JEE Main 2021 (Online) 31st August Evening Shift — Question Paper

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Physics

• A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the…
• Statement - I : To get a steady dc output from the pulsating voltage received from a…
• A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two…
• If V A and V B are the input voltages (either 5V or 0V) and V₀ is the output voltage…
• Choose the incorrect statement : (1) The electric lines of force entering into a…
• Two thin metallic spherical shells of radii r₁ and r₂ (r₁ < r₂) are placed with their…
• The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of…
• A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field…
• A parallel plate capacitor of capacitance 200 μF is connected to a battery of 200 V. A…
• A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it…
• If R E be the radius of Earth, then the ratio between the acceleration due to gravity at…
• Consider two separate ideal gases of electrons and protons having same number of…
• Four identical hollow cylindrical columns of mild steel support a big structure of mass…
• At very high frequencies, the effective impendence of the given circuit will be…
• Statement I : Two forces (P⃗+Q⃗) and (P⃗-Q⃗) where P⃗⊥ Q⃗, when act at an angle θ₁ to…
• A sample of gas with γ = 1.5 is taken through an adiabatic process in which the volume…
• A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic…
• If velocity [V], time [T] and force [F] are chosen as the base quantities, the…
• A free electron of 2.6 eV energy collides with a H⁺ ion. This results in the formation…
• A long solenoid with 1000 turns/m has a core material with relative permeability 500 and…
• In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is…
• For a body executing S.H.M. : (1) Potential energy is always equal to its K.E. (2)…
• The equivalent resistance of the given circuit between the terminals A and B is :
• A particle is moving with constant acceleration 'a'. Following graph shows v² versus…
• Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum…
• A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300 K, pressure 400 kPa…
• The magnetic field vector of an electromagnetic wave is given by B = B₀(î + ĵ)/√2 cos…

Chemistry

• The value of magnetic quantum number of the outermost electron of Zn⁺ ion is…
• Which one of the following statements is incorrect?
• The number of S = O bonds present in sulphurous acid, peroxodisulphuric acid and…
• CH₄ is absorbed on 1g charcoal at 0°C following the Freundlich adsorpiton isotherm 10.0…
• The transformation occurring in Duma's method is given below : C₂H₇N+(2x+y/2)CuO→…
• Match List - I with List - II : List - I (Metal Ion) | List - II (Group of Qualitative…
• Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is…
• The incorrect expression among the following is :
• Spin only magnetic moment in BM of [Fe(CO)₄(C₂O₄)]⁺ is :
• The major products A and B formed in the following reaction sequence are :
• Which of the following is not an example of fibrous protein?
• In the electrolytic refining of blister copper, the total number of main impurities…
• The Eu²⁺ ion is a strong reducing agent in spite of its ground state electronic…
• The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M NaOH is x ×…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Which one of the following correctly represents the order of stability of oxides, X₂O…
• The empirical formula for a compound with a cubic close packed arrangement of anions and…
• Identify correct A, B and C in the reaction sequence given below :
• 1.22 g of an organic acid is separately dissolved in 100 g of benzene (K b = 2.6 K kg…
• For the reaction A → B, the rate constant k(in s⁻¹) is given by log ₁₀k = 20.35 - (2.47…
• Which among the following is not a polyester?
• Arrange the following conformational isomers of n-butane in order of their increasing…
• According to molecular orbital theory, the number of unpaired electron(s) in O₂²⁻ is :
• Match List - I with List - II List - I (Parmeter) | List - II (Unit); (a) | Cell…
• The structures A and B formed in the following reaction are : [Ph = -C₆H₅]

Mathematics

• Let a₁, a₂, a₃, ..... be an A.P. If (a₁ + a₂ + .... + a₁₀)/(a₁ + a₂ + .... + aₚ) =…
• Let A be the set of all points (α, β) such that the area of triangle formed by the…
• Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) =…
• A tangent line L is drawn at the point (2, -4) on the parabola y² = 8x. If the line L is…
• If α = lim _(x → π/4) (tan ³x - tan x)/(cos ( x + π/4 )) and β = lim _(x → 0) (cos…
• Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g…
• An angle of intersection of the curves, x²/a² + y²/b² = 1 and x² + y² = ab, a > b, is :
• The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is…
• If S = 7/5 + 9/5² + 13/5³ + 19/5⁴ + ...., then 160 S is equal to ________.
• If ∫ (sin x)/(sin³x+cos³x)dx= αlogₑ|1+tan x|+βlogₑ|1-tan x+tan²x|+γtan⁻¹((2 tan…
• The mean and variance of 7 observations are 8 and 16 respectively. If two observations…
• If ydy/dx = x[ y²/x² + (φ ( y²/x² ))/(φ '( y²/x² )) ], x > 0, φ > 0, and y(1) = -1, then…
• The number of solutions of the equation 32^(tan ²x) + 32^(sec ²x) = 81, 0 ≤ x ≤ π/4 is :
• Let f : N → N be a function such that f(m + n) = f(m) + f(n) for every m, n∈N. If f(6) =…
• The domain of the function f(x) = sin ⁻¹( (3x² + x - 1)/(x - 1)² ) + cos ⁻¹( (x - 1)/(x…
• Let f(x) be a cubic polynomial with f(1) = -10, f(-1) = 6, and has a local minima at x =…
• The number of elements in the set { A = ( a, b; 0, d ):a,b,d ∈ { - 1,0,1} and (I - A)³ =…
• The sum of the roots of the equation x + 1 - 2log ₂(3 + 2ˣ) + 2log ₄(10 - 2⁻ˣ) = 0, is :
• Suppose, the line (x - 2)/α = (y - 2)/(- 5) = (z + 2)/2 lies on the plane x + 3y - 2z +…
• If α + β + γ = 2π, then the system of equations x + (cos γ)y + (cos β)z = 0 (cos γ)x + y…
• The locus of mid-points of the line segments joining (-3, -5) and the points on the…
• The distance of the point (-1, 2, -2) from the line of intersection of the planes 2x +…
• Let B be the centre of the circle x² + y² - 2x + 4y + 1 = 0. Let the tangents at two…
• If the coefficient of a⁷b⁸ in the expansion of (a + 2b + 4ab)¹⁰ is K.2¹⁶, then K is…
• Let a⃗ ,b⃗ ,c⃗ three vectors mutually perpendicular to each other and have same…
• If [x] is the greatest integer ≤ x, then π ²∫₀² ( sin (π x)/2 )(x - [x] )^([x])dx is…
• If z is a complex number such that (z - i)/(z - 1) is purely imaginary, then the minimum…
• If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3/2 and the…
• If dy/dx = (2ˣy + 2ʸ.2ˣ)/(2ˣ + 2ˣ⁺ʸlog ₑ2), y(0) = 0, then for y = 1, the value of x…

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