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JEE Main 2021 20 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202120 Jul, Evening shift

Physics 24Chemistry 24Mathematics 30

Physics

Q56A series LCR circuit of R = 5 Ω, L = 20 mH and C = 0.5 μ F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at…Electromagnetic Induction and Alternating Currents
Q57A radioactive substance decays to (1/16)^(th) of its initial activity in 80 days. The half life of the radioactive substance expressed in days is _ _ _ _ _ _.Atoms and Nuclei
Q60A certain metallic surface is illuminated by monochromatic radiation of wavelength λ. The stopping potential for photoelectric current for this radiation is…Dual Nature of Matter and Radiation
Q65A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane…Laws of Motion
Q72Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of…Rotational Motion
Q73A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is _ _ _ _ _ _.Rotational Motion
Q5894For a series LCR circuit with R = 100 Ω, L = 0.5 mH and C = 0.1 pF connected across 220V - 50 Hz AC supply, the phase angle between current and supplied…Electromagnetic Induction and Alternating Currents
Q6239If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be:Rotational Motion
Q6561An electron having de-Broglie wavelength λ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:Dual Nature of Matter and Radiation
Q6776In an electromagnetic wave the electric field vector and magnetic field vector are given as E = E₀ i and B = B₀ k respectively. The direction of propagation…Electromagnetic Waves
Q7198A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The…Gravitation
Q7267Consider a binary star system of star A and star B with masses m A and m B revolving in a circular orbit of radii r A an r B, respectively. If T A and T B are…Gravitation
Q7308The correct relation between the degrees of freedom f and the ratio of specific heat γ is:Kinetic Theory of Gases
Q7623At an angle of 30° to the magnetic meridian, the apparent dip is 45°. Find the true dip:Magnetic Effects of Current and Magnetism
Q7644The magnetic susceptibility of a material of a rod is 499. Permeability in vacuum is 4 π × 10⁻⁷ H/m. Absolute permeability of the material of the rod is:Magnetic Effects of Current and Magnetism
Q7875A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t₁. If he remains stationary on a moving…Kinematics
Q7942The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is:Properties of Solids and Liquids
Q8016Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is:Properties of Solids and Liquids
Q8071A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is:Rotational Motion
Q8160A particle is making simple harmonic motion along the X-axis. If at a distances x₁ and x₂ from the mean position the velocities of the particle are v₁ and v₂…Oscillations and Waves
Q8246If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is:Units and Measurements
Q8377Two vectors P and Q have equal magnitudes. If the magnitude of P + Q is n times the magnitude of P - Q, then angle between P and Q is:Kinematics
Q8402With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 A^(o) is observed at 5896 A^(o) ?Optics
Q8607A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional…Work, Energy and Power

Chemistry

Q1When 0.15 g of an organic compound was analyzed using Carius method for estimation of bromine, 0.2397 g of AgBr was obtained. The percentage of bromine in the…Some Basic Principles of Organic Chemistry
Q4PC l₅ (g) → PC l₃ (g) + C l₂ (g) In the above first order reaction the concentration of PCl₅ reduces from initial concentration 50 mol L⁻¹ to 10 mol L⁻¹ in…Chemical Kinetics
Q7An aqueous solution of NiCl₂ was heated with excess sodium cyanide in presence of strong oxidizing agent to form [Ni(CN)₆]² -. The total change in number of…Coordination Compounds
Q8Potassium chlorate is prepared by electrolysis of KCl in basic solution as shown by following equation. 6OH⁻⁺ Cl^ - → ClO₃⁻⁺ 3H₂O + 6e^(- A) current of xA has…Redox Reactions and Electrochemistry
Q18Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the…Solid State
Q19The vapour pressures of A and B at 25° C are 90 mm Hg and 15 mm Hg respectively. If A and B are mixed such that the mole fraction of A in the mixture is 0.6…Solutions
Q204g equimolar mixture of NaOH and Na₂CO₃ contains x g of NaOH and y g of Na₂CO₃. The value of x is _ _ _ _ _ _ g. (Nearest integer)Some Basic Concepts in Chemistry
Q22The wavelength of electrons accelerated from rest through a potential difference of 40 kV is x × 10⁻¹2 m. The value of x is _ _ _ _ _ _. (Nearest integer)…Atomic Structure
Q23100 ml of 0.0018% (w/v) solution of Cl⁻ⁱon was the minimum concentration of Cl^(- r)equired to precipitate a negative sol in one h. The coagulating value of…Surface Chemistry
Q24For a given chemical reaction A → B at 300 K the free energy change is - 49.4 kJ mol⁻¹ and the enthalpy of reaction is 51.4 kJ mol⁻¹. The entropy change of…Chemical Thermodynamics
Q206Which one of the following statements is not true about enzymes?Biomolecules
Q304The hybridisations of the atomic orbitals of nitrogen in NO ₂^ -, NO ₂⁺ and NH ₄⁺ respectively are.Chemical Bonding and Molecular Structure
Q732Spin only magnetic moment of an octahedral complex of Fe²⁺ in the presence of a strong field ligand in BM is:Coordination Compounds
Q733Which one of the following species doesn't have a magnetic moment of 1.73 BM, (spin only value)?Coordination Compounds
Q1069Which one of the following gases is reported to retard photosynthesis?Environmental Chemistry
Q1166Benzene on nitration gives nitrobenzene in presence of HNO₃ and H₂SO₄ mixture, where:Hydrocarbons
Q1191Metallic sodium does not react normally with:Hydrocarbons
Q1248The single largest industrial application of dihydrogen is:Hydrogen
Q1343A solution is 0.1 M in Cl^(- a)nd 0.001 M in CrO ₄²⁻. Solid AgNO₃ is gradually added to it. Assuming that the addition does not change in volume and K s…Equilibrium
Q1353Consider two chemical reactions (A) and (B) that take place during metallurgical process: (A) ZnC O 3(s) Δ Zn O (s) + C O 2(g) (B) 2Zn S (s) + 3O 2(g) Δ 2Zn O…Isolation of Elements
Q1691Bakelite is a cross-linked polymer of formaldehyde and:Polymers
Q1750In Carius method, halogen containing organic compound is heated with fuming nitric acid in the presence of:Purification and Characterisation of Organic Compounds
Q1770Cu²⁺ salt reacts with potassium iodide to givePrinciples Related to Practical Chemistry
Q2144Outermost electronic configuration of a group 13 element, E, is 4s², 4p¹. The electronic configuration of an element of p-block period-five placed diagonally…Atomic Structure

Mathematics

Q34Let a curve y = y(x) be given by the solution of the differential equation cos (1/2 cos ⁻¹(e⁻ˣ))dx = √(e²ˣ - 1) dy. If it intersects y-axis at y = - 1, and…Differential Equations
Q38Let a function g: [ 0, 4 ] → R be defined as g(x) = \ max 0 ≤ t ≤ x t³ - 6t² + 9t - 3), 0 ≤ x ≤ 3 4 - x, 3 < x ≤ 4., then the number of points in the interval…Limit, Continuity and Differentiability
Q39If lim x → 0 α x eˣ - β log e (1 + x) + γ x²e⁻ˣ x sin ² x = 10,α,β,γ R, then the value of α + β + γ is _ _ _ _ _ _ _.Limit, Continuity and Differentiability
Q41The number of solutions of the equation log (x + 1) (2x² + 7x + 5) + log (2x + 5) (x + 1)² - 4 = 0, x > 0, is:Limit, Continuity and Differentiability
Q43Let A = a ij be a 3 × 3 matrix, where a ij = \ (- 1)^(j - i) if i < j, 2 if i = j, (- 1)^(i + j) if i > j. then det (3Adj(2A⁻¹)) is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q46If the point on the curve y² = 6x, nearest to the point (3,3/2) is (α, β), then 2(α + β) is equal to _ _ _ _ _ _ _.Coordinate Geometry
Q49For k N, let 1/(α (α + 1)(α + 2).........(α + 20)) = Σ K = 0 ²⁰ A k /(α + k), where α > 0. Then the value of 100((A₁₄ + A₁₅)/(A₁₃))² is equal to _ _ _ _ _ _ _.Sequence and Series
Q50Let a n n = 1 ^∞ be a sequence such that a₁ = 1, a₂ = 1 and a n + 2 = 2a n + 1 + a n for all n ≥ 1. Then the value of 47Σ n = 1 ^∞ a n /(2³ⁿ) is equal to _ _…Sequence and Series
Q52Consider a triangle having vertices A(- 2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and…Coordinate Geometry
Q54For p > 0, a vector v ₂ = 2 i + (p + 1) j is obtained by rotating the vector v ₁ = 3 p i + j by an angle θ about origin in counter clockwise direction. If tan…Vector Algebra
Q2430Consider the line L given by the equation (x - 3)/2 = (y - 1)/1 = (z - 2)/1. Let Q be the mirror image of the point (2, 3, - 1) with respect to L. Let a plane…Three Dimensional Geometry
Q2498The lines x = ay - 1 = z - 2 and x = 3y - 2 = bz - 2, (ab ≠ 0) are coplanar, if:Three Dimensional Geometry
Q2657The sum of all the local minimum values of the twice differentiable function f: R → R defined by f(x) = x³ - 3x² - (3f''(2))/2x + f''(1) is:Limit, Continuity and Differentiability
Q2997For the natural numbers m, n, if (1 - y)^(m) (1 + y)ⁿ = 1 + a₁y + a₂y² +.... + a m + n y^(m + n) and a₁ = a₂ = 10, then the value of (m + n) is equal to:Binomial Theorem and Its Simple Applications
Q3073Let r₁ and r₂ be the radii of the largest and smallest circles, respectively, which pass through the point (- 4, 1) and having their centres on the…Coordinate Geometry
Q3407If [x] denotes the greatest integer less than or equal to x, then the value of the integral ∫ - π /2 ^(π /2) [[x] - sin x]dx is equal to:Integral Calculus
Q3408If the real part of the complex number (1 - cos θ + 2i sin θ)⁻¹ is 1/5 for θ (0,π), then the value of the integral ∫₀^θ sin x dx is equal to:Integral Calculus
Q3409Let g(t) = ∫ - π /2 ^(π /2) cos ((π)/4t + f(x)) dx, where f(x) = log e (x + √(x² + 1)),x R. Then which one of the following is correct?Integral Calculus
Q3532Let y = y(x) satisfies the equation dy/dx - |A| = 0, for all x > 0, where A = [ y sin x 1 0 - 1 1 2 0 1/x ]. If y(π) = π + 2, then the value of y((π)/2) is:Differential Equations
Q3824Let f:R - (α)/6 → R be defined by f(x) = (5x + 3)/(6x - α). Then the value of α for which (fof)(x) = x, for all x R - (α)/6, is:Sets, Relations and Functions
Q3924Let in a right angled triangle, the smallest angle be θ. If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then sin…Height and Distance
Q4103The value of tan (2 tan ⁻¹(3/5) + sin ⁻¹(5/13)) is equal to:Trigonometry
Q4235If f:R → R is given by f(x) = x + 1, then the value of lim n → ∞ 1/n[ f(0) + f(5/n) + f(10/n) +...... + f((5(n - 1))/n) ] is:Limit, Continuity and Differentiability
Q4416Consider the following three statements: (A) If 3 + 3 = 7 then 4 + 3 = 8 (B) If 5 + 3 = 8 then earth is flat. (C) If both (A) and (B) are true then 5 + 6 =…Mathematical Reasoning
Q4594The value of k R, for which the following system of linear equations 3x - y + 4z = 3, x + 2y - 3z = - 2 6x + 5y + kz = - 3, has infinitely many solutions, is:Matrices and Determinants
Q4698Let P be a variable point on the parabola y = 4x² + 1. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point…Coordinate Geometry
Q5020Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 - k), the probability that exactly one of B and C occurs is…Statistics and Probability
Q5323If sum of the first 21 terms of the series log 9^(1/2) x + log 9^(1/3) x + log 9^(1/4) x +......., where x > 0 is 504, then x is equal toSequence and Series
Q5464If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and 20/3, respectively, then the value of | a - b | is equal to:Statistics and Probability
Q5775In a triangle ABC, if | BC | = 3, | CA | = 5 and | BA | = 7, then the projection of the vector BA on BC is equal to:Vector Algebra