JEE Main 2021 (Online) 18th March Evening Shift — Question Paper

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Physics

• A ball of mass 4 kg, moving with a velocity of 10 ms⁻¹, collides with a spring of length…
• For an adiabatic expansion of an ideal gas, the fractional change in its pressure is…
• If the angular velocity of earth's spin is increased such that the bodies at the equator…
• Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ…
• The correct relation between α (ratio of collector current to emitter current) and β…
• An object of mass m₁ collides with another object of mass m₂, which is at rest. After…
• Two wires of same length and thickness having specific resistances 6Ω cm and 3Ω cm…
• The function of time representing a simple harmonic motion with a period of π/ω is :
• The typical output characteristics curve for a transistor working in the common-emitter…
• The decay of a proton to neutron is :
• A particle of mass m moves in a circular orbit under the central potential field, U(r) =…
• The projectile motion of a particle of mass 5 g is shown in the figure. The initial…
• The speed of electrons in a scanning electron microscope is 1 × 10⁷ ms⁻¹. If the protons…
• Which of the following statements are correct? (A) Electric monopoles do not exist…
• An infinite number of point charges, each carrying 1 μC charge, are placed along the…
• Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment…
• A proton and an α-particle, having kinetic energies Kₚ and K α respectively, enter into…
• The radius of a sphere is measured to be (7.50 ± 0.85) cm. Suppose the percentage error…
• The velocity - displacement graph of a particle is shown in the figure. The acceleration…
• The angular momentum of a planet of mass M moving around the sun in an elliptical orbit…
• A galaxy is moving away from the earth at a speed of 286 kms⁻¹. The shift in the…
• Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m². The…
• The time taken for the magnetic energy to reach 25% of its maximum value, when a…
• A solid cylinder of mass m is wrapped with an inextensible light string and, is placed…
• An ideal gas in a cylinder is separated by a piston in such a way that the entropy of…
• Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean…
• Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed…
• In a series LCR circuit, the inductive reactance (X L ) is 10Ω and the capacitive…
• A plane electromagnetic wave propagating along y-direction can have the following pair…

Chemistry

• Match List - I with List - II : List - I | List - II; (a) | Mercury | (i) | Vapour phase…
• Given below are two statements : Statement I : Bohr's theory accounts for the stability…
• 10.0 mL of Na₂CO₃ solution is titrated against 0.2 M HCl solution. The following titre…
• A reaction has a half life of 1 min. The time required for 99.9% completion of the…
• The solubility of CdSO₄ in water is 8.0 × 10⁻⁴ mol L⁻¹. Its solubility in 0.01 M H₂SO₄…
• Consider the above reaction where 6.1 g of Benzoic acid is used to get 7.8 g of m-bromo…
• Deficiency of vitamin K causes :
• The oxide that shows magnetic property is :
• The secondary valency and the number of hydrogen bonded water molecule(s) in CuSO₄…
• Match List - I with List - II : List - I | List - II; (a) | Be | (i) | treatment of…
• The gas phase reaction 2A(g)⇌ A₂(g) at 400 K has ΔGᵒ = + 25.2 kJ mol⁻¹. The equilibrium…
• The first ionization energy of magnesium is smaller as compared to that of elements X…
• In the reaction of hypobromite with amide, the carbonyl carbon is lost as :
• The number of species below that have two lone pairs of electrons in their central atom…
• The molar conductivities at infinite dilution of barium chloride, sulphuric acid and…
• In Tollen's test for aldehyde, the overall number of electron(s) transferred to the…
• Given below are two statements : Statement I : C₂H₅OH and AgCN both can generate…
• A xenon compound 'A' upon partial hydrolysis gives XeO₂F₂. The number of lone pair of…
• The charges on the colloidal CdS sol and TiO₂ sol are, respectively :
• In basic medium, H₂O₂ exhibits which of the following reactions? (A) Mn²⁺ → Mn⁴⁺ (B) I²…
• An organic compound "A" on treatment with benzene sulphonyl chloride gives compound B. B…
• In the following molecule, Hybridisation of Carbon a, b, and c respectively are :
• The oxidation states of nitrogen in NO, NO₂, N₂O and NO₃ - are in the order of :
• Match List - I with List - II : List - I (Class of Chemicals) | List - II (Example); (a)…
• A solute A dimerizes in water. The boiling point of a 2 molal solution of A is 100.52°C…
• Consider the given reaction, percentage yield of :
• A hard substance melts at high temperature and is an insulator in both solid and in…
• Main products formed during a reaction of 1-methoxy naphthalene with hydroiodic acid are :

Mathematics

• Let g(x) = ∫₀ˣ f(t)dt, where f is continuous function in [ 0, 3 ] such that 1/3 ≤ f(t) ≤…
• Let S₁ : x² + y² = 9 and S₂ : (x - 2)² + y² = 1. Then the locus of center of a variable…
• The term independent of x in the expansion of [ (x + 1)/(x^(2/3) - x^(1/3) + 1) - (x -…
• Let I be an identity matrix of order 2 × 2 and P = [ 2, - 1; 5, - 3 ]. Then the value of…
• Let ⁿCᵣ denote the binomial coefficient of xʳ in the expansion of (1 + x)ⁿ. If Σₖ₌₀¹⁰…
• Let in a Binomial distribution, consisting of 5 independent trials, probabilities of…
• Let in a series of 2n observations, half of them are equal to a and remaining half are…
• Let f : R - 3 → R - 1 be defined by f(x) = (x - 2)/(x - 3). Let g : R → R be given as…
• In a triangle ABC, if |BC⃗ | = 8,|CA⃗ | = 7,|AB⃗ | = 10, then the projection of the…
• If 15sin⁴α + 10cos⁴α = 6, for some α ∈R, then the value of 27sec⁶α + 8cosec⁶α is equal…
• Let P be a plane containing the line (x - 1)/3 = (y + 6)/4 = (z + 5)/2 and parallel to…
• Let a⃗ and b⃗ be two non-zero vectors perpendicular to each other and |a⃗ | = |b⃗ |. If…
• Let the system of linear equations 4x + λy + 2z = 0 2x - y + z = 0 μx + 2y + 3z = 0, λ…
• The area bounded by the curve 4y² = x²(4 - x)(x - 2) is equal to :
• Consider a hyperbola H : x² - 2y² = 4. Let the tangent at a point P(4, √6 ) meet the…
• Let f : R → R be a function defined as f(x) = { (sin (a + 1)x + sin 2x)/2x,if x < 0; b…
• Let P(x) be a real polynomial of degree 3 which vanishes at x = -3. Let P(x) have local…
• Let y = y(x) be the solution of the differential equation dy/dx = (y + 1)( (y +…
• Define a relation R over a class of n × n real matrices A and B as "ARB iff there exists…
• Let f : R → R satisfy the equation f(x + y) = f(x) . f(y) for all x, y ∈R and f(x) ≠ 0…
• Let y = y(x) be the solution of the differential equation xdy - ydx = √(x² - y²) dx, x ≥…
• Let a tangent be drawn to the ellipse x²/27 + y² = 1 at (3√3 cos θ ,sin θ ) where 0 ∈ (…
• If Σᵣ₌₁¹⁰ r!(r³ + 6r² + 2r + 5) = α (11!), then the value of α is equal to ___________.
• Let S₁ be the sum of first 2n terms of an arithmetic progression. Let S₂ be the sum of…
• If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x g(x³) is…
• Let a complex number be w = 1 - √3 i. Let another complex number z be such that |zw| = 1…
• Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides…
• Let the mirror image of the point (1, 3, a) with respect to the plane r⃗ .( 2î - ĵ + k̂…

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