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JEE Main 2021 16 Mar Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202116 Mar, Morning shift

Physics 18Chemistry 22Mathematics 29

Physics

Q52A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8 Ω, L = 24 mH and C = 60 μ F. The value of power dissipated at…Electromagnetic Induction and Alternating Currents
Q53The first three spectral lines of H-atom in the Balmer series are given λ ₁, λ ₂, λ ₃ considering the Bohr atomic model, the wave lengths of first and third…Atoms and Nuclei
Q67The resistance R = V/I, where V = (50 ± 2)V and I = (20 ± 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _ _ _ _ _.Units and Measurements
Q69A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value…Optics
Q6154For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the…Electrostatics
Q6270A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to…Kinematics
Q6312A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m. The wavelength (in meter) of the signal transmitted by this…Communication Systems
Q6496A conducting wire of length 'l', area of cross-section A and electric resistivity ρ is connected between the terminals of a battery. A potential difference V…Current Electricity
Q6637The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation:Dual Nature of Matter and Radiation
Q6772A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, B = 8.0 × 10⁻⁸ z T. The…Electromagnetic Waves
Q6773For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (U e) and magnetic (U m) fields is:Electromagnetic Waves
Q7264The maximum and minimum distances of a comet from the Sun are 1.6 × 10¹² m and 8.0 × 10¹⁰ m respectively. If the speed of the comet at the nearest point is 6…Gravitation
Q7381The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T…Thermodynamics
Q7533In thermodynamics, heat and work are:Thermodynamics
Q7622A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at…Magnetic Effects of Current and Magnetism
Q7991The pressure acting on a submarine is 3 × 10⁵ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine…Properties of Solids and Liquids
Q8203Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of…Oscillations and Waves
Q8355One main scale division of a vernier callipers is 'a' cm and n^(t)h division of the vernier scale coincide with (n - 1)^(t)h division of the main scale. The…Experimental Skills

Chemistry

Q5For the reaction A(g) B(g) at 495 K, Δ r G° = - 9.478 kJ mol⁻¹. If we start the reaction in a closed container at 495 K with 22 millimoles of A, the amount of…Equilibrium
Q6The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 × 10⁻³ s⁻¹ and the activation energy E a =…Chemical Kinetics
Q7The equivalents of ethylene diamine required to replace the neutral ligands from the coordination sphere of the trans-complex of CoCl₃. 4NH₃ is _ _ _ _ _…Coordination Compounds
Q13Two salts A₂X and MX have the same value of solubility product of 4.0 × 10⁻¹2. The ratio of their molar solubilities i.e. (S(A₂X))/(S(MX)) = _ _ _ _ _. (Round…Equilibrium
Q17A certain element crystallises in a bcc lattice of unit cell edge length 27 A^(o). If the same element under the same conditions crystallises in the fcc…Solid State
Q18AB₂ is 10% dissociated in water to A²⁺ and B^ -. The boiling point of a 10.0 molal aqueous solution of AB₂ is _ _ _ _ _° C. (Round off to the Nearest…Solutions
Q19A 6.50 molal solution of KOH (aq.) has a density of 1.89 g cm⁻³. The molarity of the solution is _ _ _ _ _ _ mol dm⁻³. (Round off to the Nearest Integer)…Some Basic Concepts in Chemistry
Q202MnO₄⁻⁺ b C₂ O₄²⁻ + c H⁺ → xM n²⁺ + yC O₂ + z H₂ O If the above equation is balanced with integer coefficients, the value of c is _ _ _ _ _ _. (Round off to…Some Basic Concepts in Chemistry
Q21Complete combustion of 750 g of an organic compound provides 420 g of CO₂ and 210 g of H₂O. The percentage composition of carbon and hydrogen in organic…Some Basic Concepts in Chemistry
Q22When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electrons is _ _ _ _ A^(o). (Round off to…Atomic Structure
Q47Assertion A: Enol form of acetone [CH₃COCH₃] exists in < 0.1% quantity. However, the enol form of acetyl acetone [CH₃COCH₂OCCH₃] exists in approximately 15%…Organic Compounds Containing Oxygen
Q127In chromotography technique, the purification of compound is independent of:Some Basic Principles of Organic Chemistry
Q236Which among the following pairs of Vitamins is stored in our body relatively for longer duration?Biomolecules
Q253Given below are two statements: one is labeled as Assertion A and the other is labelled as Reason R: Assertion A: The H - O - H bond angle in water molecule…Chemical Bonding and Molecular Structure
Q822Given below are two statements: Statement I: The E^(o) value for Ce⁴⁺ / Ce³⁺ is + 1.74 V. Statement II: Ce is more stable in Ce⁴⁺ state than Ce³⁺ state. In…d- and f-Block Elements
Q823Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Size of Bk³⁺ ion is less than Np³⁺ ion…d- and f-Block Elements
Q1028The type of pollution that gets increased during the day time and in the presence of O₃ is:Environmental Chemistry
Q1190Which of the following is Lindlar catalyst?Hydrocarbons
Q1220Given below are two statements: Statement I: H₂O₂ can act as both oxidising and reducing agent in basic medium. Statement II: In the hydrogen economy, the…Hydrogen
Q1389The process that involves the removal of sulphur from the ores is:Isolation of Elements
Q1487A group of 15 element, which is a metal and forms a hydride with strongest reducing power among group 15 hydrides. The element is:p-Block Elements
Q1883Given below are two statements: Statement I: Both CaCl₂. 6H₂O and MgCl₂. 8H₂O undergo dehydration on heating. Statement II: BeO is amphoteric whereas the…S Block Elements

Mathematics

Q28Let z and ω be two complex numbers such that ω = z z - 2z + 2,| (z + i)/(z - 3i) | = 1 and Re(ω) has minimum value. Then, the minimum value of n N for which ω…Complex Numbers and Quadratic Equations
Q30Let f: (0, 2) → R be defined as f(x) = log₂ (1 + tan ((π x)/4)). Then, lim n → ∞ 2/n(f(1/n) + f(2/n) +... + f(1)) is equal to _ _ _ _ _ _.Integral Calculus
Q31If the normal to the curve y(x) = ∫₀ˣ (2t² - 15t + 10)dt at a point (a, b) is parallel to the line x + 3y = - 5, a > 1, then the value of | a + 6b | is equal…Integral Calculus
Q32Let f: R → R be a continuous function such that f(x) + f(x + 1) = 2, for all x R. If I₁ = ∫₀⁸ f(x)dx and I₂ = ∫₋₁³ f(x)dx, then the value of I₁ + 2I₂ is equal…Integral Calculus
Q34Let the curve y = y(x) be the solution of the differential equation, dy/dx = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis…Differential Equations
Q39If lim x → 0 a eˣ - b cos x + c e⁻ˣ x sin x = 2, then a + b + c is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q41Let P = [ - 30 20 56 90 140 112 120 60 14 ] and A = [ 2 7 ω ² - 1 - ω 1 0 - ω - ω + 1 ] where ω = (- 1 + i 3)/2, and I₃ be the identity matrix of order 3. If…Matrices and Determinants
Q43The total number of 3 × 3 matrices A having entries from the set 0, 1, 2, 3 such that the sum of all the diagonal entries of AA^(T) is 9, is equal to _ _ _ _…Matrices and Determinants
Q46Let ABCD be a square of side of unit length. Let a circle C₁ centered at A with unit radius is drawn. Another circle C₂ which touches C₁ and the lines AD and…Properties of Triangle
Q47Consider an arithmetic series and a geometric series having four initial terms from the set 11, 8, 21, 16, 26, 32, 4. If the last terms of these series are…Sequence and Series
Q2428Let P be a plane lx + my + nz = 0 containing the line, (1 - x)/1 = (y + 4)/2 = (z + 2)/3. If plane P divides the line segment AB joining points A(- 3, - 6, 1)…Three Dimensional Geometry
Q2496Let the position vectors of two points P and Q be 3 i - j + 2 k and i + 2 j - 4 k, respectively. Let R and S be two points such that the direction ratios of…Three Dimensional Geometry
Q2583If for a > 0, the feet of perpendiculars from the points A(a, - 2a, 3) and B(0, 4, 5) on the plane lx + my + nz = 0 are points C(0, - a, - 1) and D…Three Dimensional Geometry
Q2930If n is the number of irrational terms in the expansion of (3^(1/4) + 5^(1/8))⁶⁰, then (n - 1) is divisible by:Binomial Theorem and Its Simple Applications
Q2993Let [ x ] denote greatest integer less than or equal to x. If for n N, (1 - x + x³)ⁿ = Σ j = 0 ³ⁿ a j x^(j), then Σ j = 0 ^([ 3n/2 ]) a 2j + 4 Σ j = 0 ^([ (3n…Binomial Theorem and Its Simple Applications
Q3258Let a complex number z, |z| ≠ 1, satisfy log 1/(2) ((|z| + 11)/((|z| - 1)²)) ≤ 2. Then, the largest value of |z| is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q3527If y = y(x) is the solution of the differential equation, dy/dx + 2y tan x = sin x,y((π)/3) = 0, then the maximum value of the function y(x) over R is equal to:Differential Equations
Q3890The range of a R for which the function f(x) = (4a - 3)(x + log e 5) + 2(a - 7) cot (x/2) sin² (x/2), x ≠ 2n π, n N has critical points, is:Sets, Relations and Functions
Q3943The locus of the midpoints of the chord of the circle, x² + y² = 25 which is tangent to the hyperbola, (x²)/9 - (y²)/16 = 1 is:Coordinate Geometry
Q4200Let the functions f: R → R and g: R → R be defined as: f(x) = \ x + 2, x < 0 x², x ≥ 0. and g(x) = \ x³, x < 1 3x - 2, x ≥ 1. Then, the number of points in R…Limit, Continuity and Differentiability
Q4282Let S k = Σ r = 1 ^(k) tan ⁻¹((6^(r))/(2^(2r + 1) + 3^(2r + 1))). Then lim k → ∞ S k is equal to:Limit, Continuity and Differentiability
Q4344Which of the following Boolean expression is a tautology?Mathematical Reasoning
Q4590Let A = [ i - i - i i ],i = √(- 1). Then, the system of linear equations A⁸[ x y ] = [ 8 64 ] has:Matrices and Determinants
Q4709If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a ≠ 0, then 'a' must be greater than:Coordinate Geometry
Q4958A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:Statistics and Probability
Q5360The number of elements in the set x R: (|x| - 3) |x + 4| = 6 is equal to:Sets, Relations and Functions
Q5461Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?Statistics and Probability
Q5646If for x (0,(π)/2), log₁₀sinx + log₁₀cosx = - 1 and log₁₀(sinx + cosx) = 1/2 (log₁₀ n - 1), n > 0, then the value of n is equal to:Trigonometry
Q5692Let a vector α i + β j be obtained by rotating the vector 3 i + j by an angle 45° about the origin in counterclockwise direction in the first quadrant. Then…Vector Algebra