JEE Main 2024 (Online) 5th April Morning Shift — Question Paper

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Physics

• Three blocks M₁, M₂, M₃ having masses 4 kg, 6 kg and 10 kg respectively are hanging from…
• The density and breaking stress of a wire are 6 × 10⁴ kg / m³ and 1.2 × 10⁸ N / m²…
• A 2A current carrying straight metal wire of resistance 1 Ω, resistivity 2 × 10⁻⁶ Ω m…
• In the given figure R₁=10 Ω, R₂=8 Ω, R₃=4 Ω and R₄=8 Ω. Battery is ideal with emf 12 V…
• Three capacitors of capacitances 25 μ F, 30 μ F and 45 μ F are connected in parallel to…
• If three helium nuclei combine to form a carbon nucleus then the energy released in this…
• An ac source is connected in given series LCR circuit. The rms potential difference…
• The angle between vector Q⃗ and the resultant of (2Q⃗+2P⃗) and (2Q⃗-2P⃗) is :
• An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across…
• Light emerges out of a convex lens when a source of light kept at its focus. The shape…
• In hydrogen like system the ratio of coulombian force and gravitational force between an…
• In a co-axial straight cable, the central conductor and the outer conductor carry equal…
• In the experiment to determine the galvanometer resistance by half-deflection method…
• Two conducting circular loops A and B are placed in the same plane with their centres…
• A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of…
• A simple pendulum doing small oscillations at a place R height above earth surface has…
• If the collision frequency of hydrogen molecules in a closed chamber at 27° C is Z, then…
• Match List I with List II : LIST I | LIST II; A. | Kinetic energy of planet | I. | -GMm…
• The electric field between the two parallel plates of a capacitor of 1.5 μ F capacitance…
• Given below are two statements : Statement I : Figure shows the variation of stopping…
• A body moves on a frictionless plane starting from rest. If Sₙ is distance moved between…
• An electron rotates in a circle around a nucleus having positive charge Ze. Correct…
• Given below are two statements : Statement I : When a capillary tube is dipped into a…
• A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different…
• If G be the gravitational constant and u be the energy density then which of the…
• Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal…
• The heat absorbed by a system in going through the given cyclic process is :
• Time periods of oscillation of the same simple pendulum measured using four different…
• In Young's double slit experiment, carried out with light of wavelength 5000 Aᵒ, the…

Chemistry

• The number of neutrons present in the more abundant isotope of boron is 'x'. Amorphous…
• Which of the following gives a positive test with ninhydrin ?
• The value of Rydberg constant (R_H) is 2.18 × 10⁻¹⁸ J. The velocity of electron having…
• The number of halobenzenes from the following that can be prepared by Sandmeyer's…
• The metal that shows highest and maximum number of oxidation state is :
• The incorrect postulates of the Dalton's atomic theory are : (A) Atoms of different…
• Number of σ and π bonds present in ethylene molecule is respectively :
• The following reaction occurs in the Blast furnance where iron ore is reduced to iron…
• For the Compounds : (A) H₃ C-CH₂-O-CH₂-CH₂-CH₃ (B) H₃ C-CH₂-CH₂-CH₂-CH₃ (C)…
• An organic compound has 42.1 % carbon, 6.4 % hydrogen and remainder is oxygen. If its…
• Given below are two statements: One is labelled as Assertion (A) and the other is…
• Which one of the following complexes will exhibit the least paramagnetic behaviour ?…
• Given below are two statements: Statement I: In group 13, the stability of +1 oxidation…
• The spin-only magnetic moment value of the ion among Ti²⁺, V²⁺, Co³⁺ and Cr²⁺, that acts…
• Given below are two statement : Statements I : Bromination of phenol in solvent with low…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• In the lewis dot structure for NO₂⁻, total number of valence electrons around nitrogen…
• The correct order of ligands arranged in increasing field strength.
• 9.3 g of pure aniline is treated with bromine water at room temperature to give a white…
• Given below are two statements : Statement I : Nitration of benzene involves the…
• The statement(s) that are correct about the species O²⁻, F⁻, Na⁺ and Mg²⁺. (A) All are…
• Identify compound (Z) in the following reaction sequence.
• An artificial cell is made by encapsulating 0.2 M glucose solution within a…
• The heat of combustion of solid benzoic acid at constant volume is -321.30 kJ at 27° C…
• The reaction at cathode in the cells commonly used in clocks involves.
• Molar ionic conductivities of divalent cation and anion are 57 S cm² mol⁻¹ and 73 S cm²…
• During Kinetic study of reaction 2 A+B → C+D, the following results were obtained : A…

Mathematics

• Let the line 2 x+3 y-k=0, k>0, intersect the x-axis and y-axis at the points A and B…
• The number of ways of getting a sum 16 on throwing a dice four times is ________.
• If y=y(x) is the solution of the differential equation (d y)/(d x)+2 y=sin (2 x)…
• For the function f(x)=sin x+3 x-2/π(x²+x), where x ∈[0, π/2], consider the following two…
• The coefficients a, b, c in the quadratic equation a x²+b x+c=0 are chosen from the set…
• Let d be the distance of the point of intersection of the lines (x+6)/3=y/2=(z+1)/1 and…
• The integral ∫0^(π / 4) (136 sin x)/(3 sin x+5 cos x) d x is equal to :
• If 1/(√1+√2)+1/(√2+√3)+…+1/(√99+√100)=m and 1/(1 · 2)+1/(2 · 3)+…+1/(99 · 100)=n, then…
• Suppose θ∈ [0,π/4] is a solution of 4 cos θ-3 sin θ=1. Then cos θ is equal to :
• If A(1,-1,2), B(5,7,-6), C(3,4,-10) and D(-1,-4,-2) are the vertices of a quadrilateral…
• If the function f(x)=(sin 3 x+α sin x-β cos 3 x)/x³, x ∈ R, is continuous at x=0, then…
• Consider the following two statements : Statement I: For any two non-zero complex…
• Let f be a differentiable function in the interval (0, ∞) such that f(1)=1 and lim t → x…
• If the line (2-x)/3=(3 y-2)/(4 λ+1)=4-z makes a right angle with the line (x+3)/(3…
• Suppose AB is a focal chord of the parabola y²=12 x of length l and slope m<√3. If the…
• Let f(x)=x⁵+2 x³+3 x+1, x ∈ R, and g(x) be a function such that g(f(x))=x for all x ∈ R…
• The value of ∫-π^π (2 y(1+sin y))/(1+cos ² y) d y is :
• Let a circle C of radius 1 and closer to the origin be such that the lines passing…
• Let A={1,3,7,9,11} and B={2,4,5,7,8,10,12}. Then the total number of one-one maps f: A →…
• If the constant term in the expansion of (1+2 x-3 x³)(3/2 x²-1/(3 x))⁹ is p, then 108 p…
• If the system of equations 11 x+y+λ z=-5; 2 x+3 y+5 z=3; 8 x-19 y-39 z=μ has infinitely…
• If S={a ∈ R:|2 a-1|=3[a]+2{a }}, where [t] denotes the greatest integer less than or…
• Let a⃗=î-3 ĵ+7 k̂, b⃗=2 î-ĵ+k̂ and c⃗ be a vector such that (a⃗+2 b⃗) × c⃗=3(c⃗ × a⃗)…
• From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at…
• Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2. Then |Aᵀ…
• Let a₁, a₂, a₃, … be in an arithmetic progression of positive terms. Let…
• Let two straight lines drawn from the origin O intersect the line 3x+4y=12 at the points…
• The area of the region enclosed by the parabolas y=x²-5x and y=7x-x² is ________.
• Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that…

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