JEE Main 2024 (Online) 29th January Morning Shift — Question Paper

Download this paper as a PDF (15 pages, with answer key)

Physics

• A capacitor of capacitance 100 μ F is charged to a potential of 12 V and connected to a…
• A 16 Ω wire is bend to form a square loop. A 9 V battery with internal resistance 1 Ω is…
• A body starts moving from rest with constant acceleration covers displacement S₁ in…
• A thermodynamic system is taken from an original state A to an intermediate state B by a…
• If the radius of curvature of the path of two particles of same mass are in the ratio 3…
• The explosive in a Hydrogen bomb is a mixture of ₁ H², ₁ H³ and ₃ Li⁶ in some condensed…
• Match List I with List II List - I | List - II; (A) | ∮ B⃗ · d l⃗=μₒ i_c+μₒ εₒ (d…
• A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the…
• A cylinder is rolling down on an inclined plane of inclination 60°. It's acceleration…
• When a hydrogen atom going from n=2 to n=1 emits a photon, its recoil speed is x/5 m /…
• The potential energy function (in J ) of a particle in a region of space is given as…
• Given below are two statements: Statement I : If a capillary tube is immersed first in…
• A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal…
• An electron is moving under the influence of the electric field of a uniformly charged…
• In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper…
• The electric current through a wire varies with time as I=I₀+β t, where I₀=20 A and β=3…
• Two vessels A and B are of the same size and are at same temperature. A contains 1 g of…
• The magnetic potential due to a magnetic dipole at a point on its axis situated at a…
• The resistance R=V/I where V=(200± 5)V and I=(20± 0.2)A, the percentage error in the…
• In the given circuit, the breakdown voltage of the Zener diode is 3.0 V. What is the…
• When the displacement of a simple harmonic oscillator is one third of its amplitude, the…
• At what distance above and below the surface of the earth a body will have same weight…
• The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of…
• A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current…
• The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a…
• A square loop of side 10 cm and resistance 0.7 Ω is placed vertically in east-west…
• A convex mirror of radius of curvature 30 cm forms an image that is half the size of the…
• A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m…
• Two charges of 5 Q and -2 Q are situated at the points (3 a, 0) and (-5 a, 0)…

Chemistry

• Given below are two statements : one is labelled as Assertion A and the other is…
• In which one of the following metal carbonyls, CO forms a bridge between metal atoms?
• The correct set of four quantum numbers for the valence electron of rubidium atom (Z=37)…
• Number of compounds among the following which contain sulphur as heteroatom is…
• the arenium ion which is not involved in the bromination of Aniline is __________.
• Number of compounds with one lone pair of electrons on central atom amongst following is…
• Appearance of blood red colour, on treatment of the sodium fusion extract of an organic…
• KMnO₄ decomposes on heating at 513 K to form O₂ along with
• From the compounds given below, number of compounds which give positive Fehling's test…
• Match List I with List II List - I (Substances) | List - II (Element Present); (A) |…
• Identify the incorrect pair from the following :
• In alkaline medium, MnO₄⁻ oxidises I⁻ to
• Given below are two statements : one is labelled as Assertion A and the other is…
• Type of amino acids obtained by hydrolysis of proteins is :
• A solution of H₂ SO₄ is 31.4 % H₂ SO₄ by mass and has a density of 1.25 g / mL. The…
• Which of the following is not correct?
• The mass of zinc produced by the electrolysis of zine sulphate solution with a steady…
• Chlorine undergoes disproportionation in alkaline medium as shown below : aCl_(2( g))+b…
• Given below are two statements : Statement I : The electronegativity of group 14…
• The difference in energy between the actual structure and the lowest energy resonance…
• For a reaction taking place in three steps at same temperature, overall rate constant…
• The osmotic pressure of a dilute solution is 7 × 10⁵ Pa at 273 K. Osmotic pressure of…
• The interaction between π bond and lone pair of electrons present on an adjacent atom is…
• For the reaction N₂O_(4( g))⇄ 2NO_(2( g)),Kₚ=0.492 atm at 300 K.K_c for the reaction at…
• The number of species from the following which are paramagnetic and with bond order…
• In chromyl chloride test for confirmation of Cl⁻ ion, a yellow solution is obtained…

Mathematics

• lim _(x → π/2) ( 1/( x - π/2 )²∫_(x³)^(( π/2 )³) cos ( t^(1/3) )dt ) is equal to
• Suppose f(x)=((2ˣ+2⁻ˣ) tan x √(tan ⁻¹(x²-x+1)))/(7 x²+3 x+1)³. Then the value of f′(0)…
• Let O be the origin and the position vectors of A and B be 2 î+2 ĵ+k̂ and 2 î+4 ĵ+4 k̂…
• If z=1/2-2 i is such that |z+1|=α z+β(1+i), i=√-1 and α, β ∈ ℝ, then α+β is equal to
• In an A.P., the sixth term a₆=2. If the product a₁ a₄ a₅ is the greatest, then the…
• If α,-π/2<α<π/2 is the solution of 4 cos θ+5 sin θ=1, then the value of tan α is
• If the points of intersection of two distinct conics x²+y²=4b and x²/16+y²/b²=1 lie on…
• If the mean and variance of the data 65,68,58,44,48,45,60, α, β, 60 where α> β, are 56…
• If the solution curve y=y(x) of the differential equation (1+y²)(1+log ₑ x) d x+x d y=0…
• Let A be a square matrix such that AAᵀ=I. Then 1/2 A[(A+Aᵀ)²+(A-Aᵀ)²] is equal to
• Let R be a relation on Z × Z defined by (a, b) R(c, d) if and only if a d-b c is…
• Consider the function f:[1/2, 1] → ℝ defined by f(x)=4 √2 x³-3 √2 x-1. Consider the…
• A fair die is thrown until 2 appears. Then the probability, that 2 appears in even…
• Let f(x)=2ˣ-x², x ∈ ℝ. If m and n are respectively the number of points at which the…
• Let P Q R be a triangle with R(-1,4,2). Suppose M(2,1,2) is the mid point of PQ. The…
• Equations of two diameters of a circle are 2 x-3 y=5 and 3 x-4 y=7. The line joining the…
• Let A=[1, 0, 0; 0, α, β; 0, β, α] and |2 A|³=2²¹ where α, β ∈ Z , Then a value of α is
• If f(x)={2+2 x,, -1 ≤ x < 0; 1-x/3,, 0 ≤ x ≤ 3 ; g(x)={-x,, -3 ≤ x ≤ 0; x,, 0 < x ≤ 1…
• The area (in sq. units) of the part of the circle x²+y²=169 which is below the line…
• Let α, β be the roots of the equation x²-x+2=0 with Im(α)>Im(β). Then α⁶+α⁴+β⁴-5 α² is…
• If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms…
• If the value of the integral ∫-π/2^(π/2)((x² cos x)/(1+πˣ)+(1+sin ² x)/(1+e^(sin…
• A line with direction ratios 2,1,2 meets the lines x=y+2=z and x+2=2 y=2 z respectively…
• A function y=f(x) satisfies f(x) sin 2 x+sin x-(1+cos ² x) f′(x)=0 with condition…
• Let a⃗, b⃗ and c⃗ be three non-zero vectors such that b⃗ and c⃗ are non-collinear. If…
• For x∈ (-π/2,π/2), if y(x)=∫ (cosecx+sin x)/(cosecx sec x+tan x sin² x)dx, and limy(x)=0…
• All the letters of the word "GTWENTY" are written in all possible ways with or without…
• If (¹¹ C₁)/2+(¹¹ C₂)/3+…+(¹¹ C₉)/10=n/m with gcd(n, m)=1 , then n+m is equal to _______.
• In a △ ABC, suppose y=x is the equation of the bisector of the angle B and the equation…

Download all JEE Main 2024 PYQs chapter-wise as free PDFs