JEE Main 2021 (Online) 24th February Morning Shift — Question Paper

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Physics

• The work done by a gas molecule in an isolated system is given by, W=αβ²e^(-x²/(α kT))…
• A current through a wire depends on time as i = α₀t + βt² where α₀ = 20 A/s and β = 8…
• A cube of side 'a' has point charges +Q located at each of its vertices except at the…
• If the velocity-time graph has the shape AMB, what would be the shape of the…
• A cell E₁ of emf 6V and internal resistance 2Ω is connected with another cell E₂ of emf…
• The focal length f is related to the radius of curvature r of the spherical convex…
• A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is…
• Two equal capacitors are first connected in series and then in parallel. The ratio of…
• In the given figure, a mass M is attached to a horizontal spring which is fixed on one…
• Consider two satellites S₁ and S₂ with periods of revolution 1 hr. and 8 hr…
• Given below are two statements : Statement I : Two photons having equal linear momenta…
• In a Young's double slit experiment, the width of the one of the slit is three times the…
• n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the…
• An inclined plane is bent in such a way that the vertical cross-section is given by y =…
• Two stars of masses m and 2m at a distance d rotate about their common centre of mass in…
• In connection with the circuit drawn below, the value of current flowing through 2 kΩ…
• If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of…
• Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T'…
• The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical…
• An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative…
• A ball with a speed of 9 m/s collides with another identical ball at rest. After the…
• A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It…
• In the given figure, the energy levels of hydrogen atom have been shown along with some…
• Match List I with List II. List I | List II; (a) | Isothermal | (i) | Pressure constant…
• Four identical particles of equal masses 1 kg made to move along the circumference of a…
• Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as…
• If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The…
• An unpolarised light beam is incident on the polarizer of a polarization experiment and…
• A resonance circuit having inductance and resistance 2 × 10⁻⁴ H and 6.28Ω respectively…

Chemistry

• 'A' and 'B' in the following reactions are :
• In Freundlich adsorption isotherm, slope of AB line is :
• Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k'…
• Which of the following ore is concentrated using group 1 cyanide salt ?
• The electrode potential of M²⁺/M of 3d-series elements shows positive value for :
• Al₂O₃ was leached with alkali to get X. The solution of X on passing of gas Y, forms Z…
• Given below are two statements : Statement I : Colourless cupric metaborate is reduced…
• When 9.45 g of CICH₂COOH is added to 500 mL of water, its freezing point drops by 0.5°C…
• At 1990 K and 1 atm pressure, there are equal number of Cl₂, molecules and Cl atoms in…
• Match List I with List II . List I (Monomer Unit) | List II (Polymer); (a) Caprolactum |…
• The reaction of sulphur in alkaline medium is given below: S₈₍ₛ₎ + a OH⁻_((aq)) → b…
• Which of the following are isostructural pairs ? A. SO₄²⁻ and CrO₄²⁻ B. SiCl₄, and TiCl₄…
• Out of the following, which type of interaction is reponsible for the stabilisation of…
• Consider the elements Mg, Al, S, P and Si, the correct increasing order of their first…
• The coordination number of an atom in a body-centered cubic structure is _______…
• Which of the following reagent is used for the following reaction ? CH₃ CH₂ CH₃ →(?) CH₃…
• 4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The…
• A proton and a Li³⁺ nucleus are accelerated by the same potential. If λ _(Li) and λ ₚ…
• Which of the following compound gives pink colour on reaction with phthalic anhydride in…
• The major components in "Gun Metal” are :
• For the reaction A (g) → B (g) the value of the equilibrium constant at 300 K and 1 atm…
• In the following reaction the reason why meta-nitro product also formed is :
• (A) HOCI + H₂O₂ → H₃O⁺ + Cl⁻ + O₂ (B) I₂ + H₂O₂ + 2OH⁻ → 2I⁻ + 2H₂O + O₂ Choose the…
• The stepwise formation of [Cu(NH₃)₄]²⁺ is given below: Cu²⁺ + NH₃ ⇌(K₁) [Cu(NH₃)]²⁺…
• Number of amphoteric compounds among the following is ________. (A) BeO (B) BaO (C)…

Mathematics

• The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is…
• The distance of the point (1, 1, 9) from the point of intersection of the line (x - 3)/1…
• lim _(x → 0) (∫₀^(x²) ( sin √t )dt)/x³ is equal to :
• A man is walking on a straight line. The arithmetic mean of the reciprocals of the…
• If ∫ (cos x-sin x)/√(8-sin 2x)dx=asin⁻¹((sin x+cos x)/b)+c, where c is a constant of…
• The minimum value of α for which the equation 4/(sin x) + 1/(1 - sin x) = α has at least…
• The function f(x) = (4x³ - 3x²)/6 - 2 sin x + ( 2x - 1 )cos x :
• If e^((cos²x+cos⁴x+cos⁶x+...∞)logₑ2) satisfies the equation t² - 9t + 8 = 0, then the…
• Let f : R → R be defined as f (x) = 2x – 1 and g : R - 1 → R be defined as g(x) = (x -…
• The equation of the plane passing through the point (1, 2, -3) and perpendicular to the…
• Let p and q be two positive numbers such that p + q = 2 and p⁴+q⁴ = 272. Then p and q…
• The population P = P(t) at time 't' of a certain species follows the differential…
• The value of -¹⁵C₁ + 2.¹⁵C₂ – 3.¹⁵C₃ + ... - 15.¹⁵C₁₅ + ¹⁴C₁ + ¹⁴C₃ + ¹⁴C₅ + ...+ ¹⁴C₁₁…
• A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes…
• If f : R → R is a function defined by f(x)= [x - 1] cos ( (2x - 1)/2 )π, where [.]…
• If the tangent to the curve y = x³ at the point P(t, t³) meets the curve again at Q…
• If ∫₋ₐᵃ ( | x | + | x - 2 | ) dx = 22, (a > 2) and [x] denotes the greatest integer ≤ x…
• The locus of the mid-point of the line segment joining the focus of the parabola y² =…
• An ordinary dice is rolled for a certain number of times. If the probability of getting…
• Let Bᵢ (i = 1, 2, 3) be three independent events in a sample space. The probability that…
• Let M be any 3 × 3 matrix with entries from the set 0, 1, 2. The maximum number of such…
• Let A = n ∈ N: n is a 3-digit number B = 9k + 2: k ∈ N and C = 9k + l: k ∈ N for some l…
• If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord of another…
• Let three vectors a⃗ ,b⃗ and c⃗ be such that c⃗ is coplanar with a⃗ and b⃗, a⃗ .c⃗ = 7…
• lim _(n → ∞) tan { Σᵣ₌₁ⁿ tan ⁻¹( 1/(1 + r + r²) ) } is equal to ______.
• The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the…
• Let P = [ 3, - 1, - 2; 2, 0, α; 3, - 5, 0 ], where α ∈ R. Suppose Q = [ qᵢⱼ] is a matrix…

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