JEE Main 2022 (Online) 25th June Morning Shift — Question Paper

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Physics

• The photodiode is used to detect the optical signals. These diodes are preferably…
• The terminal velocity (vₜ) of the spherical rain drop depends on the radius (r) of the…
• The first overtone frequency of an open organ pipe is equal to the fundamental frequency…
• The total current supplied to the circuit as shown in figure by the 5 V battery is…
• The height of any point P above the surface of earth is equal to diameter of earth. The…
• The two light beams having intensities I and 9I interfere to produce a fringe pattern on…
• A 0.5 kg block moving at a speed of 12 ms⁻¹ compresses a spring through a distance 30 cm…
• If wattless current flows in the AC circuit, then the circuit is :
• The ratio for the speed of the electron in the 3ʳᵈ orbit of He⁺ to the speed of the…
• In the figure, a very large plane sheet of positive charge is shown. P₁ and P₂ are two…
• The difference of speed of light in the two media A and B (v A - v B ) is 2.6 × 10⁷ m/s…
• A uniform chain of 6 m length is placed on a table such that a part of its length is…
• A teacher in his physics laboratory allotted an experiment to determine the resistance…
• Which of the following relations is true for two unit vector A and B making an angle θ…
• If Z=A²B³/C⁴, then the relative error in Z will be :
• The velocity of upper layer of water in a river is 36 kmh⁻¹. Shearing stress between…
• A light wave travelling linearly in a medium of dielectric constant 4, incidents on the…
• Given below are two statements : Statement I : Davisson-Germer experiment establishes…
• A long straight wire with a circular cross-section having radius R, is carrying a steady…
• Match List-I with List-II. List - I | List -II; (A) | AC generator | (I) | Detects the…
• A⃗ is a vector quantity such that |A⃗| = non-zero constant. Which of the following…
• A steam engine intakes 50 g of steam at 100°C per minute and cools it down to 20°C. If…
• A force on an object of mass 100 g is ( 10î + 5ĵ ) N. The position of that object at t =…
• If force F⃗ = 3î + 4ĵ - 2k̂ acts on a particle position vector 2î + ĵ + 2k̂ then, the…
• The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t²)…
• The electric field in an electromagnetic wave is given by E = 56.5 sin ω(t - x/c) NC⁻¹…
• A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed…
• The relation between root mean square speed (vᵣₘₛ) and most probable sped (vₚ) for the…

Chemistry

• Which one of the following alkaline earth metal ions has the highest ionic mobility in…
• Among the following, which is the strongest oxidizing agent?
• Using very little soap while washing clothes, does not serve the purpose of cleaning of…
• Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives…
• Phenol on reaction with dilute nitric acid, gives two products. Which method will be…
• The longest wavelength of light that can be used for the ionisation of lithium atom (Li)…
• Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is…
• Number of electron deficient molecules among the following PH₃, B₂H₆, CCl₄, NH₃, LiH and…
• Incorrect statement for Tyndall effect is :
• Which one of the following is an example of artificial sweetner?
• If [Cu(H₂O)₄]²⁺ absorbs a light of wavelength 600 nm for d-d transition, then the value…
• White precipitate of AgCl dissolves in aqueous ammonia solution due to formation of :
• For a given chemical reaction γ₁A + γ₂B → γ₃C + γ₄D Concentration of C changes from 10…
• The pair, in which ions are isoelectronic with AI³⁺ is :
• The IUPAC name of ethylidene chloride is :
• The standard free energy change (ΔG°) for 50% dissociation of N₂O₄ into NO₂ at 27°C and…
• Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis…
• The number of N atoms in 681 g of C₇H₅N₃O₆ is x × 10²¹. The value of x is (N A = 6.02 ×…
• In a cell, the following reactions take place Fe²⁺ → Fe³⁺ + e -, E_(Fe³⁺/Fe²⁺)ᵒ = 0.77…
• The distance between Na⁺ and Cl⁻ ions in solid NaCl of density 43.1 g cm⁻³ is…
• The intermediate X, in the reaction :
• In the following structures, which on is having staggered conformation with maximum…
• Cerium (IV) has a noble gas configuration. Which of the following is correct statement…
• The standard entropy change for the reaction 4Fe(s) + 3O₂(g) → 2Fe₂O₃(s) is -550 J K⁻¹…

Mathematics

• Let a⃗ = a₁î + a₂ĵ + a₃k̂ aᵢ > 0, i = 1,2,3 be a vector which makes equal angles with…
• For a natural number n, let α ₙ = 19ⁿ - 12ⁿ. Then, the value of (31α ₉ - α ₁₀)/(57α ₈)…
• Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃…
• The number of values of x in the interval ( π/4,7π/4 ) for which 14 cos ec²x - 2sin ²x =…
• Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y +…
• Let A = [ 0, - 2; 2, 0 ]. If M and N are two matrices given by M = Σₖ₌₁¹⁰ A²ᵏ and N =…
• Let x = 2t, y = t²/3 be a conic. Let S be the focus and B be the point on the axis of…
• Let A be a 3 × 3 matrix having entries from the set -1, 0, 1. The number of all such…
• The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is…
• Let f(x) be a polynomial function such that f(x) + f'(x) + f''(x) = x⁵ + 64. Then, the…
• Let f:R → R and g:R → R be two functions defined by f(x) = log ₑ(x² + 1) - e⁻ˣ + 1 and…
• Let y = y(x) be the solution of the differential equation (x + 1)y' - y = e³ˣ(x + 1)²…
• Let A be a 3 × 3 real matrix such that A( 1; 1; 0 ) = ( 1; 1; 0 );A( 1; 0; 1 ) = ( - 1…
• Let θ be the angle between the vectors a⃗ and b⃗, where |a⃗ | = 4, |b⃗ | = 3 and θ ∈ (…
• If the solution curve y = y(x) of the differential equation y²dx + (x² - xy + y²)dy = 0…
• The value of ∫₀^π (eᶜᵒˢˣ sin x)/(1 + cos ²x)(eᶜᵒˢˣ + e⁻ᶜᵒˢˣ)dx is equal to:
• Let g:(0,∞ ) → R be a differentiable function such that ∫ ( x(cos x - sin x)/(eˣ + 1) +…
• Let f : N → R be a function such that f(x + y) = 2f(x)f(y) for natural numbers x and y…
• The greatest integer less than or equal to the sum of first 100 terms of the sequence…
• Let f : R → R be defined as f(x) = x³ + x - 5. If g(x) is a function such that f(g(x)) =…
• If 1/(2 . 3¹⁰) + 1/(2² . 3⁹) + ..... + 1/(2¹⁰ . 3) = K/(2¹⁰ . 3¹⁰), then the remainder…
• Let a circle C touch the lines L₁:4x - 3y + K₁ = 0 and L₂ = 4x - 3y + K₂ = 0, K₁,K₂ ∈ R…
• Let f:R → R be a function defined by f(x) = ( 2( 1 - x²⁵/2 )(2 + x²⁵) )^(1/50). If the…
• Let the lines L₁:r⃗ = λ ( î + 2ĵ + 3k̂ ), λ ∈ R L₂:r⃗ = ( î + 3ĵ + k̂ ) + μ ( î + ĵ +…
• Let Cᵣ denote the binomial coefficient of xʳ in the expansion of (1 + x)¹⁰. If for α, β…
• Let the abscissae of the two points P and Q be the roots of 2x² - rx + p = 0 and the…
• Let E₁ and E₂ be two events such that the conditional probabilities P(E₁|E₂) = 1/2…
• If y = m₁x + c₁ and y = m₂x + c₂, m₁ ≠ m₂ are two common tangents of circle x² + y² = 2…

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