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

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Physics

• One end of a massless spring of spring constant k and natural length l₀ is fixed while…
• If a wave gets refracted into a denser medium, then which of the following is true?
• A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force…
• In the given circuit 'a' is an arbitrary constant. The value of m for which the…
• A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic…
• Given below are two statements : Statement I : In hydrogen atom, the frequency of…
• According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0°C…
• The distance of the Sun from earth is 1.5 × 10¹¹ m and its angular diameter is (2000) s…
• A metallic rod of length 20 cm is placed in North-South direction and is moved at a…
• For a perfect gas, two pressures P₁ and P₂ are shown in figure. The graph shows :
• The equation of a particle executing simple harmonic motion is given by x = sin π ( t +…
• The SI unit of a physical quantity is pascal-second. The dimensional formula of this…
• A parallel plate capacitor is made up of stair like structure with a plate area A of…
• When a ball is dropped into a lake from a height 4.9 m above the water level, it hits…
• A convex lens has power P. It is cut into two halves along its principal axis. Further…
• Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere…
• A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6…
• The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The…
• A stone tide to a spring of length L is whirled in a vertical circle with the other end…
• Given below are two statements : Statement I : A time varying electric field is a source…
• A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic…
• If a charge q is placed at the centre of a closed hemispherical non-conducting surface…
• If L, C and R are the self inductance, capacitance and resistance respectively, which of…
• A diatomic gas (γ = 1.4) does 400J of work when it is expanded isobarically. The heat…
• For a transistor to act as a switch, it must be operated in
• Three identical charged balls each of charge 2 C are suspended from a common point P by…
• The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 × 10⁶ A/m². The…
• Two long parallel conductors S₁ and S₂ are separated by a distance 10 cm and carrying…

Chemistry

• Arrange the following coordination compounds in the increasing order of magnetic…
• Which is true about Buna-N?
• Given below are two statements : one is labelled as Assertion A and the other is…
• The correct order of increasing ionic radii is
• It has been found that for a chemical reaction with rise in temperature by 9 K the rate…
• Statement I : Leaching of gold with cyanide ion in absence of air / O₂ leads to cyano…
• Which of the following is most stable?
• In 3d series, the metal having the highest M²⁺/M standard electrode potential is :
• The correct order of increasing intermolecular hydrogen bond strength is :
• The 'f' orbitals are half and completely filled, respectively in lanthanide ions…
• Match List-I with List-II List-I | List-II; (A) | Antipyretic | I. | Reduces pain; (B) |…
• 0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in…
• If the initial pressure of a gas is 0.03 atm, the mass of the gas adsorbed per gram of…
• Given below are two statements. Statement I : Maltose has two α-D-glucose units linked…
• pH value of 0.001 M NaOH solution is ____________.
• A solution containing 2.5 × 10⁻³ kg of a solute dissolved in 75 × 10⁻³ kg of water boils…
• When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20…
• Decarboxylation of all six possible forms of diaminobenzoic acids C₆H₃(NH₂)₂COOH yields…
• Match List I with List II. List-I (Anion) | List-II (gas evolved on reaction with…
• BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition…
• 116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of…
• The gas produced by treating an aqueous solution of ammonium chloride with sodium…
• Identify the incorrect statement for PCl₅ from the following.
• Consider the following set of quantum numbers. n | 1 | m₁; A. | 3 | 3 | -3; B. | 3 | 2 |…

Mathematics

• Let y = y(x) be the solution of the differential equation (1 - x²)dy = ( xy + (x³ +…
• If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6…
• α=sin 36° is a root of which of the following equation?
• Let a⃗ and b⃗ be the vectors along the diagonals of a parallelogram having area 2√2. Let…
• The set of values of k, for which the circle C:4x² + 4y² - 12x + 8y + k = 0 lies inside…
• Let f be a differentiable function in ( 0,π/2 ). If ∫_(cos x)¹ t² f(t)dt = sin ³x + cos…
• Let [t] denote the greatest integer ≤ t and t denote the fractional part of t. The…
• Let A and B be two 3 × 3 matrices such that AB = I and |A| = 1/8. Then |adj (B adj(2A))|…
• The value of cot ( Σₙ₌₁⁵⁰ tan ⁻¹( 1/(1 + n + n²) ) ) is :
• Let S = 2 + 6/7 + 12/7² + 20/7³ + 30/7⁴ + ...... Then 4S is equal to
• If the sum of the coefficients of all the positive powers of x, in the Binomial…
• Let the foot of the perpendicular from the point (1, 2, 4) on the line (x + 2)/4 = (y -…
• Let α, β be the roots of the equation x² - 4λ x + 5 = 0 and α, γ be the roots of the…
• If the solution curve of the differential equation ((tan ⁻¹y) - x)dy = (1 + y²)dx passes…
• If m and n respectively are the number of local maximum and local minimum points of the…
• Let S = E₁, E₂, ........., E₈ be a sample space of a random experiment such that P(Eₙ) =…
• If the area of the region {(x,y):x^(2/3)+y^(2/3)≤ 1, x+y≥ 0, y≥ 0} is A, then 256A/π is…
• If y(x) = ( xˣ )ˣ, x > 0, then d²x/dy² + 20 at x = 1 is equal to ____________.
• The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and 9/4…
• Let f(x) = | a, - 1, 0; ax, a, - 1; ax², ax, a |, a ∈ R. Then the sum of the squares of…
• Let a circle C of radius 5 lie below the x-axis. The line L₁ : 4x + 3y + 2 = 0 passes…
• If the equation of the parabola, whose vertex is at (5, 4) and the directrix is 3x + y -…
• The integral ∫₀¹ 1/7^([ 1/x ])dx, where [ . ] denotes the greatest integer function, is…
• Let A be a matrix of order 2 × 2, whose entries are from the set 0, 1, 2, 3, 4, 5. If…
• The shortest distance between the lines (x - 3)/2 = (y - 2)/3 = (z - 1)/(- 1) and (x +…
• If a₁, a₂, a₃ ...... and b₁, b₂, b₃ ....... are A.P., and a₁ = 2, a₁₀ = 3, a₁b₁ = 1 =…
• The number of points of intersection of |z - (4 + 3i)| = 2 and |z| + |z - 4| = 6, z ∈ C…
• Let for some real numbers α and β, a = α - iβ. If the system of equations 4ix + (1 + i)y…
• Let S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Define f : S → S as f(n) = { 2n, ,, if n =…

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