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JEE Main 2026 24 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202624 Jan, Morning shift

Physics 22Chemistry 18Mathematics 25

Physics

Q26Density of water at 4°C and 20°C are 1000 kg/m ³ and 998 kg/m ³ respectively. The increase in internal energy of 4 kg of water when it is heated from 4°C to…Thermodynamics
Q27Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger…Gravitation
Q29In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for…Optics
Q30A brass wire of length 2 m and radius 1 mm at 27°C is held taut between two rigid supports. Initially it was cooled to a temperature of -43°C creating a…Properties of Solids and Liquids
Q31Two electrons are moving in orbits of two hydrogen like atoms with speeds 3 × 10⁵ m/s and 2.5 × 10⁵ m/s respectively. If the radii of these orbits are nearly…Atoms and Nuclei
Q32A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece is _ _ _ N/m.Oscillations and Waves
Q33Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass…Rotational Motion
Q34Two resistors of 100 Ω each are connected in series with a 9 V battery. A voltmeter of 400 Ω resistance is connected to measure the voltage drop across one of…Current Electricity
Q35There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charge q₁, q₂ and q₃…Electrostatics
Q36Match the LIST-I with LIST-II. LIST-I: (A) Radio-wave; (B) Micro-wave; (C) Infrared-wave; (D) X-ray. LIST-II: (I) is produced by Magnetron valve; (II) due to…Electromagnetic Waves
Q37Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin is _ _ _.Electrostatics
Q38Given below are two statements: Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon. Statement II: For…Atoms and Nuclei
Q39The electrostatic potential in a charged spherical region of radius r varies as V = ar³ + b, where a and b are constants. The total charge in the sphere of…Electrostatics
Q40An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and 2√(3) (medium) respectively. To…Optics
Q41A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and…Oscillations and Waves
Q42A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on…Kinematics
Q43Match the LIST-I with LIST-II. LIST-I: (A) Magnetic induction; (B) Magnetic flux; (C) Magnetic permeability; (D) Self inductance. LIST-II: (I) [ MLT⁻²A⁻² ]…Units and Measurements
Q44The exit surface of a prism with refractive index n is coated with a material having refractive index n/2. When this prism is set for minimum angle of…Optics
Q45Two resistors 2 Ω and 3 Ω are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire…Current Electricity
Q48A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The…Electronic Devices
Q49Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger…Properties of Solids and Liquids
Q50A short bar magnet placed with its axis at 30° with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most…Magnetic Effects of Current and Magnetism

Chemistry

Q51Consider three metal chlorides x, y and z, where x is water soluble at room temperature, y is sparingly soluble in water at room temperature and z is soluble…Principles Related to Practical Chemistry
Q53Given below are two statements: Statement I: The number of paramagnetic species among [CoF₆]³⁻, [TiF₆]³⁻, V₂O₅ and [Fe(CN)₆]³⁻ is 3. Statement II: K₄[Fe(CN)₆]…Coordination Compounds
Q54A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute 'A' of molar mass 60 g mol ⁻¹ and 0.9 g of a non-volatile non-electrolyte…Solutions
Q55Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of NF₃ is higher than that of NH₃. B. The…Chemical Bonding and Molecular Structure
Q56The correct stability order of the following diazonium salts is (A) p-CH₃O-C₆H₄N₂⁺Cl^- (B) p-O₂N-C₆H₄N₂⁺Cl^- (C) C₆H₅N₂⁺Cl^- (D) p-NC-C₆H₄N₂⁺Cl^-Organic Compounds Containing Nitrogen
Q57Match the LIST-I with LIST-II. LIST-I (Chloro derivative): (A) Vinyl Chloride; (B) Benzyl Chloride; (C) Alkyl Chloride; (D) Allyl Chloride. LIST-II (Example)…Organic Compounds Containing Halogens
Q58Given below are two statements: Statement I: K > Mg > Al > B is the correct order in terms of metallic character. Statement II: Atomic radius is always…Classification of Elements and Periodicity in Properties
Q61Match the LIST-I with LIST-II. LIST-I (Isothermal process for ideal gas system): (A) Reversible expansion; (B) Free expansion; (C) Irreversible expansion; (D)…Chemical Thermodynamics
Q62'W' g of a non-volatile electrolyte solid solute of molar mass 'M' g mol ⁻¹ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg…Solutions
Q63Among the following, the CORRECT combinations are A. IF₃ → T-shaped (sp³d) B. IF₅ → Square pyramidal (sp³d²) C. IF₇ → Pentagonal bipyramidal (sp³d³) D. ClO₄^…Chemical Bonding and Molecular Structure
Q64Consider the following two reactions A and B. (A) C₆H₅OH Na Main Product + gas (x) (B) C₆H₅COOH NaHCO₃ Main Product + gas (y). Numerical value of [molar mass…Organic Compounds Containing Oxygen
Q65Consider a mixture 'X' which is made by dissolving 0.4 mol of [Co(NH₃)₅SO₄]Br and 0.4 mol of [Co(NH₃)₅Br]SO₄ in water to make 4 L of solution. When 2 L of…Coordination Compounds
Q67Arrange the following carbanions in the decreasing order of stability. I. p-Br-C₆H₄- C H₂ II. C₆H₅- C H₂ III. p-CH₃O-C₆H₄- C H₂ IV. p-CHO-C₆H₄- C H₂ V…Some Basic Principles of Organic Chemistry
Q69At 27°C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol ⁻¹. The logarithm of ratio of (k(catalysed))/(k(uncatalysed))…Chemical Kinetics
Q70A hydroxy compound (X) with molar mass 122 g mol ⁻¹ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of…Organic Compounds Containing Oxygen
Q71The hydrogen spectrum consists of several spectral lines in Lyman series (L₁, L₂, L₃; L₁ has lowest energy among Lyman series). Similarly it consists of…Atomic Structure
Q72Electricity is passed through an acidic solution of Cu²⁺ till all the Cu²⁺ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current…Redox Reactions and Electrochemistry
Q75Consider two Group IV metal ions X²⁺ and Y²⁺. A solution containing 0.01 M X²⁺ and 0.01 M Y²⁺ is saturated with H₂S. The pH at which the metal sulphide YS…Equilibrium

Mathematics

Q1If cot x = 5/12 for some x (π, (3π)/2), then sin 7x(cos 13x/2 + sin 13x/2) + cos 7x(cos 13x/2 - sin 13x/2) is equal toTrigonometry
Q2Let A(1, 0), B(2, -1) and C(7/3, 4/3) be three points. If the equation of the bisector of the angle ABC is α x + β y = 5, then the value of α² + β² isCoordinate Geometry
Q3Consider an A.P.: a₁, a₂,, a n; a₁ > 0. If a₂ - a₁ = (-3)/4, a n = 1/4a₁, and Σ i=1 ⁿ a i = 525/2, then Σ i=1 ¹⁷ a i is equal toSequence and Series
Q4Let α, β R be such that the function f(x) = 2α(x² - 2) + 2β x, x < 1 (α + 3)x + (α - β), x ≥ 1 be differentiable at all x R. Then 34(α + β) is equal toLimit, Continuity and Differentiability
Q5Let a = 2i + j - 2k, b = i + j and c = a × b. Let d be a vector such that |d - a| = √(11), |c × d| = 3 and the angle between c and d is (π)/4. Then a · d is…Vector Algebra
Q6Let R be a relation defined on the set \1, 2, 3, 4 × \1, 2, 3, 4 by R = \((a, b), (c, d)): 2a + 3b = 3c + 4d. Then the number of elements in R isSets, Relations and Functions
Q7If the function f(x) = (eˣ(e^(tan x - x) - 1) + log e (sec x + tan x) - x)/(tan x - x) is continuous at x = 0, then the value of f(0) is equal toLimit, Continuity and Differentiability
Q8Let a circle of radius 4 pass through the origin O, the points A(-√(3)a, 0) and B(0, -√(2)b), where a and b are real parameters and ab ≠ 0. Then the locus of…Coordinate Geometry
Q9Let each of the two ellipses E₁: (x²)/(a²) + (y²)/(b²) = 1, (a > b) and E₂: (x²)/(A²) + (y²)/(B²) = 1, (A < B) have eccentricity 4/5. Let the lengths of the…Coordinate Geometry
Q10Let the lines L₁: r = i + 2j + 3k + λ(2i + 3j + 4k), λ R and L₂: r = (4i + j) + μ(5i + 2j + k), μ R, intersect at the point R. Let P and Q be the points lying…Three Dimensional Geometry
Q11Let S = 1/(25!) + 1/(3! 23!) + 1/(5! 21!) + up to 13 terms. If 13S = (2^(k))/(n!), k N, then n + k is equal toBinomial Theorem and Its Simple Applications
Q12If the domain of the function f(x) = log (10x² - 17x + 7) (18x² - 11x + 1) is (-∞, a) (b, c) (d, ∞) -, then 90(a + b + c + d + e) equals:Sets, Relations and Functions
Q13Let A₁ be the bounded area enclosed by the curves y = x² + 2, x + y = 8 and y -axis that lies in the first quadrant. Let A₂ be the bounded area enclosed by…Integral Calculus
Q14Let 729, 81, 9, 1, be a sequence and P n denote the product of the first n terms of this sequence. If 2Σ n=1 ⁴⁰ (P n)^(1/n) = (3^α - 1)/(3^β) and gcd (α, β) =…Sequence and Series
Q15Let f(t) = ∫ ((1 - sin (log e t))/(1 - cos (log e t)))dt, t > 1. If f(e^(π/2)) = -e^(π/2) and f(e^(π/4)) = α e^(π/4), then α equalsIntegral Calculus
Q16The number of the real solutions of the equation: x|x + 3| + |x - 1| - 2 = 0 isComplex Numbers and Quadratic Equations
Q17From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7…Statistics and Probability
Q18The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation α in this data is replaced by β, then the mean and variance…Statistics and Probability
Q19Let S = C: |(z - 6i)/(z - 2i)| = 1 and |(z - 8 + 2i)/(z + 2i)| = 3/5. Then Σ z S |z|² is equal toComplex Numbers and Quadratic Equations
Q20The value of (√(3) cosec 20° - sec 20°)/(cos 20° cos 40° cos 60° cos 80°) is equal toTrigonometry
Q21Let a differentiable function f satisfy the equation ∫₀³⁶ f(tx/36)dt = 4α f(x). If y = f(x) is a standard parabola passing through the points (2, 1) and (-4…Integral Calculus
Q22The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits…Permutations and Combinations
Q23The number of 3 × 2 matrices A, which can be formed using the elements of the set \-2, -1, 0, 1, 2 such that the sum of all the diagonal elements of A^(T)A is…Matrices and Determinants
Q24Let (2α, α) be the largest interval in which the function f(t) = (|t + 1|)/(t²), t < 0, is strictly decreasing. Then the local maximum value of the function…Limit, Continuity and Differentiability
Q25Let a line L passing through the point P(1, 1, 1) be perpendicular to the lines (x - 4)/4 = (y - 1)/1 = (z - 1)/1 and (x - 17)/1 = (y - 71)/1 = z/0. Let the…Three Dimensional Geometry