JEE Main 2021 (Online) 26th February Morning Shift — Question Paper

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Physics

• In a typical combustion engine the workdone by a gas molecule is given by…
• In a series LCR resonant circuit, the quality factor is measured as 100. If the…
• Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance…
• Find the electric field at point P (as shown in figure) on the perpendicular bisector of…
• A short straight object of height 100 cm lies before the central axis of a spherical…
• Consider the combination of 2 capacitors C₁ and C₂ with C₂ > C₁, when connected in…
• A large number of water drops, each of radius r, combine to have a drop of radius R. If…
• If λ₁ and λ₂ are the wavelengths of the third member of Lyman and first member of the…
• A radiation is emitted by 1000W bulb and it generates an electric field and magnetic…
• A particle is moving with uniform speed along the circumference of a circle of radius R…
• A planet revolving in elliptical orbit has : A. a constant velocity of revolution. B…
• The circuit contains two diodes each with a forward resistance of 50Ω and with infinite…
• Given below are two statements : one is labelled as Assertion A and the other is…
• A container is divided into two chambers by a partition. The volume of first chamber is…
• In a Young's double slit experiment two slits are separated by 2 mm and the screen is…
• Five equal resistances are connected in a network as shown in figure. The net resistance…
• A person standing on a spring balance inside a stationary lift measures 60 kg. The…
• If two similar springs each of spring constant K₁ are joined in series, the new spring…
• In an electrical circuit, a battery is connected to pass 20C of charge through it in a…
• Four identical solid spheres each of mass 'm' and radius 'a' are placed with their…
• The normal density of a material is ρ and its bulk modulus of elasticity is K. The…
• The temperature θ at the junction of two insulating sheets, having thermal resistances…
• An alternating current is given by the equation i = i₁ sin ωt + i₂ cos ωt. The rms…
• LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is…
• Given below are two statements : one is labeled as Assertion A and the other is labelled…
• A boy pushes a box of mass 2 kg with a force F⃗ = ( 20î + 10ĵ )N on a frictionless…
• The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form…
• Find the gravitational force of attraction between the ring and sphere as shown in the…

Chemistry

• Compound A used as a strong oxidizing agent is amphoteric in nature. It is the part of…
• Statements about heavy water are given below : A. Heavy water is used in exchange…
• Which one of the following lanthanoids does not form MO₂? [M is lanthanoid metal]
• Given below are two statements : Statement I : o-Nitrophenol is steam volatile due to…
• Match List - I with List - II. List I Electronic configuration | List II Δ ᵢH in kJ…
• Dichromate ion is treated with base, the oxidation number of Cr in the product formed is…
• An amine on reaction with benzensulphonyl chloride produces a compound insoluble in…
• Given below are two statements : Statement I : A mixture of chloroform and aniline can…
• The orbital having two radial as well as two angular nodes is :
• The number of significant figures in 50000.020 × 10⁻³ is _____________.
• Find A, B and C in the following reactions : NH₃ + A + CO₂ → (NH₄)₂CO₃ (NH₄)₂CO₃ + H₂O +…
• A →(Hydrolysis) B B reacts with Hydroxyl amine but does not give Tollen's test. Identify…
• Which of the following is 'a' FALSE statement ?
• Number of bridging CO ligands in [Mn₂(CO)₁₀] is __________.
• For a chemical reaction A + B ⇌ C + D (Δ ᵣH^Θ = 80 kJ mol⁻¹) the entropy change Δ ᵣS^Θ…
• The structure of Neoprene is :
• On treating a compound with warm dil. H₂SO₄, gas X is evolved which turns K₂Cr₂O₇ paper…
• An exothermic reaction X → Y has an activation energy 30 kJ mol⁻¹. If energy change ΔE…
• Identify the major products A and B respectively in the following reactions of phenol :
• Given below are two statements : one is labelled as Assertion A and the other is…
• Which of the following vitamin is helpful in delaying the blood clotting?
• Match List - I with List - II. List - I (Ore) | List - II (Element Present); (a) |…
• 224 mL of SO 2(g) at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution…
• Consider the following reaction MnO₄ - + 8H + + 5e - → Mn⁺² + 4H₂O,Eᵒ = 1.51V. The…

Mathematics

• The value of lim _(h → 0) 2{ (√3 sin ( π/6 + h ) - cos ( π/6 + h ))/(√3 h( √3 cosh -…
• The value of the integral ∫₀^π |sin 2x|dx is ___________.
• Let R = (P, Q) | P and Q are at the same distance from the origin be a relation, then…
• The difference between degree and order of a differential equation that represents the…
• The value of | (a + 1)(a + 2), a + 2, 1; (a + 2)(a + 3), a + 3, 1; (a + 3)(a + 4), a +…
• The maximum slope of the curve y = 1/2x⁴ - 5x³ + 18x² - 19x occurs at the point :
• The number of seven digit integers with sum of the digits equal to 10 and formed by…
• In an increasing geometric series, the sum of the second and the sixth term is 25/2 and…
• The area bounded by the lines y = || x - 1 | - 2 | is ___________.
• The maximum value of the term independent of 't' in the expansion of ( tx^(1/5) + (1 -…
• Let f be any function defined on R and let it satisfy the condition : |f(x) - f(y)| ≤…
• A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is…
• The sum of the infinite series 1 + 2/3 + 7/3² + 12/3³ + 17/3⁴ + 22/3⁵ + ...... is equal…
• If (1, 5, 35), (7, 5, 5), (1, λ, 7) and (2λ, 1, 2) are coplanar, then the sum of all…
• Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal…
• If √3 (cos ²x) = (√3 - 1)cos x + 1, the number of solutions of the given equation when x…
• The value of ∫_(- π /2)^(π /2) (cos ²x)/(1 + 3ˣ) dx is :
• If a⃗ and b⃗ are perpendicular, then a⃗ × ( a⃗ × ( a⃗ × ( a⃗ × b⃗ ) ) ) is equal to :
• The rate of growth of bacteria in a culture is proportional to the number of bacteria…
• Consider the three planes P₁ : 3x + 15y + 21z = 9, P₂ : x - 3y - z = 5, and P₃ : 2x +…
• The value of Σₙ₌₁¹⁰⁰ ∫ₙ₋₁ⁿ e^(x - [x])dx , where [ x ] is the greatest integer ≤ x, is :
• If (sin ¹x)/a = (cos ⁻¹x)/b = (tan ⁻¹y)/c; 0 < x < 1, then the value of cos ( (π c)/(a +…
• In the circle given below, let OA = 1 unit, OB = 13 unit and PQ ⊥ OB. Then, the area of…
• The number of integral values of 'k' for which the equation 3 sin x+4 cos x=k+1 has a…
• The sum of 162ᵗʰ power of the roots of the equation x³ - 2x² + 2x - 1 = 0 is ________.
• If y = y(x) is the solution of the equation eˢⁱⁿʸ cos ydy/dx + eˢⁱⁿʸ cos x = cos x, y(0)…
• Let (λ, 2, 1) be a point on the plane which passes through the point (4, -2, 2). If the…
• The intersection of three lines x - y = 0, x + 2y = 3 and 2x + y = 6 is a :
• Let m, n∈N and gcd (2, n) = 1. If 30( 30; 0 ) + 29( 30; 1 ) + ...... + 2( 30; 28 ) + 1(…

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