JEE Main 2025 (Online) 4th April Evening Shift — Question Paper

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Physics

• In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of…
• Displacement of a wave is expressed as x(t)=5 cos (628 t+π/2) m. The wavelength of the…
• An inductor of self inductance 1 H is connected in series with a resistor of 100 π ohm…
• An object is kept at rest at a distance of 3 R above the earth's surface where R is…
• A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45°…
• A solid sphere with uniform density and radius R is rotating initially with constant…
• Three parallel plate capacitors C₁, C₂ and C₃ each of capacitance 5 μ F are connected as…
• In an electromagnetic system, a quantity defined as the ratio of electric dipole moment…
• A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually…
• A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected…
• Given below are two statements : Statement (I) : The dimensions of Planck's constant and…
• From the combination of resistors with resistances values R₁=R₂=R₃=5 Ω and R₄=10 Ω…
• If an optical medium possesses a relative permeability of 10/π and relative permittivity…
• There are two vessels filled with an ideal gas where volume of one is double the volume…
• Two polarisers P₁ and P₂ are placed in such a way that the intensity of the transmitted…
• A wheel is rolling on a plane surface. The speed of a particle on the highest point of…
• A radioactive material P first decays into Q and then Q decays to non-radioactive…
• The displacement x versus time graph is shown below. (A) The average velocity during 0…
• Match List - I with List - II. List - I | List - II ; (A) | Isobaric | (I) | Δ Q=Δ W…
• For the determination of refractive index of glass slab, a travelling microscope is used…
• Consider a n-type semiconductor in which nₑ and nₕ are number of electrons and holes…
• There are ' n ' number of identical electric bulbs, each is designed to draw a power p…
• A finite size object is placed normal to the principal axis at a distance of 30 cm from…
• Consider a rectangular sheet of solid material of length l=9 cm and width d=4 cm. The…

Chemistry

• Given below are two statements : Statement (I) : Alcohols are formed when alkyl…
• x mg of Mg(OH)₂( molar mass =58) is required to be dissolved in 1.0 L of water to…
• A toxic compound " A " when reacted with NaCN in aqueous acidic medium yields an edible…
• The incorrect relationship in the following pairs in relation to ionisation enthalpies…
• Given below are two statements: Statement (I): For Cl(··)F₃, all three possible…
• Half life of zero order reaction A → product is 1 hour, when initial concentration of…
• Which among the following compounds give yellow solid when reacted with NaOI / NaOH ?…
• Consider the following plots of log of rate constant k(log k) vs 1/T for three different…
• Consider the ground state of chromium atom (Z=24). How many electrons are with Azimuthal…
• The molar conductance of an infinitely dilute solution of ammonium chloride was found to…
• Match List - I with List - II List - I (Separation of) | List - II (Separation…
• The amount of calcium oxide produced on heating 150 kg limestone ( 75 % pure) is…
• The IUPAC name of the following compound is: HC≡C-CH₂-C(|)(OH)H-CH₂-CH=CH₂
• A dipeptide, " x " on complete hydrolysis gives " y " and " z ". " y " on treatment with…
• Sea water, which can be considered as a 6 molar (6 M) solution of NaCl , has a density…
• The elements of Group 13 with highest and lowest first ionisation enthalpies are…
• Consider the given data : (a) HCl(g)+10 H₂ O(l) → HCl .10 H₂ O Δ H=-69.01 kJ mol⁻¹ (b)…
• Given below are two statements: Statement (I) : Molal depression constant K_f is given…
• In which pairs, the first ion is more stable than the second?
• Given below are two statements : Statement (I) : The first ionisation enthalpy of group…
• The correct order of [FeF₆]³⁻,[CoF₆]³⁻,[Ni(CO)₄] and [Ni(CN)₄]²⁻ complex species based…
• Consider the following molecule(X). The major product formed when the given molecule (X)…
• A metal complex with a formula MCl₄ · 3 NH₃ is involved in sp³ d² hybridisation. It upon…

Mathematics

• If the sum of the first 20 terms of the series (4 · 1)/(4+3 · 1²+1⁴)+(4 · 2)/(4+3 ·…
• The sum of the infinite series cot ⁻¹(7/4)+cot ⁻¹(19/4)+cot ⁻¹(39/4)+cot ⁻¹(67/4)+…. is :
• Let the mean and the standard deviation of the observation 2,3,3,4,5,7, a, b be 4 and √2…
• If a curve y=y(x) passes through the point (1, π/2) and satisfies the differential…
• Let the three sides of a triangle ABC be given by the vectors 2 î-ĵ+k̂, î-3 ĵ-5 k̂ and 3…
• The centre of a circle C is at the centre of the ellipse E: x²/a²+y²/b²=1, a>b. Let C…
• Let A={-3,-2,-1,0,1,2,3} and R be a relation on A defined by x R y if and only if 2 x-y…
• Let A be the point of intersection of the lines L₁: (x-7)/1=(y-5)/0=(z-3)/-1 and L₂…
• A line passing through the point A(-2,0), touches the parabola P: y²=x-2 at the point B…
• Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x²/a²-y²/b²=1…
• Let for two distinct values of p the lines y=x+p touch the ellipse E: x²/4²+y²/3²=1 at…
• Let the matrix A=[1, 0, 0; 1, 0, 1; 0, 1, 0] satisfy Aⁿ=Aⁿ⁻²+A²-I for n ≥ 3. Then the…
• A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn…
• Let the values of p , for which the shortest distance between the lines (x+1)/3=y/4=z/5…
• If 1² ·( ¹⁵ C₁)+2² ·( ¹⁵ C₂)+3² ·( ¹⁵ C₃)+…+15² ·( ¹⁵ C₁₅)=2ᵐ · 3ⁿ · 5ᵏ, where m, n, k ∈…
• Let f(x)+2 f(1/x)=x²+5 and 2 g(x)-3 g(1/2)=x, x>0. If α=∫₁² f(x) d x, and β=∫₁² g(x) d…
• Let the product of ω₁=(8+i) sin θ+(7+4 i) cos θ and ω₂=(1+8 i) sin θ+(4+7 i) cos θ be…
• Let f be a differentiable function on R such that f(2)=1, f′(2)=4. Let lim _(x →…
• The axis of a parabola is the line y=x and its vertex and focus are in the first…
• Let m and n,(m<n), be two 2-digit numbers. Then the total numbers of pairs (m, n), such…
• Let the domains of the functions f(x)=log ₄ log ₃ log ₇(8-log ₂(x²+4 x+5)) and g(x)=sin…
• Let a>0. If the function f(x)=6 x³-45 a x²+108 a² x+1 attains its local maximum and…
• If α is a root of the equation x²+x+1=0 and Σk=1ⁿ(αᵏ+1/αᵏ)²=20, then n is equal to…
• If ∫ (√(1+x²)+x)¹⁰/(√(1+x²)-x)⁹ dx=1/m((√(1+x²)+x)ⁿ(n√(1+x²)-x))+C where C is the…
• Consider two sets A and B, each containing three numbers in A.P. Let the sum and the…

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