JEE Main 2025 (Online) 29th January Morning Shift — Question Paper

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Physics

• Two projectiles are fired with same initial speed from same point on ground at angles of…
• The maximum speed of a boat in still water is 27 km/h. Now this boat is moving…
• If λ and K are de Broglie wavelength and kinetic energy, respectively, of a particle…
• An electric dipole of mass m, charge q, and length l is placed in a uniform electric…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Consider a long straight wire of a circular cross-section (radius a ) carrying a steady…
• The fractional compression ( (Δ V)/V ) of water at the depth of 2.5 km below the sea…
• Match List - I with List - II. List - I | List - II; (A) Electric field inside (distance…
• In a hydraulic lift, the surface area of the input piston is 6 cm² and that of the…
• Given below are two statements: one is labelled as Assertion (A) and the other is…
• Given below are two statements: one is labelled as Assertion (A) and the other is…
• The work done in an adiabatic change in an ideal gas depends upon only :
• Two light beams fall on a transparent material block at point 1 and 2 with angle θ₁ and…
• Given below are two statements: one is labelled as Assertion (A) and the other is…
• The coordinates of a particle with respect to origin in a given reference frame is (1…
• A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical…
• For the circuit shown above, equivalent GATE is :
• A container of fixed volume contains a gas at 27°C. To double the pressure of the gas…
• The pair of physical quantities not having the same dimensions is :
• As shown below, bob A of a pendulum having massless string of length 'R' is released…
• The expression given below shows the variation of velocity ( v ) with time ( t )…
• Consider I₁ and I₂ are the currents flowing simultaneously in two nearby coils 1 & 2…
• A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic…
• Let u and v be the distances of the object and the image from a lens of focal length f…

Chemistry

• If A₂B is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is…
• Given below are two statements : Statement (I) : The radii of isoelectronic species…
• The molar mass of the water insoluble product formed from the fusion of chromite ore…
• 1.24 g of AX₂ (molar mass 124 g mol⁻¹) is dissolved in 1 kg of water to form a solution…
• The correct option with order of melting points of the pairs (Mn, Fe), (Tc, Ru) and (Re…
• The steam volatile compounds among the following are : Choose the correct answer from…
• In the following substitution reaction : Product 'P' formed is :
• Match List - I with List - II. List - I (Structure) | List - II (IUPAC Name); (A) H₃C…
• The molar conductivity of a weak electrolyte when plotted against the square root of its…
• The standard reduction potential values of some of the p-block ions are given below…
• Choose the correct statements. (A) Weight of a substance is the amount of matter present…
• At temperature T, compound AB_(2(g)) dissociates as AB_(2(g))⇌ AB_((g))+1/2B_(2(g))…
• Match List - I with List - II. List - I (Carbohydrate) | List - II (Linkage Source); (A)…
• An element ‘E’ has the ionisation enthalpy value of 374 kJ mol⁻¹. ‘E’ reacts with…
• The reaction A₂ + B₂ → 2AB follows the mechanism: A₂ ⇌(k₁) A + A (fast) A + B₂ →(k₂) AB…
• For a Mg | Mg²⁺ (aq) || Ag⁺ (aq) | Ag the correct Nernst Equation is :
• Given below are some nitrogen containing compounds : Each of them is treated with HCl…
• Match List - I with List - II. List - I (Complex) | List - II (Hybridisation & Magnetic…
• 500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm…
• If a₀ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie…
• The sum of sigma (σ) and pi (π) bonds in Hex-1,3-dien-5-yne is ________.

Mathematics

• The value of lim _(n → ∞)(Σₖ₌₁ⁿ (k³+6 k²+11 k+5)/(k+3)!) is :
• The number of 6-letter words, with or without meaning, that can be formed using the…
• The integral 80 ∫₀^(π/4)((sin θ+cos θ)/(9+16 sin 2 θ)) d θ is equal to :
• Let M and m respectively be the maximum and the minimum values of f(x)=|1+sin ² x, cos ²…
• Let x₁, x₂, ..., x₁₀ be ten observations such that Σᵢ₌₁¹⁰ (xᵢ - 2) = 30, Σᵢ₌₁¹⁰ (xᵢ -…
• Let S={m ∈ Z: A^(m²)+Aᵐ=3 I-A⁻⁶}, where A=[2, -1; 1, 0]. Then n(S) is equal to __________.
• Let P be the set of seven digit numbers with sum of their digits equal to 11. If the…
• Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the…
• Let S = { x : cos⁻¹ x = π + sin⁻¹ x + sin⁻¹ [2x + 1] } . Then Σ_(x ∈ S) (2x - 1)² is…
• Let A = [aᵢⱼ] = [log₅ 128, log₄ 5; log₅ 8, log₄ 25] . If Aᵢⱼ is the cofactor of aᵢⱼ…
• Let a⃗=î+2 ĵ+k̂ and b⃗=2 î+7 ĵ+3 k̂. Let L₁ : r⃗=(-î+2 ĵ+k̂)+λ a⃗, λ ∈ R and L₂…
• Let the area of the region (x,y):2y≤ x²+3, y+|x|≤ 3, y≥ |x-1| be A. Then 6A is equal to :
• Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y…
• Define a relation R on the interval [0, π/2) by x R y if and only if sec² x - tan² y = 1…
• Let |z₁ − 8−2i| ≤ 1 and |z₂−2+6i| ≤ 2 , z₁, z₂ ∈ ℂ . Then the minimum value of |z₁ − z₂|…
• Let L₁: (x-1)/1=(y-2)/-1=(z-1)/2 and L₂: (x+1)/-1=(y-2)/2=z/1 be two lines. Let L₃ be a…
• Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N…
• Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the…
• Let f:(0, ∞) → R be a twice differentiable function. If for some a≠ 0, ∫₀¹ f(λ x) d λ=a…
• Let the ellipse E₁: x²/a² + y²/b² = 1, a > b and E₂: x²/A² + y²/B² = 1, A < B have same…
• The least value of n for which the number of integral terms in the Binomial expansion of…
• Let the line x+y=1 meet the circle x²+y²=4 at the points A and B. If the line…
• The number of solutions of the equation ( 9/x - 9/√x + 2 ) ( 2/x - 7/√x + 3 ) = 0 is :
• Let y = y(x) be the solution of the differential equation : cos x(log ₑ(cos x))² d…
• Let a⃗ = 2î - ĵ + 3k̂, b⃗ = 3î - 5ĵ + k̂ and c⃗ be a vector such that a⃗ × c⃗ = a⃗ × b⃗…

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