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JEE Main 2024 8 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20248 Apr, Morning shift

Physics 24Chemistry 18Mathematics 29

Physics

Q49In an alpha particle scattering experiment distance of closest approach for the α particle is 4.5 × 10⁻¹⁴ ~m. If target nucleus has atomic number 80, then…Atoms and Nuclei
Q53Resistance of a wire at 0^(°) C, 100^(°) C and t^(°) C is found to be 10 Ω, 10.2 Ω and 10.95 Ω respectively. The temperature t in Kelvin scale is _ _ _ _ _.Current Electricity
Q57An electric field, E=(2 i+6 j+8 k)/(√(6)) passes through the surface of 4 ~m² area having unit vector n=((2 i+j+k)/(√(6))). The electric flux for that surface…Electrostatics
Q64An electron with kinetic energy 5 ~eV enters a region of uniform magnetic field of 3 μ T perpendicular to its direction. An electric field E is applied…Magnetic Effects of Current and Magnetism
Q67A liquid column of height 0.04 ~cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 × 10³ ~kg ~m⁻³ and surface tension…Properties of Solids and Liquids
Q70A parallel beam of monochromatic light of wavelength 600 ~nm passes through single slit of 0.4 ~mm width. Angular divergence corresponding to second order…Optics
Q71A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ((a-1)/a) then the value of a is _ _ _ _ _.Oscillations and Waves
Q5931A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The…Electromagnetic Induction and Alternating Currents
Q6067Binding energy of a certain nucleus is 18 × 10⁸ ~J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:Atoms and Nuclei
Q6230A stationary particle breaks into two parts of masses m A and m B which move with velocities v A and v B respectively. The ratio of their kinetic energies (K…Rotational Motion
Q6297A clock has 75 ~cm, 60 ~cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the…Kinematics
Q6593A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h = 6.63 × 10⁻³⁴ ~J ~s, ~m e =9.0 ×…Dual Nature of Matter and Radiation
Q6828Average force exerted on a non-reflecting surface at normal incidence is 2.4 × 10⁻⁴ ~N. If 360 ~W / cm² is the light energy flux during span of 1 hour 30…Electromagnetic Waves
Q6935Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:Electrostatics
Q7128Critical angle of incidence for a pair of optical media is 45^(°). The refractive indices of first and second media are in the ratio:Optics
Q7287Two planets A and B having masses m₁ and m₂ move around the sun in circular orbits of r₁ and r₂ radii respectively. If angular momentum of A is L and that of…Gravitation
Q7327A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27^(°) C). The ratio of specific heat of gases at…Thermodynamics
Q7601A player caught a cricket ball of mass 150 ~g moving at a speed of 20 ~m / s. If the catching process is completed in 0.1 ~s, the magnitude of force exerted…Laws of Motion
Q7602Three bodies A, B and C have equal kinetic energies and their masses are 400 ~g, 1.2 ~kg and 1.6 ~kg respectively. The ratio of their linear momenta is:Laws of Motion
Q7655Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has…Magnetic Effects of Current and Magnetism
Q7922Correct Bernoulli's equation is (symbols have their usual meaning):Properties of Solids and Liquids
Q7968Young's modulus is determined by the equation given by Y=49000 m/l dyne/(cm²) where M is the mass and l is the extension of wire used in the experiment. Now…Properties of Solids and Liquids
Q8350In an expression a × 10^(b):Units and Measurements
Q8366The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division…Experimental Skills

Chemistry

Q2Number of molecules from the following which are exceptions to octet rule is _ _ _ _ _. CO₂, NO₂, H₂ SO₄, BF₃, CH₄, SiF₄, ClO₂, PCl₅, BeF₂, C₂ H₆, CHCl₃, CBr₄Chemical Bonding and Molecular Structure
Q4Consider the following reaction A+B → C The time taken for A to become 1 / 4^(th) of its initial concentration is twice the time taken to become 1 / 2 of the…Chemical Kinetics
Q5If 279 ~g of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be _ _ _ _ g. (nearest…Organic Compounds Containing Nitrogen
Q10The 'spin only' magnetic moment value of MO₄ ²⁻ is _ _ _ _ BM. (Where M is a metal having least metallic radii. among Sc, Ti, V, Cr, Mn and Zn). (Given atomic…Coordination Compounds
Q17A solution containing 10 ~g of an electrolyte AB₂ in 100 ~g of water boils at 100.52^(°) C. The degree of ionization of the electrolyte (α) is _ _ _ _ _ ×…Solutions
Q327Match List I with List II LIST I (Molecule) LIST II (Shape) A. NH₃ I. Square pyramid B. BrF₅ II. Tetrahedral C. PCl₅ III. Trigonal pyramidal D. CH₄ IV…Chemical Bonding and Molecular Structure
Q426For the given hypothetical reactions, the equilibrium constants are as follows: X Y; K₁=1.0 Y Z; K₂=2.0 Z W; K₃=4.0 The equilibrium constant for the reaction…Equilibrium
Q577Given below are two statements: Statement I: N(CH₃)₃ and P(CH₃)₃ can act as ligands to form transition metal complexes. Statement II: As N and P are from same…Coordination Compounds
Q578Match List I with List II LIST I (Compound) LIST II (Colour] A. Fe₄[Fe(CN)₆]₃ · xH₂O I. Violet B. [Fe(CN)₅ NOS]⁴⁻ II. Blood Red C. [Fe(SCN)]²⁺ III. Prussian…Coordination Compounds
Q602An octahedral complex with the formula CoCl₃ · nNH₃ upon reaction with excess of AgNO₃ solution gives 2 moles of AgCl. Consider the oxidation state of Co in…Coordination Compounds
Q660Number of Complexes with even number of electrons in t 2 g orbitals is - [Fe(H₂ O)₆]²⁺,[Co(H₂ O)₆]²⁺,[Co(H₂ O)₆]³⁺,[Cu(H₂ O)₆]²⁺,[Cr(H₂ O)₆]²⁺Coordination Compounds
Q907Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. Fe³⁺ oxidises the iodide ion B. Fe³⁺ oxidises the persulphate ion C. Fe²⁺…d- and f-Block Elements
Q1462Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The stability order of +1 oxidation state of…p-Block Elements
Q1537Among the following halogens F₂, Cl₂, Br₂ and I₂ Which can undergo disproportionation reactions?p-Block Elements
Q1668Match List I with List II LIST I (Elements) LIST II (Properties in their respective groups) A. Cl,S I. Elements with highest electronegativity B. Ge,As II…Classification of Elements and Periodicity in Properties
Q1783Match List I with List II LIST I (Name of the test) LIST II (Reaction sequence involved) [M is metal] A. Borax bead test I. MCO₃ → MO [+Δ]Co(NO₃)₂ CoO · MO B…Principles Related to Practical Chemistry
Q1802Thiosulphate reacts differently with iodine and bromine in the reactions given below: 2 ~S₂ O₃²⁻+I₂ → S₄ O₆²⁻+2 I⁻ S₂ O₃²⁻+5 Br₂+5 H₂ O → 2 SO₄²⁻+4 Br⁻+10 H⁺…Redox Reactions and Electrochemistry
Q2105Combustion of glucose (C₆ H₁₂ O₆) produces CO₂ and water. The amount of oxygen (in g) required for the complete combustion of 900 ~g of glucose is: [Molar…Some Basic Concepts in Chemistry

Mathematics

Q24Let the area of the region enclosed by the curve y= min sin x, cos x and the x axis between x=-π to x=π be A. Then A² is equal to _ _ _ _ _.Integral Calculus
Q31If the range of f(θ)=(sin ⁴ θ+3 cos ² θ)/(sin ⁴ θ+ cos ² θ), θ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the common ratio is…Sets, Relations and Functions
Q34The value of lim x → 0 2((1- cos x √(cos 2 x) 3√(cos 3 x). 10√(cos 10 x))/(x²)) is _ _ _ _ _.Limit, Continuity and Differentiability
Q36Let A=[ cc2 -1 1 1 ]. If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to _ _ _ _.Matrices and Determinants
Q38The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is…Permutations and Combinations
Q40Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and…Statistics and Probability
Q42Let α=Σ r=0 ⁿ(4 r²+2 r+1) ⁿ C r and β=(Σ r=0 ⁿ (ⁿ C r)/(r+1))+1/(n+1). If 140<(2 α)/(β)<281, then the value of n is _ _ _ _ _.Sequence and Series
Q43If the orthocentre of the triangle formed by the lines 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-1=0, is the centroid of another triangle, whose circumcentre and…Coordinate Geometry
Q47Let a=9 i-13 j+25 k, b=3 i+7 j-13 k and c=17 i-2 j+k be three given vectors. If r is a vector such that r × a=(b+c) × a and r ·(b-c)=0, then (|593 r+67…Vector Algebra
Q2384Let P(x, y, z) be a point in the first octant, whose projection in the x y -plane is the point Q. Let O P=γ; the angle between O Q and the positive x -axis be…Three Dimensional Geometry
Q2538If the shortest distance between the lines ll L₁: r=(2+λ) i+(1-3 λ) j+(3+4 λ) k, λ R L₂: r=2(1+μ) i+3(1+μ) j+(5+μ) k, μ R is m/(√(n)), where gcd(m, n)=1, then…Three Dimensional Geometry
Q2688Let f(x)=4 cos ³ x+3 √(3) cos ² x-10. The number of points of local maxima of f in interval (0,2 π) isLimit, Continuity and Differentiability
Q2689The number of critical points of the function f(x)=(x-2)^(2 / 3)(2 x+1) isLimit, Continuity and Differentiability
Q2735For the function f(x)=(cos x)-x+1, x R, between the following two statements (S1) f(x)=0 for only one value of x in [0, π]. (S2) f(x) is decreasing in [0…Limit, Continuity and Differentiability
Q3102Let the circles C₁:(x-α)²+(y-β)²=r₁² and C₂:(x-8)²+(y-15/2)²=r₂² touch each other externally at the point (6,6). If the point (6,6) divides the line segment…Coordinate Geometry
Q3171Let z be a complex number such that |z+2|=1 and lm((z+1)/(z+2))=1/5. Then the value of |Re(z+2)| isComplex Numbers and Quadratic Equations
Q3277If the set R=\(a, b): a+5 b=42, a, b N has m elements and Σ n=1 ^(m)(1-i^(n !))=x+i y, where i=√(-1), then the value of m+x+y isComplex Numbers and Quadratic Equations
Q3484The value of k N for which the integral I n =∫₀¹(1-x^(k))ⁿ d x, n N, satisfies 147 I₂₀=148 I₂₁ isIntegral Calculus
Q3503Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to x=a>0 is e^(-a)+4 a²+a-1. Then the differential equation, whose general…Differential Equations
Q3650Let y=y(x) be the solution of the differential equation (1+y²) e^(tan x) d x+ cos ² x(1+e^(2 tan x)) d y=0, y(0)=1. Then y((π)/4) is equal toDifferential Equations
Q3982Let H: (-x²)/(a²)+(y²)/(b²)=1 be the hyperbola, whose eccentricity is √(3) and the length of the latus rectum is 4 √(3). Suppose the point (α, 6), α>0 lies on…Coordinate Geometry
Q4040Let I(x)=∫ 6/(sin ² x(1- cot x)²) d x. If I(0)=3, then I((π)/12) is equal toIntegral Calculus
Q4513Let A=[ lll2 a 0 1 3 1 0 5 b ]. If A³=4 A²-A-21 I, where I is the identity matrix of order 3 × 3, then 2 a+3 b is equal toMatrices and Determinants
Q4854Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f: A → Z be the function f(x)=[ log…Permutations and Combinations
Q4933Let the sum of two positive integers be 24. If the probability, that their product is not less than 3/4 times their greatest possible product, is m/n, where…Statistics and Probability
Q5171The sum of all the solutions of the equation (8)²ˣ-16 ·(8)ˣ+48=0 is:Complex Numbers and Quadratic Equations
Q5591The equations of two sides AB and AC of a triangle ABC are 4 x+y=14 and 3 x-2 y=5, respectively. The point (2,-4/3) divides the third side BC internally in…Coordinate Geometry
Q5648If sin x=-3/5, where π< x <(3 π)/2, then 80(tan ² x- cos x) is equal toTrigonometry
Q5789The set of all α, for which the vectors a=α t i+6 j-3 k and b=t i-2 j-2 α t k are inclined at an obtuse angle for all t R, isVector Algebra