JEE Main 2024 (Online) 8th April Morning Shift — Question Paper

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Physics

• Average force exerted on a non-reflecting surface at normal incidence is 2.4 × 10⁻⁴ N…
• A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes…
• A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain…
• A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept…
• Two charged conducting spheres of radii a and b are connected to each other by a…
• Critical angle of incidence for a pair of optical media is 45°. The refractive indices…
• A proton and an electron are associated with same de-Broglie wavelength. The ratio of…
• Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg…
• Resistance of a wire at 0° C, 100° C and t° C is found to be 10 Ω, 10.2 Ω and 10.95 Ω…
• An electric field, E⃗=(2 î+6 ĵ+8 k̂)/√6 passes through the surface of 4 m² area having…
• A stationary particle breaks into two parts of masses m_A and m_B which move with…
• An electron with kinetic energy 5 eV enters a region of uniform magnetic field of 3 μ T…
• A closed and an open organ pipe have same lengths. If the ratio of frequencies of their…
• Young's modulus is determined by the equation given by Y=49000 m/l dyne/cm² where M is…
• In an alpha particle scattering experiment distance of closest approach for the α…
• Binding energy of a certain nucleus is 18 × 10⁸ J. How much is the difference between…
• A player caught a cricket ball of mass 150 g moving at a speed of 20 m / s. If the…
• In an expression a× 10ᵇ :
• A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the…
• The output Y of following circuit for given inputs is :
• In the given circuit, the terminal potential difference of the cell is :
• A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y…
• Paramagnetic substances: A. align themselves along the directions of external magnetic…
• Three vectors OP⃗,OQ⃗ and OR⃗ each of magnitude A are acting as shown in figure. The…
• Correct Bernoulli's equation is (symbols have their usual meaning) :
• The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main…
• Two different adiabatic paths for the same gas intersect two isothermal curves as shown…
• Two planets A and B having masses m₁ and m₂ move around the sun in circular orbits of r₁…

Chemistry

• Match List I with List II LIST I (Molecule) | LIST II (Shape); A. | NH₃ | I. | Square…
• Match List I with List II LIST I (Elements) | LIST II (Properties in their respective…
• If 279 g of aniline is reacted with one equivalent of benzenediazonium chloride, the…
• Number of amine compounds from the following giving solids which are soluble in NaOH…
• Give below are two statements: One is labelled as Assertion A and the other is labelled…
• A hypothetical electromagnetic wave is show below. The frequency of the wave is x × 10¹⁹…
• Given below are two statements: Statement I: N(CH₃)₃ and P(CH₃)₃ can act as ligands to…
• Number of Complexes with even number of electrons in t_(2 g) orbitals is - [Fe(H₂…
• The number of optical isomers in following compound is : __________.
• For the given hypothetical reactions, the equilibrium constants are as follows : X⇌…
• A solution containing 10 g of an electrolyte AB₂ in 100 g of water boils at 100.52° C…
• Combustion of glucose (C₆ H₁₂ O₆) produces CO₂ and water. The amount of oxygen (in g)…
• Consider the following reaction A+B → C The time taken for A to become 1 / 4ᵗʰ of its…
• Identify the major products A and B respectively in the following set of reactions.
• Match List I with List II LIST I (Name of the test) | LIST II (Reaction sequence…
• Consider the figure provided. 1 mol of an ideal gas is kept in a cylinder, fitted with a…
• Which among the following compounds will undergo fastest S N 2 reaction.
• Thiosulphate reacts differently with iodine and bromine in the reactions given below: 2…
• Among the following halogens F₂, Cl₂, Br₂ and I₂ Which can undergo disproportionation…
• An octahedral complex with the formula CoCl₃ · nNH₃ upon reaction with excess of AgNO₃…
• The 'spin only' magnetic moment value of MO₄ ²⁻ is ________ BM. (Where M is a metal…
• Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. Fe³⁺…
• Number of molecules from the following which are exceptions to octet rule is _________…
• Match List I with List II LIST I (Compound) | LIST II (Colour]; A. | Fe₄[Fe(CN)₆]₃ ·…

Mathematics

• Let H: -x²/a²+y²/b²=1 be the hyperbola, whose eccentricity is √3 and the length of the…
• Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the…
• The set of all α, for which the vectors a⃗=α t î+6 ĵ-3 k̂ and b⃗=t î-2 ĵ-2 α t k̂ are…
• Let P(x, y, z) be a point in the first octant, whose projection in the x y-plane is the…
• If sin x=-3/5, where π<x<3π/2, then 80(tan² x-cos x) is equal to
• The value of lim x → 0 2((1-cos x √(cos 2 x) ∛(cos 3 x) … … . ¹⁰√(cos 10 x))/x²) is…
• Let A=[2, a, 0; 1, 3, 1; 0, 5, b]. If A³=4 A²-A-21 I, where I is the identity matrix of…
• Let the circles C₁:(x-α)²+(y-β)²=r₁² and C₂:(x-8)²+(y-15/2)²=r₂² touch each other…
• If the set R={(a, b): a+5 b=42, a, b ∈ ℕ} has m elements and Σn=1ᵐ(1-i^(n !))=x+i y…
• Let the positive integers be written in the form : 1; 2, 3; 4, 5, 6; 7, 8, 9, 10; ..., ⋱…
• Let the area of the region enclosed by the curve y=min{sin x,cos x} and the x axis…
• Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to…
• The sum of all the solutions of the equation (8)²ˣ-16 ·(8)ˣ+48=0 is :
• The equations of two sides AB and AC of a triangle ABC are 4x+y=14 and 3x-2y=5…
• Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime…
• Let α=Σr=0ⁿ(4 r²+2 r+1) ⁿ Cᵣ and β=(Σr=0ⁿ (ⁿ Cᵣ)/(r+1))+1/(n+1). If 140<(2 α)/β<281…
• The number of critical points of the function f(x)=(x-2)^(2 / 3)(2 x+1) is
• Let a⃗=9 î-13 ĵ+25 k̂, b⃗=3 î+7 ĵ-13 k̂ and c⃗=17 î-2 ĵ+k̂ be three given vectors. If r⃗…
• Let the sum of two positive integers be 24 . If the probability, that their product is…
• If 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…
• Let y=y(x) be the solution of the differential equation (1+y²) eᵗᵃⁿˣ d x+cos ²…
• For the function f(x)=(cos x)-x+1, x ∈ ℝ, between the following two statements (S1)…
• Let f(x)=4 cos ³ x+3 √3 cos ² x-10. The number of points of local maxima of f in…
• Let z be a complex number such that |z+2|=1 and lm((z+1)/(z+2))=1/5. Then the value of…
• Let A=[2, -1; 1, 1]. If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal…
• If the orthocentre of the triangle formed by the lines 2x+3y-1=0,x+2y-1=0 and ax+by-1=0…
• Let I(x)=∫ 6/(sin² x(1-cot x)²)dx. If I(0)=3, then I(π/12) is equal to
• If the shortest distance between the lines L₁: r⃗=(2+λ) î+(1-3 λ) ĵ+(3+4 λ) k̂,, λ ∈ ℝ…
• The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the…
• The value of k ∈ ℕ for which the integral Iₙ=∫₀¹(1-xᵏ)ⁿ d x, n ∈ ℕ, satisfies 147…

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