JEE Main 2022 (Online) 27th June Morning Shift — Question Paper

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Physics

• The area of cross-section of a large tank is 0.5 m². It has a narrow opening near the…
• Two blocks of masses 10 kg and 30 kg are placed on the same straight line with…
• A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is…
• A girl standing on road holds her umbrella at 45° with the vertical to keep the rain…
• A beam of monochromatic light is used to excite the electron in Li + + from the first…
• The current density in a cylindrical wire of radius 4 mm is 4 × 10⁶ Am⁻². The current…
• A force of 10 N acts on a charged particle placed between two plates of a charged…
• The velocity of a small ball of mass 'm' and density d₁, when dropped in a container…
• What percentage of kinetic energy of a moving particle is transferred to a stationary…
• A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to…
• An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their…
• A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04)…
• The susceptibility of a paramagnetic material is 99. The permeability of the material in…
• Identify the correct Logic Gate for the following output (Y) of two inputs A and B.
• A 72 Ω galvanometer is shunted by a resistance of 8 Ω. The percentage of the total…
• A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300 K, pressure 100…
• The current flowing through an ac circuit is given by I = 5 sin(120πt)A How long will…
• In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference…
• A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of…
• A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3…
• In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If…
• An observer moves towards a stationary source of sound with a velocity equal to…
• Given below are two statements : Statement I : The law of gravitation holds good for any…
• A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R…
• Consider a light ray travelling in air is incident into a medium of refractive index…
• The displacement of simple harmonic oscillator after 3 seconds starting from its mean…
• A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as…
• A projectile is launched at an angle 'α' with the horizontal with a velocity 20 ms⁻¹…

Chemistry

• L-isomer of a compound 'A' (C₄H₈O₄) gives a positive test with [Ag(NH₃)₂]⁺. Treatment of…
• 2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different…
• Match List - I with List - II. List - I (Si-Compounds) | List - II (Si-Polymeric/Other…
• BeCl₂ reacts with LiAlH₄ to give :
• Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the…
• Match List-I with List-II List - I | List - II; (A) | Concentration of gold ore | (I) |…
• Given below are two statements : Statement I : In Hofmann degradation reaction, the…
• The number of statements correct from the following for Copper (at. no. 29) is/are…
• Two elements A and B which form 0.15 moles of A₂B and AB₃ type compounds. If both A₂B…
• The rate constant for a first order reaction is given by the following equation: ln k =…
• The limiting molar conductivities of NaI, NaNO₃ and AgNO₃ are 12.7, 12.0 and 13.3 mS m²…
• Match List - I with List - II List - I (Polymer) | List - II (Used in); (A) | Bakelite |…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Match List-I with List-II. List - I | List - II; (A) | Spontaneous process | (I) | Δ H <…
• If the uncertainty in velocity and position of a minute particle in space are, 2.4 ×…
• Which of the following is structure of a separating funnel?
• Which of the following reactions will yield benzaldehyde as a product?
• Addition of H₂SO₄ to BaO₂ produces :
• Metal deficiency defect is shown by Fe 0.93 O. In the crystal, some Fe²⁺ cations are…
• 'A' and 'B' respectively are: A →((1) O₃) Ethane-1,2-dicarbaldehyde +…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Heating white phosphorus with conc. NaOH solution gives mainly :
• Match List-I with List-II List - I | List - II; (A) | Lyophilic colloid | (I) |…
• Which of the following will have maximum stabilization due to crystal field?
• Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic…
• 2NOCl(g) ⇌ 2NO(g) + Cl₂(g) In an experiment, 2.0 moles of NOCl was placed in a one-litre…

Mathematics

• The value of cos (2π/7)+cos (4π/7)+cos (6π/7) is equal to :
• If cos ⁻¹( y/2 ) = log ₑ( x/5 )⁵, |y| < 2, then :
• The number of distinct real roots of x⁴ - 4x + 1 = 0 is :
• Let f : R → R be a function defined by f(x) = 2e²ˣ/(e²ˣ + e). Then f( 1/100 ) + f( 2/100…
• Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x =…
• Let a be an integer such that lim _(x → 7) (18 - [1 - x])/[x - 3a] exists, where [t] is…
• sin ¹( sin 2π/3 ) + cos ⁻¹( cos 7π/6 ) + tan ⁻¹( tan 3π/4 ) is equal to :
• Let the eccentricity of an ellipse x²/a² + y²/b² = 1, a > b, be 1/4. If this ellipse…
• Let a⃗ = î + ĵ - k̂ and c⃗ = 2î - 3ĵ + 2k̂. Then the number of vectors b⃗ such that b⃗ ×…
• In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is…
• If the sum of the first ten terms of the series 1/5 + 2/65 + 3/325 + 4/1025 + 5/2501 +…
• Let dy/dx = (ax - by + a)/(bx + cy + a), where a, b, c are constants, represent a circle…
• The positive value of the determinant of the matrix A, whose Adj(Adj(A)) = ( 14, 28, -…
• The value of the integral ∫₋₂² (|x³ + x|)/(e^(x|x|) + 1)dx is equal to :
• If the sum of all the roots of the equation e²ˣ - 11eˣ - 45e⁻ˣ + 81/2 = 0 is log ₑp…
• Let the mirror image of the point (a, b, c) with respect to the plane 3x - 4y + 12z + 19…
• If dy/dx + 2ˣ⁻ʸ(2ʸ - 1)/(2ˣ - 1) = 0, x, y > 0, y(1) = 1, then y(2) is equal to :
• Let the system of linear equations x + 2y + z = 2, α x + 3y - z = α, - α x + y + 2z = -…
• If ∫ (x²+1)eˣ/(x+1)²dx=f(x)eˣ+C, where C is a constant, then d³f/dx³ at x = 1 is equal…
• A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a…
• Five numbers x₁,x₂,x₃,x₄,x₅ are randomly selected from the numbers 1, 2, 3, ......., 18…
• Let A₁={(x,y):|x|≤ y²,|x|+2y≤ 8} and A₂={(x,y):|x|+|y|≤ k}. If 27 (Area A₁) = 5 (Area…
• If two straight lines whose direction cosines are given by the relations l + m - n = 0…
• If the coefficient of x¹⁰ in the binomial expansion of ( √x/5^(1/4) + √5/x^(1/3) )⁶⁰ is…
• x = Σₙ₌₀^∞ aⁿ,y = Σₙ₌₀^∞ bⁿ,z = Σₙ₌₀^∞ cⁿ , where a, b, c are in A.P. and |a| < 1, |b| <…
• The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be…
• The area of the polygon, whose vertices are the non-real roots of the equation z̅ = iz²…
• A circle of radius 2 unit passes through the vertex and the focus of the parabola y² =…

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