JEE Main 2021 (Online) 26th February Evening Shift — Question Paper

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Physics

• An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a…
• A particle executes S.H.M., the graph of velocity as a function of displacement is :
• The incident ray, reflected ray and the outward drawn normal are denoted by the unit…
• The trajectory of a projectile in a vertical plane is y = αx - βx², where α and β are…
• A radioactive sample is undergoing α decay. At any time t₁, its activity is A and…
• 27 similar drops of mercury are maintained at 10V each. All these spherical drops…
• The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U =…
• The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to…
• Two masses A and B, each of mass M are fixed together by a massless spring. A force acts…
• Given below are two statements : Statement I : A second's pendulum has a time period of…
• Draw the output signal Y in the given combination of gates.
• The volume V of a given mass of monoatomic gas changes with temperature T according to…
• The zener diode has a V z = 30V. The current passing through the diode for the following…
• Given below are two statements: Statement I : An electric dipole is placed at the center…
• A scooter accelerates from rest for time t₁ at constant rate a₁ and then retards at…
• Find the peak current and resonant frequency of the following circuit (as shown in…
• A point source of light S, placed at a distance 60cm in front of the centre of a plane…
• Two stream of photons, possessing energies equal to twice and ten times the work…
• In the reported figure of earth, the value of acceleration due to gravity is same at…
• If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions…
• The length of metallic wire is l₁ when tension in it is T₁. It is l₂ when the tension is…
• A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of…
• A wire of 1Ω has a length of 1 m. It is stretched till its length increases by 25%. The…
• A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency…
• 1 mole of rigid diatomic gas performs a work of Q/5 when heat Q is supplied to it. The…
• A cord is wound round the circumference of wheel of radius r. The axis of the wheel is…
• An inclined plane making an angle of 30° with the horizontal is placed in a uniform…

Chemistry

• Match List - I with List - II. List - I | List - II; (a) | Siderite | (i) | Cu; (b) |…
• The correct order of electron gain enthalpy is :
• Which pair of oxides is acidic in nature?
• When 12.2 g of benzoic acid is dissolved in 100 g of water, the freezing point of…
• In mildly alkaline medium, thiosulphate ion is oxidized by MnO₄ - to "A". The oxidation…
• If the activation energy of a reaction is 80.9 kJ mol⁻¹, the fraction of molecules at…
• The nature of charge on resulting colloidal particles when FeCl₃ is added to excess of…
• Seliwanoff test and Xanthoproteic test are used for the identification of ___________…
• Which of the following forms of hydrogen emits low energy β⁻ particles?
• The average S-F bond energy in kJ mol⁻¹ of SF₆ is _____________. (Rounded off to the…
• The number of octahedral voids per lattice site in a lattice is _________. (Rounded off…
• A. Phenyl methanamine B. N,N-Dimethylaniline C. N-Methyl aniline D. Benzenamine Choose…
• Match List - I with List - II. List - I (Molecule) | List - II (Bond order); (a) | Ne₂ |…
• In C¹ H₂ = C² = C³ H - C⁴ H₃ molecule, the hybridization of carbon 1, 2, 3 and 4…
• A ball weighing 10 g is moving with a velocity of 90 ms⁻¹. If the uncertainty in its…
• The number of stereoisomers possible for [Co(ox)₂(Br)(NH₃)]²⁻ is ___________. [ox =…
• The NaNO₃ weighed out to make 50 mL of an aqueous solution containing 70.0 mg Na⁺ per mL…
• Given below are two statements : one is labelled as Assertion A and the other is…
• The pH of ammonium phosphate solution, if pkₐ of phosphoric acid and pk b of ammonium…
• Calgon is used for water treatment. Which of the following statement is NOT true about…
• Emf of the following cell at 298K in V is x × 10⁻². Zn|Zn²⁺(0.1 M)||Ag⁺ (0.01 M)|Ag The…
• Ceric ammonium nitrate and CHCl₃/alc. KOH are used for the identification of functional…
• Match List - I with List - II. List - I | List - II; (a) | Sodium Carbonate | (i) |…
• 2, 4-DNP test can be used to identify :
• Match List - I with List - II. List - I | List - II; (a) | Sucrose | (i) | β-D-Galactose…

Mathematics

• If the mirror image of the point (1, 3, 5) with respect to the plane 4x - 5y + 2z = 8 is…
• If the locus of the mid-point of the line segment from the point (3, 2) to a point on…
• Let α and β be two real numbers such that α + β = 1 and αβ = -1. Let pₙ = (α)ⁿ + (β)ⁿ…
• Let f(x) = sin ⁻¹x and g(x) = (x² - x - 2)/(2x² - x - 6). If g(2) = lim _(x → 2) g(x)…
• Consider the following system of equations : x + 2y - 3z = a 2x + 6y - 11z = b x - 2y +…
• Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z =…
• Let X₁, X₂, ......., X₁₈ be eighteen observations such that Σᵢ₌₁¹⁸ (Xᵢ - α ) = 36 and…
• Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle (x - 1)² + (y -…
• The sum of the series Σₙ₌₁^∞ (n² + 6n + 10)/(2n + 1)! is equal to :
• Let f : R → R be defined as f(x) = { 2 sin ( - (π x)/2 ),if x < - 1; |ax² + x + b|, if -…
• If the arithmetic mean and geometric mean of the pᵗʰ and qᵗʰ terms of the sequence -16…
• A natural number has prime factorization given by n = 2ˣ3ʸ5ᶻ, where y and z are such…
• Let a be an integer such that all the real roots of the polynomial 2x⁵ + 5x⁴ + 10x³ +…
• Let z be those complex numbers which satisfy | z + 5 | ≤ 4 and z(1 + i) + z̅(1 - i) ≥…
• For x > 0, if f(x) = ∫₁ˣ (log ₑt)/(1 + t)dt, then f(e) + f( 1/e ) is equal to :
• Let slope of the tangent line to a curve at any point P(x, y) be given by (xy² + y)/x…
• Let L be a common tangent line to the curves 4x² + 9y² = 36 and (2x)² + (2y)² = 31. Then…
• Let the normals at all the points on a given curve pass through a fixed point (a, b). If…
• Let A = { 1,2,3,....,10} and f:A → A be defined as f(k) = { k + 1, if k is odd; k, if k…
• If I_(m,n) = ∫₀¹ xᵐ⁻¹(1 - x)ⁿ⁻¹dx, for m, n ≥ 1, and ∫₀¹ (xᵐ⁻¹ + xⁿ⁻¹)/(1 + x)ᵐ⁺ⁿ dx = α…
• Let A₁ be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in…
• If the matrix A = [ 1, 0, 0; 0, 2, 0; 3, 0, - 1 ] satisfies the equation A²⁰ + α A¹⁹ + β…
• Let f(x) be a differentiable function at x = a with f'(a) = 2 and f(a) = 4. Then lim _(x…
• If 0 < a, b < 1, and tan⁻¹a + tan⁻¹b = π/4, then the value of (a + b) - ( (a² + b²)/2 )…
• If vectors a₁⃗ = xî - ĵ + k̂ and a₂⃗ = î + yĵ + zk̂ are collinear, then a possible unit…
• The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is…
• Let f(x) = ∫₀ˣ eᵗf(t)dt + eˣ be a differentiable function for all x∈R. Then f(x) equals :
• A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that…

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