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JEE Main 2024 9 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20249 Apr, Morning shift

Physics 27Chemistry 19Mathematics 30

Physics

Q51When a coil is connected across a 20 ~V dc supply, it draws a current of 5 ~A. When it is connected across 20 ~V, 50 ~Hz ac supply, it draws a current of 4…Electromagnetic Induction and Alternating Currents
Q53A star has 100% helium composition. It starts to convert three ⁴ He into one ¹² C via triple alpha process as ⁴ He+ ⁴ He+ ⁴ He → ¹² C+Q. The mass of the star…Atoms and Nuclei
Q58At the centre of a half ring of radius R=10 ~cm and linear charge density 4 ~nC ~m⁻¹, the potential is x π V. The value of x is _ _ _ _ _.Electrostatics
Q66A square loop of edge length 2 ~m carrying current of 2 ~A is placed with its edges parallel to the x - y axis. A magnetic field is passing through the x - y…Magnetic Effects of Current and Magnetism
Q68Two persons pull a wire towards themselves. Each person exerts a force of 200 ~N on the wire. Young's modulus of the material of wire is 1 × 10¹¹ ~N ~m⁻²…Properties of Solids and Liquids
Q70A string is wrapped around the rim of a wheel of moment of inertia 0.40 ~kgm² and radius 10 ~cm. The wheel is free to rotate about its axis. Initially the…Rotational Motion
Q71The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 ~m, 2 ~ms⁻¹ and 16 ~ms⁻² at a certain…Oscillations and Waves
Q74If a and b makes an angle cos ⁻¹(5/9) with each other, then |a+b|=√(2)|a-b| for |a|=n|b| The integer value of n is _ _ _ _ _.Kinematics
Q75In a Young's double slit experiment, the intensity at a point is (1/4)^(th) of the maximum intensity, the minimum distance of the point from the central…Optics
Q5928A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:Electromagnetic Induction and Alternating Currents
Q6063The energy equivalent of 1 ~g of substance is:Atoms and Nuclei
Q6483A galvanometer has a coil of resistance 200 Ω with a full scale deflection at 20 μ A. The value of resistance to be added to use it as an ammeter of range…Current Electricity
Q6591A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:Dual Nature of Matter and Radiation
Q6826A plane EM wave is propagating along x direction. It has a wavelength of 4 ~mm. If electric field is in y direction with the maximum magnitude of 60 ~Vm⁻¹…Electromagnetic Waves
Q6888A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42 ~eV. The wavelength of light emitted from the LED is:Electronic Devices
Q7055Given below are two statements: Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of…Optics
Q7222An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 ~km. From earth's…Gravitation
Q7503The volume of an ideal gas (γ=1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:Thermodynamics
Q7504A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiab constant for the gas is γ=3/2, then the work done by the gas…Thermodynamics
Q7544A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The…Laws of Motion
Q7567A light unstretchable string passing over a smooth light pulley connects two blocks of masses m₁ and m₂. If the acceleration of the system is g/8, then the…Laws of Motion
Q7661Given below are two statements: Statement (I): When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field…Magnetic Effects of Current and Magnetism
Q7830A particle moving in a straight line covers half the distance with speed 6 ~m / s. The other half is covered in two equal time intervals with speeds 9 ~m / s…Kinematics
Q7999A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank is:Properties of Solids and Liquids
Q8281The dimensional formula of latent heat is:Units and Measurements
Q8364One main scale division of a vernier caliper is equal to m units. If n^(th) division of main scale coincides with (n+1)^(th) division of vernier scale, the…Experimental Skills
Q8626A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v=α √(x), where α is a constant. The total…Work, Energy and Power

Chemistry

Q2Total number of essential amino acid among the given list of amino acids is _ _ _ _. Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine…Biomolecules
Q5The total number of species from the following in which one unpaired electron is present, is _ _ _ _. N₂, O₂, C₂⁻, O₂⁻, O₂²⁻, H₂⁺, CN⁻, He₂⁺Chemical Bonding and Molecular Structure
Q7Number of ambidentate ligands among the following is _ _ _ _ _. NO₂⁻, SCN⁻, C₂ O₄²⁻, NH₃, CN⁻, SO₄²⁻, H₂ O.Coordination Compounds
Q8Number of colourless lanthanoid ions among the following is _ _ _ _ _. Eu³⁺, Lu³⁺, Nd³⁺, La³⁺, Sm³⁺d- and f-Block Elements
Q10The standard reduction potentials at 298 ~K for the following half cells are given below: Cr₂ O₇²⁻+14 H⁺+6 e⁻ → 2 Cr³⁺+7 H₂ O, E^(°)=1.33 ~V ll Fe³⁺(aq)+3 e⁻…Redox Reactions and Electrochemistry
Q16Molarity (M) of an aqueous solution containing x ~g of anhyd. CuSO₄ in 500 ~mL solution at 32^(°) C is 2 × 10⁻¹ M. Its molality will be _ _ _ _ _ × 10⁻³ ~m…Some Basic Concepts in Chemistry
Q18When equal volume of 1 ~M ~HCl and 1 ~M ~H₂ SO₄ are separately neutralised by excess volume of 1 M NaOH solution. x and y ~kJ of heat is liberated…Chemical Thermodynamics
Q19The heat of solution of anhydrous CuSO₄ and CuSO₄ · 5 H₂ O are -70 ~kJ ~mol⁻¹ and +12 ~kJ ~mol⁻¹ respectively. The heat of hydration of CuSO₄ to CuSO₄ · 5 H₂…Chemical Thermodynamics
Q142Methods used for purification of organic compounds are based on:Some Basic Principles of Organic Chemistry
Q248The F⁻ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the…Biomolecules
Q323In which one of the following pairs the central atoms exhibit sp² hybridization ?Chemical Bonding and Molecular Structure
Q695Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The total number of geometrical…Coordination Compounds
Q905The electronic configuration of Cu(II) is 3 ~d⁹ whereas that of Cu(I) is 3 ~d¹⁰. Which of the following is correct?d- and f-Block Elements
Q1155Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): S N 2 reaction of C₆ H₅ CH₂ Br occurs…Organic Compounds Containing Halogens
Q1522Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Both rhombic and monoclinic sulphur…p-Block Elements
Q1523On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed?p-Block Elements
Q1584Given below are two statements: Statement (I): The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of…Classification of Elements and Periodicity in Properties
Q1743Identify the incorrect statements regarding primary standard of titrimetric analysis. (A) It should be purely available in dry form. (B) It should not undergo…Principles Related to Practical Chemistry
Q2216Compare the energies of following sets of quantum numbers for multielectron system. (A) n=4,1=1 (B) n=4,1=2 (C) n=3, l=1 (D) n=3,1=2 (E) n=4,1=0 Choose the…Atomic Structure

Mathematics

Q22Let the set of all positive values of λ, for which the point of local minimum of the function (1+x(λ²-x²)) satisfies (x²+x+2)/(x²+5 x+6)<0, be (α, β). Then…Limit, Continuity and Differentiability
Q24The remainder when 428²⁰²⁴ is divided by 21 is _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q27Let the centre of a circle, passing through the points (0,0),(1,0) and touching the circle x²+y²=9, be (h, k). Then for all possible values of the coordinates…Coordinate Geometry
Q28The sum of the square of the modulus of the elements in the set =a+ib: a, b Z, z C,|z-1| ≤ 1,|z-5| ≤|z-5 i| is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q29Let lim n → ∞ (n/(√(n⁴+1))-(2 n)/((n²+1) √(n⁴+1))+n/(√(n⁴+16))-(8 n)/((n²+4) √(n⁴+16))..+ +n/(√(n⁴+n⁴))-(2 n · n²)/((n²+n²) √(n⁴+n⁴))) be (π)/k, using only…Integral Calculus
Q35If a function f satisfies f(~m+n)=f(~m)+f(n) for all m, n N and f(1)=1, then the largest natural number λ such that Σ k=1 ²⁰²² f(λ+k) ≤(2022)² is equal to _ _…Sets, Relations and Functions
Q37Let f:(0, π) → R be a function given by f(x)=\ cc(8/7)^((tan 8 x)/(tan 7 x)), 0< x<(π)/2 a-8, x=(π)/2 (1+ cot x)^(b/a| tan x|), (π)/2 < x < π. where a, b Z…Limit, Continuity and Differentiability
Q38Let A be a non-singular matrix of order 3. If det(3 adj(2 adj((det A) A)))=3⁻¹³ · 2⁻¹⁰ and det(3adj(2 A))=2^(m) · 3ⁿ, then |3 ~m+2 n| is equal to _ _ _ _ _.Matrices and Determinants
Q40Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,4. If the probability that a x²+b…Statistics and Probability
Q43Let A=\2,3,6,7 and B=\4,5,6,8. Let R be a relation defined on A × B by (a₁, b₁) R(a₂, b₂) if and only if a₁+a₂=b₁+b₂. Then the number of elements in R is _ _…Sets, Relations and Functions
Q2533The shortest distance between the lines (x-3)/4=(y+7)/(-11)=(z-1)/5 and (x-5)/3=(y-9)/(-6)=(z+2)/1 is:Three Dimensional Geometry
Q2534Let the line L intersect the lines x-2=-y=z-1,2(x+1)=2(y-1)=z+1 and be parallel to the line (x-2)/3=(y-1)/1=(z-2)/2. Then which of the following points lies…Three Dimensional Geometry
Q2870The parabola y²=4 x divides the area of the circle x²+y²=5 in two parts. The area of the smaller part is equal to:Integral Calculus
Q3015The coefficient of x⁷⁰ in x²(1+x)⁹⁸+x³(1+x)⁹⁷+x⁴(1+x)⁹⁶+ +x⁵⁴(1+x)⁴⁶ is ⁹⁹ C p - ⁴⁶ C q. Then a possible value of p+q is:Binomial Theorem and Its Simple Applications
Q3028Let a circle passing through (2,0) have its centre at the point (h, k). Let (x c, y c) be the point of intersection of the lines 3 x+5 y=1 and (2+c) x+5 c²…Coordinate Geometry
Q3567The solution of the differential equation (x²+y²) d x-5 x y ~d y=0, y(1)=0, is:Differential Equations
Q3568The solution curve, of the differential equation 2 y (d y)/(~d x)+3=5 (d y)/(~d x), passing through the point (0,1) is a conic, whose vertex lies on the line:Differential Equations
Q3703Let f(x)=a x³+b x²+c x+41 be such that f(1)=40, f^()(1)=2 and f^()(1)=4. Then a²+b²+c² is equal to:Limit, Continuity and Differentiability
Q3771Let f(x)=x²+9, g(x)=x/(x-9) and a=f° g(10), b=g° f(3). If e and l denote the eccentricity and the length of the latus rectum of the ellipse…Coordinate Geometry
Q3851If the domain of the function f(x)= sin ⁻¹((x-1)/(2 x+3)) is R-(α, β), then 12 α β is equal to:Sets, Relations and Functions
Q4039Let ∫ (2- tan x)/(3+ tan x) ~d x=1/2(α x+ log e |β sin x+γ cos x|)+C, where C is the constant of integration. Then α+(γ)/(β) is equal to:Integral Calculus
Q4637Let λ, μ R. If the system of equations 3 x+5 y+λ z=3 7 x+11 y-9 z=2 97 x+155 y-189 z=μ has infinitely many solutions, then μ+2 λ is equal to:Matrices and Determinants
Q5169Let α, β be the roots of the equation x²+2 √(2) x-1=0. The quadratic equation, whose roots are α⁴+β⁴ and 1/10(α⁶+β⁶), is:Complex Numbers and Quadratic Equations
Q5348If the sum of the series 1/(1 ·(1+d))+1/((1+d)(1+2 ~d))+ +1/((1+9 ~d)(1+10 ~d)) is equal to 5, then 50 ~d is equal to:Sequence and Series
Q5495The frequency distribution of the age of students in a class of 40 students is given below. Age 15 16 17 18 19 20 No of Students 5 8 5 12 x y If the mean…Statistics and Probability
Q5526A variable line L passes through the point (3,5) and intersects the positive coordinate axes at the points A and B. The minimum area of the triangle OAB…Coordinate Geometry
Q5624A ray of light coming from the point P(1,2) gets reflected from the point Q on the x -axis and then passes through the point R(4,3). If the point S(h, k) is…Coordinate Geometry
Q5632Let | cos θ cos (60-θ) cos (60+θ)| ≤ 1/8, θ ε[0,2 π]. Then, the sum of all θ [0,2 π], where cos 3 θ attains its maximum value, is:Trigonometry
Q5854Let three vectors, a=α i+4 j+2 k, b=5 i+3 j+4 k, c=x i+y j+z k form a triangle such that c=a-b and the area of the triangle is 5 √(6). If α is a positive real…Vector Algebra
Q5855Let O A=2 a, O B=6 a+5 b and O C=3 b, where O is the origin. If the area of the parallelogram with adjacent sides O A and O C is 15 sq. units, then the area…Vector Algebra