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JEE Main 2021 18 Mar Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202118 Mar, Evening shift

Physics 22Chemistry 22Mathematics 30

Physics

Q56A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at. (i) ground level (ii) a height of 5 m. The increase in…Communication Systems
Q57Two wires of same length and thickness having specific resistances 6 Ω cm and 3 Ω cm respectively are connected in parallel. The effective resistivity is ρ Ω…Current Electricity
Q62An infinite number of point charges, each carrying 1 μ C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m............... The total force on a 1C…Electrostatics
Q72The radius of a sphere is measured to be (7.50 ± 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is _ _ _ _ _.Units and Measurements
Q73A galaxy is moving away from the earth at a speed of 286 kms⁻¹. The shift in the wavelength of a redline at 630 nm is x × 10⁻¹0 m. The value of x, to the…Optics
Q74A ball of mass 4 kg, moving with a velocity of 10 ms⁻¹, collides with a spring of length 8 m and force constant 100 Nm⁻¹. The length of the compressed spring…Work, Energy and Power
Q5892In a series LCR circuit, the inductive reactance (X L) is 10 Ω and the capacitive reactance (X C) is 4 Ω. The resistance (R) in the circuit is 6 Ω. The power…Electromagnetic Induction and Alternating Currents
Q6107The decay of a proton to neutron is:Atoms and Nuclei
Q6224An object of mass m₁ collides with another object of mass m₂, which is at rest. After the collision the objects move with equal speeds in opposite direction…Rotational Motion
Q6529The speed of electrons in a scanning electron microscope is 1 × 10⁷ ms⁻¹. If the protons having the same speed are used instead of electrons, then the…Dual Nature of Matter and Radiation
Q6686The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is:Electromagnetic Induction and Alternating Currents
Q6775A plane electromagnetic wave propagating along y-direction can have the following pair of electric field (E) and magnetic field (B) components.Electromagnetic Waves
Q6905The correct relation between α (ratio of collector current to emitter current) and β (ratio of collector current to base current) of a transistor is:Electronic Devices
Q7142If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately: [Take…Gravitation
Q7266The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is:Gravitation
Q7331An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S₁ and that of the other part is S₂. Given that S₁ > S₂. If…Thermodynamics
Q7383Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would…Kinetic Theory of Gases
Q7485For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats):Thermodynamics
Q7643Which of the following statements are correct? (A) Electric monopoles do not exist whereas magnetic monopoles exist. (B) Magnetic field lines due to a…Magnetic Effects of Current and Magnetism
Q7756A proton and an α -particle, having kinetic energies K p and K_ α respectively, enter into a magnetic field at right angles. The ratio of the radii of…Magnetic Effects of Current and Magnetism
Q8100Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire…Rotational Motion
Q8159The function of time representing a simple harmonic motion with a period of (π)/(ω) is:Oscillations and Waves

Chemistry

Q1In Tollen's test for aldehyde, the overall number of electron(s) transferred to the Tollen's reagent formula [Ag(NH₃)₂]⁺ per aldehyde group to form silver…Organic Compounds Containing Oxygen
Q3The number of species below that have two lone pairs of electrons in their central atom is _ _ _ _ _. (Round off to the Nearest Integer). SF₄, BF ₄^ -, ClF₃…Chemical Bonding and Molecular Structure
Q4The gas phase reaction 2A(g) A₂(g) at 400 K has Δ G^(o) = + 25.2 kJ mol⁻¹. The equilibrium constant K C for this reaction is _ _ _ _ × 10⁻². (Round off to the…Equilibrium
Q5A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _ _ _ _ m in. (Round off to the Nearest Integer). [Use: ln 2 =…Chemical Kinetics
Q9The molar conductivities at infinite dilution of barium chloride, sulphuric acid and hydrochloric acid are 280, 860 and 426 S cm² mol⁻¹ respectively. The…Redox Reactions and Electrochemistry
Q13The solubility of CdSO₄ in water is 8.0 × 10⁻⁴ mol L⁻¹. Its solubility in 0.01 M H₂SO₄ solution is _ _ _ _ _ × 10⁻⁶ mol L⁻¹. (Round off to the Nearest…Equilibrium
Q19A solute A dimerizes in water. The boiling point of a 2 molal solution of A is 100.52° C. The percentage association of A is _ _ _ _ _. (Round off to the…Solutions
Q2010.0 mL of Na₂CO₃ solution is titrated against 0.2 M HCl solution. The following titre values were obtained in 5 readings: 4.8 mL, 4.9 mL, 5.0 mL, 5.0 mL and…Some Basic Concepts in Chemistry
Q237Deficiency of vitamin K causes:Biomolecules
Q532In the reaction of hypobromite with amide, the carbonyl carbon is lost as:Organic Compounds Containing Nitrogen
Q592The secondary valency and the number of hydrogen bonded water molecule(s) in CuSO₄. 5H₂O, respectively, are:Coordination Compounds
Q767The oxide that shows magnetic property is:d- and f-Block Elements
Q1068Given below are two statements: Statement I: Non-biodegradable wastes are generated by the thermal power plants. Statement II: Bio-degradable detergents leads…Environmental Chemistry
Q1158Given below are two statements: Statement I: C₂H₅OH and AgCN both can generate nucleophile. Statement II: KCN and AgCN both will generate nitrile nucleophile…Organic Compounds Containing Halogens
Q1222In basic medium, H₂O₂ exhibits which of the following reactions? (A) Mn²⁺ → Mn⁴⁺ (B) I² → I^ - (C) PbS → PbSO₄ Choose the most appropriate answer from the…Hydrogen
Q1440Match List - I with List - II: List - I List - II (a) Mercury (i) Vapour phase refining (b) Copper (ii) Distillation refining (c) Silicon (iii) Electrolytic…Isolation of Elements
Q1610The first ionization energy of magnesium is smaller as compared to that of elements X and Y, but higher than that of Z. The elements X, Y and Z, respectively…Classification of Elements and Periodicity in Properties
Q1807The oxidation states of nitrogen in NO, NO₂, N₂O and NO ₃^(- a)re in the order of:Redox Reactions and Electrochemistry
Q1885Match List - I with List - II: List - I List - II (a) Be (i) treatment of cancer (b) Mg (ii) extraction of metals (c) Ca (iii) incendiary bombs and signals…S Block Elements
Q1946A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/an:Solid State
Q2120Given below are two statements: Statement I: Bohr's theory accounts for the stability and line spectrum of Li⁺ ion. Statement II: Bohr's theory was unable to…Atomic Structure
Q2258The charges on the colloidal CdS sol and TiO₂ sol are, respectively:Surface Chemistry

Mathematics

Q23Let P be a plane containing the line (x - 1)/3 = (y + 6)/4 = (z + 5)/2 and parallel to the line (x - 1)/4 = (y - 2)/(- 3) = (z + 5)/7. If the point (1, - 1…Three Dimensional Geometry
Q24Let the mirror image of the point (1, 3, a) with respect to the plane r.(2 i - j + k) - b = 0 be (- 3, 5, 2). Then, the value of | a + b | is equal to _ _ _ _…Three Dimensional Geometry
Q26The term independent of x in the expansion of [ (x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2)) ]¹⁰, x ≠ 1, is equal to _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q27Let ⁿ C r denote the binomial coefficient of x^(r) in the expansion of (1 + x)ⁿ. If Σ k = 0 ¹⁰ (2² + 3k) ¹⁰C k = α.3¹⁰ + β.2¹⁰,α,β R, then α + β is equal to _…Binomial Theorem and Its Simple Applications
Q31Let P(x) be a real polynomial of degree 3 which vanishes at x = - 3. Let P(x) have local minima at x = 1, local maxima at x = - 1 and ∫₋₁¹ P(x)dx = 18, then…Integral Calculus
Q33Let y = y(x) be the solution of the differential equation xdy - ydx = √((x² - y²)) dx, x ≥ 1, with y(1) = 0. If the area bounded by the line x = 1, x = e^ π…Differential Equations
Q35If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x g(x³) is divisible by x² + x + 1, then P(1) is equal to _ _ _ _ _ _.Sets, Relations and Functions
Q40Let f: R → R satisfy the equation f(x + y) = f(x). f(y) for all x, y R and f(x) ≠ 0 for any x R. If the function f is differentiable at x = 0 and f'(0) = 3…Limit, Continuity and Differentiability
Q42Let I be an identity matrix of order 2 × 2 and P = [ 2 - 1 5 - 3 ]. Then the value of n N for which Pⁿ = 5I - 8P is equal to _ _ _ _ _ _.Matrices and Determinants
Q44If Σ r = 1 ¹⁰ r!(r³ + 6r² + 2r + 5) = α (11!), then the value of α is equal to _ _ _ _ _ _.Permutations and Combinations
Q2884The area bounded by the curve 4y² = x²(4 - x)(x - 2) is equal to:Integral Calculus
Q3072Let S₁: x² + y² = 9 and S₂: (x - 2)² + y² = 1. Then the locus of center of a variable circle S which touches S₁ internally and S₂ externally always passes…Coordinate Geometry
Q3188Let a complex number be w = 1 - 3 i. Let another complex number z be such that |zw| = 1 and arg(z) - arg(w) = (π)/2. Then the area of the triangle with…Complex Numbers and Quadratic Equations
Q3404Let g(x) = ∫₀ˣ f(t)dt, where f is continuous function in [ 0, 3 ] such that 1/3 ≤ f(t) ≤ 1 for all t [0, 1] and 0 ≤ f(t) ≤ 1/2 for all t (1, 3]. The largest…Integral Calculus
Q3531Let y = y(x) be the solution of the differential equation dy/dx = (y + 1)((y + 1)e^(x²/2) - x), 0 < x < 2.1, with y(2) = 0. Then the value of dy/dx at x = 1…Differential Equations
Q3781Let a tangent be drawn to the ellipse (x²)/27 + y² = 1 at (3 3 cos θ, sin θ) where 0 (0,(π)/2). Then the value of θ such that the sum of intercepts on axes…Coordinate Geometry
Q3883Let f: R - 3 → R - 1 be defined by f(x) = (x - 2)/(x - 3). Let g: R → R be given as g(x) = 2x - 3. Then, the sum of all the values of x for which f⁻¹(x) +…Sets, Relations and Functions
Q3923A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be (π)/3. If the radius…Height and Distance
Q3989Consider a hyperbola H: x² - 2y² = 4. Let the tangent at a point P(4, 6) meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁ > 0. If F is a focus of H…Coordinate Geometry
Q4145Let f: R → R be a function defined as f(x) = \ (sin (a + 1)x + sin 2x)/2x,if x < 0 b, if x = 0 x + b x³ - x b x^(5/2), if x > 0. If f is continuous at x = 0…Limit, Continuity and Differentiability
Q4347If P and Q are two statements, then which of the following compound statement is a tautology?Mathematical Reasoning
Q4593Let the system of linear equations 4x + λ y + 2z = 0 2x - y + z = 0 μ x + 2y + 3z = 0, λ, μ R. has a non-trivial solution. Then which of the following is true?Matrices and Determinants
Q4884Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the…Statistics and Probability
Q5219Let S₁ be the sum of first 2n terms of an arithmetic progression. Let S₂ be the sum of first 4n terms of the same arithmetic progression. If (S₂ - S₁) is…Sequence and Series
Q5377Define a relation R over a class of n × n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP⁻¹ = B". Then which of the…Sets, Relations and Functions
Q5462Let in a series of 2n observations, half of them are equal to a and remaining half are equal to - a. Also by adding a constant b in each of these…Statistics and Probability
Q5537Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R…Coordinate Geometry
Q5647If 15sin⁴ α + 10cos⁴ α = 6, for some α R, then the value of 27sec⁶ α + 8cosec⁶ α is equal to:Trigonometry
Q5774In a triangle ABC, if |BC | = 8,|CA | = 7,|AB | = 10, then the projection of the vector AB on AC is equal to:Vector Algebra
Q5814Let a and b be two non-zero vectors perpendicular to each other and | a | = | b |. If | a × b | = | a |, then the angle between the vectors (a + b + (a × b))…Vector Algebra