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JEE Main 2026 21 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202621 Jan, Morning shift

Physics 20Chemistry 21Mathematics 25

Physics

Q26An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of…Properties of Solids and Liquids
Q27A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C. The rate of consumption of the gas is _ _ _ g/s. (Take heat of…Thermodynamics
Q28Initially a satellite of 100 kg is in a circular orbit of radius 1.5R E. This satellite can be moved to a circular orbit of radius 3R E by supplying α×10⁶ J…Gravitation
Q30Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of…Properties of Solids and Liquids
Q31A 4 kg mass moves under the influence of a force F=(4t³ i-3t j) N where t is the time in second. If mass starts from origin at t=0, the velocity and position…Kinematics
Q32Two strings (A, B) having linear densities μ A =2×10⁻⁴ kg/m and μ B =4×10⁻⁴ kg/m and lengths L A =2.5 m and L B =1.5 m respectively are joined. Free ends of A…Oscillations and Waves
Q33A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid…Magnetic Effects of Current and Magnetism
Q34A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness (1/3)^(rd) of the separation between…Electrostatics
Q35Consider a modified Bernoulli equation. (P+A/(Bt²))+ρ g(h+Bt)+1/2ρ V²= constant. If t has the dimension of time then the dimensions of A and B are _ _ _, _ _…Units and Measurements
Q36A point charge of 10⁻⁸ C is placed at origin. The work done in moving a point charge 2 μ C from point A(4, 4, 2) m to B(2, 2, 1) m is _ _ _ J. (1/(4πε₀)=9×10⁹…Electrostatics
Q38The electric field in a plane electromagnetic wave is given by: E y =69 sin [0.6×10³x-1.8×10¹¹t] V/m. The expression for magnetic field associated with this…Electromagnetic Waves
Q39If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is _ _ _ m. (Atomic number of gold…Atoms and Nuclei
Q40In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a…Optics
Q41A conducting circular loop of area 1.0 m ² is placed perpendicular to a magnetic field which varies as B= sin (100t) Tesla. If the resistance of the loop is…Electromagnetic Induction and Alternating Currents
Q42A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of…Electromagnetic Induction and Alternating Currents
Q44In an experiment the values of two spring constants were measured as k₁=(10±0.2) N/m and k₂=(20±0.3) N/m. If these springs are connected in parallel, then the…Units and Measurements
Q45A light wave described by E=60[ sin (3×10¹⁵)t+ sin (12×10¹⁵)t] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of…Dual Nature of Matter and Radiation
Q4610 mole of oxygen is heated at constant volume from 30°C to 40°C. The change in the internal energy of the gas is _ _ _ cal. (The molecular specific heat of…Thermodynamics
Q49In a microscope the objective is having focal length f₀=2 cm and eye-piece is having focal length f e =4 cm. The tube length is 32 cm. The magnification…Optics
Q50A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a…Optics

Chemistry

Q51Given below are two statements: Statement I: The number of species among SF₄, NH₄⁺, [NiCl₄]²⁻, XeF₄, [PtCl₄]²⁻, SeF₄ and [Ni(CN)₄]²⁻, that have tetrahedral…Chemical Bonding and Molecular Structure
Q52Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and PQ₂. When 1 g of PQ is dissolved in 50 g of solvent 'A', Δ T b was 1.176 K…Solutions
Q53A hydrocarbon 'P' (C₄H₈) on reaction with HCl gives an optically active compound 'Q' (C₄H₉Cl) which on reaction with one mole of ammonia gives compound 'R'…Organic Compounds Containing Nitrogen
Q54Which of the following represents the correct trend for the mentioned property ? A. F>P>S>B - First Ionization Energy; B. Cl>F>S>P - Electron Affinity; C…Classification of Elements and Periodicity in Properties
Q56MnO₄²⁻, in acidic medium, disproportionates to:d- and f-Block Elements
Q5780 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The residual gases after cooling to 273 K occupy 224…Some Basic Concepts in Chemistry
Q58Given below are two statements: Statement I: Among [Cu(NH₃)₄]²⁺, [Ni(en)₃]²⁺, [Ni(NH₃)₆]²⁺ and [Mn(H₂O)₆]²⁺, [Mn(H₂O)₆]²⁺ has the maximum number of unpaired…Coordination Compounds
Q59Given below are two statements: Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the…Atomic Structure
Q60An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with Br₂ and KOH forms compound (R) having…Organic Compounds Containing Nitrogen
Q62Given below are two statements: Statement I: The number of pairs among [SiO₂,CO₂], [SnO,SnO₂], [PbO,PbO₂] and [GeO,GeO₂], which contain oxides that are both…p-Block Elements
Q63Identify correct statements from the following: A. Propanal and propanone are functional isomers. B. Ethoxyethane and methoxypropane are metamers. C…Some Basic Principles of Organic Chemistry
Q64In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar mass 32 g mol ⁻¹). Molar mass of barium…Purification and Characterisation of Organic Compounds
Q65An organic compound 'P' of molecular formula C₆H₁₂O₃ gives positive Iodoform test but negative Tollen's test. When 'P' is treated with dilute acid, it…Organic Compounds Containing Oxygen
Q6614.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K. Which of the following statements is incorrect ? [Given: Molar mass…Some Basic Concepts in Chemistry
Q67Identify the correct statements. A. Arginine and Tryptophan are essential amino acids. B. Histidine does not contain heterocyclic ring in its structure. C…Biomolecules
Q70Consider the following reactions. PbCl₂+K₂CrO₄→ A+2KCl (Hot solution); A+NaOH B+Na₂CrO₄; PbSO₄+4CH₃COONH₄→(NH₄)₂SO₄+X. In the above reactions, A, B and X are…Principles Related to Practical Chemistry
Q71The pH and conductance of a weak acid (HX) was found to be 5 and 4×10⁻⁵ S, respectively. The conductance was measured under standard condition using a cell…Redox Reactions and Electrochemistry
Q72Consider the following reactions: NaCl+K₂Cr₂O₇+H₂SO₄→ A+KHSO₄+NaHSO₄+H₂O; A+NaOH→ B+NaCl+H₂O; B+H₂SO₄+H₂O₂→ C+Na₂SO₄+H₂O. In the product 'C', 'X' is the…d- and f-Block Elements
Q73Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of…Chemical Kinetics
Q74Use the following data: Δ f H^ (500 K) / kJ mol ⁻¹ and S^ (500 K) / J K ⁻¹ mol ⁻¹: AB(g): 32, 222; A₂ (g): 6, 146; B₂ (g): x, 280. One mole each of A₂ (g) and…Chemical Thermodynamics
Q75Consider the following reaction sequence: Benzene conc. HNO₃+conc. H₂SO₄, 333 K P 1. Sn/HCl/Δ; 2. pH neutralised Q (CH₃CO)₂O R conc. HNO₃+conc. H₂SO₄ S (major…Organic Compounds Containing Nitrogen

Mathematics

Q1Let f:R→(0,∞) be a twice differentiable function such that f(3)=18, f'(3)=0 and f''(3)=4. Then lim x→1 (log e ((f(2+x))/(f(3)))^(18/((x-1)²))) is equal to:Limit, Continuity and Differentiability
Q2Let a=- i+2 j+2 k, b=8 i+7 j-3 k and c be a vector such that a× c= b. If c·(i+ j+ k)=4, then | a+ c|² is equal to:Vector Algebra
Q3If the domain of the function f(x)= cos ⁻¹((2x-5)/(11-3x))+ sin ⁻¹(2x²-3x+1) is the interval [α,β], then α+2β is equal to:Sets, Relations and Functions
Q4The sum of all the roots of the equation (x-1)²-5|x-1|+6=0, is:Complex Numbers and Quadratic Equations
Q5Let a₁,a₂,a₃, be a G.P. of increasing positive terms such that a₂· a₃· a₄=64 and a₁+a₃+a₅=813/7. Then a₃+a₅+a₇ is equal to:Sequence and Series
Q6If the coefficient of x in the expansion of (ax²+bx+c)(1-2x)²⁶ is -56 and the coefficients of x² and x³ are both zero, then a+b+c is equal to:Binomial Theorem and Its Simple Applications
Q7The area of the region, inside the ellipse x²+4y²=4 and outside the region bounded by the curves y=|x|-1 and y=1-|x|, is:Integral Calculus
Q8If x²+x+1=0, then the value of (x+1/x)⁴+(x²+1/(x²))⁴+(x³+1/(x³))⁴+ +(x²⁵+1/(x²⁵))⁴ is:Complex Numbers and Quadratic Equations
Q9Let PQ and MN be two straight lines touching the circle x²+y²-4x-6y-3=0 at the points A and B respectively. Let O be the centre of the circle and AOB=π/3…Coordinate Geometry
Q10The number of strictly increasing functions f from the set \1,2,3,4,5,6 to the set \1,2,3,,9 such that f(i)≠ i for 1≤ i≤6, is equal to:Permutations and Combinations
Q11Let O be the vertex of the parabola x²=4y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio…Coordinate Geometry
Q12Let c and d be vectors such that | c+ d|=√(29) and c×(2 i+3 j+4 k)=(2 i+3 j+4 k)× d. If λ₁,λ₂ (λ₁>λ₂) are the possible values of (c+ d)·(-7 i+2 j+3 k), then…Coordinate Geometry
Q13Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x>y, be 8 and 16 respectively. Two numbers are chosen from \1,2,3,x-4,y,5 one after…Statistics and Probability
Q14The number of relations, defined on the set,b,c,d, which are both reflexive and symmetric, is equal to:Sets, Relations and Functions
Q15Let the foci of a hyperbola coincide with the foci of the ellipse (x²)/36+(y²)/16=1. If the eccentricity of the hyperbola is 5, then the length of its latus…Coordinate Geometry
Q16Let y=y(x) be the solution curve of the differential equation (1+x²)dy+(y- tan ⁻¹x) dx=0, y(0)=1. Then the value of y(1) is:Differential Equations
Q17The value of ∫ -π/6 ^(π/6)((π+4x¹¹)/(1- sin (|x|+(π)/6)))dx is equal to:Integral Calculus
Q18Let a point A lie between the parallel lines L₁ and L₂ such that its distances from L₁ and L₂ are 6 and 3 units, respectively. Then the area (in sq. units) of…Coordinate Geometry
Q19The value of cosec 10°- 3 sec 10° is equal to:Trigonometry
Q20Let (α,β,γ) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4,2) on the line r=(- i+3 j+ k)+λ(2 i+3 j- k). Then the length of the…Three Dimensional Geometry
Q21Let a₁=1 and for n≥1, a n+1 =1/2a n +(n²-2n-1)/(n²(n+1)²). Then |Σ n=1 ^(∞)(a n -2/(n²))| is equal to _ _ _.Sequence and Series
Q22Let S=\(m,n):m,n \1,2,3,,50. If the number of elements (m,n) in S such that 6^(m)+9ⁿ is a multiple of 5 is p and the number of elements (m,n) in S such that…Permutations and Combinations
Q236∫₀^(π)| sin 3x+ sin 2x+ sin x| dx is equal to _ _ _.Integral Calculus
Q24For some α,β, let A= α 2 1 2 and B= 1 1 1 β be such that A²-4A+2I=B²-3B+I=O. Then (det (adj(A³-B³)))² is equal to _ _ _.Matrices and Determinants
Q25Let f:R be a twice differentiable function such that the quadratic equation f(x)m²-2f'(x)m+f''(x)=0 in m, has two equal roots for every x. If f(0)=1, f'(0)=2…Limit, Continuity and Differentiability