JEE Main 2021 (Online) 25th February Morning Shift — Question Paper

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Physics

• The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale…
• A solid sphere of radius R gravitationally attracts a particle placed at 3R from its…
• The potential energy (U) of a diatomic molecule is a function dependent on r…
• 512 identical drops of mercury are charged to a potential of 2V each. The drops are…
• A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 μF is…
• An α particle and a proton are accelerated from rest by a potential difference of 200V…
• Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and…
• A small bob tied at one end of a thin string of length 1 m is describing a vertical…
• A coil of inductance 2 H having negligible resistance is connected to a source of supply…
• Given below are two statements : one is labelled as Assertion A and the other is…
• A 5V battery is connected across the points X and Y. Assume D₁ and D₂ to be normal…
• A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving…
• In an octagon ABCDEFGH of equal side, what is the sum of AB⃗+AC⃗+AD⃗+AE⃗+AF⃗+AG⃗+AH⃗…
• If the time period of a two meter long simple pendulum is 2s, the acceleration due to…
• The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The…
• A diatomic gas, having Cₚ = 7/2R and Cᵥ = 5/2R, is heated at constant pressure. The…
• Two coherent light sources having intensity in the ratio 2x produce an interference…
• Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at…
• In the given circuit of potentiometer, the potential difference E across AB (10 m…
• A student is performing the experiment of resonance column. The diameter of the column…
• An engine of a train, moving with uniform acceleration, passes the signal-post with…
• The same size images are formed by a convex lens when the object is placed at 20 cm or…
• Given below are two statements : one is labelled as Assertion A and the other is…
• A proton, a deuteron and an α particle are moving with same momentum in a uniform…
• Match List - I with List - II : List I | List II; (a) | h (Planck's constant) | (i) |…
• Two radioactive substances X and Y originally have N₁ and N₂ nuclei respectively. Half…
• The electric field in a region is given by E⃗ = ( 3/5E₀î + 4/5E₀ĵ )N/C. The ratio of…
• In a certain thermodynamical process, the pressure of a gas depends on its volume as…

Chemistry

• The ionization enthalpy of Na⁺ formation from Na (g) is 495.8 kJ mol⁻¹, while the…
• Ellingham diagram is a graphical representation of :
• In basic medium CrO₄²⁻ oxidises S₂O₃²⁻ to form SO₄²⁻ and itself changes into Cr(OH)₄ -…
• 1 molal aqueous solution of an electrolyte A₂B₃ is 60% ionised. The boiling point of the…
• In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption ( x/m )…
• The solubility of AgCN in a buffer solution of pH = 3 is x. The value of x is : [Assume…
• Which of the glycosidic linkage between galactose and glucose is present in lactose?
• Consider the following chemical reaction. CH≡CH →(1) Red hot Fe tube, 873 K) Product The…
• The hybridization and magnetic nature of [Mn(CN)₆]⁴⁻ and [Fe(CN)₆]³⁻, respectively are :
• Which one of the following reactions will not form acetaldehyde?
• The plots of radial distribution functions for various orbitals of hydrogen atom against…
• Which statement is correct?
• 0.4 g mixture of NaOH, Na₂CO₃ and some inert impurities was first titrated with N/10 HCl…
• Given below are two statements : Statement I : CeO₂ can be used for oxidation of…
• Using the provided information in the following paper chromatogram : Fig : Paper…
• Complete combustion of 1.80 g of an oxygen containing compound (CₓH y O z ) gave 2.64 g…
• The reaction of cyanamide, NH₂CN₍ₛ₎ with oxygen was run in a bomb calorimeter and ΔU was…
• For the reaction, aA + bB → cC + dD, the plot of log k vs 1/T is given below : The…
• In which of the following pairs, the outer most electronic configuration will be the same?
• According to molecular orbital theory, the species among the following that does not…
• The correct statement about B₂H₆ is :
• Which of the following equation depicts the oxidizing nature of H₂O₂?
• Among the following, the number of halide(s) which is/are inert to hydrolysis is…
• Which of the following reaction/s will not give p-aminoazobenzene?
• Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are :

Mathematics

• If a curve passes through the origin and the slope of the tangent to it at any point (x…
• If Rolle's theorem holds for the function f(x) = x³ - ax² + bx - 4, x ∈ [1,2] with f'(…
• If the system of equations kx + y + 2z = 1 3x - y - 2z = 2 -2x -2y -4z = 3 has…
• lim _(n → ∞) ( 1 + (1 + 1/2 + ........ + 1/n)/n² )ⁿ is equal to :
• The number of points, at which the function f(x) = | 2x + 1 | - 3| x + 2 | + | x² + x -…
• Let a⃗ = î + 2ĵ - k̂, b⃗ = î - ĵ and c⃗ = î - ĵ - k̂ be three given vectors. If r⃗ is a…
• Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x⁶ is unity and…
• Let α be the angle between the lines whose direction cosines satisfy the equations l + m…
• All possible values of θ ∈ [0, 2π] for which sin 2θ + tan 2θ > 0 lie in :
• Let A₁, A₂, A₃, ....... be squares such that for each n ≥ 1, the length of the side of…
• If 0 < θ ,φ < π/2,x = Σₙ₌₀^∞ cos ²ⁿθ ,y = Σₙ₌₀^∞ sin ²ⁿφ and z = Σₙ₌₀^∞ cos ²ⁿθ .sin ²ⁿφ…
• The integer 'k', for which the inequality x² - 2(3k - 1)x + 8k² - 7 > 0 is valid for…
• The graphs of sine and cosine functions, intersect each other at a number of points and…
• A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y =…
• The total number of numbers, lying between 100 and 1000 that can be formed with the…
• If the curves, x²/a + y²/b = 1 and x²/c + y²/d = 1 intersect each other at an angle of…
• Let the lines (2 - i)z = (2 + i)z̅ and (2 + i)z + (i - 2)z̅ - 4i = 0, (here i² = -1) be…
• Let f, g : N → N such that f(n + 1) = f(n) + f(1) ∀ n∈N and g be any arbitrary function…
• The value of ∫₋₁¹ x²e^([x³]) dx, where [ t ] denotes the greatest integer ≤ t, is :
• The total number of positive integral solutions (x, y, z) such that xyz = 24 is :
• Let A = [ x, y, z; y, z, x; z, x, y ], where x, y and z are real numbers such that x + y…
• The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by…
• The value of the integral ∫ (sin θ.sin 2θ(sin⁶θ+sin⁴θ+sin²θ)√(2sin⁴θ+3sin²θ+6))/(1-cos…
• The image of the point (3, 5) in the line x - y + 1 = 0, lies on :
• The locus of the point of intersection of the lines ( √3 )kx + ky - 4√3 = 0 and √3 x - y…
• The equation of the line through the point (0, 1, 2) and perpendicular to the line (x -…
• If A = [ 0, - tan ( θ/2 ); tan ( θ/2 ), 0 ] and (I₂ + A)(I₂ - A)⁻¹ = [ a, - b; b, a ]…
• When a missile is fired from a ship, the probability that it is intercepted is 1/3 and…

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