JEE Main 2021 (Online) 17th March Evening Shift — Question Paper

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Physics

• The velocity of a particle is v = v₀ + gt + Ft². Its position is x = 0 at t = 0; then…
• If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of…
• A hairpin like shape as shown in figure is made by bending a long current carrying wire…
• A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient…
• A sound wave of frequency 245 Hz travels with the speed of 300 ms⁻¹ along the positive…
• A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms⁻¹ goes…
• A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of…
• The electric field in a region is given by E⃗ = 2/5E₀î + 3/5E₀ĵ with E₀ = 4.0 × 10³N/C…
• The disc of mass M with uniform surface mass density σ is shown in the figure. The…
• Two identical photocathodes receive the light of frequencies f₁ and f₂ respectively. If…
• Seawater at a frequency f = 9 × 10² Hz, has permittivity ε = 80ε₀ and resistivity ρ =…
• Two cells of emf 2E and E with internal resistance r₁ and r₂ respectively are connected…
• Which one is the correct option for the two different thermodynamic processes?
• The atomic hydrogen emits a line spectrum consisting of various series. Which series of…
• A 2μF capacitor C₁ is first charged to a potential difference of 10V using a battery…
• Match List - I with List - II List - I | List - II; (a) | Phase difference between…
• Two particles A and B of equal masses are suspended from two massless springs of spring…
• A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude…
• A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R…
• Suppose you have taken a dilute solution of oleic acid in such a way that its…
• Two identical blocks A and B each of mass m resting on the smooth horizontal floor are…
• What happens to the inductive reactance and the current in a purely inductive circuit if…
• An object is located at 2 km beneath the surface of the water. If the fractional…
• A rubber ball is released from a height of 5 m above the floor. It bounces back…
• A particle of mass m moves in a circular orbit in a central potential field U(r) = U₀r⁴…
• The four arms of a Wheatstone bridge have resistances as shown in the figure. A…
• The electric field intensity produced by the radiation coming from a 100 W bulb at a…
• Which one of the following will be the output of the given circuit?
• The image of an object placed in air formed by a convex refracting surface is at a…

Chemistry

• The common positive oxidation states for an element with atomic number 24, are :
• The correct pair(s) of the ambident nucleophiles is(are) (A) AgCN/KCN (B) RCOOAg/RCOOK…
• The functional groups that are responsible for the ion-exchange property of cation and…
• One of the by-products formed during the recovery of NH₃ from Solvay process is :
• Nitrogen can be estimated by Kjeldahl's method for which of the following compound?
• Match List - I with List - II : List - I | List - II ; (a) | [Co(NH₃)₆][Cr(CN)₆] | (i) |…
• Choose the correct statement regarding the formation of carbocations A and B given…
• Amongst the following, the linear species is :
• Primary, secondary and tertiary amines can be separated using:
• KBr is doped with 10⁻⁵ mole percent of SrBr₂. The number of cationic vacancies in 1g of…
• The reaction 2A + B₂ → 2AB is an elementary reaction. For a certain quantity of…
• Consider the reaction N₂O₄(g)⇌ 2NO₂(g) The temperature at which K C = 20.4 and K P =…
• The set that represents the pair of neutral oxides of nitrogen is :
• Match List - I with List - II. List - I Chemical Compound | List - II Used as; (a) |…
• In the above reaction, the structural formula of (A), ''X'' and ''Y'' respectively are :
• Given below are two statements : Statement I : 2-methylbutane on oxidation with KMnO₄…
• The total number of C-C sigma bond/s in mesityl oxide (C₆H₁₀O) is __________. (Round off…
• During which of the following processes, does entropy decrease? (A) Freezing of water to…
• Match List - I with List - II : List - I | List - II; (a) | Haematite | (i) | Al₂O₃…
• In the ground state of atomic Fe(Z = 26), the spin-only magnetic moment is ____________…
• C₁₂H₂₂O₁₁ + H₂O→(Enzyme A) C₆H₁₂O₆_(Glu cos e) + C₆H₁₂O₆_(Fructose) C₆H₁₂O₆_(Glu cos e)…
• Fructose is an example of :
• The set of elements that differ in mutual relationship from those of the other sets is :
• For the coagulation of a negative sol, the species below, that has the highest…
• A KCl solution of conductivity 0.14 S m⁻¹ shows a resistance of 4.19Ω in a conductivity…
• Consider the above reaction. The percentage yield of amide product is __________. (Round…
• A 1 molal K₄Fe(CN)₆ solution has a degree of dissociation of 0.4. Its boiling point is…
• On complete reaction of FeCl₃ with oxalic acid in aqueous solution containing KOH…

Mathematics

• If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points…
• If x, y, z are in arithmetic progression with common difference d, x ≠ 3d, and the…
• Let the tangent to the circle x² + y² = 25 at the point R(3, 4) meet x-axis and y-axis…
• Let y = y(x) be the solution of the differential equation cos x(3 sin x + cos x + 3)dy =…
• Two tangents are drawn from a point P to the circle x² + y² - 2x - 4y + 4 = 0, such that…
• The number of solutions of the equation x + 2tanx = π/2 in the interval [0, 2π] is :
• Let x⃗ be a vector in the plane containing vectors a⃗ = 2î - ĵ + k̂ and b⃗ = î + 2ĵ -…
• Let P be an arbitrary point having sum of the squares of the distances from the planes x…
• Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n…
• The value of the limit lim _(θ → 0) (tan (π cos ²θ ))/(sin (2π sin ²θ )) is equal to :
• Consider the function f : R → R defined by f(x) = { ( 2 - sin ( 1/x ) )|x|,x ≠ 0; 0, x =…
• Let A = [ a, b; c, d ] and B = [ α; β ] ≠ [ 0; 0 ] such that AB = B and a + d = 2021…
• If the integral ∫₀¹⁰ [sin 2π x]/e^(x - [x]) dx = α e⁻¹ + β e^(- 1/2) + γ , where α, β, γ…
• Let L be a tangent line to the parabola y² = 4x - 20 at (6, 2). If L is also a tangent…
• Let the coefficients of third, fourth and fifth terms in the expansion of ( x + a/x²…
• If 1, log₁₀(4ˣ - 2) and log₁₀( 4ˣ + 18/5 ) are in arithmetic progression for a real…
• If the equation of plane passing through the mirror image of a point (2, 3, 1) with…
• Let f : [-3, 1] → R be given as f(x)={min {(x+6),x²},-3≤ x≤ 0; max {√x,x²}, 0≤ x≤ 1. If…
• Let f : R → R be defined as f(x) = e⁻ˣsinx. If F : [0, 1] → R is a differentiable…
• Let Iₙ = ∫₁ᵉ x¹⁹(log |x|)ⁿ dx, where n∈N. If (20)I₁₀ = αI₉ + βI₈, for natural numbers α…
• Let tanα, tanβ and tanγ; α, β, γ ≠ (2n-1)π/2, n∈N be the slopes of three line segments…
• Let S₁, S₂ and S₃ be three sets defined as S₁ = z∈C : |z - 1| ≤ √2 S₂ = z∈C : Re((1 -…
• The value of lim _(n → ∞) ([r] + [2r] + ... + [nr])/n², where r is a non-zero real…
• Let O be the origin. Let OP⃗ = xî + yĵ - k̂ and OQ⃗ = - î + 2ĵ + 3xk̂, x, y∈R, x > 0, be…
• Let f : [-1, 1] → R be defined as f(x) = ax² + bx + c for all x∈[-1, 1], where a, b, c∈R…
• Let a computer program generate only the digits 0 and 1 to form a string of binary…
• If the curve y = y(x) is the solution of the differential equation 2(x² + x^(5/4))dy -…
• The number of solutions of the equation sin ⁻¹[ x² + 1/3 ] + cos ⁻¹[ x² - 2/3 ] = x²…
• The value of Σᵣ₌₀⁶ ( ⁶Cᵣ . ⁶C₆₋ᵣ ) is equal to :

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