JEE Main 2020 (Online) 9th January Evening Slot — Question Paper

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Physics

• A small spherical droplet of density d is floating exactly half immersed in a liquid of…
• A wire of length L and mass per unit length 6.0 × 10 –3 kgm –1 is put under tension of…
• A small circular loop of conducting wire has radius a and carries current I. It is…
• An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by…
• A plane electromagnetic wave is propagating along the direction (î + ĵ)/√2 , with its…
• There is a small source of light at some depth below the surface of water (refractive…
• Planet A has mass M and radius R. Planet B has half the mass and half the radius of…
• A particle starts from the origin at t = 0 with an initial velocity of 3.0 î m/s and…
• A spring mass system (mass m, spring constant k and natural length l) rest in…
• A particle of mass m is projected with a speed u from the ground at an angle θ = π/3…
• Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1…
• Starting at temperature 300 K, one mole of an ideal diatomic gas (γ = 1.4) is first…
• A rod of length L has non-uniform linear mass density given by ρ(x) = a + b( x/L )²…
• In a Young's double slit experiment 15 fringes are observed on a small portion of the…
• In LC circuit the inductance L = 40 mH and capacitance C = 100 μF. If a voltage V(t) =…
• The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs…
• For the four sets of three measured physical quantities as given below. Which of the…
• The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is…
• A uniformly thick wheel with moment of inertia I and radius R is free to rotate about…
• Two identical capacitors A and B, charged to the same potential 5V are connected in two…
• An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid…
• In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is…
• The current i in the network is :
• Two steel wires having same length are suspended from a ceiling under the same load. If…

Chemistry

• The decreasing order of basicity of the following amines is :
• 10.30 mg of O₂ is dissolved into a liter of sea water of density 1.03 g/mL. The…
• Which polymer has 'chiral' monomer(s) ?
• The reaction of H₃N₃B₃Cl₃ (A) with LiBH₄ in tetrahydrofuran gives inorganic benzene (B)…
• 5 g of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b)…
• Consider the following reactions, [P]{→((i) NaNO₂/HCl, 0-5°C (ii) β-naphthol/NaOH)…
• In the figure shown below reactant A (represented by square) is in equilibrium with…
• The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol –1…
• The solubility product of Cr(OH)₃ at 298 K is 6.0 × 10 –31 . The concentration of…
• Amongst the following, the form of water with the lowest ionic conductance at 298 K is :
• A mixture of gases O₂, H₂ and CO are taken in a closed vessel containing charcoal. The…
• Which of the following has the shortest C-Cl bond?
• The correct order of the spin-only magnetic moments of the following complexes is : (I)…
• A, B and C are three biomolecules. The results of the tests performed on them are given…
• The number of sp² hybrid orbitals in a molecule of benzene is :
• A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the…
• The isomer(s) of [Co(NH₃)₄Cl₂] that has/have a Cl–Co–Cl angle of 90°, is/are :
• Among the statements (a)-(d) the correct ones are : (a) Lithium has the highest…
• The true statement amongst the following is :

Mathematics

• Let ƒ and g be differentiable functions on R such that fog is the identity function. If…
• If one end of a focal chord AB of the parabola y² = 8x is at A( 1/2, - 2 ), then the…
• Given : f(x)={x ,, 0≤ x<1/2; 1/2 ,, x=1/2; 1-x ,, 1/2<x≤ 1 and g(x)=(x-1/2)²,x∈ R Then…
• If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the…
• Let a, b ∈ R, a ≠ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root α…
• If A = x ∈ R : |x| < 2 and B = x ∈ R : |x – 2| ≥ 3; then :
• If x = 2 sin θ - sin 2θ and y = 2 cos θ - cos 2θ, θ ∈ [ 0,2π ], then d²y/dx² at θ = π is :
• Let a function ƒ : [0, 5] → R be continuous, ƒ(1) = 3 and F be defined as : F(x) = ∫₁ˣ…
• If dy/dx = xy/(x² + y²); y(1) = 1; then a value of x satisfying y(x) = e is :
• The number of terms common to the two A.P.'s 3, 7, 11, ....., 407 and 2, 9, 16…
• In the expansion of ( x/(cos θ) + 1/(x sin θ) )¹⁶, if ℓ ₁ is the least value of the term…
• Let [t] denote the greatest integer ≤ t and lim _(x → 0) x[ 4/x ] = A. Then the…
• The following system of linear equations 7x + 6y – 2z = 0 3x + 4y + 2z = 0 x – 2y – 6z =…
• If ∫ dθ/cos²θ(tan 2θ+sec 2θ)=λ tan θ+2logₑ|f(θ)|+C where C is a constant of integration…
• A random variable X has the following probability distribution : X: | 1 | 2 | 3 | 4 | 5…
• Let aₙ be the nᵗʰ term of a G.P. of positive terms. Σₙ₌₁¹⁰⁰ a₂ₙ₊₁ = 200 and Σₙ₌₁¹⁰⁰ a₂ₙ…
• If Cᵣ ≡ ²⁵Cᵣ and C₀ + 5.C₁ + 9.C₂ + .... + (101).C₂₅ = 2²⁵.k, then k is equal to _____.
• Let a – 2b + c = 1. If f(x)=| x + a, x + 2, x + 1; x + b, x + 3, x + 2; x + c, x + 4, x…
• If the curves, x² – 6x + y² + 8 = 0 and x² – 8y + y² + 16 – k = 0, (k > 0) touch each…
• If x=Σₙ₌₀^∞(-1)ⁿtan²ⁿθ and y=Σₙ₌₀^∞cos²ⁿθ for 0 < θ < π/4, then :
• The length of the minor axis (along y-axis) of an ellipse in the standard form is 4/√3…
• If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be :
• Let a⃗, b⃗ and c⃗ be three vectors such that | a⃗ | = √3, | b⃗ | = 5,b⃗ .c⃗ = 10 and the…

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