JEE Main 2021 (Online) 18th March Morning Shift — Question Paper

Download this paper as a PDF (17 pages, with answer key)

Physics

• The voltage across the 10Ω resistor in the given circuit is x volt. The value of 'x' to…
• A constant power delivering machine has towed a box, which was initially at rest, along…
• A parallel plate capacitor has plate area 100 m² and plate separation of 10 m. The space…
• A thin circular ring of mass M and radius r is rotating about its axis with an angular…
• A loop of flexible wire of irregular shape carrying current is placed in an external…
• A radioactive sample disintegrates via two independent decay processes having half lives…
• A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops…
• The position, velocity and acceleration of a particle moving with a constant…
• A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the…
• A ball of mass 10 kg moving with a velocity 10√3 m/s along the x-axis, hits another ball…
• Your friend is having eye sight problem. She is not able to see clearly a distant…
• Four identical long solenoids A, B, C and D are connected to each other as shown in the…
• The time period of a satellite in a circular orbit of radius R is T. The period of…
• The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in…
• A particle performs simple harmonic motion with a period of 2 second. The time taken by…
• In a series LCR resonance circuit, if we change the resistance only, from a lower to…
• In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the…
• The time period of a simple pendulum is given by T = 2π √(l/g). The measured value of…
• The circuit shown in the figure consists of a charged capacitor of capacity 3 μF and a…
• An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the…
• An npn transistor operates as a common emitter amplifier with a power gain of 10⁶. The…
• A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and…
• What will be the average value of energy along one degree of freedom for an ideal gas in…
• Imagine that the electron in a hydrogen atom is replaced by a muon (μ). The mass of muon…
• Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are…
• An oil drop of radius 2 mm with a density 3g cm⁻³ is held stationary under a constant…
• A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie…
• In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the…
• As shown in the figure, a particle of mass 10 kg is placed at a point A. When the…

Chemistry

• In order to prepare a buffer solution of pH 5.74, sodium acetate is added to acetic…
• The chemical that is added to reduce the melting point of the reaction mixture during…
• A non-reducing sugar "A" hydrolyses to give two reducing mono saccharides. Sugar A is
• The total number of unpaired electrons present in the complex K₃[Cr(oxalate)₃] is…
• Match the list - I with list - II List - I (Class of Drug) | List - II (Example); (a) |…
• Compound with molecular formula C₃H₆O can show :
• Match List - I with List - II : List - I (Chemicals) (a) Alcoholic potassium hydroxide…
• The number of ionisable hydrogens present in the product obtained from a reaction of…
• Match List - I with List - II List - I (process) | List - II (catalyst); (a) | Deacron's…
• In a binary compound, atoms of element A form a hcp structure and those of element M…
• Given below are two statements : One is labelled as Assertion A and the other labelled…
• A certain orbital has no angular nodes and two radial nodes. The orbital is :
• 2 molal solution of a weak acid HA has a freezing point of 3.885°C. The degree of…
• 2NO(g) + Cl₂(g) ⇌ 2NOCl(s) This reaction was studied at -10° and the following data was…
• Match List - I with List - II List - I | List - II ; (a) | Chlorophyll | (i) |…
• The ionic radius of Na⁺ ions is 1.02 Aᵒ. The ionic radii (in Aᵒ) of Mg²⁺ and Al³⁺…
• For the reaction 2Fe³⁺(aq) + 2I⁻(aq) → 2Fe²⁺(aq) + I₂(s) the magnitude of the standard…
• Considering the above reaction, X and Y respectively are :
• For the reaction C₂H₆ → C₂H₄ + H₂ the reaction enthalpy ΔᵣH = __________ kJ mol⁻¹…
• Complete combustion of 3g of ethane gives x × 10²² molecules of water. The value of x is…
• AX is a covalent diatomic molecule where A and X are second row elements of periodic…
• Reagent, 1-napthylamine and sulphanilic acid in acetic acid is used for the detection of
• A reaction of 0.1 mole of Benzylamine with bromomethane gave 23 g of Benzyl trimethyl…
• __________ grams of 3-Hydroxy propanal (MW = 74) must be dehydrated to produce 7.8 g of…
• Match List - I with List - II List - I | List - II ; (a) | Ca(OCl)₂ | (i) | Antacid; (b)…
• Reaction of Grignard reagent, C₂H₅MgBr with C₈H₈O followed by hydrolysis gives compound…
• The correct structures of trans-[NiBr₂(PPh₃)₂] and meridonial-[Co(NH₃)₃(NO₂)₃]…

Mathematics

• If f(x) = { 1/|x|, ; |x| ≥ 1; ax² + b, ; |x| < 1 is differentiable at every point of the…
• If lim _(x → 0) (sin ⁻¹x - tan ⁻¹x)/3x³ is equal to L, then the value of (6L + 1) is
• The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :
• If the functions are defined as f(x) = √x and g(x) = √(1 - x), then what is the common…
• Let (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² + .... + a₄₀x⁴⁰. Then a₁ + a₃ + a₅ + ..... + a₃₇…
• The equation of the planes parallel to the plane x - 2y + 2z - 3 = 0 which are at unit…
• The equation of one of the straight lines which passes through the point (1, 3) and…
• Choose the correct statement about two circles whose equations are given below : x² + y²…
• Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, -3, 1) and (2…
• The solutions of the equation | 1 + sin ²x, sin ²x, sin ²x; cos ²x, 1 + cos ²x, cos ²x…
• A vector a⃗ has components 3p and 1 with respect to a rectangular cartesian system. This…
• 1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + .... + 1/((201)² - 1) is equal to
• The value of 3 + 1/(4 + 1/(3 + 1/(4 + 1/(3 + ....∞)))) is equal to
• The integral ∫ ((2x-1)cos √((2x-1)²+5))/√(4x²-4x+6)dx is equal to (where c is a constant…
• The number of integral values of m so that the abscissa of point of intersection of…
• Let f(x) and g(x) be two functions satisfying f(x²) + g(4 - x) = 4x³ and g(4 - x) + g(x)…
• A square ABCD has all its vertices on the curve x²y² = 1. The midpoints of its sides…
• Let z₁, z₂ be the roots of the equation z² + az + 12 = 0 and z₁, z₂ form an equilateral…
• Let A + 2B = [ 1, 2, 0; 6, - 3, 3; - 5, 3, 1 ] and 2A - B = [ 2, - 1, 5; 2, - 1, 6; 0…
• The number of times the digit 3 will be written when listing the integers from 1 to 1000…
• Let α, β, γ be the real roots of the equation, x³ + ax² + bx + c = 0, (a, b, c ∈ R and…
• If f(x)=∫ (5x⁸+7x⁶)/(x²+1+2x⁷)²dx,(x≥ 0),f(0)=0 and f(1)=1/K, then the value of K is
• The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2…
• If α, β are natural numbers such that 100 α - 199β = (100)(100) + (99)(101) + (98)(102)…
• For the four circles M, N, O and P, following four equations are given : Circle M : x² +…
• The real valued function f(x) = (cos ec⁻¹x)/√(x - [x]), where [x] denotes the greatest…
• The number of solutions of the equation |cot x| = cot x + 1/(sin x) in the interval [ 0…
• The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60…
• If the equation a|z|² + α̅ z + α z̅̅ + d = 0 represents a circle where a, d are real…

Download all JEE Main 2021 PYQs chapter-wise as free PDFs