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JEE Main 2026 6 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20266 Apr, Morning shift

Physics 19Chemistry 22Mathematics 25

Physics

Q26The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42±0.02 g…Units and Measurements
Q27The potential energy of a particle changes with distance x from a fixed origin as V=(A x)/(x+B), where A and B are constant with appropriate dimensions. The…Units and Measurements
Q28The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive…Work, Energy and Power
Q30A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4×10⁸ N/m² and its radius is 4 mm, then maximum…Properties of Solids and Liquids
Q31A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It…Rotational Motion
Q32A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force…Work, Energy and Power
Q34The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When…Properties of Solids and Liquids
Q35Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the…Kinetic Theory of Gases
Q36In interference experiment the path difference between two interfering waves at a point A on the screen is λ/3, where λ is the wavelength of these waves, and…Optics
Q37A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x=A to x=A/(2) is _ _ _ _ sec.Oscillations and Waves
Q38A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is…Electrostatics
Q40A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as I₀. The detector is now shifted to…Electromagnetic Waves
Q42A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is…Magnetic Effects of Current and Magnetism
Q43An inductor of inductance 10 mH having resistance of 100 Ω is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch…Electromagnetic Induction and Alternating Currents
Q44The ratio of momentum of the photons of the 1^(st) and 2^(nd) line of Balmer series of Hydrogen atoms is α/β. The possible values of α and β are:-Atoms and Nuclei
Q45A LCR series circuit driven with E rms =90 V at frequency f d =30 Hz has resistance R=80 Ω, an inductance with inductive reactance X L =20.0 Ω and capacitance…Electromagnetic Induction and Alternating Currents
Q47An unpolarized light of intensity I₀ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the…Optics
Q48The energy released when 7/17.13 kg of ⁷₃Li is converted into ⁴₂He by proton bombardment is α×10³² eV. The value of α is _ _. (Nearest integer) (Mass of…Atoms and Nuclei
Q49A three coulomb charge moves from the point (0,-2,-5) to the point (5,1,2) in an electric field expressed as E=2x i+3y² j+4 k N/C. The work done in moving the…Electrostatics

Chemistry

Q51An oxide of iron contains 69.9% iron, its empirical formula, is: (Given: Molar mass of Fe and O are 56 and 16 g mol ⁻¹ respectively.)Some Basic Concepts in Chemistry
Q52If shortest wavelength of hydrogen atom in Lyman series is x, then longest wavelength in Balmer series of He⁺ is:Atomic Structure
Q53Match the LIST-I with LIST-II. List-I (Orbital): A. 2s; B. 3s; C. 3p; D. 4d. List-II (Radial nodes and nodal plane): I. 1 Radial node + two nodal planes; II…Atomic Structure
Q54The pairs among A=[ SO₃²⁻,CO₃²⁻ ], B=[ O₂²⁻,F₂ ], C=[CN^-,CO], D=[NH₃,H₃O⁺] and E=[ MnO₄²⁻,CrO₄²⁻ ] that do not have similar Lewis dot structure areChemical Bonding and Molecular Structure
Q55Arrange the following isothermal processes in order of the magnitude of the work (p - V) involved between states 1 and 2. A. Expansion in single stage w A; B…Chemical Thermodynamics
Q56When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was x% of vapor pressure of pure…Solutions
Q57One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium. A(g) B(g). K c for this reaction at…Equilibrium
Q59Given below are two statements: Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of E°_ Al³⁺/Al is…p-Block Elements
Q60The correct statements among the following are. A. Basic vanadium oxide is used in the manufacture of H₂SO₄. B. The spin-only magnetic moment value of the…d- and f-Block Elements
Q61Match the LIST-I with LIST-II. List-I (Electronic configuration of tetrahedral metal ion): A. d²; B. d⁴; C. d⁶; D. d⁸. List-II (Crystal Field Stabilization…Coordination Compounds
Q62Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex? A. d xy =d xz >d x²-y²; B. d xy =d yz >d z²; C. d x²-y² >d…Coordination Compounds
Q63R f value for 2-methylpropene in a solvent system (Ethyl acetate + ether) is 0.42. 2-methylpropene is treated with dilute H₂SO₄ to give major organic product…Purification and Characterisation of Organic Compounds
Q64Given below are two statements: Statement I: 2,6-diethylcyclohexanone and 6-methyl-2-n-propylcyclohexanone are metamers. Statement II…Some Basic Principles of Organic Chemistry
Q65Given below are two statements: Statement I: Methane can be prepared by decarboxylation of sodium ethanoate, Kolbe's electrolysis of sodium acetate and…Hydrocarbons
Q68Arrange the following compounds according to increasing order of boiling points. n-C₄H₉OH (A), n-C₄H₉NH₂ (B), n-C₄H₁₀ (C) and C₂H₅NHC₂H₅ (D).Organic Compounds Containing Nitrogen
Q69Match the LIST-I with LIST-II. List-I (Deficiency Disease): A. Scurvy; B. Convulsions; C. Cheilosis; D. Xerophthalmia. List-II (Vitamin): I. Pyridoxine; II…Biomolecules
Q70Match the LIST-I with LIST-II. List-I (Amino acid): A. Glutamine; B. Lysine; C. Tyrosine; D. Serine. List-II (Positive reaction/Test for functional group…Biomolecules
Q71First and second ionization enthalpies of lithium are 520 kJ mol ⁻¹ and 7297 kJ mol ⁻¹ respectively. Energy required to convert 3.5 mg lithium (g) into…Classification of Elements and Periodicity in Properties
Q72Consider the following sequence of reactions. C₆H₅-N = N - NH - C₆H₅ (i) HCl, (ii) Aniline (in excess), (iii) Warm 40–45°C, (iv) Cool, acetic acid Yellow…Organic Compounds Containing Nitrogen
Q734.7 g of phenol is heated with Zn to give product X. If this reaction goes to 60% completion then the number of moles of compound X formed will be _ _ ×10⁻²…Organic Compounds Containing Oxygen
Q74Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with t 1/2 =3 hour. The percentage of sucrose remaining after 6 hours is…Chemical Kinetics
Q75Consider the reaction X Y at 300 K. If Δ H^θ and K are 28.40 kJ mol ⁻¹ and 1.8×10⁻⁷ at the same temperature, then the magnitude of Δ S^θ for the reaction in J…Chemical Thermodynamics

Mathematics

Q1Let [·] denote the greatest integer function. If the domain of the function f(x)= sin ⁻¹((x+[x])/3) is [α,β), then α²+β² is equal to:Sets, Relations and Functions
Q2Let one root of the quadratic equation in x: (k²-15k+27)x²+9(k-1)x+18=0 be twice the other. Then the length of the latus rectum of the parabola y²=6kx is…Complex Numbers and Quadratic Equations
Q3Let e₁ and e₂ be two distinct roots of the equation x²-ax+2=0. Let the sets: e₁ and e₂ are the eccentricities of hyperbolas \=(α,β), and: e₁ and e₂ are the…Coordinate Geometry
Q4Let the set of all values of k such that the equation z(z+2+i)+k(2+3i)=0, z, has at least one solution, be the interval [α,β]. Then 9(α+β) is equal to:Complex Numbers and Quadratic Equations
Q5The value of 1³-2³+3³- +15³ is:Sequence and Series
Q6The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio…Sequence and Series
Q7The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word…Permutations and Combinations
Q8If the coefficients of the middle terms in the binomial expansions of (1+α x)²⁶ and (1-α x)²⁸, α≠0, are equal, then the value of α is:Binomial Theorem and Its Simple Applications
Q9A data consists of 20 observations x₁,x₂,,x₂₀. If Σ i=1 ²⁰(x i +5)²=2500 and Σ i=1 ²⁰(x i -5)²=100, then the ratio of mean to standard deviation of this data…Statistics and Probability
Q10A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting…Statistics and Probability
Q11If the eccentricity e of the hyperbola (x²)/(a²)-(y²)/(b²)=1, passing through (6,4 3), satisfies 15(e²+1)=34e, then the length of the latus rectum of the…Coordinate Geometry
Q12Let chord PQ of length 3√(13) of the parabola y²=12x be such that the ordinates of points P and Q are in the ratio 1:2. If the chord PQ subtends an angle α at…Coordinate Geometry
Q13Let 0<α<1, β=1/(3α) and tan ⁻¹(1-α)+ tan ⁻¹(1-β)=(π)/4. Then 6(α+β) is equal to:Trigonometry
Q14Let S=\θ (-2π,2π): cos θ+1= 3 sin θ. Then Σ θ S θ is equal to:Trigonometry
Q15Let the image of the point P(1,6,a) in the line L:x/1=(y-1)/2=(z-a+1)/b, b>0, be (a/3,0,a+c). If S(α,β,γ), α>0, is the point on L such that the distance of S…Three Dimensional Geometry
Q16Let a line L be perpendicular to both the lines L₁:(x+1)/3=(y+3)/5=(z+5)/7 and L₂:(x-2)/1=(y-4)/4=(z-6)/7. If θ is the acute angle between the lines L and…Three Dimensional Geometry
Q17The value of lim x→0 ((x² sin ²x)/(x²- sin ²x)) is:Limit, Continuity and Differentiability
Q18The value of the integral ∫ -π/4 ^(π/4)((32 cos ⁴x)/(1+e^(sin x)))dx is:Integral Calculus
Q19The area of the region \(x,y):0≤ y≤ 6-x, y²≥ 4x-3, x≥0 is:Integral Calculus
Q20Let e be the base of natural logarithm and let f:\1,2,3,4\→\1,e,e²,e³ and g:\1,e,e²,e³\→\1,1/2,1/3,1/4 be two bijective functions such that f is strictly…Integral Calculus
Q21Let A= -1 1 -1 1 0 1 0 0 1 satisfy A²+α(adj(adj(A)))+β(adj(A)(adj(adj(A))))= 2 -2 2 -2 0 -1 0 0 -1 for some α,β. Then (α-β)² is equal to _ _ _ _Matrices and Determinants
Q22Let the centre of the circle x²+y²+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x-y=4. Let the area of an equilateral triangle inscribed in the…Coordinate Geometry
Q23If a= i+ j+ k, b= j- k and c be three vectors such that a× c= b and a· c=3, then c·(a-2 b) is equal to _ _ _ _.Vector Algebra
Q24For the functions f(θ)=α tan ²θ+β cot ²θ, and g(θ)=α sin ²θ+β cos ²θ, α>β>0, let min 0<θ< π2 f(θ)= max 0<θ<π g(θ). If the first term of a G.P. is ((α)/(2β))…Sequence and Series
Q25Let y=y(x) be the solution of the differential equation (x²-x√(x²-1))dy+(y(x-√(x²-1))-x)dx=0, x≥1. If y(1)=1, then the greatest integer less than y(5) is _ _…Differential Equations