JEE Main 2021 (Online) 27th July Evening Shift — Question Paper

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Physics

• The expected graphical representation of the variation of angle of deviation 'δ' with…
• In the given figure, two wheels P and Q are connected by a belt B. The radius of P is…
• A particle executes simple harmonic motion represented by displacement function as x(t)…
• An electron and proton are separated by a large distance. The electron starts…
• What will be the magnitude of electric field at point O as shown in the figure? Each…
• A physical quantity 'y' is represented by the formula y=m²r⁻⁴gˣl^(-3/2) If the…
• Find the truth table for the function Y of A and B represented in the following figure.
• Two identical particles of mass 1 kg each go round a circle of radius R, under the…
• A 100Ω resistance, a 0.1 μF capacitor and an inductor are connected in series across a…
• An automobile of mass 'm' accelerates starting from origin and initially at rest, while…
• Two Carnot engines A and B operate in series such that engine A absorbs heat at T₁ and…
• The difference in the number of waves when yellow light propagates through air and…
• The resistance of a conductor at 15°C is 16Ω and at 100°C is 20Ω. What will be the…
• One mole of an ideal gas is taken through an adiabatic process where the temperature…
• The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is…
• Given below is the plot of a potential energy function U(x) for a system, in which a…
• A particle of mass M originally at rest is subjected to a force whose direction is…
• A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the…
• For the circuit shown, the value of current at time t = 3.2 s will be _________ A…
• A small block slides down from the top of hemisphere of radius R = 3 m as shown in the…
• Figure A and B shown to long straight wires of circular cross-section (a and b with a <…
• Match List I with List II. List - I | List - II; (a) | Capacitance, C | (i) |…
• The K α X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms…
• The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an…
• An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and…
• Consider the following statements : A. Atoms of each element emit characteristics…
• A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30°…
• In the given figure the magnetic flux through the loop increases according to the…

Chemistry

• The equilibrium constant for the reaction A(s) ⇌ M(s) + 1/2O₂(g) is Kₚ = 4. At…
• The addition of silica during the extraction of copper from its sulphide ore :-
• Given below are two statements : Statement I : Penicillin is a bacteriostatic type…
• The total number of electrons in all bonding molecular orbitals of O₂²⁻ is…
• R-CN →((i)DIBAL-H)R-Y Consider the above reaction and identify "Y"
• If the Thompson model of the atom was correct, then the result of Rutherford's gold foil…
• 10.0 mL of 0.05 M KMnO₄ solution was consumed in a titration with 10.0 mL of given…
• Which one of the following set of elements can be detected using sodium fusion extract?
• Match List - I with List - II : List - I | List - II; (a) | Li | (i) | photoelectric…
• Given below are two statements : Statement I : Hyperconjugation is a permanent effect…
• Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is :
• 2SO₂(g) + O₂(g) → 2SO₃(g) The above reaction is carried out in a vessel starting with…
• The number of neutrons and electrons, respectively, present in the radioactive isotope…
• Select the correct statements (A) Crystalline solids have long range order. (B)…
• The dihedral angle in staggered form of Newman projection of 1, 1, 1-Trichloro ethane is…
• To an aqueous solution containing ions such as Al³⁺, Zn²⁺, Ca²⁺, Fe³⁺, Ni²⁺, Ba²⁺ and…
• Given below are two statements : Statement I : [Mn(CN)₆]³⁻, [Fe(CN)₆]³⁻ and…
• Number of Cl = O bonds in chlorous acid, chloric acid and perchloric acid respectively…
• 3 moles of metal complex with formula Co(en)₂Cl₃ gives 3 moles of silver chloride on…
• Match List - I with List - II : List - I (compound) | List - II (effect/affected…
• What is A in the following reaction?
• The correct order of first ionisation enthalpy is :
• For the cell Cu(s) | Cu²⁺ (aq) (0.1 M) || Ag⁺(aq) (0.01 M) | Ag(s) the cell potential E₁…
• When 400 mL of 0.2 M H₂SO₄ solution is mixed with 600 mL of 0.1 M NaOH solution, the…
• In a solvent 50% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor…
• Given below are two statement : one is labelled as Assertion A and the other is labelled…

Mathematics

• Let f:[0,∞ ) → [0,3] be a function defined by f(x) = { max { sin t:0 ≤ t ≤ x} ,, 0 ≤ x ≤…
• Let C be the set of all complex numbers. Let S₁ = z∈C : |z - 2| ≤ 1 and S₂ = z∈C : z(1 +…
• A possible value of 'x', for which the ninth term in the expansion of { 3^(log ₃√(25ˣ⁻¹…
• The value of lim _(x → 0) ( x/(⁸√(1 - sin x) - ⁸√(1 + sin x)) ) is equal to :
• A student appeared in an examination consisting of 8 true-false type questions. The…
• If A = [ 1, 1, 1; 0, 1, 1; 0, 0, 1 ] and M = A + A² + A³ + ....... + A²⁰, then the sum…
• Let y = y(x) be the solution of the differential equation (x - x³)dy = (y + yx² -…
• Let f : R → R be defined as f(x + y) + f(x - y) = 2f(x)f(y),f( 1/2 ) = - 1. Then, the…
• If tan (π/9),x,tan (7π/18) are in arithmetic progression and tan (π/9),y,tan (5π/18) are…
• Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the…
• Let the mean and variance of the frequency distribution x:, x₁ = 2, x₂ = 6, x₃ = 8, x₄ =…
• Let α = max _(x ∈ R) { 8²ˢⁱⁿ³ˣ.4⁴ᶜᵒˢ³ˣ} and β = min _(x ∈ R) { 8²ˢⁱⁿ³ˣ.4⁴ᶜᵒˢ³ˣ}. If 8x²…
• Let a⃗ = î - α ĵ + β k̂, b⃗ = 3î + β ĵ - α k̂ and c⃗ = -α î - 2ĵ + k̂, where α and β are…
• The distance of the point P(3, 4, 4) from the point of intersection of the line joining…
• The number of real roots of the equation e⁴ˣ - e³ˣ - 4e²ˣ - eˣ + 1 = 0 is equal to…
• Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center…
• If the real part of the complex number z = (3 + 2i cos θ)/(1 - 3i cos θ),θ ∈ ( 0,π/2 )…
• The area of the region bounded by y - x = 2 and x² = y is equal to :
• Let a⃗, b⃗ and c⃗ be three vectors such that a⃗ = b⃗ × (b⃗ × c⃗). If magnitudes of the…
• Let A = n ∈ N | n² ≤ n + 10,000, B = 3k + 1 | k∈ N an dC = 2k | k∈N, then the sum of all…
• For real numbers α and β ≠ 0, if the point of intersection of the straight lines (x -…
• Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6√5 on…
• If ∫₀^π (sin ³x)e^(- sin ²x)dx = α - β/e∫₀¹ √t eᵗdt , then α + β is equal to ____________.
• Let y = y(x) be the solution of the differential equation dy = e αx + y dx; α ∈ N. If…
• Let A and B be two 3 × 3 real matrices such that (A² - B²) is invertible matrix. If A⁵ =…
• Let f : (a, b) → R be twice differentiable function such that f(x) = ∫ₐˣ g(t)dt for a…
• The point P (a, b) undergoes the following three transformations successively : (a)…
• Let N be the set of natural numbers and a relation R on N be defined by R = { (x,y) ∈ N…
• Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the…

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