JEE Main 2021 (Online) 27th July Morning Shift — Question Paper

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Physics

• List-I | List-II; (a) MI of the rod (length L, Mass M, about an axis ⊥ to the rod…
• The figure shows two solid discs with radius R and r respectively. If mass per unit area…
• Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a…
• Two capacitors of capacities 2C and C are joined in parallel and charged up to potential…
• In the given figure, a battery of emf E is connected across a conductor PQ of length 'l'…
• A transistor is connected in common emitter circuit configuration, the collector supply…
• In the reported figure, a capacitor is formed by placing a compound dielectric between…
• If 'f' denotes the ratio of the number of nuclei decayed (N d ) to the number of nuclei…
• Consider an electrical circuit containing a two way switch 'S'. Initially S is open and…
• Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M…
• Assertion A : If in five complete rotations of the circular scale, the distance…
• Three objects A, B and C are kept in a straight line on a frictionless horizontal…
• In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a…
• A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of…
• A particle of mass 9.1 × 10⁻³¹ kg travels in a medium with a speed of 10⁶ m/s and a…
• In Young's double slit experiment, if the source of light changes from orange to blue…
• The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure…
• A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of…
• A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the…
• In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius…
• Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O'…
• A prism of refractive index n₁ and another prism of refractive index n₂ are stuck…
• A 0.07 H inductor and a 12Ω resistor are connected in series to a 220V, 50 Hz ac source…
• A radioactive sample has an average life of 30 ms and is decaying. A capacitor of…
• The relative permittivity of distilled water is 81. The velocity of light in it will be…
• A capacitor of capacitance C = 1 μF is suddenly connected to a battery of 100 volt…
• A body takes 4 min. to cool from 61° C to 59° C. If the temperature of the surroundings…
• In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 × 10⁻² A/m²…
• A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total…

Chemistry

• CO₂ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount…
• The correct order of stability of given carbocation is :
• The statement is incorrect about Ellingham diagram is
• Given below are two statements : Statement I : Aniline is less basic than acetamide…
• 1.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure…
• The difference between bond orders of CO and NO ⊕ is x/2 where x = _____________. (Round…
• Given below are two statements : Statement I : Rutherford's gold foil experiment cannot…
• Given below are two statements : One is labelled as Assertion A and the other labelled…
• The compound 'A' is a complementary base of _______________ in DNA stands.
• The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, α = 90°, β…
• The type of hybridisation and magnetic property of the complex [MnCl₆]³⁻, respectively…
• Match List - I with List - II : List - I | List - II; (a) | NaOH | (i) | Acidic; (b) |…
• Which one among the following chemical tests is used to distinguish monosaccharide from…
• Presence of which reagent will affect the reversibility of the following reaction, and…
• An organic compound is subjected to chlorination to get compound A using 5.0 g of…
• The density of NaOH solution is 1.2 g cm⁻³. The molality of this solution is…
• Match List - I with List - II : List-I (Drug) | List-II (Class of Drug); (a) | Furacin |…
• The conductivity of a weak acid HA of concentration 0.001 mol L⁻¹ is 2.0 × 10⁻⁵ S cm⁻¹…
• Which one of the following compounds will give orange precipitate when treated with 2…
• For water at 100° C and 1 bar, Δᵥₐₚ H - Δᵥₐₚ U = _____________ × 10² J mol⁻¹. (Round off…
• For a reaction of order n, the unit of the rate constant is :
• PCl₅ ⇌ PCl₃ + Cl₂ K c = 1.844 3.0 moles of PCl₅ is introduced in a 1 L closed reaction…
• In gaseous triethyl amine the "-C-N-C-" bond angle is _________ degree.
• The product obtained from the electrolytic oxidation of acidified sulphate solutions, is :
• The oxidation states of 'P' in H₄P₂O₇, H₄P₂O₅ and H₄P₂O₆, respectively, are :
• The number of geometrical isomers possible in triamminetrinitrocobalt (III) is X and in…
• Staggered and eclipsed conformers of ethane are :

Mathematics

• Let a⃗ = î + ĵ + 2k̂ and b⃗ = - î + 2ĵ + 3k̂. Then the vector product ( a⃗ + b⃗ ) × ( (…
• Let P and Q be two distinct points on a circle which has center at C(2, 3) and which…
• Let C be the set of all complex numbers. Let S₁ = { z ∈ C||z - 3 - 2i|² = 8} S₂ = { z ∈…
• If the coefficients of x⁷ in ( x² + 1/bx )¹¹ and x⁻⁷ in ( x - 1/bx² )¹¹, b ≠ 0, are…
• Let y = y(x) be solution of the differential equation log ( dy/dx ) = 3x + 4y, with y(0)…
• If log ₃2,log ₃(2ˣ - 5),log ₃( 2ˣ - 7/2 ) are in an arithmetic progression, then the…
• Let α, β be two roots of the equation x² + (20) 1/4 x + (5) 1/2 = 0. Then α⁸ + β⁸ is…
• Let f:( - π/4,π/4 ) → R be defined as f(x) = { (1 + |sin x|)^(3a/(|sin x|)), ,, - π/4 <…
• Let f:[0,3] → R be defined by f(x) = min { x - [x],1 + [x] - x} where [x] is the…
• Two tangents are drawn from the point P(-1, 1) to the circle x² + y² - 2x - 6y + 6 = 0…
• The probability that a randomly selected 2-digit number belongs to the set n ∈ N : (2ⁿ -…
• Let F:[3,5] → R be a twice differentiable function on (3, 5) such that F(x) = e⁻ˣ∫₃ˣ…
• A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes…
• Let f(x) = | sin ²x, - 2 + cos ²x, cos 2x; 2 + sin ²x, cos ²x, cos 2x; sin ²x, cos ²x, 1…
• The value of lim _(n → ∞) 1/nΣⱼ₌₁ⁿ ((2j - 1) + 8n)/((2j - 1) + 4n) is equal to :
• Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the…
• Let f : R → R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of lim _(x…
• Let S = 1, 2, 3, 4, 5, 6, 7. Then the number of possible functions f : S → S such that…
• If sin θ+cos θ=1/2, then 16(sin(2θ) + cos(4θ) + sin(6θ)) is equal to :
• Let a⃗ = î + ĵ + k̂,b⃗ and c⃗ = ĵ - k̂ be three vectors such that a⃗ × b⃗ = c⃗ and a⃗…
• If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and…
• If y = y(x),y ∈ [ 0,π/2 ) is the solution of the differential equation sec ydy/dx - sin…
• Let A = [ 1, 2; - 1, 4 ]. If A⁻¹ = αI + βA, α, β ∈ R, I is a 2 × 2 identity matrix then…
• Let a plane P pass through the point (3, 7, -7) and contain the line, (x - 2)/(- 3) = (y…
• For real numbers α and β, consider the following system of linear equations : x + y - z…
• Let the domain of the function f(x) = log ₄( log ₅( log ₃(18x - x² - 77) ) ) be (a, b)…
• The value of the definite integral ∫_(- π/4)^(π/4) dx/(1 + eˣᶜᵒˢˣ)(sin ⁴x + cos ⁴x) is…
• If the area of the bounded region R={(x,y):max{0,logₑx}≤ y≤ 2ˣ,1/2≤ x≤ 2} is…
• Let A = { (x,y) ∈ R × R|2x² + 2y² - 2x - 2y = 1}, B = { (x,y) ∈ R × R|4x² + 4y² - 16y +…

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