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JEE Main 2026 22 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202622 Jan, Morning shift

Physics 14Chemistry 22Mathematics 25

Physics

Q27A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the…Electrostatics
Q28A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair…Rotational Motion
Q30Match the LIST-I with LIST-II. LIST-I: A. Spring constant; B. Thermal conductivity; C. Boltzmann constant; D. Inductive reactance. LIST-II: I. ML²T⁻²K⁻¹; II…Units and Measurements
Q31Electric field in a region is given by E=Axi+Byj, where A=10 V/m² and B=5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric…Electrostatics
Q33Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere…Properties of Solids and Liquids
Q36The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is…Gravitation
Q38The volume of an ideal gas increases 8 times and temperature becomes (1/4)^(th) of initial temperature during a reversible change. If there is no exchange of…Thermodynamics
Q40Consider an equilateral prism (refractive index 2). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze…Optics
Q41A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the…Kinematics
Q42The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 α particles is _ _ _ kHz. [mass of He nucleus = 4.002 amu, 1 amu…Atoms and Nuclei
Q43Three identical coils C₁, C₂ and C₃ are closely placed such that they share a common axis. C₂ is exactly midway. C₁ carries current I in anti-clockwise…Electromagnetic Induction and Alternating Currents
Q46The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, E y =20 sin (3×10⁶x-4.5×10¹⁴t) V/m (where x, t…Electromagnetic Waves
Q48A circular disc has radius R₁ and thickness T₁. Another circular disc made of the same material has radius R₂ and thickness T₂. If the moment of inertia of…Rotational Motion
Q49A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive…Optics

Chemistry

Q52Given below are two statements: Statement I: The Henry's law constant K H is constant with respect to variations in solution's concentration over the range…Solutions
Q53The correct order of reactivity of CH₃Br in methanol with the following nucleophiles is F^-, I^-, C₂H₅O^(- a)nd C₆H₅O^-Organic Compounds Containing Halogens
Q54Given below are two statements: Statement I: The halogen that makes longest bond with hydrogen in HX, has the smallest covalent radius in its group. Statement…p-Block Elements
Q55Given below are two statements: Statement I: Sucrose is dextrorotatory. However, sucrose upon hydrolysis gives a solution having mixture of products. This…Biomolecules
Q56In the reaction, 2Al(s)+6HCl(aq)→ 2Al³⁺(aq)+6Cl^-(aq)+3H₂(g)Some Basic Concepts in Chemistry
Q57A→ product (First order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions: Run 1 ⇒ 100 mL of 10 M…Chemical Kinetics
Q58Match the LIST-I (Reagents) with LIST-II (Name of Reaction involving carbonyl compounds). LIST-I: A. NH₂-NH₂, KOH; B. Ag(NH₃)₂OH; C. Aq. CuSO₄, Sodium…Organic Compounds Containing Oxygen
Q59A first row transition metal (M) does not liberate H₂ gas from dilute HCl. 1 mol of aqueous solution of MSO₄ is treated with excess of aqueous KCN and then…Coordination Compounds
Q60Match the LIST-I (Thermodynamic Process) with LIST-II (Magnitude in kJ). LIST-I: A. Work done in reversible, isothermal expansion of 2 mol of ideal gas from 2…Chemical Thermodynamics
Q61Given below are two statements: Statement I: Phenol on treatment with CHCl₃ /aq. KOH under refluxing condition, followed by acidification produces p -hydroxy…Organic Compounds Containing Oxygen
Q62A 'p'-block element (E) and hydrogen form a binary cation (EH x)⁺, while EH₃ on treatment with K₂HgI₄ in alkaline medium gives a precipitate of basic…p-Block Elements
Q65As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene? A. The magnitude of negative charge is more on…Organic Compounds Containing Halogens
Q66Consider the transition metal ions Mn³⁺, Cr³⁺, Fe³⁺ and Co³⁺ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in…Coordination Compounds
Q67Given below are two statements: Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with CH₃COCl/AlCl₃ will give…Hydrocarbons
Q68Two p-block elements X and Y form fluorides of the type EF₃. The fluoride compound XF₃ is a Lewis acid and YF₃ is a Lewis base. The hybridizations of the…Chemical Bonding and Molecular Structure
Q69The formal charges on the atoms marked as (1) to (4) in the Lewis representation of HNO₃ molecule respectively are [Lewis structure: H- O (1)-N(2)=O(3) with…Chemical Bonding and Molecular Structure
Q70The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is _ _ _ J mol⁻¹. Given: R H =2.18×10⁻¹¹…Atomic Structure
Q71The temperature at which the rate constants of the given below two gaseous reactions become equal is _ _ _ K. (Nearest integer) X→ Y, k₁=10⁶e^(-30000/T); P→…Chemical Kinetics
Q72Sodium fusion extract of an organic compound (Y) with CHCl₃ and chlorine water gives violet color to the CHCl₃ layer. 0.15g of (Y) gave 0.12 g of the silver…Purification and Characterisation of Organic Compounds
Q73Dissociation of a gas A₂ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1 bar at 300K. A₂(g) 2A(g). The…Equilibrium
Q74The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C:Br ratio is 3:1. The percentage of…Hydrocarbons
Q75Consider the following electrochemical cell at 298K: Pt|HSnO₂^-(aq)|Sn(OH)₆²⁻(aq)|OH^-(aq)|Bi₂O₃(s)|Bi(s). If the reaction quotient at a given time is 10⁶…Redox Reactions and Electrochemistry

Mathematics

Q1If the chord joining the points P₁(x₁, y₁) and P₂(x₂, y₂) on the parabola y² = 12x subtends a right angle at the vertex of the parabola, then x₁x₂ - y₁y₂ is…Coordinate Geometry
Q2If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms isSequence and Series
Q3If the domain of the function f(x)= sin ⁻¹((5-x)/(3+2x))+1/(log e (10-x)) is (-∞, α] [β, γ)-\δ, then 6(α+β+γ+δ) is equal toSets, Relations and Functions
Q4The coefficient of x⁴⁸ in (1+x)+2(1+x)²+3(1+x)³+ +100(1+x)¹⁰⁰ is equal toBinomial Theorem and Its Simple Applications
Q5Let AB=2i+4j-5k and AD=i+2j+, λ. Let the projection of the vector v=i+j+k on the diagonal AC of the parallelogram ABCD be of length one unit. If α, β, where…Vector Algebra
Q6Let the relation R on the set M=\1, 2, 3,, 16 be given by R=\(x, y): 4y=5x-3, x, y. Then the minimum number of elements required to be added in R, in order to…Sets, Relations and Functions
Q7If the line α x+2y=1, where α, does not meet the hyperbola x²-9y²=9, then a possible value of α is:Coordinate Geometry
Q8Let the set of all values of r, for which the circles (x+1)²+(y+4)²=r² and x²+y²-4x-2y-4=0 intersect at two distinct points be the interval (α, β). Then αβ is…Coordinate Geometry
Q9The number of distinct real solutions of the equation x|x+4|+3|x+2|+10=0 isComplex Numbers and Quadratic Equations
Q10If a random variable x has the probability distribution [Table — x: 0, 1, 2, 3, 4, 5, 6, 7; P(x): 0, 2k, k, 3k, 2k², 2k, k²+k, 7k² ] then P(3<x≤ 6) is equal toStatistics and Probability
Q11Let f(x)=x²⁰²⁵-x²⁰⁰⁰, x [0, 1] and the minimum value of the function f(x) in the interval [0, 1] be (80)⁸⁰(n)⁻⁸¹. Then n is equal toLimit, Continuity and Differentiability
Q12Let the line x=-1 divide the area of the region \(x, y): 1+x²≤ y≤ 3-x in the ratio m:n, gcd (m, n)=1. Then m+n is equal toIntegral Calculus
Q13Let f:[1, ∞) be a differentiable function. If 6∫₁ˣ f(t) dt=3xf(x)+x³-4 for all x≥ 1, then the value of f(2)-f(3) isDifferential Equations
Q14Two distinct numbers a and b are selected at random from 1, 2, 3,, 50. The probability, that their product ab is divisible by 3, isStatistics and Probability
Q15If A= 2 3 3 5, then the determinant of the matrix (A²⁰²⁵-3A²⁰²⁴+A²⁰²³) isMatrices and Determinants
Q16The number of solutions of tan ⁻¹4x+ tan ⁻¹6x=(π)/6, where -1/(2 6)<x<1/(2 6), is equal toTrigonometry
Q17Let the solution curve of the differential equation x dy-y dx=√(x²+y²) dx, x>0, y(1)=0, be y=y(x). Then y(3) is equal toDifferential Equations
Q18Let P(α, β, γ) be the point on the line (x-1)/2=(y+1)/(-3)=z at a distance 4√(14) from the point (1, -1, 0) and nearer to the origin. Then the shortest…Three Dimensional Geometry
Q19If the image of the point P(1, 2, a) in the line (x-6)/3=(y-7)/2=(7-z)/2 is Q(5, b, c), then a²+b²+c² is equal toThree Dimensional Geometry
Q20The value of ∫ -(π)/2 ^((π)/2)(1/([x]+4))dx, where [·] denotes the greatest integer function, isIntegral Calculus
Q21If (cos ² 48°- sin ² 12°)/(sin ² 24°- sin ² 6°)=(α+β 5)/2, where α, β, then α+β is equal toTrigonometry
Q22Let α=(-1+i 3)/2 and β=(-1-i 3)/2, i=√(-1). If (7-7α+9β)²⁰+(9+7α-7β)²⁰+(-7+9α+7β)²⁰+(14+7α+7β)²⁰=m¹⁰, then m isComplex Numbers and Quadratic Equations
Q23If ∫(sin x)^(-11/2)(cos x)^(-5/2) dx=-p₁/q₁(cot x)^(9/2)-p₂/q₂(cot x)^(5/2)-p₃/q₃(cot x)^(1/2)+p₄/q₄(cot x)^(-3/2)+C, where p i and q i are positive integers…Integral Calculus
Q24Let A be a 3×3 matrix such that A+A^(T)=O. If A 1 -1 0 = 3 3 2, A² 1 -1 0 = -3 19 -24 and det (adj(2 adj(A+I)))=(2)^(α)·(3)^(β)·(11)^(γ), α, β, γ are…Matrices and Determinants
Q25Let ABC be a triangle. Consider four points p₁, p₂, p₃, p₄ on the side AB, five points p₅, p₆, p₇, p₈, p₉ on the side BC, and four points p₁₀, p₁₁, p₁₂, p₁₃…Permutations and Combinations