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JEE Main 2020 9 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20209 Jan, Evening shift

Physics 17Chemistry 15Mathematics 25

Physics

Q59In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed…Optics
Q5881In LC circuit the inductance L = 40 mH and capacitance C = 100 μ F. If a voltage V(t) = 10sin(314t) is applied to the circuit, the current in the circuit is…Electromagnetic Induction and Alternating Currents
Q5996The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this…Atoms and Nuclei
Q6198A rod of length L has non-uniform linear mass density given by ρ (x) = a + b (x/L)², where a and b are constants and 0 ≤ x ≤ L. The value of x for the centre…Rotational Motion
Q6219A particle of mass m is projected with a speed u from the ground at an angle θ = (π)/3 w.r.t. horizontal (x-axis). When it has reached its maximum height, it…Rotational Motion
Q6545An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie…Dual Nature of Matter and Radiation
Q6766A plane electromagnetic wave is propagating along the direction (i + j)/(2), with its polarization along the direction k. The correct form of the magnetic…Electromagnetic Waves
Q7103There is a small source of light at some depth below the surface of water (refractive index = 4/3) in a tank of large cross sectional surface area. Neglecting…Optics
Q7193Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are v A and v…Gravitation
Q7378Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same…Thermodynamics
Q7702A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that…Magnetic Effects of Current and Magnetism
Q7818A particle starts from the origin at t = 0 with an initial velocity of 3.0 i m/s and moves in the x-y plane with a constant acceleration (6 i + 4 j) m/s². The…Kinematics
Q8004Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1: 4, the ratio of…Properties of Solids and Liquids
Q8011A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of the droplet is (take…Properties of Solids and Liquids
Q8195A spring mass system (mass m, spring constant k and natural length l) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the…Oscillations and Waves
Q8302For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A₁ = 24.36, B₁ = 0.0724, C₁ = 256.2…Units and Measurements
Q8551A wire of length L and mass per unit length 6.0 × 10^–3 kgm^–1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and…Oscillations and Waves

Chemistry

Q7The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is _ _ _ _ _ _.d- and f-Block Elements
Q1610.30 mg of O₂ is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of O₂ in ppm is _ _ _ _ _.Some Basic Concepts in Chemistry
Q82Which of the following has the shortest C-Cl bond?Some Basic Principles of Organic Chemistry
Q299The number of sp² hybrid orbitals in a molecule of benzene is:Chemical Bonding and Molecular Structure
Q622The correct order of the spin-only magnetic moments of the following complexes is: (I) [Cr(H₂O)₆]Br₂ (II) Na₄[Fe(CN)₆] (III) Na₃[Fe(C₂O₄)₃] (Δ ₀ > P) (IV)…Coordination Compounds
Q686The isomer(s) of [Co(NH₃)₄Cl₂] that has/have a Cl–Co–Cl angle of 90°, is/are:Coordination Compounds
Q7625 g of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b) aqueous sodium hydroxide. The ratio of the volumes of H₂ evolved in…d- and f-Block Elements
Q1088Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm):Environmental Chemistry
Q1197Amongst the following, the form of water with the lowest ionic conductance at 298 K is:Hydrogen
Q1339The solubility product of Cr(OH)₃ at 298 K is 6.0 × 10^–31. The concentration of hydroxide ions in a saturated solution of Cr(OH)₃ will be:Equilibrium
Q1451The reaction of H₃N₃B₃Cl₃ (A) with LiBH₄ in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A) with (C) leads to H₃N₃B₃(Me)₃. Compounds…p-Block Elements
Q1604The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol^–1, respectively. How many moles of HCl and H₂SO₄, respectively, will be needed…Classification of Elements and Periodicity in Properties
Q1747A, B and C are three biomolecules. The results of the tests performed on them are given below: |l|l|l|l| l Molisch's Test l Barfoed Test l Biuret Test A…Principles Related to Practical Chemistry
Q1850Among the statements (a)-(d) the correct ones are: (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is insoluble…S Block Elements
Q2367The true statement amongst the following is:Chemical Thermodynamics

Mathematics

Q18If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines (x + 1)/2 = (y - 3)/4 = (z + 1)/3 and (x + 3)/2 = (y + 2)/6 = (z…Three Dimensional Geometry
Q21If C r ²⁵C r and C₀ + 5.C₁ + 9.C₂ +.... + (101).C₂₅ = 2²⁵.k, then k is equal to _ _ _.Binomial Theorem and Its Simple Applications
Q22If the curves, x² – 6x + y² + 8 = 0 and x² – 8y + y² + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is _ _ _.Coordinate Geometry
Q38The number of terms common to the two A.P.'s 3, 7, 11,....., 407 and 2, 9, 16,....., 709 is _ _ _.Sequence and Series
Q42Let a, b and c be three vectors such that | a | = 3, | b | = 5, b. c = 10 and the angle between b and c is (π)/3. If a is perpendicular to the vector b × c…Vector Algebra
Q2827Given: 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 the area (in sq. units) of the region bounded by the curves, y…Integral Calculus
Q2926In the expansion of (x/(cos θ) + 1/(x sin θ))¹⁶, if ₁ is the least value of the term independent of x when (π)/8 ≤ θ ≤ (π)/4 and ₂ is the least value of the…Binomial Theorem and Its Simple Applications
Q3257If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be:Complex Numbers and Quadratic Equations
Q3307Let a function ƒ: [0, 5] → R be continuous, ƒ(1) = 3 and F be defined as: F(x) = ∫₁ˣ t²g(t)dt, where g(t) = ∫₁^(t) f(u)du Then for the function F, the point x…Integral Calculus
Q3600If dy/dx = xy/(x² + y²); y(1) = 1; then a value of x satisfying y(x) = e is:Differential Equations
Q3695If x = 2 sin θ - sin 2θ and y = 2 cos θ - cos 2θ, θ [ 0,2π ], then d²y d x² at θ = π is:Limit, Continuity and Differentiability
Q3698Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to:Limit, Continuity and Differentiability
Q3778The length of the minor axis (along y-axis) of an ellipse in the standard form is 4/(3). If this ellipse touches the line, x + 6y = 8; then its eccentricity is:Coordinate Geometry
Q3863Let a – 2b + c = 1. If f(x)=| x + a x + 2 x + 1 x + b x + 3 x + 2 x + c x + 4 x + 3 |, then:Sets, Relations and Functions
Q4021If ∫ (dθ)/(cos ²θ (tan 2θ + sec 2θ)) = λ tan θ + 2 log e | f(θ) | + C where C is a constant of integration, then the ordered pair (λ, ƒ(θ)) is equal to:Integral Calculus
Q4140Let [t] denote the greatest integer ≤ t and lim x → 0 x[ 4/x ] = A. Then the function, f(x) = [x²]sin(π x) is discontinuous, when x is equal to:Limit, Continuity and Differentiability
Q4334If p → (p ~q) is false, then the truth values of p and q are respectively:Mathematical Reasoning
Q4574The following system of linear equations 7x + 6y – 2z = 0 3x + 4y + 2z = 0 x – 2y – 6z = 0, hasMatrices and Determinants
Q4742If one end of a focal chord AB of the parabola y² = 8x is at A(1/2, - 2), then the equation of the tangent to it at B is:Coordinate Geometry
Q4977If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is:Statistics and Probability
Q4998A random variable X has the following probability distribution: X: 1 2 3 4 5 P(X): K² 2K K 2K 5K² Then P(X > 2) is equal to:Statistics and Probability
Q5056Let a, b R, a ≠ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root α, which is also a root of the equation, x² – 2bx – 10 = 0. If β is the…Complex Numbers and Quadratic Equations
Q5257Let a n be the n^(t)h term of a G.P. of positive terms. Σ n = 1 ¹⁰⁰ a 2n + 1 = 200 and Σ n = 1 ¹⁰⁰ a 2n = 100, then Σ n = 1 ²⁰⁰ a n is equal to:Sequence and Series
Q5403If A = x R: |x| < 2 and B = x R: |x – 2| ≥ 3; then:Sets, Relations and Functions
Q5663If x = Σ n = 0 ^∞ (- 1)ⁿ tan ²ⁿ θ and y = Σ n = 0 ^∞ cos ²ⁿθ for 0 < θ < (π)/4, then:Trigonometry