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JEE Main 2026 4 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20264 Apr, Morning shift

Physics 17Chemistry 21Mathematics 24

Physics

Q26In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least…Experimental Skills
Q27The increase in the pressure required to decrease the volume (Δ V) of water is 6.3×10⁷ N/m ². The percentage decrease in the volume is _ _ _. (Bulk modulus of…Properties of Solids and Liquids
Q28The time taken by a block of mass m to slide down from the highest point to the lowest point on a rough inclined plane is 50% more compared to the time taken…Laws of Motion
Q29Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass…Atoms and Nuclei
Q30A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the…Rotational Motion
Q31The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The…Kinematics
Q33A slit of width a is illuminated by light of wavelength λ. The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen…Optics
Q34A string A of length 0.314 m and Young's modulus 2×10¹⁰ N/m ² is connected to another string B of length and Young's modulus both twice of those of A. This…Properties of Solids and Liquids
Q35One gas of n₁ mole of molecules at temperature T₁, volume V₁, and pressure P₁, and another gas of n₂ mole of molecules at temperature T₂, volume V₂, and…Kinetic Theory of Gases
Q37A voltmeter with internal resistance of x Ω can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is…Current Electricity
Q40A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any…Electrostatics
Q41An insulated wire is wound so that it forms a flat coil with N=200 turns. The radius of the innermost turn is r₁=3 cm, and of the outermost turn r₂=6 cm. If…Magnetic Effects of Current and Magnetism
Q44A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of 5×10⁻⁷ radian. The value of R…Optics
Q46A 1 kg block subjected to two simultaneous forces (2i+3j+4k) N and (3i-j-2k) N is moved a distance of 25 m along (3i-4j) direction. The work done in this…Work, Energy and Power
Q47The surface tension of a soap solution is 3.5×10⁻² N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is α×10⁻⁶ J. The value of…Properties of Solids and Liquids
Q48The velocity of a particle executing simple harmonic motion along x -axis is described as v²=50-x², where x represents displacement. If the time period of…Oscillations and Waves
Q49A body of mass 2 kg begins to move under the influence of time dependent force F=(2ti+6t²j) N, where i and j are unit vectors along x and y -axis…Work, Energy and Power

Chemistry

Q51Number of moles and number of molecules in 1.4187 L of SO₂ at STP respectively areSome Basic Concepts in Chemistry
Q52What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?Atomic Structure
Q53Which of the following is correct set of 4 quantum numbers of 19th electron in Chromium (Atomic number =24) in accordance with Aufbau principle?Atomic Structure
Q54Given below are two statements: Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure…Chemical Thermodynamics
Q55At T(K), the equilibrium constant of A₂(g)+B₂(g) C(g) is 2.7×10⁻⁵. What is the equilibrium constant for 1/3A₂(g)+1/3B₂(g) 1/3C(g) at the same temperature?Equilibrium
Q56In order to oxidise a mixture of 1 mole each of FeC₂O₄, Fe₂(C₂O₄)₃, FeSO₄ and Fe₂(SO₄)₃ in acidic medium, the number of moles of KMnO₄ required isRedox Reactions and Electrochemistry
Q57Consider the first order reaction R→ P. The fraction of molecules decomposed in the given first order reaction can be expressed asChemical Kinetics
Q58A monoatomic anion (A^-) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A)…Classification of Elements and Periodicity in Properties
Q59Given below are two statements: Statement I: The covalency of oxygen is generally two but it can exceed upto four. The oxidation state of oxygen in SO₂ is -2…p-Block Elements
Q60The correct statements among the following are, A. Mo(VI) and W(VI) are less stable than Cr(VI). B. Ce⁴⁺ and Tb⁴⁺ are oxidant while Eu²⁺ and Yb²⁺ are…d- and f-Block Elements
Q61Correct statements from the following are A. Potassium dichromate is an oxidising agent and it oxidises FeSO₄ to Fe₂(SO₄)₃ in acidic medium. B. Sodium…d- and f-Block Elements
Q62Match the LIST-I with LIST-II. LIST-I (Complex ion): A. [Cr(H₂O)₆]²⁺ B. [Co(H₂O)₆]²⁺ C. [Cu(H₂O)₆]²⁺ D. [Mn(H₂O)₆]²⁺. LIST-II (Calculated spin only magnetic…Coordination Compounds
Q63Increasing order of electron withdrawing power of following functional groups is: a. -CN b. -COOH c. -NO₂ d. -ISome Basic Principles of Organic Chemistry
Q65Match the LIST-I with LIST-II. LIST-I (Name of reaction): A. Finkelstein reaction B. Swarts reaction C. Sandmeyer's reaction D. Fittig reaction. LIST-II…Organic Compounds Containing Halogens
Q67Product C of the following reaction sequence will be: aniline Br₂/water A (Major product) NaNO₂/HCl, 273-278 K B (i) HBF₄ (ii) NaNO₂,Cu,Δ COrganic Compounds Containing Nitrogen
Q69Match the LIST-I with LIST-II. LIST-I (Name of amino acid): A. Arginine B. Aspartic acid C. Lysine D. Glutamic acid. LIST-II (One letter symbol/type): I…Biomolecules
Q71According to Lewis theory, the total number of σ bond-pairs and lone pair of electrons around the central atom of XeO₆⁴⁻ ion is _ _ _.Chemical Bonding and Molecular Structure
Q72Consider the following sequence of reactions to give the major product (X): benzene (i) CH₃Cl/anhydrous AlCl₃ (ii) Cl₂/FeCl₃ (iii) K₂Cr₂O₇/H₂SO₄ (X) Major…Organic Compounds Containing Oxygen
Q732.0 g of a bromo hydrocarbon (X) was subjected to Carius analysis, gave 3.36 g of AgBr. The percentage of carbon in the compound (X) is 26.7%. Total number of…Purification and Characterisation of Organic Compounds
Q74The pH of a solution obtained by mixing 5 mL of 0.1 M NH₄OH solution with 250 mL of 0.1 M NH₄Cl solution is _ _ _ ×10⁻². (Nearest integer) Given: pK b…Equilibrium
Q75A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased from 760 mm Hg to 750 mm Hg. If…Solutions

Mathematics

Q1Let [·] denote the greatest integer function. If the domain of the function f(x)= cos ⁻¹((4x+2[x])/3) is [α, β], then 12(α+β) is equal to:Sets, Relations and Functions
Q2If the set of all solutions of |x²+x-9|=|x|+|x²-9| is [α, β] [γ, ∞), then (α²+β²+γ²) is equal to:Complex Numbers and Quadratic Equations
Q3Let z be a complex number such that |z+2|=|z-2| and arg ((z+3)/(z-i))=(π)/4. Then |z|² is equal to:Complex Numbers and Quadratic Equations
Q4The number of functions f:\1,2,3,4\→,b,c, which are not onto, is:Sets, Relations and Functions
Q5Let S= = a b c d: a,b,c,d \0,1,2,3,4 and A²-4A+3I=0 be a set of 2×2 matrices. Then the number of matrices in S, for which the sum of the diagonal elements is…Matrices and Determinants
Q6Let A= 1 1 2 -2 0 1 1 3 5. Then the sum of all elements of the matrix adj(adj(2(adjA)⁻¹)) is equal to:Matrices and Determinants
Q7The first term of an A.P. of 30 non-negative terms is 10/3. If the sum of this A.P. is the cube of its last term, then its common difference is:Sequence and Series
Q8The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:Permutations and Combinations
Q9Let the smallest value of k, for which the coefficient of x³ in (1+x)³+(1+x)⁴+(1+x)⁵+ +(1+x)⁹⁹+(1+kx)¹⁰⁰, x≠0, is (43n+101/4)(¹⁰⁰C₃) for some n, be p. Then…Binomial Theorem and Its Simple Applications
Q10Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a>b), are 40 and 21, respectively. If the mean deviation about…Statistics and Probability
Q11Let the line L₁: x+3=0 intersect the lines L₂: x-y=0 and L₃: 3x+y=0 at the points A and B, respectively. Let the bisector of the obtuse angle between the…Coordinate Geometry
Q12Let the vertex A of a triangle ABC be (1,2), and the mid-point of the side AB be (5,-1). If the centroid of this triangle is (3,4) and its circumcenter is…Coordinate Geometry
Q13Suppose that two chords, drawn from the point (1,2) on the circle x²+y²+x-3y=0 are bisected by the y -axis. If the other ends of these chords are R and S, and…Coordinate Geometry
Q14A line with direction ratios 1,-1,2 intersects the lines x/2=y/3=(z+1)/3 and (x+1)/(-1)=(y-2)/1=z/4 at the points P and Q, respectively. If the length of the…Three Dimensional Geometry
Q15The square of the distance of the point (-2,-8,6) from the line (x-1)/1=(y-1)/2=z/(-1) along the line (x+5)/1=(y+5)/(-1)=z/2 is equal to:Three Dimensional Geometry
Q16If y= tan ⁻¹((3 cos x-4 sin x)/(4 cos x+3 sin x))+2 tan ⁻¹(x/(1+√(1-x²))), then dy/dx at x=(3)/2 is equal to:Limit, Continuity and Differentiability
Q17Let f be a real polynomial of degree n such that f(x)=f'(x)f''(x), for all x. If f(0)=0, then 36(f'(2)+f''(2)+∫₀² f(x) dx) is equal to:Limit, Continuity and Differentiability
Q18The area of the region \(x,y): y≤π-|x|, y≤|x sin x|, y≥0 is:Integral Calculus
Q19Let ∫₋₂²(| sin x|+[x sin x])dx=2(3- cos 2)+β, where [·] is the greatest integer function. Then β sin ((β)/2) equals:Integral Calculus
Q21A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p, then…Statistics and Probability
Q22Consider the parabola P: y²=4kx and the ellipse E: (x²)/(a²)+(y²)/(b²)=1. Let the line segment joining the points of intersection of P and E, be their latus…Coordinate Geometry
Q23If A=(sin 3°)/(cos 9°)+(sin 9°)/(cos 27°)+(sin 27°)/(cos 81°) and B= tan 81°- tan 3°, then B/A is equal to _ _ _.Trigonometry
Q24Let a k =(tan θ k)i+j and b k =i-(cot θ k)j, where θ k =(2^(k-1)π)/(2ⁿ+1), for some n, n>5. Then the value of (Σ k=1 ⁿ|a k |²)/(Σ k=1 ⁿ|b k |²) is _ _ _.Vector Algebra
Q25The number of points, at which the function f(x)= max \6x, 2+3x²\+|x-1| cos |x²-1/4|, x (-π,π), is not differentiable, is _ _ _.Limit, Continuity and Differentiability