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

Download this paper as a PDF (16 pages, with answer key)

Physics

• Considering the Bohr model of hydrogen like atoms, the ratio of the radius of 5ᵗʰ orbit…
• Two liquids A and B have θ_A and θ_B as contact angles in a capillary tube. If K=cos θ_A…
• Two small spherical balls of mass 10 g each with charges -2 μ C and 2 μ C, are attached…
• Four capacitors each of capacitance 16 μ F are connected as shown in the figure. The…
• Consider the sound wave travelling in ideal gases of He, CH₄, and CO₂. All the gases…
• In an experiment with a closed organ pipe, it is filled with water by (1/5) th of its…
• Two slabs with square cross section of different materials (1,2) with equal sides (l)…
• Given below are two statements : one is labelled as Assertion A and the other is…
• A body of mass m is suspended by two strings making angles θ₁ and θ₂ with the horizontal…
• Distance between object and its image (magnified by -1/3 ) is 30 cm . The focal length…
• Which of the following are correct expression for torque acting on a body? A. τ⃗=r⃗ × L⃗…
• If L⃗ and P⃗ represent the angular momentum and linear momentum respectively of a…
• An alternating current is represented by the equation, i=100 √2 sin (100 π t) ampere…
• Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of 1/√2…
• The Boolean expression Y=A B̄ C+Ā C̄ can be realised with which of the following gate…
• The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 ×…
• A small mirror of mass m is suspended by a massless thread of length l. Then the small…
• In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits…
• Two infinite identical charged sheets and a charged spherical body of charge density ' ρ…
• When an object is placed 40 cm away from a spherical mirror an image of magnification…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• Two simple pendulums having lengths l₁ and l₂ with negligible string mass undergo…
• A circular ring and a solid sphere having same radius roll down on an inclined plane…
• Current passing through a wire as function of time is given as I(t)=0.02 t+0.01 A. The…
• In an electromagnetic system, the quantity representing the ratio of electric flux and…

Chemistry

• The pH of a 0.01 M weak acid HX(Kₐ=4 × 10⁻¹⁰) is found to be 5 . Now the acid solution…
• The total number of hydrogen bonds of a DNA-double Helix strand whose one strand has the…
• Which one of the following complexes will have Δₒ=0 and μ=5.96 B.M?
• On charging the lead storage battery, the oxidation state of lead changes from x₁ to y₁…
• Given below are two statements: Statement I: Nitrogen forms oxides with +1 to +5…
• The major product (A) formed in the following reaction sequence is
• Aldol condensation is a popular and classical method to prepare α, β-unsaturated…
• For A₂+B₂ ⇌ 2 AB Eₐ for forward and backward reaction are 180 and 200 kJ mol⁻¹…
• One mole of an ideal gas expands isothermally and reversibly from 10 dm³ to 20 dm³ at…
• KMnO₄ acts as an oxidising agent in acidic medium. ' X ' is the difference between the…
• Which one of the following about an electron occupying the 1 s orbital in a hydrogen…
• Which of the following molecule(s) show/s paramagnetic behavior? A. O₂ B. N₂ C. F₂ D. S₂…
• An organic compound (X) with molecular formula C₃ H₆ O is not readily oxidised. On…
• Number of stereoisomers possible for the complexes, [CrCl₃(py)₃] and [CrCl₂(ox)₂]³⁻ are…
• Rate law for a reaction between A and B is given by r=k[ A]ⁿ[ B]ᵐ If concentration of A…
• Given below are the pairs of group 13 elements showing their relation in terms of atomic…
• X Y is the membrane/partition between two chambers 1 and 2 containing sugar solutions of…
• Fortification of food with iron is done using FeSO₄ · 7 H₂ O. The mass in grams of the…
• In Dumas' method for estimation of nitrogen 1 g of an organic compound gave 150 mL of…
• Let us consider a reversible reaction at temperature, T. In this reaction, both Δ H and…
• Identify the pair of reactants that upon reaction, with elimination of HCl will give…
• Pair of transition metal ions having the same number of unpaired electrons is
• Benzene is treated with oleum to produce compound (X) which when further heated with…

Mathematics

• If 10 sin⁴ θ+15 cos⁴ θ=6, then the value of (27cosec⁶θ+8 sec⁶ θ)/(16 sec⁸ θ) is
• Let A and B be two distinct points on the line L: (x-6)/3=(y-7)/2=(z-7)/-2. Both A and B…
• The value of ∫-1¹ ((1+√(|x|-x)) eˣ+(√(|x|-x)) e⁻ˣ)/(eˣ+e⁻ˣ) d x is equal to
• Considering the principal values of the inverse trigonometric functions, sin ⁻¹(√3/2…
• If lim x → 1⁺ ((x-1)(6+λ cos (x-1))+μ sin (1-x))/(x-1)³=-1, where λ, μ ∈ ℝ, then λ+μ is…
• Consider the equation x²+4 x-n=0, where n ∈[20,100] is a natural number. Then the number…
• In the expansion of (∛2+1/∛3)ⁿ, n ∈ N, if the ratio of 15ᵗʰ term from the beginning to…
• The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and…
• If the area of the region {(x,y):|x-5|≤ y≤ 4√x} is A, then 3A is equal to _________.
• 1+3+5²+7+9²+… upto 40 terms is equal to
• Consider two vectors u⃗=3 î-ĵ and v⃗=2 î+ĵ-λ k̂, λ>0. The angle between them is given by…
• A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random…
• Let the three sides of a triangle are on the lines 4x-7y+10=0,x+y=5 and 7x+4y=15. Then…
• For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial…
• Let the shortest distance between the lines (x-3)/3=(y-α)/-1=(z-3)/1 and…
• Let C be the circle x²+(y-1)²=2, E₁ and E₂ be two ellipses whose centres lie at the…
• Let f, g:(1, ∞) → ℝ be defined as f(x)=(2 x+3)/(5 x+2) and g(x)=(2-3 x)/(1-x). If the…
• Let A=[cos θ, 0, -sin θ; 0, 1, 0; sin θ, 0, cos θ]. If for some θ ∈(0, π), A²=Aᵀ, then…
• Let A={z ∈ C:|z-2-i|=3}, B={z ∈ C: Re(z-i z)=2} and S=A ∩ B. Then Σ_(z ∈ S)|z|² is equal…
• Consider the sets A={(x, y) ∈ ℝ × ℝ: x²+y²=25}, B={(x, y) ∈ ℝ × ℝ: x²+9 y²=144}, C={(x…
• Let f: ℝ → ℝ be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x ∈ ℝ…
• The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10…
• Let f:[0,∞)→ ℝ be a differentiable function such that f(x)=1-2x+∫₀ˣeˣ⁻ᵗf(t)dt for all x∈…
• Let A={1,6,11,16, …} and B={9,16,23,30, …} be the sets consisting of the first 2025…
• Let m and n be the number of points at which the function f(x)=max {x, x³, x⁵, … x²¹}, x…

Download all JEE Main 2025 PYQs chapter-wise as free PDFs