Statement I: The second ionization enthalpy of B, Al and Ga is in the order of B > Al > Ga. Statement II: The correct order in…Classification of Elements and Periodicity in Properties
Q60Given below are two statements: Statement I: Among Zn, Mn, Sc and Cu, the energy required to remove the third valence electron is highest for Zn and lowest…Coordination Compounds
Q61Which of the following complexes will show coordination isomerism ? A. [Ag(NH₃)₂][Ag(CN)₂] B. [Co(NH₃)₆][Cr(CN)₆] C. [Co(NH₃)₆][Co(CN)₆] D…Coordination Compounds
Q62Complete combustion of X g of an organic compound gave 0.25 g of CO₂ and 0.12 g of H₂O. If the% of carbon is 25% and of hydrogen is 4.89%, then X = _ _ _…Purification and Characterisation of Organic Compounds
Q63Given below are two statements: Statement I: In O₂N-C₆H₄- C H-C₆H₄-OCH₃ (both groups para), the carbocation is stabilised by +R effect of -OCH₃ group…Some Basic Principles of Organic Chemistry
Q64The compound (X) on (i) on heating in the presence of anhydrous AlCl₃ and HCl gas gives 2,4-dimethyl pentane (ii) aromatization gives toulene and (iii)…Hydrocarbons
Q65Correct statements regarding alkyl halides (R - X) among the following are: A. Alcohol being less polar solvent as compared to water, alcoholic KOH favours…Organic Compounds Containing Halogens
Q66An organic compound “x” where molar ratio of C, O and H are equal, on treatment with 50% KOH under reflux followed by acidification produced “y”. The most…Organic Compounds Containing Oxygen
Q67A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z)…Organic Compounds Containing Oxygen
Q69Identify the correct pair having amino acid (A) and the hormone (B) that is iodinated derivative of the amino acid (A). (T and Y represent one letter code for…Biomolecules
Q71The surface of sodium metal is irradiated with radiation of wavelength x nm. The kinetic energy of ejected electrons is 2.8×10⁻²⁰ J. The work function of…Atomic Structure
Q72Consider the following gas phase reaction being carried out in a closed vessel at 25° C. 2A(g)→4B(g)+C(g). Time (min) and total pressure of the system (mm…Chemical Kinetics
Q73Consider the following two half-cell reactions along with the standard reduction potential given: CO₂+6H⁺+6e^-→ CH₃OH+H₂O, E° red =0.02 V; 1/2O₂+2H⁺+2e^-→…Redox Reactions and Electrochemistry
Q74Number of paramagnetic ions among the following d- and f-block metal ions is _ _ _. Mn²⁺, Cu²⁺, Zn²⁺, Yb²⁺, Sc³⁺, La³⁺, Gd³⁺, Lu³⁺, Ti⁴⁺, Ce⁴⁺ (Atomic number…d- and f-Block Elements
Q75Consider the following reactions sequence: 4-nitrotoluene (H₃C-C₆H₄-NO₂, para) (i) Sn/HCl; OH^- (ii) (CH₃CO)₂O (iii) Br₂/AlBr₃ (iv) H₃O⁺ Major Product (P)…Organic Compounds Containing Nitrogen

Mathematics

Q1Let α, β be the roots of the equation x²-3x+r=0, and (α)/2, 2β be the roots of the equation x²+3x+r=0. If the roots of the equation x²+6x=m are 2α+β+2r and…Complex Numbers and Quadratic Equations
Q2Let the circles C₁: |z|=r and C₂: |z-3-4i|=5, z, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ moves on C₂ and min |z₁-z₂|=2, then max |z₁-z₂| is…Complex Numbers and Quadratic Equations
Q3If the system of equations x+5y+6z=4, 2x+3y+4z=7, x+6y+az=b has infinitely many solutions, then the point (a, b) lies on the lineMatrices and Determinants
Q4Let a₁, a₂, a₃, be an A.P. and g₁=a₁, g₂, g₃, be an increasing G.P. If a₁=a₂+g₂=1 and a₃+g₃=4, then a₁₀+g₅ is equal to:Sequence and Series
Q5The sum (1³)/1+(1³+2³)/(1+3)+(1³+2³+3³)/(1+3+5)+ up to 8 terms, is:Sequence and Series
Q6If for 3≤ r≤ 30, (³⁰C 30-r)+3(³⁰C 31-r)+3(³⁰C 32-r)+(³⁰C 33-r)=^(m)C r, then m equals:Binomial Theorem and Its Simple Applications
Q7Let p n denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If p n+1 -p n =66, then the sum of all distinct…Permutations and Combinations
Q8A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly…Statistics and Probability
Q9The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n-1) observations is 48 and the sum of squares of the first (n-1)…Statistics and Probability
Q10Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x+(k-1)y+3=0 and 2x+k²y-4=0. If the line…Coordinate Geometry
Q11Let O be the origin, and P and Q be two points on the rectangular hyperbola xy=12 such that the mid point of the line segment PQ is (1/2, -1/2). Then the area…Coordinate Geometry
Q12Let the parabola y=x²+px+q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p²+q²…Coordinate Geometry
Q13Let P=\θ [0, 4π]: tan ²θ≠1 and S=: 2(cos ⁸θ- sin ⁸θ) sec 2θ=a², θ P. Then n(S) is:Trigonometry
Q14Let the vectors a=- i+ j+3 k and b= i+3 j+ k. For some λ, μ, let c=λ a+μ b. If c·(3 i-6 j+2 k)=10 and c·(i+ j+ k)=-2, then | c|² is equal to:Vector Algebra
Q15Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line (x-1)/2=(y-2)/1=(z-α)/3. If the midpoint of the line segment PA is…Three Dimensional Geometry
Q16Two adjacent sides of a parallelogram PQRS are given by PQ= j+ k and PS= i- j. If the side PS is rotated about the point P by an acute angle α in the plane of…Vector Algebra
Q17The value of ∫₀^(20π)(sin ⁴x+ cos ⁴x) dx is equal to:Integral Calculus
Q18Let f(x) be a polynomial of degree 5, and have extrema at x=1 and x=-1. If lim x→0 ((f(x))/(x³))=-5, then f(2)-f(-2) is equal to:Limit, Continuity and Differentiability
Q19Let f(x)=∫((16x+24)/(x²+2x-15))dx. If f(4)=14 log e (3) and f(7)= log e (2^α·3^β), α, β, then α+β is equal to:Integral Calculus
Q20Let x=x(y) be the solution of the differential equation 2y²dx/dy-2xy+x²=0, y>1, x(e)=e. Then x(e²) is equal to:Differential Equations
Q21Let A=\2, 3, 4, 5, 6. Let R be a relation on the set A× A given by (x, y)R(z, w) if and only if x divides z and y≤ w. Then the number of elements in R is _ _ _.Sets, Relations and Functions
Q22Consider the matrices A= 2 -2 4 -2 and B= 3 9 1 3. If matrices P and Q are such that PA=B and AQ=B, then the absolute value of the sum of the diagonal…Matrices and Determinants
Q23Let A be the point (3, 0) and circles with variable diameter AB touch the circle x²+y²=36 internally. Let the curve C be the locus of the point B. If the…Coordinate Geometry
Q24If the area of the region bounded by 16x²-9y²=144 and 8x-3y=24 is A, then 3(A+6 log e (3)) is equal to _ _ _.Integral Calculus
Q25The number of points in the interval [2, 4], at which the function f(x)=[x²-x-1/2], where [·] denotes the greatest integer function, is discontinuous, is _ _ _.Limit, Continuity and Differentiability