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

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Physics

• The depth below the surface of sea to which a rubber ball be taken so as to decrease its…
• Two conductors have the same resistances at 0° C but their temperature coefficients of…
• The fundamental frequency of a closed organ pipe is equal to the first overtone…
• When a metal surface is illuminated by light of wavelength λ, the stopping potential is…
• The parameter that remains the same for molecules of all gases at a given temperature is :
• If the wavelength of the first member of Lyman series of hydrogen is λ. The wavelength…
• A small steel ball is dropped into a long cylinder containing glycerine. Which one of…
• A small square loop of wire of side l is placed inside a large square loop of wire of…
• If the percentage errors in measuring the length and the diameter of a wire are 0.1%…
• A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is…
• The given figure represents two isobaric processes for the same mass of an ideal gas, then
• A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of…
• A rigid wire consists of a semicircular portion of radius R and two straight sections…
• A coil is places perpendicular to a magnetic field of 5000 T. When the field is changed…
• The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is n ×…
• In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 ×…
• Identify the logic operation performed by the given circuit.
• An electron moves through a uniform magnetic field B⃗=B₀ î+2 B₀ ĵ T. At a particular…
• A body starts falling freely from height H hits an inclined plane in its path at height…
• The relation between time 't' and distance 'x' is t=α x²+β x, where α and β are…
• An artillery piece of mass M₁ fires a shell of mass M₂ horizontally. Instantaneously…
• Two charges q and 3 q are separated by a distance 'r' in air. At a distance x from…
• In the given arrangement of a doubly inclined plane two blocks of masses M and m are…
• A force is represented by F=ax²+bt^(1/2) where x= distance and t= time. The dimensions…
• Two waves of intensity ratio 1: 9 cross each other at a point. The resultant intensities…
• A coin is placed on a disc. The coefficient of friction between the coin and the disc is…
• The refractive index of a prism with apex angle A is cot A / 2. The angle of minimum…
• A particle performs simple harmonic motion with amplitude A. Its speed is increased to…
• Four identical particles of mass m are kept at the four corners of a square. If the…

Chemistry

• The product (C) in the below mentioned reaction is : CH₃-CH₂-CH₂-Br →(KOH_((alc))) A…
• The compound that is white in color is
• Number of moles of methane required to produce 22 g CO_(2( g)) after combustion is x ×…
• Identify the factor from the following that does not affect electrolytic conductance of…
• The ionization energy of sodium in kJ mol⁻¹, if electromagnetic radiation of wavelength…
• Number of alkanes obtained on electrolysis of a mixture of CH₃ COONa and C₂ H₅ COONa is…
• Match List I with List II List - I (Technique) | List - II (Application; (A) |…
• For the given reaction, choose the correct expression of K_C from the following :-…
• Given below are two statements: Statement I: IUPAC name of HO-CH₂-(CH₂)₃-CH₂-COCH₃ is…
• Consider the following reaction at 298 K · 3/2 O_(2(g)) ⇌ O_(3(g)) · K_P=2.47 × 10⁻²⁹…
• 'Adsorption' principle is used for which of the following purification method?
• The metals that are employed in the battery industries are A. Fe B. Mn C. Ni D. Cr E. Cd…
• Identify the mixture that shows positive deviations from Raoult's Law
• Molar mass of the salt from NaBr, NaNO₃, KI and CaF₂ which does not evolve coloured…
• Give below are two statements: Statement - I: Noble gases have very high boiling points…
• One Faraday of electricity liberates x × 10⁻¹ gram atom of copper from copper sulphate…
• The linear combination of atomic orbitals to form molecular orbitals takes place only…
• Identify correct statements from below: A. The chromate ion is square planar. B…
• The number of species from the following in which the central atom uses sp³ hybrid…
• Given below are two statements: One is labelled as Assertion A and the other is labelled…
• The correct statements from following are: A. The strength of anionic ligands can be…
• Match List I with List II List - I | List - II; (A) | Glucose/NaHCO₃/Δ | (I) | Gluconic…
• A species having carbon with sextet of electrons and can act as electrophile is called
• Integrated rate law equation for a first order gas phase reaction is given by (where Pᵢ…
• The 'Spin only' Magnetic moment for [Ni(NH₃)₆]²⁺ is _________ × 10⁻¹ BM. (given = Atomic…
• Given below are two statements: One is labelled as Assertion A and the other is labelled…
• Consider the oxides of group 14 elements SiO₂, GeO₂, SnO₂, PbO₂, CO and GeO. The…
• The correct sequence of electron gain enthalpy of the elements listed below is A. Ar B…

Mathematics

• Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x=y…
• If the system of linear equations x-2 y+z=-4 ; 2 x+α y+3 z=5 ; 3 x-y+β z=3 has…
• Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and…
• Three rotten apples are accidently mixed with fifteen good apples. Assuming the random…
• For α, β, γ ≠ 0, if sin ⁻¹ α+sin ⁻¹ β+sin ⁻¹ γ=π and (α+β+γ)(α-γ+β)=3 α β, then γ equals
• If α denotes the number of solutions of |1-i|ˣ=2ˣ and β=(|z|/(arg (z))), where…
• Let a⃗=3 î+ĵ-2 k̂, b⃗=4 î+ĵ+7 k̂ and c⃗=î-3 ĵ+4 k̂ be three vectors. If a vectors p⃗…
• Let the foci and length of the latus rectum of an ellipse x²/a²+y²/b²=1, a>b b e( ± 5,0)…
• Let S be the set of positive integral values of a for which (a x²+2(a+1) x+9 a+4)/(x²-8…
• For 0 < c < b < a, let (a+b-2 c) x²+(b+c-2 a) x+(c+a-2 b)=0 and α ≠ 1 be one of its…
• The total number of words (with or without meaning) that can be formed out of the…
• The sum of the series 1/(1-3 · 1²+1⁴)+2/(1-3 · 2²+2⁴)+3/(1-3 · 3²+3⁴)+… up to 10 -terms is
• The area of the region {(x,y):y²≤ 4x,x<4,xy(x-1)(x-2)/(x-3)(x-4)>0,x≠ 3} is
• Let f: ℝ → ℝ be a function defined by f(x)=4ˣ/(4ˣ+2) and M=∫f(a)ᶠ⁽¹⁻ᵃ⁾ x sin ⁴(x(1-x)) d…
• In the expansion of (1+x)(1-x²)(1+3/x+3/x²+1/x³)⁵, x ≠ 0, the sum of the coefficients of…
• lim x → 0 (e^(2|sin x|)-2|sin x|-1)/x²
• If f(x)=(4 x+3)/(6 x-4), x ≠ 2/3 and (f ° f)(x)=g(x), where g: ℝ-{2/3} → ℝ-{2/3}, then…
• If the foci of a hyperbola are same as that of the ellipse x²/9+y²/25=1 and the…
• Let A={1,2,3,4} and R={(1,2),(2,3),(1,4)} be a relation on A. Let S be the equivalence…
• If one of the diameters of the circle x²+y²-10 x+4 y+13=0 is a chord of another circle…
• Let S=(-1, ∞) and f: S → ℝ be defined as f(x)=∫-1ˣ(eᵗ-1)¹¹(2 t-1)⁵(t-2)⁷(t-3)¹²(2…
• Let g(x) be a linear function and f(x)={g(x), , x ≤ 0; ((1+x)/(2+x))^(1/x), , x>0, is…
• The solution curve of the differential equation y (d x)/(d y)=x(log ₑ x-log ₑ y+1), x>0…
• Let y=y(x) be the solution of the differential equation (d y)/(d x)=((tan x)+y)/(sin…
• If the integral 525 ∫0^(π/2) sin 2 x cos ^(11/2) x(1+Cos^(5/2) x)^(1/2) d x is equal to…
• Let α,β,γ,δ∈ ℤ and let A(α,β),B(1,0),C(γ,δ) and D(1,2) be the vertices of a…
• If f(x)=|x³, 2 x²+1, 1+3 x; 3 x²+2, 2 x, x³+6; x³-x, 4, x²-2| for all x ∈ ℝ , then 2…
• Let a be the sum of all coefficients in the expansion of (1-2 x+2 x²)²⁰²³(3-4 x²+2…
• The distance of the point Q(0,2,-2) form the line passing through the point P(5,-4, 3)…
• Let a⃗ and b⃗ be two vectors such that |a⃗|=1,|b⃗|=4, and a⃗ · b⃗=2. If c⃗=(2 a⃗ × b⃗)-3…

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