JEE Main 2024 (Online) 6th April Morning Shift — Question Paper

Download this paper as a PDF (17 pages, with answer key)

Physics

• For three vectors A⃗=(-xî-6ĵ-2k̂),B⃗=(-î+4ĵ+3k̂) and C⃗=(-8î-ĵ+3k̂), if A⃗· (B⃗× C⃗)=0…
• A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ₀. After…
• A wire of resistance R and radius r is stretched till its radius became r / 2. If new…
• The specific heat at constant pressure of a real gas obeying P V²=R T equation is:
• A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed…
• A train starting from rest first accelerates uniformly up to a speed of 80 km / h for…
• A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface…
• The correct truth table for the following logic circuit is :
• Given below are two statements : Statement I : In an LCR series circuit, current is…
• The value of unknown resistance (x) for which the potential difference between B and D…
• Four particles A, B, C, D of mass m/2, m, 2 m, 4 m, have same momentum, respectively…
• If the radius of earth is reduced to three-fourth of its present value without change in…
• The ratio of the shortest wavelength of Balmer series to the shortest wavelength of…
• A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s…
• Which of the following phenomena does not explain by wave nature of light. A. reflection…
• Electromagnetic waves travel in a medium with speed of 1.5 × 10⁸ m s⁻¹. The relative…
• In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The…
• To find the spring constant (k) of a spring experimentally, a student commits 2%…
• A circular coil having 200 turns, 2.5 × 10⁻⁴ m² area and carrying 100 μ A current is…
• An element Δ l=Δ xî is placed at the origin and carries a large current I=10 A. The…
• A light string passing over a smooth light pulley connects two blocks of masses m₁ and…
• σ is the uniform surface charge density of a thin spherical shell of radius R. The…
• Radius of a certain orbit of hydrogen atom is 8.48 Aᵒ. If energy of electron in this…
• A bullet of mass 50 g is fired with a speed 100 m / s on a plywood and emerges with 40 m…
• Three infinitely long charged thin sheets are placed as shown in figure. The magnitude…
• To project a body of mass m from earth's surface to infinity, the required kinetic…
• When a d c voltage of 100 V is applied to an inductor, a d c current of 5 A flows…
• The refractive index of prism is μ=√3 and the ratio of the angle of minimum deviation to…
• While measuring diameter of wire using screw gauge the following readings were noted…
• Match List I with List II LIST I | LIST II; A. | Torque | I. | [M¹L¹T⁻²A⁻²]; B. |…

Chemistry

• Given below are two statements : Statement I : Gallium is used in the manufacturing of…
• Which of the following is metamer of the given compound (X) ?
• Which of the following material is not a semiconductor.
• A conductivity cell with two electrodes (dark side) are half filled with infinitely…
• Which among the following aldehydes is most reactive towards nucleophilic addition…
• The difference in the 'spin-only' magnetic moment values of KMnO₄ and the manganese…
• Consider the dissociation of the weak acid HX as given below HX(aq) ⇌ H⁺(aq)+X⁻(aq)…
• The major product of the following reaction is P. CH₃ C≡C-CH₃ →((i) Na /liq. NH₃) 'P'…
• 9.3 g of pure aniline upon diazotisation followed by coupling with phenol gives an…
• Functional group present in sulphonic acids is :
• Number of molecules from the following which can exhibit hydrogen bonding is _________…
• In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an…
• Consider the following complexes (A) [CoCl(NH₃)₅]²⁺, (B) [Co(CN)₆]³⁻, (C) [Co(NH₃)₅(H₂…
• Given below are two statements : Statement I : Piciric acid is 2,4,6 - trinitrotoluene…
• Match List I with List II LIST I (Compound/Species) | LIST II (Shape/Geometry); A. | SF₄…
• Time required for 99.9 % completion of a first order reaction is _________ times the…
• Match List I with List II LIST I (Molecule/Species) | LIST II (Property/Shape); A. |…
• The electron affinity value are negative for A. Be → Be⁻ B. N → N⁻ C. O → O²⁻ D. Na →…
• Match List I with List II LIST I (Hybridization) | LIST II (Orientation in Shape); A. |…
• The density of 'x' M solution ('x' molar) of NaOH is 1.12 g mL⁻¹, while in molality, the…
• Match List I with List II LIST I (Compound) | LIST II (Uses); A. | Idoform | I. | Fire…
• Match List I with List II LIST I (Precipitating reagent and conditions) | LIST II…
• At -20°C and 1 atm pressure, a cylinder is filled with equal number of H₂,I₂ and HI…
• An ideal gas, C̅ᵥ=5/2 R, is expanded adiabatically against a constant pressure of 1 atm…
• Which of the following statements are correct? A. Glycerol is purified by vacuum…
• The number of element from the following that do not belong to lanthanoids is Eu, Cm…
• Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is…
• Among CrO, Cr₂ O₃ and CrO₃, the sum of spin-only magnetic moment values of basic and…
• DNA molecule contains 4 bases whose structure are shown below. One of the structures is…

Mathematics

• A company has two plants A and B to manufacture motorcycles. 60 % motorcycles are…
• Let P be the point (10,-2,-1) and Q be the foot of the perpendicular drawn from the…
• Let A={n ∈[100,700] ∩ N: n is neither a multiple of 3 nor a multiple of 4}. Then the…
• Let y=y(x) be the solution of the differential equation (2 x log ₑ x) (d y)/(d x)+2…
• ∫0^(π / 4) (cos ² x sin ² x)/(cos ³ x+sin ³ x)² d x is equal to
• Let C be the circle of minimum area touching the parabola y=6-x² and the lines y=√3|x|…
• Let L₁, L₂ be the lines passing through the point P(0,1) and touching the parabola 9…
• Let α, β be the distinct roots of the equation x²-(t²-5 t+6) x+1=0, t ∈ ℝ and aₙ=αⁿ+βⁿ…
• If the second, third and fourth terms in the expansion of (x+y)ⁿ are 135, 30 and 10/3…
• Let α β γ=45 ; α, β, γ ∈ ℝ. If x(α, 1,2)+y(1, β, 2)+z(2,3, γ)=(0,0,0) for some x, y, z ∈…
• If f(x)={x³ sin (1/x),, x ≠ 0; 0, , x=0 , then
• Let x₁, x₂, x₃, x₄ be the solution of the equation 4 x⁴+8 x³-17 x²-12 x+9=0 and…
• Let y=y(x) be the solution of the differential equation (1+x²) (d y)/(d x)+y=e^(tan ⁻¹…
• The number of triangles whose vertices are at the vertices of a regular octagon but none…
• The function f(x)=(x²+2 x-15)/(x²-4 x+9), x ∈ ℝ is
• Let the relations R₁ and R₂ on the set X={1,2,3, …, 20} be given by R₁={(x, y): 2 x-3…
• Let f:(-∞, ∞)-{0} → ℝ be a differentiable function such that f′(1)=lim a → ∞ a² f(1/a)…
• Let a variable line of slope m>0 passing through the point (4,-9) intersect the…
• Let rₖ=(∫₀¹(1-x⁷)ᵏ d x)/(∫₀¹(1-x⁷)ᵏ⁺¹ d x), k ∈ ℕ. Then the value of Σk=1¹⁰ 1/7(rₖ-1) is…
• Let the first term of a series be T₁=6 and its rᵗʰ term Tᵣ=3 Tᵣ₋₁+6ʳ, r=2,3…
• Let a conic C pass through the point (4,-2) and P(x, y), x ≥ 3, be any point on C. Let…
• The shortest distance between the lines (x-3)/2=(y+15)/-7=(z-9)/5 and…
• The interval in which the function f(x)=xˣ, x>0, is strictly increasing is
• Let the area of the region enclosed by the curves y=3x,2y=27-3x and y=3x-x√x be A. Then…
• Let a⃗=2 î-3 ĵ+4 k̂, b⃗=3 î+4 ĵ-5 k̂ and a vector c⃗ be such that a⃗ ×(b⃗+c⃗)+b⃗ ×…
• A circle is inscribed in an equilateral triangle of side of length 12. If the area and…
• For n ∈ N, if cot ⁻¹ 3+cot ⁻¹ 4+cot ⁻¹ 5+cot ⁻¹ n=π/4, then n is equal to ________.
• If A(3,1,-1), B(5/3, 7/3, 1/3), C(2,2,1) and D(10/3, 2/3, -1/3) are the vertices of a…
• The mean and standard deviation of 20 observations are found to be 10 and 2…
• For α, β ∈ ℝ and a natural number n, let Aᵣ=|r, 1, n²/2+α; 2 r, 2, n²-β; 3 r-2, 3, n(3…

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