JEE Main 2021 (Online) 16th March Evening Shift — Question Paper

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Physics

• Red light differs from blue light as they have :
• Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh⁻¹ and takes…
• A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed…
• Find out the surface charge density at the intersection of point x = 3 m plane and…
• The de-Broglie wavelength associated with an electron and a proton were calculated by…
• In a parallel plate capacitor set up, the plate area of capacitor is 2 m² and the plates…
• A mosquito is moving with a velocity v⃗ = 0.5t²î + 3tĵ + 9k̂ m/s and accelerating in…
• A body of mass 2 kg moves under a force of ( 2î + 3ĵ + 5k̂ )N. It starts from rest and…
• A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has…
• A force F⃗ = 4î + 3ĵ + 4k̂ is applied on an intersection point of x = 2 plane and…
• The magnetic field in a region is given by B⃗ = Bₒ( x/a )k̂. A square loop of side d is…
• The following logic gate is equivalent to :
• A charge Q is moving dl⃗ distance in the magnetic field B⃗. Find the value of work done…
• For the given circuit, comment on the type of transformer used.
• Amplitude of a mass-spring system, which is executing simple harmonic motion decreases…
• What will be the nature of flow of water from a circular tap, when its flow rate…
• A closed organ pipe of length L and an open organ pipe contain gases of densities ρ₁ and…
• For an ideal heat engine, the temperature of the source is 127°C. In order to have 60%…
• Calculate the time interval between 33% decay and 67% decay if half-life of a substance…
• If one wants to remove all the mass of the earth to infinity in order to break it up…
• The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic…
• A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A…
• A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are…
• A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane…
• The refractive index of a converging lens is 1.4. What will be the focal length of this…
• A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal…
• Calculate the value of mean free path (λ) for oxygen molecules at temperature 27°C and…
• The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA…
• In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a…

Chemistry

• [Ti(H₂O)₆]³⁺ absorbs light of wavelength 498 nm during a d - d transition. The…
• The number of orbitals with n = 5, m₁ = +2 is ___________. (Round off to the Nearest…
• The secondary structure of protein is stabilised by:
• Statement I : Sodium hydride can be used as an oxidising agent. Statement II : The lone…
• In the above reaction, the reagent ''A'' is :
• Which of the following is least basic?
• An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with…
• In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL…
• The INCORRECT statement regarding the structure of C₆₀ is :
• Sulphurous acid (H₂SO₃) has Ka₁ = 1.7 × 10⁻² and Ka₂ = 6.4 × 10⁻⁸. The pH of 0.588 M…
• Fex₂ and Fey₃ are known when x and y are :
• Arrange the following metal complex/compounds in the increasing order of spin only…
• The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H₃PO₃…
• The correct statements about H₂O₂ are : (A) used in the treatment of effluents. (B) used…
• Which of the following reduction reaction CANNOT be carried out with coke?
• The INCORRECT statements below regarding colloidal solutions is :
• Match List - I with List - II : List - I Test/Reagents/Observation(s) | List - II…
• A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min…
• A 5.0 m mol dm⁻³ aqueous solution of KCl has a conductance of 0.55 mS when measured in a…
• The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and…
• Identify the elements X and Y using the ionisation energy values given below…
• Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total…
• Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to…
• When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic…
• Which of the following polymer is used in the manufacture of wood laminates?
• At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and…
• At 25°C, 50 g of iron reacts with HCl to form FeCl₂. The evolved hydrogen gas expands…

Mathematics

• If (x, y, z) be an arbitrary point lying on a plane P which passes through the points…
• If the distance of the point (1, -2, 3) from the plane x + 2y - 3z + 10 = 0 measured…
• Let A = 2, 3, 4, 5, ....., 30 and '≃' be an equivalence relation on A × A, defined by…
• Consider the statistics of two sets of observations as follows : Size | Mean | Variance…
• Let α ∈ R be such that the function f(x) = { (cos ⁻¹(1 - { x} ²)sin ⁻¹(1 - { x} ))/({ x}…
• Let C be the locus of the mirror image of a point on the parabola y² = 4x with respect…
• The maximum value of f(x) = | sin ²x, 1 + cos ²x, cos 2x; 1 + sin ²x, cos ²x, cos 2x…
• Let C₁ be the curve obtained by the solution of differential equation 2xydy/dx = y² -…
• Given that the inverse trigonometric functions take principal values only. Then, the…
• Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0…
• Let f be a real valued function, defined on R - -1, 1 and given by f(x) = 3 logₑ | (x -…
• Sₙ(x) = log a 1/2 x + log a 1/3 x + log a 1/6 x + log a 1/11 x + log a 1/18 x + log a…
• If y = y(x) is the solution of the differential equation dy/dx + (tan x) y = sin x, 0 ≤…
• Let f : R → R and g : R → R be defined as f(x) = { x + a,, x < 0; |x - 1|,, x ≥ 0 and…
• The least value of |z| where z is complex number which satisfies the inequality exp (…
• Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay…
• Consider the integral I = ∫₀¹⁰ [x]e^([x])/eˣ⁻¹dx, where [x] denotes the greatest integer…
• Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments…
• Let f : S → S where S = (0, ∞) be a twice differentiable function such that f(x + 1) =…
• Let 1/16, a and b be in G.P. and 1/a, 1/b, 6 be in A.P., where a, b > 0. Then 72(a + b)…
• For real numbers α, β, γ and δ, if ∫ ((x²-1)+tan⁻¹((x²+1)/x))/(x⁴+3x²+1)tan⁻¹((x²+1)/x)dx…
• Let c⃗ be a vector perpendicular to the vectors, a⃗ = î + ĵ - k̂ and b⃗ = î + 2ĵ + k̂…
• If the points of intersections of the ellipse x²/16 + y²/b² = 1 and the circle x² + y² =…
• Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without…
• If the foot of the perpendicular from point (4, 3, 8) on the line L₁:(x - a)/l = (y -…
• Let A = [ a₁; a₂ ] and B = [ b₁; b₂ ] be two 2 × 1 matrices with real entries such that…
• Let P(x) = x² + bx + c be a quadratic polynomial with real coefficients such that ∫₀¹…
• Let n be a positive integer. Let A = Σₖ₌₀ⁿ ( - 1)ᵏⁿCₖ[ ( 1/2 )ᵏ + ( 3/4 )ᵏ + ( 7/8 )ᵏ +…
• Let a⃗ = î + 2ĵ - 3k̂ and b⃗ = 2î - 3ĵ + 5k̂. If r⃗ × a⃗ = b⃗ × r⃗, r⃗ . ( α î + 2ĵ + k̂…

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