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

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Physics

• In the given figure, the block of mass m is dropped from the point 'A'. The expression…
• The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of (-0.05) cm…
• A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and…
• The speed of light in media 'A' and 'B' are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s…
• An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in…
• The combination of two identical cells, whether connected in series or parallel…
• A block of mass M placed inside a box descends vertically with acceleration 'a'. The…
• At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted…
• The displacement current of 4.425 μA is developed in the space between the plates of…
• Two resistors are connected in series across a battery as shown in figure. If a…
• A person can throw a ball upto a maximum range of 100 m. How high above the ground he…
• In an experiment to determine the velocity of sound in air at room temperature using a…
• If the electric potential at any point (x, y, z) m in space is given by V = 3x² volt…
• Given below are two statements : Statement I : The electric force changes the speed of…
• A potential barrier of 0.4 V exists across a p-n junction. An electron enters the…
• The moment of inertia of a uniform thin rod about a perpendicular axis passing through…
• A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an…
• A small spherical ball of radius 0.1 mm and density 10⁴ kg m⁻³ falls freely under…
• The time period of a satellite revolving around earth in a given orbit is 7 hours. If…
• Starting with the same initial conditions, an ideal gas expands from volume V₁ to V₂ in…
• The half life of a radioactive substance is 5 years. After x years a given sample of the…
• The electric field at a point associated with a light wave is given by E = 200 [sin (6 ×…
• Two point charges Q each are placed at a distance d apart. A third point charge q is…
• A small toy starts moving from the position of rest under a constant acceleration. If it…
• In the following nuclear reaction, D→(α) D₁→(β -) D₂→(α) D₃→(γ) D₄ Mass number of D is…
• In a double slit experiment with monochromatic light, fringes are obtained on a screen…
• Two long current carrying conductors are placed to each other at a distance of 8 cm…
• The motion of a simple pendulum executing S.H.M. is represented by the following…
• A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored…

Chemistry

• A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The…
• In Friedel-Crafts alkylation of aniline, one gets
• In the given reaction, The number of π electrons present in the product 'P' is _________.
• A 42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The…
• Match List I with List II. List-I Ore | List-II Composition; (A) | Siderite | (I) |…
• The stable carbocation formed in the above reaction is
• Number of lone pair(s) of electrons on central atom and the shape BrF₃ molecule…
• Given below are two statements. One is labelled as Assertion A and the other is labelled…
• In the given reaction, the number of sp² hybridised carbon(s) in compound 'X' is ________.
• Sulphur dioxide is one of the components of polluted air. SO₂ is also a major…
• The number of chiral alcohol(s) with molecular formula C₄H₁₀O is ________.
• For the reaction given below : CoCl₃ . xNH₃ + AgNO₃ (aq) → If two equivalents of AgCl…
• The equation k = (6.5 × 10¹²s⁻¹)e -26000K/T is followed for the decomposition of…
• Using the rules for significant figures, the correct answer for the expression (0.02858…
• Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H…
• Aqueous solution of which of the following boron compounds will be strongly basic in…
• A white precipitate was formed when BaCl₂ was added to water extract of an inorganic…
• 4.0 moles of argon and 5.0 moles of PCl₅ are introduced into an evacuated flask of 100…
• Given below are two statements. • Statement I : In CuSO₄ . 5H₂O, Cu-O bonds are present…
• Consider the species CH₄, NH₄ + and BH₄ -. Choose the correct option with respect to the…
• Which of the following carbocations is most stable?
• Which of the following is the correct plot for the probability density ψ ² (r) as a…
• Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The…
• The mixture of chloroxylenol and terpineol is an example of
• 2.2 g of nitrous oxide (N₂O) gas is cooled at a constant pressure of 1 atm from 310 K to…
• The structure of protein that is unaffected by heating is
• The cell potential for the given cell at 298 K Pt| H₂ (g, 1 bar) | H⁺ (aq) || Cu²⁺ (aq)…
• Amongst baking soda, caustic soda and washing soda, carbonate anion is present in :
• Given below are two statements : One is labelled as Assertion A and the other is…
• Spin only magnetic moment of [MnBr₆]⁴⁻ is _________ B.M. (round off to the closest…

Mathematics

• The number of solutions of the equation sin x = cos ²x in the interval (0, 10) is…
• Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) =…
• Let y = y(x), x > 1, be the solution of the differential equation (x - 1)dy/dx + 2xy =…
• The value of lim _(x → 1) ((x² - 1)sin ²(π x))/(x⁴ - 2x³ + 2x - 1) is equal to:
• Let f be a real valued continuous function on [0, 1] and f(x) = x + ∫₀¹ (x - t)f(t)dt…
• If y = y(x) is the solution of the differential equation ( 1 + e²ˣ )dy/dx + 2( 1 + y²…
• The sum of the infinite series 1 + 5/6 + 12/6² + 22/6³ + 35/6⁴ + 51/6⁵ + 70/6⁶ +…
• Let A = ( 2, - 1; 0, 2 ). If B = I - ⁵C₁(adj A) + ⁵C₂(adj A)² - ..... - ⁵C₅(adj A)⁵…
• Let f : R → R be a function defined by f(x) = (x - 3) n₁ (x - 5) n₂ , n₁, n₂ ∈ N. Then…
• Let f and g be twice differentiable even functions on (-2, 2) such that f( 1/4 ) = 0, f(…
• Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z…
• Let α be a root of the equation 1 + x² + x⁴ = 0. Then, the value of α¹⁰¹¹ + α²⁰²² -…
• Let (x - 2)/3 = (y + 1)/(- 2) = (z + 3)/(- 1) lie on the plane px - qy + z = 5, for some…
• Let n ≥ 5 be an integer. If 9ⁿ - 8n - 1 = 64α and 6ⁿ - 5n - 1 = 25β, then α - β is equal…
• The total number of four digit numbers such that each of first three digits is divisible…
• Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and…
• The number of values of a ∈ N such that the variance of 3, 7, 12, a, 43 - a is a natural…
• Let A, B, C be three points whose position vectors respectively are a⃗ = î + 4ĵ + 3k̂ b⃗…
• Let 3, 6, 9, 12, ....... upto 78 terms and 5, 9, 13, 17, ...... upto 59 terms be two…
• Let M = [ 0, - α; α, 0 ], where α is a non-zero real number an N = Σₖ₌₁⁴⁹ M²ᵏ. If (I -…
• If ∫₀² ( √2x - √(2x - x²) )dx = ∫₀¹ ( 1 - √(1 - y²) - y²/2 )dy + ∫₁² ( 2 - y²/2 )dy + I…
• Let a triangle ABC be inscribed in the circle x² - √2 (x + y) + y² = 0 such that ∠ BAC =…
• The probability that a relation R from {x, y} to {x, y} is both symmetric and…
• Let the coefficients of x⁻¹ and x⁻³ in the expansion of ( 2x^(1/5) - 1/x^(1/5) )¹⁵,x >…
• The distance of the origin from the centroid of the triangle whose two sides have the…
• Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P…

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