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

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Physics

• A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it…
• An object viewed from a near point distance of 25 cm, using a microscopic lens with…
• A body having specific charge 8 μC/g is resting on a frictionless plane at a distance 10…
• Consider a mixture of gas molecule of types A, B and C having masses m A < m B < m C…
• A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all…
• If A⃗ and B⃗ are two vectors satisfying the relation A⃗ . B⃗ = |A⃗× B⃗|. Then the value…
• A rod of mass M and length L is lying on a horizontal frictionless surface. A particle…
• A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders…
• The value of tension in a long thin metal wire has been changed from T₁ to T₂. The…
• Region I and II are separated by a spherical surface of radius 25 cm. An object is kept…
• The amplitude of wave disturbance propagating in the positive x-direction is given by y…
• A butterfly is flying with a velocity 4√2 m/s in North-East direction. Wind is slowly…
• A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into…
• In an LCR series circuit, an inductor 30 mH and a resistor 1 Ω are connected to an AC…
• In the reported figure, heat energy absorbed by a system in going through a cyclic…
• For the circuit shown below, calculate the value of I z :
• A radioactive material decays by simultaneous emissions of two particles with half lives…
• The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30° banked…
• The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from…
• The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car…
• The entropy of any system is given by S = α ²β ln [ (μ kR)/(Jβ ²) + 3 ] where α and β…
• The value of current in the 6 Ω resistance is :
• In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in…
• A certain charge Q is divided into two parts q and (Q - q). How should the charges Q and…
• The radiation corresponding to 3 → 2 transition of a hydrogen atom falls on a gold…
• A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04…
• A nucleus of mass M emits γ -ray photon of frequency 'v'. The loss of internal energy by…
• The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then…
• AC voltage V(t) = 20 sinωt of frequency 50 Hz is applied to a parallel plate capacitor…

Chemistry

• The inactivation rate of a viral preparation is proportional to the amount of virus. In…
• 250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl. The number of unreacted HCl…
• The correct order of intensity of colors of the compounds is :
• Identify the incorrect statement from the following
• Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated…
• The Azimuthal quantum number for the valence electrons of Ga⁺ ion is ___________…
• According to the valence bond theory the hybridization of central metal atom is dsp² for…
• The conditions given below are in the context of observing Tyndall effect in colloidal…
• Green chemistry in day-to-day life is in the use of :
• The correct structure of Rhumann's Purple, the compound formed in the reaction of…
• An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass…
• The species given below that does NOT show disproportionation reaction is :
• Which among the above compound/s does/do not form Silver mirror when treated with…
• The metal that can be purified economically by fractional distillation method is :
• The number of nitrogen atoms in a semicarbazone molecule of acetone is ______________.
• Given below are two statements. One is labelled as Assertion A nd the other is labelled…
• To synthesize 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate ___________…
• Given below are two statements : One is labelled as Assertion A and other is labelled as…
• The set in which compounds have different nature is :
• In the given reaction 3-Bromo-2, 2-dimethyl butane →(C₂H₅OH) 'A'_((Major Pr oduct))…
• The number of lone pairs of electrons on the central I atom in I₃ - is ____________.
• Orlon fibres are made up of :
• Compound A is converted to B on reaction with CHCl₃ and KOH. The compound B is toxic and…
• Among the given species the Resonance stabilised carbocations are :
• At 20° C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20…
• 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) In an equilibrium mixture, the partial pressures are P SO₃ =…
• An inorganic Compound 'X' on treatment with concentrated H₂SO₄ produces brown fumes and…
• A s-block element (M) reacts with oxygen to form an oxide of the formula MO₂. The oxide…

Mathematics

• Let A = [aᵢⱼ] be a 3 × 3 matrix, where aᵢⱼ = { 1, ,, if i = j; - x, ,, if | i - j | = 1…
• Let A = ( 1, - 1, 0; 0, 1, - 1; 0, 0, 1 ) and B = 7A²⁰ - 20A⁷ + 2I, where I is an…
• Let the tangent to the parabola S : y² = 2x at the point P(2, 2) meet the x-axis at Q…
• The value of the integral ∫₋₁¹ log ₑ(√(1 - x) + √(1 + x) )dx is equal to:
• The number of rational terms in the binomial expansion of ( 4^(1/4) + 5^(1/6) )¹²⁰ is…
• Let 'a' be a real number such that the function f(x) = ax² + 6x - 15, x ∈ R is…
• If z and ω are two complex numbers such that | zω | = 1 and arg (z) - arg (ω ) = 3π/2…
• Let y = y(x) be the solution of the differential equation x tan ( y/x )dy = ( y tan (…
• If the value of lim _(x → 0) (2 - cos x√(cos 2x) )^(( (x + 2)/x² )) is equal to eᵃ, then…
• Let a function f : R → R be defined as f(x) = { sin x - eˣ, if, x ≤ 0; a + [ - x], if, 0…
• Let A = [ 2, 3; a, 0 ], a∈R be written as P + Q where P is a symmetric matrix and Q is…
• Let a, b, c, d in arithmetic progression with common difference λ. If | x + a - c, x +…
• Let [ x ] denote the greatest integer ≤ x, where x ∈ R. If the domain of the real valued…
• If α and β are the distinct roots of the equation x² + (3)^(1/4)x + 3^(1/2) = 0, then…
• The number of real roots of the equation tan ⁻¹√x(x + 1) + sin ⁻¹√(x² + x + 1) = π/4 is :
• There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2…
• Let a⃗ = 2î + ĵ - 2k̂ and b⃗ = î + ĵ. If c⃗ is a vector such that a⃗ . c⃗ = | c⃗ |,| c⃗…
• Let a be a positive real number such that ∫₀ᵃ e^(x - [x]) dx = 10e - 9 where [ x ] is…
• Let P be a plane passing through the points (1, 0, 1), (1, -2, 1) and (0, 1, -2). Let a…
• Words with or without meaning are to be formed using all the letters of the word…
• The probability of selecting integers a∈[- 5, 30] such that x² + 2(a + 4)x - 5a + 64 >…
• Let y = mx + c, m > 0 be the focal chord of y² = - 64x, which is tangent to (x + 10)² +…
• The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6…
• Let y = y(x) be the solution of the differential equation eˣ√(1 - y²) dx + ( y/x )dy =…
• Let a⃗, b⃗, c⃗ be three mutually perpendicular vectors of the same magnitude and equally…
• The coefficient of x²⁵⁶ in the expansion of (1 - x)¹⁰¹ (x² + x + 1)¹⁰⁰ is :
• If the shortest distance between the lines r₁⃗ = α î + 2ĵ + 2k̂ + λ (î - 2ĵ + 2k̂), λ ∈…

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