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

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Physics

• At time t = 0, a material is composed of two radioactive atoms A and B, where N A (0) =…
• The coefficient of static friction between two blocks is 0.5 and the table is smooth…
• For the given circuit, the power across Zener diode is .............. mW.
• The two thin coaxial rings, each of radius 'a' and having charges +Q and -Q respectively…
• A cylindrical container of volume 4.0 × 10⁻³ m³ contains one mole of hydrogen and two…
• An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply…
• The temperature of equal masses of three different liquids x, y and z are 10°C, 20°C and…
• Two simple harmonic motions are represented by the equations x₁ = 5 sin ( 2π t + π/4 )…
• A source of light is placed in front of a screen. Intensity of light on the screen is I…
• A refrigerator consumes an average 35W power to operate between temperature -10°C to…
• Two waves are simultaneously passing through a string and their equations are : y₁ = A₁…
• In the given circuit the AC source has ω = 100 rad s⁻¹. Considering the inductor and…
• A parallel plate capacitor with plate area A has separation d between the plates. Two…
• The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy…
• A light beam is described by E = 800 sin ω ( t - x/c ). An electron is allowed to move…
• The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the…
• A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane…
• Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth…
• Match List - I with List - II Choose the most appropriate answer from the options given…
• An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal…
• If you are provided a set of resistances 2Ω, 4Ω, 6Ω and 8Ω. Connect these resistances so…
• The angle between vector (A⃗) and (A⃗-B⃗) is :
• Four NOR gates are connected as shown in figure. The truth table for the given figure is :
• A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the…
• If the length of the pendulum in pendulum clock increases by 0.1%, then the error in…
• A particle of mass m is suspended from a ceiling through a string of length L. The…
• A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter…
• The de-Broglie wavelength of a particle having kinetic energy E is λ. How much extra…
• If the maximum value of accelerating potential provided by a ratio frequency oscillator…

Chemistry

• 83 g of ethylene glycol dissolved in 625 g of water. The freezing point of the solution…
• The bond order and magnetic behaviour of O₂ - ion are respectively :
• Which one of the following phenols does not give colour when condensed with phthalic…
• Chalcogen group elements are :
• Which one of the following compounds is not aromatic?
• 100 mL of Na₃PO₄ solution contains 3.45 g of sodium. The molarity of the solution is…
• Indicate the complex/complex ion which did not show any geometrical isomerism :
• The class of drug to which chlordiazepoxide with above structure belongs is :
• The number of non-ionisable hydrogen atoms present in the final product obtained from…
• Given below are two statements : one is labelled as Assertion (A) and other is labelled…
• Match List - I with List - II : List - I, List - II; (Chemical Reaction), (Reagent…
• Arrange the following Cobalt complexes in the order of increasing Crystal Field…
• Consider the given reaction, identify 'X' and 'Y' :
• The major product in the above reaction is :
• The overall stability constant of the complex ion [Cu(NH₃)₄]²⁺ is 2.1 × 10¹³. The…
• For the galvanic cell, Zn(s) + Cu²⁺ (0.02 M) → Zn²⁺ (0.04 M) + Cu(s), E cell =…
• The number of stereoisomers possible for 1, 2-dimethyl cyclopropane is :
• Given below are two statements : Statement I : Sphalerite is a sulphide or of zinc and…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• The sol given below with negatively charged colloidal particles is :
• In the sulphur estimation, 0.471 g of an organic compound gave 1.44 g of barium…
• For water Δᵥₐₚ H = 41 kJ mol⁻¹ at 373 K and 1 bar pressure. Assuming that water vapour…
• A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• A chloro compound "A". (i) forms aldehydes on ozonolysis followed by the hydrolysis…
• The equilibrium constant K c at 298 K for the reaction A + B ⇌ C + D is 100. Starting…

Mathematics

• A hall has a square floor of dimension 10 m × 10 m (see the figure) and vertical walls…
• Let Q be the foot of the perpendicular from the point P(7, -2, 13) on the plane…
• Two fair dice are thrown. The numbers on them are taken as λ and μ, and a system of…
• Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively…
• If ( √3 + i )¹⁰⁰ = 2⁹⁹(p + iq), then p and q are roots of the equation :
• Let P be the plane passing through the point (1, 2, 3) and the line of intersection of…
• A fair die is tossed until six is obtained on it. Let x be the number of required…
• The sum of all 3-digit numbers less than or equal to 500, that are formed without using…
• Let a and b respectively be the points of local maximum and local minimum of the…
• If the projection of the vector î + 2ĵ + k̂ on the sum of the two vectors 2î + 4ĵ - 5k̂…
• Let y(x) be the solution of the differential equation 2x² dy + (eʸ - 2x)dx = 0, x > 0…
• The locus of the mid points of the chords of the hyperbola x² - y² = 4, which touch the…
• Let a₁, a₂, ......., a₁₀ be an AP with common difference - 3 and b₁, b₂, ........., b₁₀…
• The value of ∫_(- π/2)^(π/2) ( (1 + sin ²x)/(1 + π ˢⁱⁿˣ) ) dx is
• lim _(x → 2) ( Σₙ₌₁⁹ x/(n(n + 1)x² + 2(2n + 1)x + 4) ) is equal to :
• Let λ ≠ 0 be in R. If α and β are the roots of the equation x² - x + 2λ = 0, and α and γ…
• The domain of the function cosec ⁻¹( (1 + x)/x ) is :
• The point P( - 2√6 ,√3 ) lies on the hyperbola x²/a² - y²/b² = 1 having eccentricity…
• Let A be a 3 × 3 real matrix. If det(2Adj(2 Adj(Adj(2A)))) = 2⁴¹, then the value of…
• Let A = ( 1, 0, 0; 0, 1, 1; 1, 0, 0 ). Then A²⁰²⁵ - A²⁰²⁰ is equal to :
• The value of 2 sin (π/8)sin (2π/8)sin (3π/8)sin (5π/8)sin (6π/8)sin (7π/8) is :
• If the value of the integral ∫₀⁵ (x + [x])/e^(x - [x])dx = α e⁻¹ + β , where α, β ∈ R…
• Let ( n; k ) denotes ⁿCₖ and [ n; k ] = { ( n; k ),, if 0 ≤ k ≤ n; 0,, otherwise If Aₖ =…
• If Σᵣ₌₁⁵⁰ tan ⁻¹1/2r² = p, then the value of tan p is :
• Let [t] denote the greatest integer less than or equal to t. Let f(x) = x - [x], g(x) =…
• A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C₁ : x²…
• The least positive integer n such that (2i)ⁿ/(1 - i)ⁿ⁻²,i = √(- 1) is a positive…
• The local maximum value of the function f(x) = ( 2/x )^(x²), x > 0, is

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