JEE Main 2021 (Online) 17th March Morning Shift — Question Paper

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Physics

• Two ideal polyatomic gases at temperatures T₁ and T₂ are mixed so that there is no loss…
• The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds…
• The radius in kilometer to which the present radius of earth (R = 6400 km) to be…
• Two identical metal wires of thermal conductivities K₁ and K₂ respectively are connected…
• A triangular plate is shown. A force F⃗ = 4î - 3ĵ is applied at point P. The torque at…
• The output of the given combination gates represents :
• Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table…
• Four identical rectangular plates with length, l = 2 cm and breadth, b = 3/2 cm are…
• When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of…
• A car accelerates from rest at a constant rate α for some time after which it…
• The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of…
• A mass M hangs on a massless rod of length l which rotates at a constant angular…
• If an electron is moving in the nᵗʰ orbit of the hydrogen atom, then its velocity (vₙ)…
• The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If…
• A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms⁻¹. The…
• Consider two identical springs each of spring constant k and negligible mass compared to…
• A polyatomic ideal gas has 24 vibrational modes. What is the value of γ?
• A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a…
• The equivalent resistance of series combination of two resistors is 's'. When they are…
• An electron of mass m and a photon have same energy E. The ratio of wavelength of…
• If 2.5 × 10⁻⁶ N average force is exerted by a light wave on a non-reflecting surface of…
• The vernier scale used for measurement has a positive zero error of 0.2 mm. If while…
• A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle…
• An AC current is given by I = I₁ sinωt + I₂ cosωt. A hot wire ammeter will give a…
• A modern grand - prix racing car of mass m is travelling on a flat track in a circular…
• Which level of the single ionized carbon has the same energy as the ground state energy…
• For what value of displacement the kinetic energy and potential energy of a simple…
• A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated…
• A current of 10A exists in a wire of cross-sectional area of 5 mm² with a drift velocity…

Chemistry

• The standard enthalpies of formation of Al₂O₃ and CaO are -1675 kJ mol⁻¹ and -635 kJ…
• The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above…
• The INCORRECT statement(s) about heavy water is (are) (A) used as a moderator in nuclear…
• The mole fraction of a solute in a 100 molal aqueous solution is ___________ × 10⁻²…
• Given below are two statements : Statement I : Potassium permanganate on heating at 573K…
• A certain orbital has n = 4 and m L = -3. The number of radial nodes in this orbital is…
• Mesityl oxide is a common name of :
• 0.01 moles of a weak acid HA (Kₐ = 2.0 × 10⁻⁶) is dissolved in 1.0 L of 0.1 M HCl…
• In the above reaction, 3.9 g of benzene on nitration gives 4.92 g of nitrobenzene. The…
• Which of the following is an aromatic compound?
• Which of the following reaction is an example of ammonolysis?
• With respect to drug-enzyme interaction, identify the wrong statement.
• A central atom in a molecule has two lone pairs of electrons and forms three single…
• The absolute value of the electron gain enthalpy of halogens satisfies :
• The correct order of conductivity of ions in water is :
• What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic…
• Given below are two statements : Statement I : Retardation factor (R f ) can be measured…
• Which of the following compound CANNOT act as a Lewis base?
• A colloidal system consisting of a gas dispersed in a solid is called a/an :
• Which of the following is correct structure of tyrosine?
• 15 mL of aqueous solution of Fe²⁺ in acidic medium completely reacted with 20 mL of 0.03…
• For a certain first order reaction 32% of the reactant is left after 570s. The rate…
• Hoffmann bromomide degradation of benzamide gives product A, which upon heating with…

Mathematics

• The value of lim _(x → 0 +) (cos ⁻¹(x - [x]²).sin ⁻¹(x - [x]²))/(x - x³), where [ x ]…
• The line 2x - y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of…
• Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then…
• The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no…
• Let a⃗ = 2î - 3ĵ + 4k̂ and b⃗ = 7î + ĵ - 6k̂. If r⃗ × a⃗ = r⃗ × b⃗, r⃗ . (î + 2ĵ + k̂) =…
• The inverse of y = 5ˡᵒᵍˣ is :
• In a school, there are three types of games to be played. Some of the students play two…
• Let there be three independent events E₁, E₂ and E₃. The probability that only E₁ occurs…
• If (2021)³⁷⁶² is divided by 17, then the remainder is __________.
• The sum of possible values of x for tan⁻¹(x + 1) + cot⁻¹( 1/(x - 1) ) = tan⁻¹( 8/31 ) is :
• The value of 4 + 1/(5 + 1/(4 + 1/(5 + 1/(4 + ......∞)))) is :
• If the equation of the plane passing through the line of intersection of the planes 2x -…
• If the function f(x) = (cos (sin x) - cos x)/x⁴ is continuous at each point in its…
• If a⃗ = α î + β ĵ + 3k̂, b⃗ = - β î - α ĵ - k̂ and c⃗ = î - 2ĵ - k̂ such that a⃗ . b⃗ =…
• Which of the following statements is correct for the function g(α) for α ∈ R such that…
• The maximum value of z in the following equation z = 6xy + y², where 3x + 4y ≤ 100 and…
• The minimum distance between any two points P₁ and P₂ while considering point P₁ on one…
• If A = [ 2, 3; 0, - 1 ], then the value of det(A⁴) + det(A¹⁰ - (Adj(2A))¹⁰) is equal to…
• Choose the incorrect statement about the two circles whose equations are given below…
• Which of the following is true for y(x) that satisfies the differential equation dy/dx =…
• If cot⁻¹(α) = cot⁻¹ 2 + cot⁻¹ 8 + cot⁻¹ 18 + cot⁻¹ 32 + ...... upto 100 terms, then α is :
• If f(x) = sin ( cos ⁻¹( (1 - 2²ˣ)/(1 + 2²ˣ) ) ) and its first derivative with respect to…
• The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
• If A = ( 0, sin α; sin α, 0 ) and det ( A² - 1/2I ) = 0, then a possible value of α is :
• The equation of the plane which contains the y-axis and passes through the point (1, 2…
• If [ . ] represents the greatest integer function, then the value of | ∫₀^(√(π/2)) […
• In a triangle PQR, the co-ordinates of the points P and Q are (-2, 4) and (4, -2)…
• If the fourth term in the expansion of (x + x^(log ₂x))⁷ is 4480, then the value of x…
• Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total…

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