JEE Main 2021 (Online) 20th July Evening Shift — Question Paper

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Physics

• One mole of an ideal gas at 27° is taken from A to B as shown in the given PV indicator…
• If the Kinetic energy of a moving body becomes four times its initial Kinetic energy…
• With what speed should a galaxy move outward with respect to earth so that the sodium-D…
• A body at rest is moved along a horizontal straight line by a machine delivering a…
• An electron having de-Broglie wavelength λ is incident on a target in a X-ray tube…
• In an electromagnetic wave the electric field vector and magnetic field vector are given…
• If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units…
• A body rolls down an inclined plane without slipping. The kinetic energy of rotation is…
• At an angle of 30° to the magnetic meridian, the apparent dip is 45°. Find the true dip :
• A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in…
• A satellite is launched into a circular orbit of radius R around earth, while a second…
• A particle is making simple harmonic motion along the X-axis. If at a distances x₁ and…
• The correct relation between the degrees of freedom f and the ratio of specific heat γ…
• A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with…
• Two small drops of mercury each of radius R coalesce to form a single large drop. The…
• A radioactive substance decays to ( 1/16 )ᵗʰ of its initial activity in 80 days. The…
• A certain metallic surface is illuminated by monochromatic radiation of wavelength λ…
• A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is…
• For the forward biased diode characteristics shown in the figure, the dynamic resistance…
• The magnetic susceptibility of a material of a rod is 499. Permeability in vacuum is 4π…
• Which of the following graphs represent the behavior of an ideal gas? Symbols have their…
• A series LCR circuit of R = 5Ω, L = 20 mH and C = 0.5 μF is connected across an AC…
• The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the…
• For a certain radioactive process the graph between In R and t(sec) is obtained as shown…
• In the given figure switches S₁ and S₂ are in open condition. The resistance across ab…
• Two vectors P⃗ and Q⃗ have equal magnitudes. If the magnitude of P⃗+Q⃗ is n times the…
• A boy reaches the airport and finds that the escalator is not working. He walks up the…
• Consider a binary star system of star A and star B with masses m A and m B revolving in…
• For a series LCR circuit with R = 100 Ω, L = 0.5 mH and C = 0.1 pF connected across…
• Two bodies, a ring and a solid cylinder of same material are rolling down without…

Chemistry

• Potassium chlorate is prepared by electrolysis of KCl in basic solution as shown by…
• Which one of the following species doesn't have a magnetic moment of 1.73 BM, (spin only…
• A solution is 0.1 M in Cl⁻ and 0.001 M in CrO₄²⁻. Solid AgNO₃ is gradually added to it…
• Which one of the following statements is not true about enzymes?
• 100 ml of 0.0018% (w/v) solution of Cl⁻ ion was the minimum concentration of Cl⁻…
• Consider the above reaction, compound B is :
• The correct order of their reactivity towards hydrolysis at room temperature is :
• Outermost electronic configuration of a group 13 element, E, is 4s², 4p¹. The electronic…
• The single largest industrial application of dihydrogen is :
• PCl₅(g) → PCl₃(g) + Cl₂(g) In the above first order reaction the concentration of PCl₅…
• Metallic sodium does not react normally with :
• Bakelite is a cross-linked polymer of formaldehyde and :
• For a given chemical reaction A → B at 300 K the free energy change is -49.4 kJ mol⁻¹…
• In the above reactions, product A and product B respectively are :
• When 0.15 g of an organic compound was analyzed using Carius method for estimation of…
• Spin only magnetic moment of an octahedral complex of Fe²⁺ in the presence of a strong…
• The wavelength of electrons accelerated from rest through a potential difference of 40…
• Diamond has a three dimensional structure of C atoms formed by covalent bonds. The…
• Consider two chemical reactions (A) and (B) that take place during metallurgical…
• Benzene on nitration gives nitrobenzene in presence of HNO₃ and H₂SO₄ mixture, where :
• 4g equimolar mixture of NaOH and Na₂CO₃ contains x g of NaOH and y g of Na₂CO₃. The…
• Cu²⁺ salt reacts with potassium iodide to give
• Which one of the following pairs of isomers is an example of metamerism?
• An aqueous solution of NiCl₂ was heated with excess sodium cyanide in presence of strong…
• In Carius method, halogen containing organic compound is heated with fuming nitric acid…
• The vapour pressures of A and B at 25°C are 90 mm Hg and 15 mm Hg respectively. If A and…
• The hybridisations of the atomic orbitals of nitrogen in NO₂ -, NO₂ + and NH₄ +…

Mathematics

• In a triangle ABC, if | BC⃗ | = 3, | CA⃗ | = 5 and | BA⃗ | = 7, then the projection of…
• The sum of all the local minimum values of the twice differentiable function f : R → R…
• Let a function g : [ 0, 4 ] → R be defined as g(x) = { max _(0 ≤ t ≤ x) { t³ - 6t² + 9t…
• Let { aₙ }ₙ₌₁^∞ be a sequence such that a₁ = 1, a₂ = 1 and aₙ₊₂ = 2aₙ₊₁ + aₙ for all n ≥…
• If the point on the curve y² = 6x, nearest to the point ( 3,3/2 ) is (α, β), then 2(α +…
• If [x] denotes the greatest integer less than or equal to x, then the value of the…
• Consider the line L given by the equation (x - 3)/2 = (y - 1)/1 = (z - 2)/1. Let Q be…
• Let y = y(x) satisfies the equation dy/dx - |A| = 0, for all x > 0, where A = [ y, sin…
• For p > 0, a vector v⃗ ₂ = 2î + (p + 1)ĵ is obtained by rotating the vector v⃗ ₁ = √3 pî…
• Let P be a variable point on the parabola y = 4x² + 1. Then, the locus of the mid-point…
• For k ∈ N, let 1/(α (α + 1)(α + 2).........(α + 20)) = Σ_(K = 0)²⁰ Aₖ/(α + k) , where α…
• If f:R → R is given by f(x) = x + 1, then the value of lim _(n → ∞) 1/n[ f(0) + f( 5/n )…
• If sum of the first 21 terms of the series log _(9^(1/2))x + log _(9^(1/3))x + log…
• Let A, B and C be three events such that the probability that exactly one of A and B…
• Let a curve y = y(x) be given by the solution of the differential equation cos ( 1/2cos…
• Consider a triangle having vertices A(-2, 3), B(1, 9) and C(3, 8). If a line L passing…
• The lines x = ay - 1 = z - 2 and x = 3y - 2 = bz - 2, (ab ≠ 0) are coplanar, if :
• Let g(t) = ∫_(- π /2)^(π /2) cos ( π/4t + f(x) ) dx, where f(x) = log ₑ( x + √(x² + 1)…
• The value of k ∈R, for which the following system of linear equations 3x - y + 4z = 3, x…
• For the natural numbers m, n, if (1 - y)ᵐ(1 + y)ⁿ = 1 + a₁y + a₂y² + .... + aₘ₊ₙyᵐ⁺ⁿ and…
• The value of tan ( 2tan ⁻¹( 3/5 ) + sin ⁻¹( 5/13 ) ) is equal to :
• If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and 20/3…
• Let A = { aᵢⱼ} be a 3 × 3 matrix, where aᵢⱼ = { ( - 1)ʲ⁻ⁱ, if, i < j,; 2, if, i = j,; (…
• Let f:R - { α/6 } → R be defined by f(x) = (5x + 3)/(6x - α). Then the value of α for…
• If lim _(x → 0) (α xeˣ - β log ₑ(1 + x) + γ x²e⁻ˣ)/(xsin ²x) = 10,α ,β ,γ ∈ R, then the…
• If the real part of the complex number (1 - cos θ + 2i sin θ )⁻¹ is 1/5 for θ ∈ (0,π )…
• Let r₁ and r₂ be the radii of the largest and smallest circles, respectively, which pass…

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