JEE Main 2024 (Online) 9th April Evening Shift — Question Paper

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Physics

• A spherical ball of radius 1 × 10⁻⁴ m and density 10⁵ kg / m³ falls freely under gravity…
• A square loop of side 15 cm being moved towards right at a constant speed of 2 cm / s as…
• A force (3 x²+2 x-5) N displaces a body from x=2 m to x=4 m. Work done by this force is…
• Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An…
• The I-V characteristics of an electronic device shown in the figure. The device is :
• At room temperature (27° C), the resistance of a heating element is 50 Ω. The…
• A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio…
• A straight magnetic strip has a magnetic moment of 44 Am². If the strip is bent in a…
• A real gas within a closed chamber at 27° C undergoes the cyclic process as shown in…
• The de-Broglie wavelength associated with a particle of mass m and energy E is h/√2mE…
• To determine the resistance (R) of a wire, a circuit is designed below. The V-I…
• UV light of 4.13 eV is incident on a photosensitive metal surface having work function…
• A capacitor of reactance 4 √3 Ω and a resistor of resistance 4 Ω are connected in series…
• Five charges +q,+5 q,-2 q,+3 q and -4 q are situated as shown in the figure. The…
• The magnetic field in a plane electromagnetic wave is B_y=(3.5 × 10⁻⁷) sin (1.5 × 10³…
• In the truth table of the above circuit the value of X and Y are :
• A particle of mass 0.50 kg executes simple harmonic motion under force F=-50(Nm⁻¹) x…
• A circular disc reaches from top to bottom of an inclined plane of length l. When it…
• A satellite of 10³ kg mass is revolving in circular orbit of radius 2 R. If (10⁴ R)/6 J…
• The following figure represents two biconvex lenses L₁ and L₂ having focal length 10 cm…
• The temperature of a gas is -78° C and the average translational kinetic energy of its…
• A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines…
• A proton and a deutron (q=+e, m=2.0 u) having same kinetic energies enter a region of…
• Two cars are travelling towards each other at speed of 20 m s⁻¹ each. When the cars are…
• The energy released in the fusion of 2 kg of hydrogen deep in the sun is E_H and the…
• An electric field E⃗=(2 x î) N C⁻¹ exists in space. A cube of side 2 m is placed in the…
• The excess pressure inside a soap bubble is thrice the excess pressure inside a second…
• The resultant of two vectors A⃗ and B⃗ is perpendicular to A⃗ and its magnitude is half…
• The effective resistance between A and B, if resistance of each resistor is R, will be :
• A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force…

Chemistry

• A transition metal 'M' among Sc, Ti, V, Cr, Mn and Fe has the highest second ionisation…
• Consider the following test for a group-IV cation. M²⁺+H₂ S → A (Black precipitate)+…
• The candela is the luminous intensity, in a given direction, of a source that emits…
• The correct stability order of the following resonance structures of CH₃-CH=CH-CHO is…
• When Δ Hᵥₐₚ=30 kJ / mol and Δ Sᵥₐₚ=75 J mol⁻¹ K⁻¹, then the temperature of vapour, at…
• Which of the following compounds will give silver mirror with ammoniacal silver nitrate?…
• Match List I with List II LIST I (Cell) | LIST II (Use/Property/Reaction); A. |…
• Match List I with List II LIST I | LIST II; A. | Melting Point [K] | I. | T 1>In>Ga>A…
• Which of the following compound can give positive iodoform test when treated with…
• The correct increasing order for bond angles among BF₃, PF₃ and ClF₃ is :
• The electronic configuration of Einsteinium is : (Given atomic number of Einsteinium =99)
• For a sparingly soluble salt AB₂, the equilibrium concentrations of A²⁺ ions and B⁻ ions…
• Which out of the following is a correct equation to show change in molar conductivity…
• The incorrect statement regarding ethyne is
• Total number of electrons present in (π^*) molecular orbitals of O₂, O₂⁺ and O₂⁻ is…
• Consider the following first order gas phase reaction at constant temperature A(g) → 2…
• Number of compounds from the following which cannot undergo Friedel-Crafts reactions is…
• Match List I with List II LIST I (Test) | LIST II (Observation); A. | Br₂ water test |…
• The incorrect statement about Glucose is :
• Total number of stereo isomers possible for the given structure :
• Give below are two statements : Statement I : The higher oxidation states are more…
• Number of oxygen atoms present in chemical formula of fuming sulphuric acid is…
• Major product of the following reaction is
• The coordination environment of Ca²⁺ ion in its complex with EDTA⁴⁻ is :
• Match List I with List II LIST I (Element) | LIST II (Electronic Configuration); A. | N…
• The vapor pressure of pure benzene and methyl benzene at 27° C is given as 80 Torr and…
• Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the…

Mathematics

• The square of the distance of the image of the point (6,1,5) in the line…
• Let A, B and C be three points on the parabola y²=6 x and let the line segment A B meet…
• For a differentiable function f: ℝ → ℝ, suppose f′(x)=3 f(x)+α, where α ∈ ℝ, f(0)=1 and…
• The sum of the coefficient of x^(2 / 3) and x^(-2 / 5) in the binomial expansion of…
• lim x → 0 (e-(1+2 x)^(1/(2 x)))/x is equal to
• Let a⃗=2 î+α ĵ+k̂, b⃗=-î+k̂, c⃗=β ĵ-k̂, where α and β are integers and α β=-6. Let the…
• If the variance of the frequency distribution x | c | 2c | 3c | 4c | 5c | 6c; f | 2 | 1…
• Let the foci of a hyperbola H coincide with the foci of the ellipse E…
• Consider the matrices : A=[2, -5; 3, m], B=[20; m] and X=[x; y]. Let the set of all m…
• Between the following two statements: Statement I : Let a⃗=î+2 ĵ-3 k̂ and b⃗=2 î+ĵ-k̂…
• Two vertices of a triangle ABC are A(3,-1) and B(-2,3), and its orthocentre is P(1,1)…
• Let z be a complex number such that the real part of (z-2 i)/(z+2 i) is zero. Then, the…
• Let A={(x, y): 2 x+3 y=23, x, y ∈ ℕ} and B={x:(x, y) ∈ A}. Then the number of one-one…
• If log ₑ y=3 sin ⁻¹ x, then (1-x²) y^(′ ′)-x y′ at x=1/2 is equal to
• If (1/(α+1)+1/(α+2)+… . .+1/(α+1012))-(1/(2 · 1)+1/(4 · 3)+1/(6 · 5)+… …+1/(2024 ·…
• If an unbiased dice is rolled thrice, then the probability of getting a greater number…
• Let the range of the function f(x)=1/(2+sin 3 x+cos 3 x), x ∈ ℝ be [a, b]. If α and β ar…
• Let a, a r, a r², ............ be an infinite G.P. If Σn=0^∞ a rⁿ=57 and Σn=0^∞ a³…
• The area (in square units) of the region enclosed by the ellipse x²+3y²=18 in the first…
• Consider the line L passing through the points (1,2,3) and (2,3,5). The distance of the…
• The integral ∫1 / 4^(3 / 4) cos (2 cot ⁻¹ √((1-x)/(1+x))) d x is equal to
• The value of the integral ∫-1² log ₑ(x+√(x²+1)) d x is
• The number of integers, between 100 and 1000 having the sum of their digits equals to 14…
• Let the inverse trigonometric functions take principal values. The number of real…
• Consider the circle C: x²+y²=4 and the parabola P: y²=8 x. If the set of all values of…
• Let B=[1, 3; 1, 5] and A be a 2 × 2 matrix such that A B⁻¹=A⁻¹. If B C B⁻¹=A and C⁴+α…
• Let ∫0ˣ √(1-(y′(t))²) d t=∫₀ˣ y(t) d t, 0 ≤ x ≤ 3, y ≥ 0, y(0)=0. Then at x=2, y^(′…
• Let α, β ; α>β, be the roots of the equation x²-√2 x-√3=0. Let Pₙ=αⁿ-βⁿ, n ∈ N. Then (11…
• Let the set of all values of p, for which f(x)=(p²-6 p+8)(sin ² 2 x-cos ² 2 x)+2(2-p)…
• lim x → π/2((∫_(x³)^((π / 2)³)(sin (2 t^(1 / 3))+cos (t^(1 / 3))) d t)/(x-π/2)²) is…

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