JEE Main 2024 (Online) 4th April Evening Shift — Question Paper

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Physics

• Identify the logic gate given in the circuit :
• Given below are two statements : Statement I : The contact angle between a solid and a…
• In a system two particles of masses m₁=3 kg and m₂=2 kg are placed at certain distance…
• A bus moving along a straight highway with speed of 72 km / h is brought to halt within…
• A rod of length 60 cm rotates with a uniform angular velocity 20 rad s⁻¹ about its…
• A cyclist starts from the point P of a circular ground of radius 2 km and travels along…
• Applying the principle of homogeneity of dimensions, determine which one is correct…
• In simple harmonic motion, the total mechanical energy of given system is E. If mass of…
• A 90 kg body placed at 2 R distance from surface of earth experiences gravitational pull…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• A body of m kg slides from rest along the curve of vertical circle from point A to B in…
• The width of one of the two slits in a Young's double slit experiment is 4 times that of…
• Arrange the following in the ascending order of wavelength: A. Gamma rays (λ₁) B. x -…
• An electric bulb rated 50 W-200 V is connected across a 100 V supply. The power…
• The displacement of a particle executing SHM is given by x=10 sin (w t+π/3) m. The time…
• A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected…
• Two wires A and B are made up of the same material and have the same mass. Wire A has…
• Correct formula for height of a satellite from earths surface is :
• The magnetic moment of a bar magnet is 0.5 Am². It is suspended in a uniform magnetic…
• A sample of gas at temperature T is adiabatically expanded to double its volume…
• The translational degrees of freedom (fₜ) and rotational degrees of freedom (fᵣ) of CH₄…
• The disintegration energy Q for the nuclear fission of ²³⁵ U → ¹⁴⁰ Ce+ ⁹⁴ Zr+n is…
• A charge q is placed at the center of one of the surface of a cube. The flux linked with…
• Two parallel long current carrying wire separated by a distance 2 r are shown in the…
• Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by…
• A 2 kg brick begins to slide over a surface which is inclined at an angle of 45° with…
• According to Bohr's theory, the moment of momentum of an electron revolving in 4ᵗʰ orbit…
• A light ray is incident on a glass slab of thickness 4 √3 cm and refractive index √2 The…

Chemistry

• Choose the Incorrect Statement about Dalton's Atomic Theory
• The correct statement/s about Hydrogen bonding is/are A. Hydrogen bonding exists when H…
• The adsorbent used in adsorption chromatography is/are - A. silica gel B. alumina C…
• Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and π…
• If an iron (III) complex with the formula [Fe(NH₃)ₓ(CN)_y]⁻ has no electron in its e_g…
• Correct order of stability of carbanion is :
• Given below are two statements : Statement I : The correct order of first ionization…
• The total number of 'sigma' and 'pi' bonds in 2-oxohex-4-ynoic acid is ______.
• The maximum number of orbitals which can be identified with n=4 and mₗ=0 is _________.
• CH₃-CH₂-CH₂-Br+NaOH →(C₂ H₅ OH) Product 'A' Product A →(H₂O) Product “B”; →(Diborane)…
• The correct order of the first ionization enthalpy is
• A first row transition metal with highest enthalpy of atomisation, upon reaction with…
• 2.7 kg of each of water and acetic acid are mixed. The freezing point of the solution…
• Consider the following reaction, the rate expression of which is given below A+B → C…
• From 6.55 g of aniline, the maximum amount of acetanilide that can be prepared will be…
• When MnO₂ and H₂ SO₄ is added to a salt (A), the greenish yellow gas liberated as salt…
• Number of compounds / species from the following with non-zero dipole moment is…
• Fuel cell, using hydrogen and oxygen as fuels, A. has been used in spaceship B. has as…
• The number of species from the following that have pyramidal geometry around the central…
• The number of unpaired d-electrons in [Co(H₂ O)₆]³⁺ is ________.
• Common name of Benzene - 1,2 - diol is -
• Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant…
• A first row transition metal in its +2 oxidation state has a spin-only magnetic moment…
• The equilibrium constant for the reaction SO₃( g)⇌ SO₂( g)+1/2O₂( g) is K_c=4.9× 10⁻²…
• Match List I with List II LIST I | LIST II; A. | α - Glucose and α - Galactose | I. |…
• Phthalimide is made to undergo following sequence of reactions. Phthalimide →((i) KOH…
• For a strong electrolyte, a plot of molar conductivity against (concentration) ^(1 / 2)…

Mathematics

• Let y=y(x) be the solution of the differential equation (x+y+2)² d x=d y, y(0)=-2. Let…
• Let a⃗=î+ĵ+k̂, b⃗=2 î+4 ĵ-5 k̂ and c⃗=x î+2 ĵ+3 k̂, x ∈ ℝ. If d⃗ is the unit vector in…
• Given that the inverse trigonometric function assumes principal values only. Let x, y be…
• The value of (1 × 2²+2 × 3²+…+100 ×(101)²)/(1² × 2+2² × 3+… .+100² × 101) is
• Let f(x)=∫₀ˣ(t+sin (1-eᵗ)) d t, x ∈ ℝ. Then, lim x → 0 f(x)/x³ is equal to
• If the function f(x)= (72ˣ-9ˣ-8ˣ+1)/(√2-√(1+cos x)), x ≠ 0 ; a log ₑ 2 log ₑ 3 , x=0 is…
• In a tournament, a team plays 10 matches with probabilities of winning and losing each…
• Let three real numbers a, b, c be in arithmetic progression and a+1, b, c+3 be in…
• Let C be a circle with radius √10 units and centre at the origin. Let the line x+y=2…
• Let y=y(x) be the solution of the differential equation (x²+4)² d y+(2 x³ y+8 x y-2) d…
• If the value of the integral ∫₋₁¹ (cos α x)/(1+3ˣ) d x is 2/π.Then, a value of α is
• Consider a hyperbola H having centre at the origin and foci on the x-axis. Let C₁ be the…
• Let S={sin ² 2 θ:(sin ⁴ θ+cos ⁴ θ) x²+(sin 2 θ) x+(sin ⁶ θ+cos ⁶ θ)=0 has real roots }…
• Consider the function f: ℝ → ℝ defined by f(x)=(2 x)/√(1+9 x²). If the composition of f…
• Consider a line L passing through the points P(1,2,1) and Q(2,1,-1). If the mirror image…
• If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1+x)ⁿ are in the arithmetic…
• If the mean of the following probability distribution of a radam variable X : X | 0 | 2…
• Let A=[1, 2; 0, 1] and B=I+adj(A)+(adj A)²+…+(adj A)¹⁰. Then, the sum of all the…
• Let P be the point of intersection of the lines (x-2)/1=(y-4)/5=(z-2)/1 and…
• Let f: ℝ → ℝ be a thrice differentiable function such that f(0)=0, f(1)=1, f(2)=-1…
• For λ>0, let θ be the angle between the vectors a⃗=î+λ ĵ-3 k̂ and b⃗=3 î-ĵ+2 k̂. If the…
• Let a relation R on N × ℕ be defined as: (x₁, y₁) R(x₂, y₂) if and only if x₁ ≤ x₂ or y₁…
• Let P Q be a chord of the parabola y²=12 x and the midpoint of P Q be at (4,1). Then…
• There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons…
• The area (in sq. units) of the region S={z ∈ ℂ:|z-1| ≤ 2 ;(z+z̄)+i(z-z̄) ≤ 2, lm(z) ≥ 0}…
• Let A be a 2 × 2 symmetric matrix such that A[1; 1]=[3; 7] and the determinant of A be 1…
• The area (in sq. units) of the region described by {(x,y):y²≤ 2x, andy≥ 4x-1} is
• If ∫ cosec⁵xdx=α cot xcosecx(cosec²x+3/2)+β logₑ|tan x/2|+C where α,β∈ ℝ and C is the…
• Consider a triangle ABC having the vertices A(1,2),B(α,β) and C(γ,δ) and angles ∠…
• Let f(x)=3 √(x-2)+√(4-x) be a real valued function. If α and β are respectively the…

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