JEE Main 2022 (Online) 28th June Morning Shift — Question Paper

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Physics

• Given below are two statements : One is labelled as Assertion A and the other is…
• A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and…
• Two planets A and B of equal mass are having their period of revolutions T A and T B…
• In the following circuit, the correct relation between output (Y) and inputs A and B…
• A pendulum is suspended by a string of length 250 cm. The mass of the bob of the…
• Motion of a particle in x-y plane is described by a set of following equations x = 4 sin…
• An AC source is connected to an inductance of 100 mH, a capacitance of 100 μF and a…
• A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of…
• A telegraph line of length 100 km has a capacity of 0.01 μF/km and it carries an…
• A radar sends an electromagnetic signal of electric field (E₀) = 2.25 V/m and magnetic…
• An infinitely long hollow conducting cylinder with radius R carries a uniform current…
• The position vector of 1 kg object is r⃗ = ( 3î - ĵ )m and its velocity v⃗ = ( 3ĵ + k̂…
• The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40…
• A meter bridge setup is shown in the figure. It is used to determine an unknown…
• The de Broglie wavelengths for an electron and a photon are λₑ and λₚ respectively. For…
• For using a multimeter to identify diode from electrical components, choose the correct…
• Current measured by the ammeter (A) in the reported circuit when no current flows…
• Given below are two statements : One is labelled as Assertion A and the other is…
• The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will…
• The refracting angle of a prism is A and refractive index of the material of the prism…
• A particle of mass m is moving in a circular path of constant radius r such that its…
• Given below are two statements : Statement I : A point charge is brought in an electric…
• A hanging mass M is connected to a four times bigger mass by using a string-pulley…
• Given below are two statements : Statement I : When μ amount of an ideal gas undergoes…
• The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kₚ are…
• The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of…
• A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of…
• The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a…

Chemistry

• Number of complexes which will exhibit synergic bonding amongst, [Cr(CO)₆], [Mn(CO)₅]…
• Stability of α-Helix structure of proteins depends upon
• The quantity of electricity in Faraday needed to reduce 1 mol of Cr₂O₇²⁻ to Cr³⁺ is…
• The solubility product of a sparingly soluble salt A₂X₃ is 1.1 × 10⁻²³. If specific…
• Given below are two statements : Statement I : The pentavalent oxide of group-15…
• Nitrogen gas is obtained by thermal decomposition of :
• Which one of the following compounds is inactive towards S N 1 reaction?
• Which of the following structure are aromatic in nature?
• Which one of the following is NOT a copolymer?
• Given below are two statements : Statement I : [Ni(CN)₄]²⁻ is square planar and…
• Which one of the lanthanoids given below is the most stable in divalent form?
• Identify the major product formed in the following sequence of reactions:
• The formula of the purple colour formed in Laissaigne's test for sulphur using sodium…
• The hybridization of P exhibited in PF₅ is spˣdʸ. The value of y is __________.
• Given are two statements one is labelled as Assertion A and other is labelled as Reason…
• If the work function of a metal is 6.63 × 10⁻¹⁹J, the maximum wavelength of the photon…
• The incorrect statement about the imperfections in solids is :
• For a first order reaction A → B, the rate constant, k = 5.5 × 10⁻¹⁴ s⁻¹. The time…
• In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver…
• Element "E" belongs to the period 4 and group 16 of the periodic table. The valence…
• The Zeta potential is related to which property of colloids?
• Which amongst the following is not a pesticide?
• 4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total…
• Dihydrogen reacts with CuO to give :
• Which one of the following techniques is not used to spot components of a mixture…
• A 2.0 g sample containing MnO₂ is treated with HCl liberating Cl₂. The Cl₂ gas is passed…
• The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr…
• A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after…

Mathematics

• Let A be a matrix of order 3 × 3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is…
• If the tangents drawn at the points O(0,0) and P( 1 + √5 ,2 ) on the circle x² + y² - 2x…
• The area of the region S = (x, y) : y² ≤ 8x, y ≥ √2x, x ≥ 1 is
• Let the eccentricity of the hyperbola H:x²/a² - y²/b² = 1 be √(5/2) and length of its…
• Let A₁, A₂, A₃, ....... be an increasing geometric progression of positive real numbers…
• The mean and standard deviation of 15 observations are found to be 8 and 3 respectively…
• Let [t] denote the greatest integer less than or equal to t. Then, the value of the…
• Let R₁ and R₂ be relations on the set 1, 2, ......., 50 such that R₁ = (p, pⁿ) : p is a…
• The number of positive integers k such that the constant term in the binomial expansion…
• The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without…
• Let a function f : N → N be defined by f(n) = [ 2n,, n = 2,4,6,8,......; n - 1,, n =…
• If a⃗ = 2î + ĵ + 3k̂, b⃗ = 3î + 3ĵ + k̂ and c⃗ = c₁î + c₂ĵ + c₃k̂ are coplanar vectors…
• The number of real solutions of x⁷ + 5x³ + 3x + 1 = 0 is equal to ____________.
• If the system of linear equations 2x + 3y - z = - 2 x + y + z = 4 x - y + |λ |z = 4λ - 4…
• A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and…
• Let the solution curve y = y(x) of the differential equation [ x/√(x² - y²) + e^(y/x)…
• The number of real solutions of the equation e⁴ˣ + 4e³ˣ - 58e²ˣ + 4eˣ + 1 = 0 is…
• If Σₖ₌₁³¹ ( ³¹Cₖ )( ³¹Cₖ₋₁ ) - Σₖ₌₁³⁰ ( ³⁰Cₖ )( ³⁰Cₖ₋₁ ) = (α (60!))/(30!)(31!) , where…
• Let the plane P:r⃗ . a⃗ = d contain the line of intersection of two planes r⃗ . ( î + 3ĵ…
• Let l be a line which is normal to the curve y = 2x² + x + 2 at a point P on the curve…
• The number of elements in the set z = a + ib ∈ C : a, b ∈ Z and 1 < | z - 3 + 2i | < 4…
• Let the lines y + 2x = √11 + 7√7 and 2y + x = 2√11 + 6√7 be normal to a circle C:(x -…
• If two distinct point Q, R lie on the line of intersection of the planes - x + 2y - z =…
• Let f : R → R be defined as f(x) = [ [eˣ],, x < 0; aeˣ + [x - 1],, 0 ≤ x < 1; b + [sin…
• The probability, that in a randomly selected 3-digit number at least two digits are odd…
• Let A = 1, a₁, a₂ ....... a₁₈, 77 be a set of integers with 1 < a₁ < a₂ < ....... < a₁₈…
• The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing…
• Let y = y(x) be the solution of the differential equation x(1 - x²)dy/dx + (3x²y - y -…

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