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

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JEE Main 202116 Mar, Evening shift

Physics 22Chemistry 25Mathematics 30

Physics

Q61The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is _ _ _ _ _ _ Ω. (Round off to the…Current Electricity
Q66A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint…Optics
Q67If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be x/5 G…Gravitation
Q69A body of mass 2 kg moves under a force of (2 i + 3 j + 5 k) N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b…Laws of Motion
Q72A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow…Kinematics
Q74A force F = 4 i + 3 j + 4 k is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is _…Rotational Motion
Q77A closed organ pipe of length L and an open organ pipe contain gases of densities ρ ₁ and ρ ₂ respectively. The compressibility of gases are equal in both the…Oscillations and Waves
Q6104Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.Atoms and Nuclei
Q6105The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic weight is 198 g mol⁻¹ is, (N a = 6 × 10²³/mol).Atoms and Nuclei
Q6271Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh⁻¹ and takes a sharp circular turn along a path of radius of 2m without reducing the…Kinematics
Q6313Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving…Communication Systems
Q6431A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the…Current Electricity
Q6558The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be…Dual Nature of Matter and Radiation
Q6965Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the…Electrostatics
Q7046The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the…Optics
Q7105Red light differs from blue light as they have:Optics
Q7382Calculate the value of mean free path (λ) for oxygen molecules at temperature 27° C and pressure 1.01 × 10⁵ Pa. Assume the molecular diameter 0.3 nm and the…Kinetic Theory of Gases
Q7755A charge Q is moving dl distance in the magnetic field B. Find the value of work done by B.Magnetic Effects of Current and Magnetism
Q7820A mosquito is moving with a velocity v = 0.5t² i + 3t j + 9 k m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?Kinematics
Q7905What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity…Properties of Solids and Liquids
Q8122Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time…Oscillations and Waves
Q8304In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale…Units and Measurements

Chemistry

Q2A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A and B, the…Chemical Kinetics
Q5[Ti(H₂O)₆]³⁺ absorbs light of wavelength 498 nm during a d - d transition. The octahedral splitting energy for the above complex is _ _ _ _ _ _ × 10⁻¹9 J…Coordination Compounds
Q8A 5.0 m mol dm⁻³ aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 cm⁻¹. The molar conductivity of this…Redox Reactions and Electrochemistry
Q11Sulphurous acid (H₂SO₃) has Ka₁ = 1.7 × 10⁻² and Ka₂ = 6.4 × 10⁻⁸. The pH of 0.588 M H₂SO₃ is _ _ _ _ _. (Round off to the Nearest Integer).Equilibrium
Q17In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The…Principles Related to Practical Chemistry
Q19Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is _ _ _ _ _ × 10²¹. (Round off to the…Solid State
Q20At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is ideal, the…Solutions
Q22When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, _ _ _ _ _ × 10⁻⁵ moles of lead sulphate precipitate out…Some Basic Concepts in Chemistry
Q23The number of orbitals with n = 5, m₁ = +2 is _ _ _ _ _ _. (Round off to the Nearest Integer).Atomic Structure
Q25At 25° C, 50 g of iron reacts with HCl to form FeCl₂. The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during…Chemical Thermodynamics
Q205The secondary structure of protein is stabilised by:Biomolecules
Q530Which of the following is least basic?Organic Compounds Containing Nitrogen
Q531Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and tertiary amines. The purpose of NaOH…Organic Compounds Containing Nitrogen
Q764Fex₂ and Fey₃ are known when x and y are:d- and f-Block Elements
Q824Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system. (Atomic numbers…d- and f-Block Elements
Q1066The green house gas/es is (are): (A) Carbon dioxide (B) Oxygen (C) Water vapour (D) Methane Choose the most appropriate answer from the options given below:Environmental Chemistry
Q1221The correct statements about H₂O₂ are: (A) used in the treatment of effluents. (B) used as both oxidising and reducing agents. (C) the two hydroxyl groups lie…Hydrogen
Q1390Which of the following reduction reaction CANNOT be carried out with coke?Isolation of Elements
Q1609Identify the elements X and Y using the ionisation energy values given below: Ionization energy (kJ/mol) 1 st 2 nd X 495 4563 Y 731 1450Classification of Elements and Periodicity in Properties
Q1653The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are:Classification of Elements and Periodicity in Properties
Q1718Which of the following polymer is used in the manufacture of wood laminates?Polymers
Q1730Match List - I with List - II: List - I Test/Reagents/Observation(s) List - II Species detected (a) Lassaigne's Test (i) Carbon (b) Cu(II) oxide (ii) Sulphur…Principles Related to Practical Chemistry
Q1798Statement I: Sodium hydride can be used as an oxidising agent. Statement II: The lone pair of electrons on nitrogen in pyridine makes it basic. Choose the…Redox Reactions and Electrochemistry
Q2040The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H₃PO₃ solution and 100 mL of 2 M H₃PO₂ solution, respectively, are:Some Basic Concepts in Chemistry
Q2255The INCORRECT statements below regarding colloidal solutions is:Surface Chemistry

Mathematics

Q26If the distance of the point (1, - 2, 3) from the plane x + 2y - 3z + 10 = 0 measured parallel to the line, (x - 1)/3 = (2 - y)/m = (z + 3)/1 is √(7/2), then…Three Dimensional Geometry
Q31Let n be a positive integer. Let A = Σ k = 0 ⁿ (- 1)^(k) ⁿ C k [ (1/2)^(k) + (3/4)^(k) + (7/8)^(k) + (15/16)^(k) + (31/32)^(k) ]. If 63A = 1 - 1/(2³⁰), then n…Binomial Theorem and Its Simple Applications
Q39For real numbers α, β, γ and δ, if ∫ ((x² - 1) + tan ⁻¹((x² + 1)/x))/((x⁴ + 3x² + 1) tan ⁻¹((x² + 1)/x))dx = α log e (tan ⁻¹((x² + 1)/x)) + β tan ⁻¹((γ (x² +…Integral Calculus
Q42Let f: R → R and g: R → R be defined as f(x) = \ x + a, x < 0 |x - 1|, x ≥ 0. and g(x) = \ x + 1, x < 0 (x - 1)² + b, x ≥ 0., where a, b are non-negative real…Limit, Continuity and Differentiability
Q44Let A = [ a₁ a₂ ] and B = [ b₁ b₂ ] be two 2 × 1 matrices with real entries such that A = XB, where X = 1/(3)[ 1 - 1 1 k ], and k R. If a₁² + a₂² = 2/3 (b ₁²…Matrices and Determinants
Q48In Δ ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of Δ ABC is 30 cm² and R and r are respectively the radii of…Properties of Triangle
Q49Let 1/16, a and b be in G.P. and 1/a, 1/b, 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to _ _ _ _ _ _.Sequence and Series
Q50S n (x) = loga¹/2x + loga¹/3x + loga¹/6x + loga¹/11x + loga¹/18x + loga¹/27x +...... up to n-terms, where a > 1. If S₂₄(x) = 1093 and S₁₂(2x) = 265, then…Sequence and Series
Q52Consider the statistics of two sets of observations as follows: | Size | Mean | Variance Observation I | 10 | 2 | 2 Observation II | n | 3 | 1 If the variance…Statistics and Probability
Q54Let c be a vector perpendicular to the vectors, a = i + j - k and b = i + 2 j + k. If c. (i + j + 3 k) = 8 then the value of c. (a × b) is equal to _ _ _ _ _.Vector Algebra
Q2497If the foot of the perpendicular from point (4, 3, 8) on the line L₁:(x - a)/l = (y - 2)/3 = (z - b)/4, l ≠ 0 is (3, 5, 7), then the shortest distance between…Three Dimensional Geometry
Q2584If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of the expression…Three Dimensional Geometry
Q2654The maximum value of f(x) = | sin ²x 1 + cos ²x cos 2x 1 + sin ²x cos ²x cos 2x sin ²x cos ²x sin 2x |,x R is:Limit, Continuity and Differentiability
Q2718Let f be a real valued function, defined on R - - 1, 1 and given by f(x) = 3 log e | (x - 1)/(x + 1) | - 2/(x - 1). Then in which of the following intervals…Limit, Continuity and Differentiability
Q3083Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2 2 and 2 5, respectively. Then the shortest…Coordinate Geometry
Q3259The least value of |z| where z is complex number which satisfies the inequality exp (((|z| + 3)(|z| - 1))/(||z| + 1|) log e 2) ≥ log 2 |5 7 + 9i|,i = √(- 1)…Complex Numbers and Quadratic Equations
Q3400Consider the integral I = ∫₀¹⁰ ([x]e^([x]))/(eˣ⁻¹)dx, where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to:Integral Calculus
Q3401Let P(x) = x² + bx + c be a quadratic polynomial with real coefficients such that ∫₀¹ P(x)dx = 1 and P(x) leaves remainder 5 when it is divided by (x - 2)…Integral Calculus
Q3528If y = y(x) is the solution of the differential equation dy/dx + (tan x) y = sin x, 0 ≤ x ≤ (π)/3, with y(0) = 0, then y((π)/4) equal to:Differential Equations
Q3607Let C₁ be the curve obtained by the solution of differential equation 2xydy/dx = y² - x²,x > 0. Let the curve C₂ be the solution of 2xy/(x² - y²) = dy/dx. If…Differential Equations
Q3780If the points of intersections of the ellipse (x²)/16 + (y²)/(b²) = 1 and the circle x² + y² = 4b, b > 4 lie on the curve y² = 3x², then b is equal to:Coordinate Geometry
Q4072Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy sin ⁻¹(3x/5) + sin ⁻¹(4x/5) =…Trigonometry
Q4144Let α R be such that the function f(x) = \ (cos ⁻¹(1 - x ²) sin ⁻¹(1 - x))/(x - x ³), x ≠ 0 α, x = 0. is continuous at x = 0, where x = x - [ x ] is the…Limit, Continuity and Differentiability
Q4201Let f: S → S where S = (0, ∞) be a twice differentiable function such that f(x + 1) = xf(x). If g: S → R be defined as g(x) = log e f(x), then the value of…Limit, Continuity and Differentiability
Q4746Let C be the locus of the mirror image of a point on the parabola y² = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1) is:Coordinate Geometry
Q4761Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let α be the number of triangles having…Permutations and Combinations
Q4912Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to:Statistics and Probability
Q5361Let A = 2, 3, 4, 5,....., 30 and ' ' be an equivalence relation on A × A, defined by (a, b) (c, d), if and only if ad = bc. Then the number of ordered pairs…Sets, Relations and Functions
Q5518Let A(- 1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A₁ and A₂ be the…Coordinate Geometry
Q5813Let a = i + 2 j - 3 k and b = 2 i - 3 j + 5 k. If r × a = b × r, r. (α i + 2 j + k) = 3 and r. (2 i + 5 j - α k) = - 1, α R, then the value of α + | r |² is…Vector Algebra