JEE Main 2024 (Online) 31st January Evening Shift — Question Paper

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Physics

• An AC voltage V=20 sin 200 π t is applied to a series LCR circuit which drives a current…
• If two vectors A⃗ and B⃗ having equal magnitude R are inclined at angle θ, then
• The speed of sound in oxygen at S.T.P. will be approximately: (given, R=8.3 JK⁻¹, γ=1.4)
• A light string passing over a smooth light fixed pulley connects two blocks of masses m₁…
• Two circular coils P and Q of 100 turns each have same radius of π cm. The currents in P…
• Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a…
• Given below are two statements: Statement I: Electromagnetic waves carry energy as they…
• The mass number of nucleus having radius equal to half of the radius of nucleus with…
• A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T…
• A body of mass 2 kg begins to move under the action of a time dependent force given by…
• The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The…
• A small spherical ball of radius r, falling through a viscous medium of negligible…
• When unpolarized light is incident at an angle of 60° on a transparent medium from air…
• A body of mass 'm' is projected with a speed 'u' making an angle of 45° with the ground…
• A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If…
• The distance between charges +q and -q is 2 l and between +2 q and -2 q is 4 l. The…
• Light from a point source in air falls on a convex curved surface of radius 20 cm and…
• The time period of simple harmonic motion of mass M in the given figure is π √((α M)/(5…
• Consider two physical quantities A and B related to each other as E=(B-x²)/At where E,x…
• The resistance per centimeter of a meter bridge wire is r, with X Ω resistance in left…
• The output of the given circuit diagram is -
• In the following circuit, the battery has an emf of 2 V and an internal resistance of…
• A nucleus has mass number A₁ and volume V₁. Another nucleus has mass number A₂ and…
• Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth…
• The mass of the moon is 1/144 times the mass of a planet and its diameter is 1/16 times…
• Force between two point charges q₁ and q₂ placed in vacuum at 'r' cm apart is F. Force…
• A uniform magnetic field of 2 × 10⁻³ T acts along positive Y-direction. A rectangular…
• By what percentage will the illumination of the lamp decrease if the current drops by 20%?
• The magnetic flux φ (in weber) linked with a closed circuit of resistance 8 Ω varies…
• In a photoelectric effect experiment a light of frequency 1.5 times the threshold…

Chemistry

• If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under…
• Choose the correct statements from the following A. All group 16 elements form oxides of…
• A compound (x) with molar mass 108 g mol⁻¹ undergoes acetylation to give product with…
• Identify structure of 2,3-dibromo-1-phenylpentane.
• r=k[A] for a reaction, 50 % of A is decomposed in 120 minutes. The time taken for 90 %…
• In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.)…
• Match List I with List II List - I (Complex ion) | List - II (Electronic Configuration)…
• Select the option with correct property -
• Given below are two statements: Statement I : S₈ solid undergoes disproportionation…
• Given below are two statements : Statement I : Aniline reacts with con. H₂SO₄, followed…
• The azo-dye (Y) formed in the following reactions is Sulphanilic acid +NaNO₂+CH₃COOH→ X.
• Consider the following elements. Group, |, A′ B′, → Period; ↓, C′ D′ Which of the…
• From the vitamins A, B₁, B₆, B₁₂, C, D, E and K, the number of vitamins that can be…
• The four quantum numbers for the electron in the outer most orbital of potassium (atomic…
• The correct order of reactivity in electrophilic substitution reaction of the following…
• The molarity of 1 L orthophosphoric acid (H₃ PO₄) having 70 % purity by weight (specific…
• The fragrance of flowers is due to the presence of some steam volatile organic compounds…
• A_((g))⇌ B_((g))+C/2(g) The correct relationship between K_P,α and equilibrium pressure…
• Choose the correct statements from the following A. Mn₂ O₇ is an oil at room temperature…
• Number of moles of H⁺ ions required by 1 mole of MnO₄⁻ to oxidise oxalate ion to CO₂ is…
• Which of the following is least ionic?
• A sample of CaCO₃ and MgCO₃ weighed 2.21 g is ignited to constant weight of 1.152 g. The…
• Number of isomeric products formed by monochlorination of 2-methylbutane in presence of…
• The values of conductivity of some materials at 298.15 K⁻¹ in Sm⁻¹ are 2.1 × 10³, 1.0 ×…
• Given below are two statements: Statement I : Group 13 trivalent halides get easily…

Mathematics

• Let f: → ℝ →(0, ∞) be strictly increasing function such that lim x → ∞ f(7 x)/f(x)=1…
• If the function f:(-∞,-1] →(a, b] defined by f(x)=e^(x³-3 x+1) is one - one and onto…
• If lim x → 0 (a x² eˣ-b log ₑ(1+x)+c x e⁻ˣ)/(x² sin x)=1, then 16(a²+b²+c²) is equal to…
• If a=sin ⁻¹(sin (5)) and b=cos ⁻¹(cos (5)), then a²+b² is equal to
• Let 2ⁿᵈ, 8ᵗʰ and 44ᵗʰ terms of a non-constant A. P. be respectively the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ…
• Let the mean and the variance of 6 observations a, b, 68,44,48,60 be 55 and 194…
• Let the coefficient of xʳ in the expansion of (x+3)ⁿ⁻¹+(x+3)ⁿ⁻²(x+2)+(x+3)ⁿ⁻³(x+2)²+… ……
• Let a, b, c be the lengths of three sides of a triangle satistying the condition (a²+b²)…
• Let a variable line passing through the centre of the circle x²+y²-16 x-4 y=0, meet the…
• Let A={1,2,3, … … … …, 100}. Let R be a relation on A defined by (x, y) ∈ R if and only…
• The number of ways in which 21 identical apples can be distributed among three children…
• Let y=y(x) be the solution of the differential equation sec ² x d x+(e²ʸ tan ² x+tan x)…
• Let (α, β, γ) be the mirror image of the point (2,3,5) in the line…
• Let A(-2,-1),B(1,0),C(α,β) and D(γ,δ) be the vertices of a parallelogram ABCD. If the…
• |120/π³ ∫0^π (x² sin x cos x)/(sin ⁴ x+cos ⁴ x) d x| is equal to ________.
• A coin is biased so that a head is twice as likely to occur as a tail. If the coin is…
• A line passes through A(4,-6,-2) and B(16,-2,4). The point P(a, b, c), where a, b, c are…
• Let P be a parabola with vertex (2,3) and directrix 2 x+y=6. Let an ellipse E…
• Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid, circumcentre and…
• Consider the function f:(0, ∞) → ℝ defined by f(x)=e^(-|log ₑ x|). If m and n be…
• If for some m, n ; ⁶ Cₘ+2( ⁶ Cₘ₊₁)+ ⁶ Cₘ₊₂> ⁸ C₃ and ⁿ⁻¹ P₃: ⁿ P₄=1: 8, then ⁿ Pₘ₊₁+ ⁿ⁺¹…
• Let A be a 3 × 3 matrix and det(A)=2. If n=det(adj(adj(… . .(adj A))₂₀₂₄₋ₜᵢₘₑₛ)), then…
• The area of the region enclosed by the parabolas y=4x-x² and 3y=(x-4)² is equal to :
• The number of solutions, of the equation eˢⁱⁿˣ-2e⁻ˢⁱⁿˣ=2, is :
• Let z₁ and z₂ be two complex numbers such that z₁+z₂=5 and z₁³+z₂³=20+15 i Then…
• Let a⃗=3 î+2 ĵ+k̂, b⃗=2 î-ĵ+3 k̂ and c⃗ be a vector such that (a⃗+b⃗) × c⃗=2(a⃗ × b⃗)+24…
• The temperature T(t) of a body at time t=0 is 160° F and it decreases continuously as…
• The shortest distance, between lines L₁ and L₂, where L₁: (x-1)/2=(y+1)/-3=(z+4)/2 and…
• Let A be a 3 × 3 real matrix such that A(1; 0; 1)=2(1; 0; 1), A(-1; 0; 1)=4(-1; 0; 1)…
• Let f, g:(0, ∞) → ℝ be two functions defined by f(x)=∫₋ₓˣ(|t|-t²) e^(-t²) d t and…

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