JEE Main 2022 (Online) 29th June Morning Shift — Question Paper

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Physics

• A parallel beam of light is allowed to fall on a transparent spherical globe of diameter…
• Given below are two statements : one is labelled as Assertion A and the other is…
• Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat…
• A positive charge particle of 100 mg is thrown in opposite direction to a uniform…
• As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined…
• At a certain place the angle of dip is 30° and the horizontal component of earth's…
• A transistor is used in an amplifier circuit in common emitter mode. If the base current…
• A particle of mass 500 gm is moving in a straight line with velocity v = b x 5/2 . The…
• A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when…
• A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on…
• A longitudinal wave is represented by x = 10 sin 2π ( nt - x/λ ) cm. The maximum…
• For a series LCR circuit, I vs ω curve is shown : (a) To the left of ωᵣ, the circuit is…
• A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure)…
• Two vectors A⃗ and B⃗ have equal magnitudes. If magnitude of A⃗ + B⃗ is equal to two…
• A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2…
• 300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature…
• A charge particle moves along circular path in a uniform magnetic field in a cyclotron…
• For the network shown below, the value of V B - V A is ____________ V.
• Using Young's double slit experiment, a monochromatic light of wavelength 5000 Aᵒ…
• A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the…
• A parallel plate capacitor filled with a medium of dielectric constant 10, is connected…
• A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature…
• The variation of applied potential and current flowing through a given wire is shown in…
• The escape velocity of a body on a planet 'A' is 12 kms⁻¹. The escape velocity of the…
• The activity of a radioactive material is 2.56 × 10⁻³ Ci. If the half life of the…
• √d₁ and √d₂ are the impact parameters corresponding to scattering angles 60° and 90°…
• The intensity of the light from a bulb incident on a surface is 0.22 W/m². The amplitude…
• Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the…
• In van der Waal equation [ P + a/V² ] [V - b] = RT; P is pressure, V is volume, R is…

Chemistry

• The polymer, which can be stretched and remains its original status on releasing the…
• Production of iron in blast furnace follows the following equation Fe₃O₄(s) + 4CO(g) →…
• C₆H₁₂O₆ →(Zymase) A → _Δ ^(NaOI) B + CHI₃ The number of carbon atoms present in the…
• Observe structures of the following compounds The total number of structures/compounds…
• Sugar moiety in DNA and RNA molecules respectively are
• Which of the following statements are correct? (A) The electronic configuration of Cr is…
• Arrange the following in the decreasing order of their covalent character : (A) LiCl (B)…
• Given below are two statements : Statement I : Phenols are weakly acidic. Statement II…
• Consider the above reactions, the product A and product B respectively are
• Which of the following compound does not contain sulphur atom?
• An acidified manganate solution undergoes disproportionation reaction. The spin-only…
• Which one of the following reactions indicates the reducing ability of hydrogen peroxide…
• The solubility of AgCl will be maximum in which of the following?
• 17.0 g of NH₃ completely vapourises at -33.42°C and 1 bar pressure and the enthalpy…
• In isolation of which one of the following metals from their ores, the use of cyanide…
• A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2…
• The activation energy of one of the reactions in a biochemical process is 532611 J…
• Match List-I with List-II. List-I (Metal) | List-II (Application); (A) | Cs | (I) | High…
• Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The…
• Given below are two statements : Statement I : The esterification of carboxylic acid…
• Which of the following is a correct statement?
• The electronic configuration of Pt (atomic number 78) is :
• Two isomers 'A' and 'B' with molecular formula C₄H₈ give different products on oxidation…
• The number of terminal oxygen atoms present in the product B obtained from the following…
• The oxoacid of phosphorus that is easily obtained from a reaction of alkali and white…
• 1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in…

Mathematics

• The number of elements in the set S = { θ ∈ [ - 4π ,4π ]:3cos ²2θ + 6 cos 2θ - 10cos ²θ…
• Let P₁:r⃗ . ( 2î + ĵ - 3k̂ ) = 4 be a plane. Let P₂ be another plane which passes…
• The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of…
• Let f:R → R be a function defined by : f(x) = { max { t³ - 3t} t ≤ x, ;, x ≤ 2; x² + 2x…
• Let α and β be the roots of the equation x² + (2i - 1) = 0. Then, the value of |α⁸ + β⁸|…
• 50 tan ( 3tan ⁻¹( 1/2 ) + 2cos ⁻¹( 1/√5 ) ) + 4√2 tan ( 1/2tan ⁻¹(2√2 ) ) is equal to…
• The distance between the two points A and A' which lie on y = 2 such that both the line…
• Let PQ be a focal chord of the parabola y² = 4x such that it subtends an angle of π/2 at…
• Let d be the distance between the foot of perpendiculars of the points P(1, 2, -1) and…
• The domain of the function cos ⁻¹( (2sin ⁻¹( 1/(4x² - 1) ))/π ) is :
• Let the solution curve of the differential equation xdy/dx - y = √(y² + 16x²), y(1) = 3…
• Let c, k ∈ R. If f(x) = (c + 1)x² + (1 - c²)x + 2k and f(x + y) = f(x) + f(y) - xy, for…
• Let H:x²/a² - y²/b² = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of…
• Let b₁b₂b₃b₄ be a 4-element permutation with bᵢ ∈ 1, 2, 3, ........, 100 for 1 ≤ i ≤ 4…
• If the mirror image of the point (2, 4, 7) in the plane 3x - y + 4z = 2 is (a, b, c)…
• Let a⃗ = α î + 3ĵ - k̂, b⃗ = 3î - β ĵ + 4k̂ and c⃗ = î + 2ĵ - 2k̂ where α , β ∈ R, be…
• Let the tangent to the circle C₁ : x² + y² = 2 at the point M(-1, 1) intersect the…
• The area enclosed by y² = 8x and y = √2 x that lies outside the triangle formed by y =…
• Let A = [aᵢⱼ] be a square matrix of order 3 such that aᵢⱼ = 2ʲ⁻ⁱ, for all i, j = 1, 2…
• Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be 24/5 and 194/25…
• ∫₀⁵ cos ( π ( x - [ x/2 ] ) )dx , where [t] denotes greatest integer less than or equal…
• Let a set A = A₁ ∪ A₂ ∪ ..... ∪ Aₖ, where Aᵢ ∩ Aⱼ = φ for i ≠ j, 1 ≤ j, j ≤ k. Define…
• Let S = { z ∈ C:|z - 2| ≤ 1, z(1 + i) + z̅ (1 - i) ≤ 2}. Let |z - 4i| attains minimum…
• A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into…
• The number of solutions of the equation 2θ - cos ²θ + √2 = 0 in R is equal to ___________.
• If the system of linear equations 2x + y - z = 7 x - 3y + 2z = 1 x + 4y + δz = k, where…
• Let y = y(x) be the solution of the differential equation dy/dx + (√2 y)/(2cos ⁴x - cos…
• Let { aₙ} ₙ₌₀^∞ be a sequence such that a₀ = a₁ = 0 and aₙ₊₂ = 2aₙ₊₁ - aₙ + 1 for all n…
• If the constant term in the expansion of ( 3x³ - 2x² + 5/x⁵ )¹⁰ is 2ᵏ.l, where l is an…

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