JEE Main 2024 (Online) 30th January Morning Shift — Question Paper

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Physics

• An electric toaster has resistance of 60 Ω at room temperature (27° C). The toaster is…
• Young's modules of material of a wire of length 'L' and cross-sectional area A is Y. If…
• The gravitational potential at a point above the surface of earth is -5.12 × 10⁷ J / kg…
• The displacement and the increase in the velocity of a moving particle in the time…
• A potential divider circuit is shown in figure. The output voltage V₀ is :
• The electric field of an electromagnetic wave in free space is represented as E⃗=E₀ cos…
• A particle of mass m is projected with a velocity 'u' making an angle of 30° with the…
• A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After…
• A particle is placed at the point A of a frictionless track A B C as shown in figure. It…
• The work function of a substance is 3.0 eV. The longest wavelength of light that can…
• Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad / s…
• The horizontal component of earth's magnetic field at a place is 3.5 × 10⁻⁵ T. A very…
• A capacitor of capacitance C and potential V has energy E. It is connected to another…
• A series L.R circuit connected with an ac source E=(25 sin 1000 t) V has a power factor…
• Two thermodynamical processes are shown in the figure. The molar heat capacity for…
• In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of…
• At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an…
• Match List I with List II. List I | List II; (A) | Coefficient of viscosity | (I) | [ML²…
• A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity…
• Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of…
• The electrostatic potential due to an electric dipole at a distance 'r' varies as :
• The distance between object and its two times magnified real image as produced by a…
• A Zener diode of breakdown voltage 10 V is used as a voltage regulator as shown in the…
• All surfaces shown in figure are assumed to be frictionless and the pulleys and the…
• Two insulated circular loop A and B of radius 'a' carrying a current of 'I' in the anti…
• The ratio of the magnitude of the kinetic energy to the potential energy of an electron…
• Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A…
• The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width…
• A electron of hydrogen atom on an excited state is having energy Eₙ=-0.85 eV. The…
• Two cells are connected in opposition as shown. Cell E₁ is of 8 V emf and 2 Ω internal…

Chemistry

• Given below are two statements : Statement (I) : The gas liberated on warming a salt…
• The rate of First order reaction is 0.04 mol L⁻¹ s⁻¹ at 10 minutes and 0.03 mol L⁻¹ s⁻¹…
• This reduction reaction is known as:
• Diamagnetic Lanthanoid ions are :
• What happens to freezing point of benzene when small quantity of napthalene is added to…
• The Lassiagne's extract is boiled with dil HNO₃ before testing for halogens because,
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Structure of 4-Methylpent-2-enal is :
• Following is a confirmatory test for aromatic primary amines. Identify reagent (A) and…
• The total number of molecular orbitals formed from 2 s and 2 p atomic orbitals of a…
• Example of vinylic halide is :
• Aluminium chloride in acidified aqueous solution forms an ion having geometry
• On a thin layer chromatographic plate, an organic compound moved by 3.5 cm, while the…
• If IUPAC name of an element is "Unununnium" then the element belongs to nᵗʰ group of…
• Match List I with List II. List I Species | List II Electronic distribution; (A) | Cr⁺²…
• Given below are two statements : Statement (I) : The orbitals having same energy are…
• 2 MnO₄⁻+bI⁻+cH₂ O → x I₂+y MnO₂+z O̅ H If the above equation is balanced with integer…
• Choose the correct statements from the following : (A) Ethane-1, 2-diamine is a…
• The compound formed by the reaction of ethanal with semicarbazide contains _________…
• The pH at which Mg(OH)₂[ Kₛₚ=1 × 10⁻¹¹] begins to precipitate from a solution containing…
• 0.05 cm thick coating of silver is deposited on a plate of 0.05 m² area. The number of…
• Sugar which does not give reddish brown precipitate with Fehling's reagent, is :
• Which of the following molecule/species is most stable?
• The mass of sodium acetate (CH₃ COONa) required to prepare 250 mL of 0.35 M aqueous…
• Given below are two statements : one is labelled as Assertion (A) and the other is…

Mathematics

• Let α, β ∈ N be roots of the equation x²-70 x+λ=0, where λ/2, λ/3 ∉ N. If λ assumes the…
• Let a⃗=a₁ î+a₂ ĵ+a₃ k̂ and b⃗=b₁ î+b₂ ĵ+b₃ k̂ be two vectors such that |a⃗|=1, a⃗ · b⃗=2…
• A line passing through the point A(9,0) makes an angle of 30° with the positive…
• Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram A B C D. If the…
• Let (α, β, γ) be the foot of perpendicular from the point (1,2,3) on the line…
• Let M denote the median of the following frequency distribution Class | 0 - 4 | 4 - 8 |…
• Two integers x and y are chosen with replacement from the set {0,1,2,3, …, 10}. Then the…
• A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics…
• The value of 9 ∫0⁹[√((10 x)/(x+1))] d x, where [t] denotes the greatest integer less…
• If the circles (x+1)²+(y+2)²=r² and x²+y²-4 x-4 y+4=0 intersect at exactly two distinct…
• If the length of the minor axis of an ellipse is equal to half of the distance between…
• Let y=y(x) be the solution of the differential equation (1-x²) d y=[x y+(x³+2) √3(1-x²)]…
• Let Sₙ denote the sum of first n terms of an arithmetic progression. If S₂₀=790 and…
• Let α=1²+4²+8²+13²+19²+26²+… upto 10 terms and β=Σn=1¹⁰ n⁴. If 4 α-β=55 k+40, then k is…
• Number of integral terms in the expansion of {7^((1/2))+11^((1/6))}⁸²⁴ is equal to…
• If d₁ is the shortest distance between the lines x+1=2 y=-12 z, x=y+2=6 z-6 and d₂ is…
• The maximum area of a triangle whose one vertex is at (0,0) and the other two vertices…
• Let g: R → R be a non constant twice differentiable function such that g′(1/2)=g′(3/2)…
• Let the latus rectum of the hyperbola x²/9-y²/b²=1 subtend an angle of π/3 at the centre…
• If the domain of the function f(x)=cos ⁻¹((2-|x|)/4)+{log ₑ(3-x)}⁻¹ is [-α, β)-{γ}, then…
• If f(x)=|2 cos ⁴ x, 2 sin ⁴ x, 3+sin ² 2 x; 3+2 cos ⁴ x, 2 sin ⁴ x, sin ² 2 x; 2 cos ⁴…
• If 2 sin ³ x+sin 2 x cos x+4 sin x-4=0 has exactly 3 solutions in the interval [0, (n…
• The value of lim n → ∞ Σk=1ⁿ n³/(n²+k²)(n²+3 k²) is :
• Let f:[-π/2, π/2] → R be a differentiable function such that f(0)=1/2. If the lim x → 0…
• If the function f(x)= 1/|x|, |x| ≥ 2 ; a x²+2 b, |x|<2 is differentiable on R, then…
• Let y=y(x) be the solution of the differential equation sec x d y+{2(1-x) tan x+x(2-x)}…
• Let A={1,2,3, …, 7} and let P(A) denote the power set of A. If the number of functions…
• If z=x+i y, x y ≠ 0, satisfies the equation z²+i z̄=0, then |z²| is equal to :
• Consider the system of linear equations x+y+z=4 μ, x+2 y+2 λ z=10 μ, x+3 y+4 λ² z=μ²+15…
• The area (in square units) of the region bounded by the parabola y²=4(x-2) and the line…

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