JEE Main 2020 (Online) 8th January Morning Slot — Question Paper

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Physics

• At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area…
• Consider a uniform rod of mass M = 4m and length ℓ pivoted about its centre. A mass m…
• A particle of mass m is fixed to one end of a light spring having force constant k and…
• Effective capacitance of parallel combination of two capacitors C₁ and C₂ is 10 μF. When…
• A point object in air is in front of the curved surface of a plano-convex lens. The…
• Four resistances of 15Ω, 12Ω, 4Ω and 10Ω respectively in cyclic order to form…
• A one metre long (both ends open) organ pipe is kept in a gas that has double the…
• A leak proof cylinder of length 1m, made of a metal which has very low coefficient of…
• Consider a solid sphere of radius R and mass density ρ ( r ) = ρ ₀( 1 - r²/R² ) , 0 < r…
• A thermodynamic cycle xyzx is shown on a V-T diagram. The P-V diagram that best…
• The dimension of stopping potential V₀ in photoelectric effect in units of Planck's…
• The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of…
• Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively…
• A particle is moving along the x-axis with its coordinate with the time 't' given be…
• In finding the electric field using Gauss Law the formula | E⃗ | = q_(enc)/(ε ₀| A |) is…
• The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of…
• The plot that depicts the behavior of the mean free time t (time between two successive…
• The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a…
• A body A, of mass m = 0.1 kg has an initial velocity of 3î ms⁻¹ . It collides…
• The critical angle of a medium for a specific wavelength, if the medium has relative…
• When photon of energy 4.0 eV strikes the surface of a metal A, the ejected…
• The graph which depicts the results of Rutherford gold foil experiment with α-particales…
• Proton with kinetic energy of 1MeV moves from south to north. It gets an acceleration of…

Chemistry

• The decreasing order of reactivity towards dehydrohalogenation (E₁) reaction of the…
• The rate of a certain biochemical reaction at physiological temperature (T) occurs 10⁶…
• Which of the following statement is not true for glucose?
• The stoichiometry and solubility product of a salt with the solubility curve given below…
• The third ionization enthalpy is minimum for :
• The predominant intermolecular forces present in ethyl acetate, a liquid, are:
• As per Hardy-Schulze formulation, the flocculation values of the following for ferric…
• The number of chiral centres in penicillin is _________.
• The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :
• Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams)…
• The volume (in mL) of 0.125 M AgNO₃ required to quantitatively precipitate chloride ions…
• The complex that can show fac- and mer-isomers is :
• When gypsum is heated to 393 K, it forms :
• Arrange the following compounds in increasing order of C–OH bond length : methanol…
• A graph of vapour pressure and temperature for three different liquids X, Y, and Z is…
• The number of bonds between sulphur and oxygen atoms in S₂O₈²⁻ and the number of bonds…
• For the Balmer series in the spectrum of H atom, ν̅ = R_H{ 1/n₁² - 1/n₂² }, the correct…
• A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at…
• The strength of an aqueous NaOH solution is most accurately determined by titrating…

Mathematics

• Let the normal at a point P on the curve y² – 3x² + y + 10 = 0 intersect the y-axis at (…
• If the equation, x² + bx + 45 = 0 (b ∈ R) has conjugate complex roots and they satisfy…
• Let the volume of a parallelopiped whose coterminous edges are given by u⃗ = î + ĵ + λ…
• If ∫ (cos xdx)/sin³x(1+sin⁶x)^(2/3)=f(x)(1+sin⁶x)^(1/λ)+c where c is a constant of…
• The sum Σₖ₌₁²⁰ ( 1 + 2 + 3 + ... + k ) is :
• lim _(x → 0) ( (3x² + 2)/(7x² + 2) )^(1/x²) is equal to
• The locus of a point which divides the line segment joining the point (0, –1) and a…
• The least positive value of 'a' for which the equation 2x² + (a – 10)x + 33/2 = 2a has…
• The inverse function of f(x) = (8²ˣ - 8⁻²ˣ)/(8²ˣ + 8⁻²ˣ), x ∈ (-1, 1), is :
• The shortest distance between the lines (x - 3)/3 = (y - 8)/(- 1) = (z - 3)/1 and (x +…
• If c is a point at which Rolle's theorem holds for the function, f(x) = log ₑ( (x² +…
• Let the line y = mx and the ellipse 2x² + y² = 1 intersect at a ponit P in the first…
• If a, b and c are the greatest value of ¹⁹Cₚ, ²⁰C q and ²¹Cᵣ respectively, then :
• Let y = y(x) be a solution of the differential equation, √(1 - x²) dy/dx + √(1 - y²) =…
• Let ƒ(x) = xcos –1 (–sin|x|), x ∈ [ - π/2,π/2 ], then which of the following is true?
• For a > 0, let the curves C₁ : y² = ax and C₂ : x² = ay intersect at origin O and a…
• Let A and B be two independent events such that P(A) = 1/3 and P(B) = 1/6. Then, which…
• Let two points be A(1, –1) and B(0, 2). If a point P(x', y') be such that the area of…
• Let ƒ : R → R be such that for all x ∈ R (2¹⁺ˣ + 2 1–x ), ƒ(x) and (3ˣ + 3 –x ) are in…
• The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the…
• For which of the following ordered pairs (μ, δ), the system of linear equations x + 2y +…
• An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of…
• The mean and the standard deviation (s.d.) of 10 observations are 20 and 2…
• Let ƒ(x) = (sin(tan –1 x) + sin(cot –1 x))² – 1, |x| > 1. If dy/dx = 1/2d/dx( sin ⁻¹( f(…

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