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

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Physics

• The ratio of the equivalent resistance of the network (shown in figure) between the…
• A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring…
• A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and…
• The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth…
• A player kicks a football with an initial speed of 25 ms⁻¹ at an angle of 45° from the…
• X different wavelengths may be observed in the spectrum from a hydrogen sample if the…
• Two simple harmonic motion, are represented by the equations y₁ = 10 sin ( 3π t + π/3 )…
• A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive…
• For a transistor α and β are given as α = I_C/I_E and β = I_C/I_B. Then the correct…
• If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what…
• Two discs have moments of inertia I₁ and I₂ about their respective axes perpendicular to…
• Match List - I with List - II. List - I | List - II; (a) | R_H (Rydberg constant) | (i)…
• An ac circuit has an inductor and a resistor resistance R in series, such that X L = 3R…
• A plane electromagnetic wave with frequency of 30 MHz travels in free space. At…
• A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a…
• if the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen…
• A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of…
• Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8…
• For full scale deflection of total 50 divisions, 50 mV voltage is required in…
• Curved surfaces of a plano-convex lens of refractive index μ₁ and a plano-concave lens…
• The Colour coding on a carbon resistor is shown in the given figure. The resistance…
• The light waves from two coherent sources have same intensity I₁ = I₂ = I₀. In…
• Figure shows a rod AB, which is bent in a 120° circular arc of radius R. A charge (-Q)…
• Wires W₁ and W₂ are made of same material having the breaking stress of 1.25 × 10⁹ N/m²…
• Three capacitors C₁ = 2μF, C₂ = 6μF and C₃ = 12μF are connected as shown in figure. Find…
• A zener diode of power rating 2W is to be used as a voltage regulator. If the zener…
• A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that…
• The height of victoria falls is 63 m. What is the difference in temperature of water at…
• A heat engine operates between a cold reservoir at temperature T₂ = 400 K and a hot…

Chemistry

• Given below are two statements : Statement I : Ethyl pent-4-yn-oate on reaction with…
• 100 g of propane is completely reacted with 1000 g of oxygen. The mole fraction of…
• Which one of the following is the major product of the given reaction?
• The resistance of a conductivity cell with cell constant 1.14 cm⁻¹, containing 0.001 M…
• The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 × 10⁻³s⁻¹…
• The compound/s which will show significant intermolecular H-bonding is/are :
• The correct order of ionic radii for the ions, P³⁻, S²⁻, Ca²⁺, K⁺, Cl⁻ is :
• Which one of the following reactions will not yield propionic acid?
• When 5.1 g of solid NH₄HS is introduced into a two litre evacuated flask at 27°C, 20% of…
• Hydrolysis of sucrose gives :
• Which one of the following chemicals is responsible for the production of HCl in the…
• Match List-I with List-II : List - I (Name of ore/mineral) | List - II (Chemical…
• Choose the correct statement from the following :
• The number of species having non-pyramidal shape among the following is ___________. (A)…
• The major product of the following reaction, if it occurs by S N 2 mechanism is :
• The number of photons emitted by a monochromatic (single frequency) infrared range…
• 40 g of glucose (Molar mass = 180) is mixed with 200 mL of water. The freezing point of…
• Data given for the following reaction is as follows : FeO₍ₛ₎ + C (graphite) → Fe₍ₛ₎ + CO…
• Which one of the following tests used for the identification of functional groups in…
• The number of optical isomers possible for [Cr(C₂O₄)₃]³⁻ is ____________.
• The correct structures of A and B formed in the following reactions are :
• Potassium permanganate on heating at 513 K gives a product which is :
• Which one of the following is formed (mainly) when red phosphorus is heated in a sealed…
• The addition of dilute NaOH to Cr³⁺ salt solution will give :
• The oxide that gives H₂O₂ most readily on treatment with H₂O is :
• Lyophilic sols are more stable than lyophobic sols because :

Mathematics

• Let S be the sum of all solutions (in radians) of the equation sin ⁴θ + cos ⁴θ - sin θ…
• If 0 < x < 1 and y = 1/2x² + 2/3x³ + 3/4x⁴ + ...., then the value of e 1 + y at x = 1/2…
• Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x - y + z +…
• Let M and m respectively be the maximum and minimum values of the function f(x) = tan⁻¹…
• Let S = 1, 2, 3, 4, 5, 6, 9. Then the number of elements in the set T = A ⊆ S : A ≠ φ…
• If lim _(x → ∞) ( √(x² - x + 1) - ax ) = b, then the ordered pair (a, b) is :
• A differential equation representing the family of parabolas with axis parallel to…
• Let A(a, 0), B(b, 2b + 1) and C(0, b), b ≠ 0, |b| ≠ 1, be points such that the area of…
• 3 × 7²² + 2 × 10²² - 44 when divided by 18 leaves the remainder __________.
• Let [λ] be the greatest integer less than or equal to λ. The set of all values of λ for…
• The area of the region bounded by the parabola (y - 2)² = (x - 1), the tangent to it at…
• Let Z be the set of all integers, A = { (x,y) ∈ Z × Z:(x - 2)² + y² ≤ 4} B = { (x,y) ∈ Z…
• An online exam is attempted by 50 candidates out of which 20 are boys. The average marks…
• Two circles each of radius 5 units touch each other at the point (1, 2). If the equation…
• Let z₁ and z₂ be two complex numbers such that arg (z₁ - z₂) = π/4 and z₁, z₂ satisfy…
• If y(x) = cot ⁻¹( (√(1 + sin x) + √(1 - sin x))/(√(1 + sin x) - √(1 - sin x)) ),x ∈ (…
• Let A = ( [x + 1], [x + 2], [x + 3]; [x], [x + 3], [x + 3]; [x], [x + 2], [x + 4] )…
• The angle between the straight lines, whose direction cosines are given by the equations…
• The value of the integral ∫₀¹ (√x dx)/(1 + x)(1 + 3x)(3 + x) is :
• The set of all values of K > -1, for which the equation (3x² + 4x + 3)² - (k + 1)(3x² +…
• The equation of the plane passing through the line of intersection of the planes r⃗ .( î…
• Each of the persons A and B independently tosses three fair coins. The probability that…
• If the solution curve of the differential equation (2x - 10y³)dy + ydx = 0, passes…
• The probability distribution of random variable X is given by : X | 1 | 2 | 3 | 4 | 5…
• A box open from top is made from a rectangular sheet of dimension a × b by cutting…
• If ∫ (2eˣ+3e⁻ˣ)/(4eˣ+7e⁻ˣ)dx=1/14(ux+vlogₑ(4eˣ+7e⁻ˣ))+C, where C is a constant of…
• If two tangents drawn from a point P to the parabola y² = 16(x - 3) are at right angles…

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