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

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Physics

• A particle is moving in a circle of radius 50 cm in such a way that at any instant the…
• A small liquid drop of radius R is divided into 27 identical liquid drops. If the…
• N moles of a polyatomic gas (f=6) must be mixed with two moles of a monoatomic gas so…
• If the distance between object and its two times magnified virtual image produced by a…
• A planet takes 200 days to complete one revolution around the Sun. If the distance of…
• In an a.c. circuit, voltage and current are given by: V=100 sin (100 t) V and I=100 sin…
• The temperature of a gas having 2.0 × 10²⁵ molecules per cubic meter at 1.38 atm (Given…
• A particle is moving in a straight line. The variation of position 'x' as a function of…
• A body of mass 5 kg moving with a uniform speed 3 √2 ms⁻¹ in X-Y plane along the line…
• An electric field is given by (6 î+5 ĵ+3 k̂) N / C. The electric flux through a surface…
• The truth table for this given circuit is :
• A wire of length L and radius r is clamped at one end. If its other end is pulled by a…
• Hydrogen atom is bombarded with electrons accelerated through a potential difference of…
• Two metallic wires P and Q have same volume and are made up of same material. If their…
• In Young's double slit experiment, light from two identical sources are superimposing on…
• In the given figure, the charge stored in 6 μ F capacitor, when points A and B are…
• A charge of 4.0 μ C is moving with a velocity of 4.0 × 10⁶ ms⁻¹ along the positive y…
• Given below are two statements: Statement I : Most of the mass of the atom and all its…
• In a single slit diffraction pattern, a light of wavelength 6000Aᵒ is used. The distance…
• In the given circuit, the current in resistance R₃ is :
• A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m…
• Two particles X and Y having equal charges are being accelerated through the same…
• A simple harmonic oscillator has an amplitude A and time period 6 π second. Assuming the…
• A physical quantity Q is found to depend on quantities a,b,c by the relation Q=a⁴b³/c²…
• A plane electromagnetic wave of frequency 35 MHz travels in free space along the…
• A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum…
• Two sources of light emit with a power of 200 W. The ratio of number of photons of…
• A horizontal straight wire 5 m long extending from east to west falling freely at right…
• In the given circuit, the current flowing through the resistance 20 Ω is 0.3 A, while…
• The bob of a pendulum was released from a horizontal position. The length of the…

Chemistry

• Which of the following acts as a strong reducing agent? (Atomic number: Ce=58, Eu=63…
• On passing a gas, 'X', through Nessler's regent, a brown precipitate is obtained. The…
• Given below are two statements: Statement I : Fluorine has most negative electron gain…
• The total number of anti bonding molecular orbitals, formed from 2 s and 2 p atomic…
• The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after…
• The following concentrations were observed at 500 K for the formation of NH₃ from N₂ and…
• The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is _________.
• Chromatographic technique/s based on the principle of differential adsorption is / are…
• The correct IUPAC name of K₂ MnO₄ is
• The total number of molecules with zero dipole moment among CH₄, BF₃, H₂ O, HF, NH₃, CO₂…
• If 50 mL of 0.5 M oxalic acid is required to neutralise 25 mL of NaOH solution, the…
• Match List I with List II List - I (Bio Polymer) | List - II (Monomer); (A) | Starch |…
• Molality of 0.8 M H₂SO₄ solution (density 1.06 g cm⁻³) is ________ ×10⁻³ m.
• Match List I with List II List - I (Spectral Series for Hydrogen) | List - II (Spectral…
• A reagent which gives brilliant red precipitate with Nickel ions in basic medium is
• Standard enthalpy of vapourisation for CCl₄ is 30.5 kJ mol⁻¹. Heat required for…
• Anomalous behavior of oxygen is due to its
• According to IUPAC system, the compound is named as
• Which of the following reaction is correct?
• Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed…
• Alkyl halide is converted into alkyl isocyanide by reaction with
• The ascending acidity order of the following H atoms is
• The element having the highest first ionization enthalpy is
• Which one of the following will show geometrical isomerism?
• The oxidation number of iron in the compound formed during brown ring test for NO₃⁻ iron…
• The product A formed in the following reaction is
• A constant current was passed through a solution of AuCl₄⁻ ion between gold electrodes…
• Match List I with List II List - I (Compound) | List - II (pKₐ value); (A) | Ethanol |…
• Which of the following statements are correct about Zn, Cd and Hg ? A. They exhibit high…

Mathematics

• If the mean and variance of five observations are 24/5 and 194/25 respectively and the…
• Let O be the origin, and M and N be the points on the lines (x-5)/4=(y-4)/1=(z-5)/3 and…
• Let P(3,2,3), Q(4,6,2) and R(7,3,2) be the vertices of △ PQR. Then, the angle ∠ QPR is
• Let P(α, β) be a point on the parabola y²=4 x. If P also lies on the chord of the…
• The function f(x)=2 x+3(x)^(2/3), x ∈ ℝ, has
• Let f(x)=√(lim r → x{(2 r²[(f(r))²-f(x) f(r)])/(r²-x²)-r³ e^(f(r)/r)}) be differentiable…
• If ∫ (sin^(3/2) x+cos^(3/2) x)/√(sin³ x cos³ x sin (x-θ))dx=A√(cos θ tan x-sin θ)+B√(cos…
• Number of ways of arranging 8 identical books into 4 identical shelves where any number…
• If sin (y/x)=log ₑ|x|+α/2 is the solution of the differential equation x cos (y/x) (d…
• Let r and θ respectively be the modulus and amplitude of the complex number z=2-i(2 tan…
• If log ₑ a, log ₑ b, log ₑ c are in an A.P. and log ₑ a-log ₑ 2 b, log ₑ 2 b-log ₑ 3 c…
• Let a unit vector u=x î+y ĵ+z k̂ make angles π/2, π/3 and (2 π)/3 with the vectors 1/√2…
• An integer is chosen at random from the integers 1,2,3, …, 50. The probability that the…
• Let the slope of the line 45 x+5 y+3=0 be 27 r₁+(9 r₂)/2 for some r₁, r₂ ∈ ℝ. Then lim x…
• Let A=[2, 1, 2; 6, 2, 11; 3, 3, 2] and P=[1, 2, 0; 5, 0, 2; 7, 1, 5]. The sum of the…
• Let x=m/n (m, n are co-prime natural numbers) be a solution of the equation cos (2 sin…
• Let A be the point of intersection of the lines 3x+2y=14,5x-y=6 and B be the point of…
• The sum of the solutions x ∈ ℝ of the equation (3 cos 2 x+cos ³ 2 x)/(cos ⁶ x-sin ⁶…
• Let the area of the region {(x,y):0≤ x≤ 3,0≤ y≤ min{x²+2,2x+2}} be A. Then 12 A is equal…
• The distance of the point (2,3) from the line 2x-3y+28=0, measured parallel to the line…
• Let α, β be the roots of the equation x²-√6 x+3=0 such that Im(α)>Im(β). Let a, b be…
• Let for any three distinct consecutive terms a, b, c of an A.P, the lines a x+b y+c=0 be…
• Let the set C={(x, y) | x²-2ʸ=2023, x, y ∈ ℕ}. Then Σ(x, y) ∈ C(x+y) is equal to…
• Remainder when 64^(32³²) is divided by 9 is equal to ________.
• If ∫π/6^(π/3) √(1-sin 2 x) d x=α+β √2+γ √3, where α, β and γ are rational numbers, then…
• Let y=log ₑ((1-x²)/(1+x²)),-1 < x<1 . Then at x=1/2 , the value of 225(y′-y^(′ ′)) is…
• If R is the smallest equivalence relation on the set {1,2,3,4} such that {(1,2),(1,3)} ⊂…
• The function f(x)=x/(x²-6 x-16), x ∈ ℝ-{-2,8}
• Let O A⃗=a⃗, O B⃗=12 a⃗+4 b⃗ and O C⃗=b⃗, where O is the origin. If S is the…
• If each term of a geometric progression a₁, a₂, a₃, … with a₁=1/8 and a₂ ≠ a₁, is the…

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