JEE Main 2022 (Online) 24th June Evening Shift — Question Paper

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Physics

• The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV…
• A Carnot engine takes 5000 kcal of heat from a reservoir at 727°C and gives heat to a…
• Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio…
• A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms⁻¹. What…
• A proton, a deutron and an α-particle with same kinetic energy enter into a uniform…
• In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential…
• An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance…
• A ray of light is incident at an angle of incidence 60° on the glass slab of refractive…
• Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at…
• A circular coil of 1000 turns each with area 1m² is rotated about its vertical diameter…
• Two travelling waves of equal amplitudes and equal frequencies move in opposite…
• Identify the pair of physical quantities that have same dimensions:
• A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first…
• A monoatomic gas performs a work of Q/4 where Q is the heat supplied to it. The molar…
• Potential energy as a function of r is given by U = A/r¹⁰ - B/r⁵, where r is the…
• An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance…
• A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 25…
• The soft-iron is a suitable material for making an electromagnet. This is because…
• Given below are two statements : Statement I : The reactance of an ac circuit is zero…
• A sample contains 10⁻² kg each of two substances A and B with half lives 4 s and 8 s…
• A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform…
• The distance between Sun and Earth is R. The duration of year if the distance between…
• A body is projected from the ground at an angle of 45° with the horizontal. Its velocity…
• A long cylindrical volume contains a uniformly distributed charge of density ρ. The…
• Two identical charged particles each having a mass 10 g and charge 2.0 × 10⁻⁷C are…
• If the charge on a capacitor is increased by 2 C, the energy stored in it increases by…
• What will be the most suitable combination of three resistors A = 2Ω, B = 4Ω, C = 6Ω so…
• In the given circuit, the value of current I L will be ____________ mA. (When R L = 1kΩ)

Chemistry

• Metals generally melt at very high temperature. Amongst the following, the metal with…
• At 25°C and 1 atm pressure, the enthalpies of combustion are as given below : Substance…
• In the industrial production of which of the following, molecular hydrogen is obtained…
• For a first order reaction, the time required for completion of 90% reaction is 'x'…
• Manganese (VI) has ability to disproportionate in acidic solution. The difference in…
• Arrange the following carbocations in decreasing order of stability.
• Hex-4-ene-2-ol on treatment with PCC gives 'A'. 'A' on reaction with sodium hypoiodite…
• A company dissolves 'x' amount of CO₂ at 298 K in 1 litre of water to prepare soda…
• (a) Baryte, (b) Galena, (c) Zinc blende and (d) Copper pyrites. How many of these…
• Which of the following chemical reactions represents Hall-Heroult Process?
• The correct order of bond orders of C₂²⁻, N₂²⁻ and O₂²⁻ is, respectively
• In the flame test of a mixture of salts, a green flame with blue centre was observed…
• Transition metal complex with highest value of crystal field splitting (Δ₀) will be :
• Which one of the following compounds is used as a chemical in certain type of fire…
• The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63…
• 120 g of an organic compound that contains only carbon and hydrogen gives 330 g of CO₂…
• PCl₅ is well known, but NCl₅ is not. because,
• The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is 1750 Ω…
• Given below are two statements : Statement I : The presence of weaker π-bonds make…
• 0.2 g of an organic compound was subjected to estimation of nitrogen by Dumas method in…
• When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final…
• In alanylglycyl leucyl alanyl valine, the number of peptide linkages is ___________.
• The structure shown below is of which well-known drug molecule?
• The conversion of propan-1-ol to n-butylamine involves the sequential addition of…
• Which of the following is not an example of a condensation polymer?
• PCl₅ dissociates as PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) 5 moles of PCl₅ are placed in a 200 litre…

Mathematics

• Let P₁ be a parabola with vertex (3, 2) and focus (4, 4) and P₂ be its mirror image with…
• Let the area of the triangle with vertices A(1, α), B(α, 0) and C(0, α) be 4 sq. units…
• Let f(x) = { (sin (x - [x]))/(x - [x]), , x ∈ ( - 2, - 1); max { 2x,3[|x|]}, , |x| < 1…
• The remainder on dividing 1 + 3 + 3² + 3³ + ..... + 3²⁰²¹ by 50 is _________.
• Let a and b be two unit vectors such that |(a + b) + 2(a × b)| = 2. If θ ∈ (0, π) is the…
• If y = tan ⁻¹( sec x³ - tan x³ ),π/2 < x³ < 3π/2, then
• Let the points on the plane P be equidistant from the points (-4, 2, 1) and (2, -2, 3)…
• Let a circle C : (x - h)² + (y - k)² = r², k > 0, touch the x-axis at (1, 0). If the…
• The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by…
• The value of the integral ∫_(- π /2)^(π /2) dx/(1 + eˣ)(sin ⁶x + cos ⁶x) is equal to
• Let S = z ∈ C : |z - 3| ≤ 1 and z(4 + 3i) + z̅(4 - 3i) ≤ 24. If α + iβ is the point in S…
• Let the hyperbola H:x²/a² - y² = 1 and the ellipse E:3x² + 4y² = 12 be such that the…
• In an examination, there are 10 true-false type questions. Out of 10, a student can…
• Let the maximum area of the triangle that can be inscribed in the ellipse x²/a² + y²/4 =…
• Let x, y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is
• If the shortest distance between the lines (x - 1)/2 = (y - 2)/3 = (z - 3)/λ and (x -…
• The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line…
• Let x * y = x² + y³ and (x * 1) * 1 = x * (1 * 1). Then a value of 2sin ⁻¹( (x⁴ + x² -…
• lim _(n → ∞) ( n²/(n² + 1)(n + 1) + n²/(n² + 4)(n + 2) + n²/(n² + 9)(n + 3) + .... +…
• Let λ * be the largest value of λ for which the function f_λ (x) = 4λ x³ - 36λ x² + 36x…
• A particle is moving in the xy-plane along a curve C passing through the point (3, 3)…
• The number of distinct real roots of the equation x⁷ - 7x - 2 = 0 is
• The sum of all the real roots of the equation (e²ˣ - 4)(6e²ˣ - 5eˣ + 1) = 0 is
• The number of solutions of the equation cos ( x + π/3 )cos ( π/3 - x ) = 1/4cos ²2x, x ∈…
• Let S = { ( - 1, a; 0, b );a,b ∈ { 1,2,3,....100} } and let Tₙ = { A ∈ S:Aⁿ⁽ⁿ⁺¹⁾ = I}…
• The number of 7-digit numbers which are multiples of 11 and are formed using all the…
• Let the system of linear equations x + y + αz = 2 3x + y + z = 4 x + 2z = 1 have a…
• A random variable X has the following probability distribution : X | 0 | 1 | 2 | 3 | 4…
• The sum of all the elements of the set { α ∈ { 1,2,.....,100} :HCF(α ,24) = 1} is…

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