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JEE Main 2026 23 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202623 Jan, Evening shift

Physics 17Chemistry 21Mathematics 25

Physics

Q27An air bubble of volume 2.9 cm ³ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17°C. The volume of the…Kinetic Theory of Gases
Q29When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The…Optics
Q31A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop…Electromagnetic Induction and Alternating Currents
Q33Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I=10 sin (ω t) A, where ω=1000 rad./s. A circular…Electromagnetic Induction and Alternating Currents
Q36The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability of μ=2μ₀, is (μ₀ = permeability of vacuum)Electromagnetic Waves
Q37The current passing through a conducting loop in the form of equilateral triangle of side 4 3 cm is 2 A. The magnetic field at its centroid is α×10⁻⁵ T. The…Magnetic Effects of Current and Magnetism
Q38A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2: 2: 3. The two pieces of equal masses fly off…Laws of Motion
Q39Which of the following pair of nuclei are isobars of the element?Atoms and Nuclei
Q40A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the…Electrostatics
Q41One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27°C and does W joule of work. If the gas undergoes same magnitude…Thermodynamics
Q42A small metallic sphere of diameter 2 mm and density 10.5 g/cm ³ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm ³ respectively. The…Properties of Solids and Liquids
Q44A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m/s ². At 10 m height from ground, while…Kinematics
Q45Two charges 7 μC and −2 μC are placed at (−9, 0, 0) cm and (9, 0, 0) cm respectively in an external field E=A/(r²) r, where A=9×10⁵ N/C.m ². Considering the…Electrostatics
Q46The velocity of sound in air is doubled when the temperature is raised from 0°C to α°C. The value of α is _ _ _ _.Oscillations and Waves
Q48A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by…Units and Measurements
Q49The average energy released per fission for the nucleus of ²³⁵₉₂U is 190 MeV. When all the atoms of 47 g pure ²³⁵₉₂U undergo fission process, the energy…Atoms and Nuclei
Q50The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The…Optics

Chemistry

Q51Identify the CORRECT set of details from the following: A. [Co(NH₃)₆]³⁺: Inner orbital complex; d²sp³ hybridized B. [MnCl₆]³⁻: Outer orbital complex; sp³d²…Coordination Compounds
Q52Given below are two statements: Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg. Statement II…Classification of Elements and Periodicity in Properties
Q53Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming M⁺ (M→ M⁺+e^-). The cation M⁺ is present in two…Redox Reactions and Electrochemistry
Q54Identify the INCORRECT statements from the following: A. Notation ²⁴₁₂Mg represents 24 protons and 12 neutrons. B. Wavelength of a radiation of frequency…Atomic Structure
Q55A student has been given a compound "x" of molecular formula- C₆H₇N. 'x' is sparingly soluble in water. However, on addition of dilute mineral acid, 'x'…Organic Compounds Containing Nitrogen
Q56A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give…Organic Compounds Containing Oxygen
Q57Observe the following reactions at T(K). I. A → products. II. 5Br^-(aq)+BrO₃^-(aq)+6H⁺(aq)→3Br₂(aq)+3H₂O(l). Both the reactions are started at 10.00 am. The…Chemical Kinetics
Q58It is noticed that Pb²⁺ is more stable than Pb⁴⁺ but Sn²⁺ is less stable than Sn⁴⁺. Observe the following reactions. PbO₂+Pb→2PbO; Δ r G°(1). SnO₂+Sn→2SnO; Δ…p-Block Elements
Q59The oxidation state of chromium in the final product formed in the reaction between KI and acidified K₂Cr₂O₇ solution is:d- and f-Block Elements
Q61Given below are two statements: Statement I: (CH₃)₃ C is more stable than C H₃ as nine hyperconjugation interactions are possible in (CH₃)₃ C. Statement II: C…Some Basic Principles of Organic Chemistry
Q63Iodoform test can differentiate between A. Methanol and Ethanol B. CH₃COOH and CH₃CH₂COOH C. Cyclohexene and cyclohexanone D. Diethyl ether and Pentan-3-one…Organic Compounds Containing Oxygen
Q64Elements X and Y belong to Group 15. The difference between the electronegativity values of 'X' and phosphorus is higher than that of the difference between…p-Block Elements
Q65Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence ofBiomolecules
Q67In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound isPurification and Characterisation of Organic Compounds
Q68The work functions of two metals (M A and M B) are in the 1: 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated…Atomic Structure
Q70Which of the following statements are TRUE about Haloform reaction?: A. Sodium hypochlorite reacts with KI to give KOI. B. KOI is a reducing agent. C. α…Organic Compounds Containing Oxygen
Q71Two liquids A and B form an ideal solution. At 320 K, the vapour pressure of the solution, containing 3 mol of A and 1 mol of B is 500 mm Hg. At the same…Solutions
Q72Consider the following reaction of benzene. Benzene + H₃C-CO-CH₂-CH₂-CO-Cl anhydrous AlCl₃ (P) [Δ]aq NaOH (Q). In compound (Q), the percentage of oxygen is _…Organic Compounds Containing Oxygen
Q73200 cc of x×10⁻³ M potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt solution in acidic medium. Here x= _ _ _ _.Redox Reactions and Electrochemistry
Q74Total number of unpaired electrons present in the central metal atoms/ions of [Ni(CO)₄], [NiCl₄]²⁻, [PtCl₂(NH₃)₂], [Ni(CN)₄]²⁻ and [Pt(CN)₄]²⁻ is _ _ _ _.Coordination Compounds
Q75X₂(g)+Y₂(g) 2Z(g). X₂(g) and Y₂(g) are added to a 1 L flask and it is found that the system attains the above equilibrium at T(K) with the number of moles of…Equilibrium

Mathematics

Q1If the points of intersection of the ellipses x²+2y²-6x-12y+23=0 and 4x²+2y²-20x-12y+35=0 lie on a circle of radius r and centre (a, b), then the value of…Coordinate Geometry
Q2Let PQ be a chord of the hyperbola (x²)/4-(y²)/(b²)=1, perpendicular to the x-axis such that OPQ is an equilateral triangle, O being the centre of the…Coordinate Geometry
Q3Let A=\0,1,2,,9. Let R be a relation on A defined by (x, y) R if and only if |x-y| is a multiple of 3. Given below are two statements: Statement I: n(R)=36…Sets, Relations and Functions
Q4The area of the region enclosed between the circles x²+y²=4 and x²+(y-2)²=4 is:Integral Calculus
Q5The system of linear equations x+y+z=6, 2x+5y+az=36, x+2y+3z=b hasMatrices and Determinants
Q6Consider two sets A=: ||x-3|-3|≤1 and B= -\1,2 ((x-2)(x-4))/(x-1) log e (|x-2|)=0. Then the number of onto functions f: A→ B is equal toSets, Relations and Functions
Q7Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the…Statistics and Probability
Q8Let I(x)=∫(3 dx)/((4x+6)(√(4x²+8x+3))) and I(0)=(3)/4+20. If I(1/2)=(a 2)/b+c, where a, b, c, gcd (a, b)=1, then a+b+c is equal toIntegral Calculus
Q9Let (π)/2<θ<π and cot θ=-1/(2 2). Then the value of sin ((15θ)/2)(cos 8θ+ sin 8θ)+ cos ((15θ)/2)(cos 8θ- sin 8θ) is equal toTrigonometry
Q10Let Σ k=1 ⁿa k =α n²+β n. If a₁₀=59 and a₆=7a₁, then α+β is equal toSequence and Series
Q11If the mean and the variance of the data (Class: 4–8, 8–12, 12–16, 16–20; Frequency: 3, λ, 4, 7 respectively) are μ and 19 respectively, then the value of λ+μ…Statistics and Probability
Q12The sum of all the real solutions of the equation log (x+3) (6x²+28x+30)=5-2 log (6x+10) (x²+6x+9) is equal toComplex Numbers and Quadratic Equations
Q13Let a= i-2 j+3 k, b=2 i+ j- k, c=λ i+ j+ k and v= a× b. If v· c=11 and the length of the projection of b on c is p, then 9p² is equal toVector Algebra
Q14An equilateral triangle OAB is inscribed in the parabola y²=4x with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having…Coordinate Geometry
Q15The least value of (cos ²θ-6 sin θ cos θ+3 sin ²θ+2) isTrigonometry
Q16If f(x)= (a|x|+x²-2(sin |x|)(cos |x|))/x, x≠0 b, x=0 is continuous at x=0, then a+b is equal toLimit, Continuity and Differentiability
Q17Let A(1, 2) and C(−3, −6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7x-y=14. If B (α, β) and D (γ, δ)…Coordinate Geometry
Q18If z=(3)/2+i/2, i=√(-1), then (z²⁰¹-i)⁸ is equal toComplex Numbers and Quadratic Equations
Q19Let a, b, c be three vectors such that a× b=2(a× c). If | a|=1, | b|=4, | c|=2, and the angle between b and c is 60°, then | a· c| is equal toVector Algebra
Q20The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, isPermutations and Combinations
Q21If the image of the point P (a, 2, a) in the line x/2=(y+a)/1=z/1 is Q and the image of Q in the line (x-2b)/2=(y-a)/1=(z+2b)/(-5) is P, then a+b is equal to…Three Dimensional Geometry
Q22Let A= 0 2 -3 -2 0 1 3 -1 0 and B be a matrix such that B(I-A)=I+A. Then the sum of the diagonal elements of B^(T)B is equal to _ _Matrices and Determinants
Q23The number of elements in the set S=: x [0,100] and ∫₀ˣ t² sin (x-t) dt=x² is _ _Integral Calculus
Q24Let S denote the set of 4-digit numbers abcd such that a>b>c>d and P denote the set of 5-digit numbers having product of its digits equal to 20. Then…Permutations and Combinations
Q25If the solution curve y=f(x) of the differential equation (x²-4)y'-2xy+2x(4-x²)²=0, x>2, passes through the point (3, 15), then the local maximum value of f…Differential Equations