Loading…

Questions and solutions are free, always.

Practise

Practice
Revision queue
Revision planner
Take a test
Build a test

Browse

All topics
Blog
Notes & printables
Physics
Chemistry
Mathematics

Account

Your numbers
Study plan
Saved
Plus
Privacy
Terms
Delete account

Skip to content

JEE Main 2021 31 Aug Evening shift Question Paper with Solutions | JEE Arc

Past papers

Ctrl K

Practice
Revise
Tests
Topics
More
Dashboard Settings My progress Notes & printables Revision planner Study plan Saved questions Explore Plus

81days to JEE Main

Study

PracticePractice

Study planPlanPlus

Library

Past papersPapers

ProgressProgress

SettingsSettings

JEE Arc Plus₹49 a month. Mocks, plans, notes.→?GuestSign in to save progress

JEE Main 202131 Aug, Evening shift

Physics 24Chemistry 18Mathematics 29

Physics

Q49A parallel plate capacitor of capacitance 200 μ F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the…Electrostatics
Q50A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz…Communication Systems
Q51A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it. Now, when the current is doubled, the amount of thermal energy…Current Electricity
Q60A sample of gas with γ = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm³ to 300 cm³. If the initial pressure is 200…Thermodynamics
Q63A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 10³ cm³. If the core material is replaced by another material…Magnetic Effects of Current and Magnetism
Q69The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of…Units and Measurements
Q71In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of slits. Distance between fourth bright…Optics
Q6568Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the…Dual Nature of Matter and Radiation
Q6602A free electron of 2.6 eV energy collides with a H⁺ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released…Dual Nature of Matter and Radiation
Q6782The magnetic field vector of an electromagnetic wave is given by B = B₀(i + j)/(2) cos (kz - ω t); where i, j represents unit vector along x and y-axis…Electromagnetic Waves
Q6877Statement - I: To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel…Electronic Devices
Q6983Choose the incorrect statement: (1) The electric lines of force entering into a Gaussian surface provide negative flux. (2) A charge 'q' is placed at the…Electrostatics
Q7144If R E be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is…Gravitation
Q7344Two thin metallic spherical shells of radii r₁ and r₂ (r₁ < r₂) are placed with their centres coinciding. A material of thermal conductivity K is filled in…Properties of Solids and Liquids
Q7393A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be:-Thermodynamics
Q7542Statement: 1 If three forces F ₁, F ₂ and F ₃ are represented by three sides of a triangle and F ₁ + F ₂ = - F ₃, then these three forces are concurrent…Laws of Motion
Q7685A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is: (Assume that the current is…Magnetic Effects of Current and Magnetism
Q7945Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 10³ kg. The inner and outer radii of each column are 50 cm and…Properties of Solids and Liquids
Q8103A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres…Rotational Motion
Q8164For a body executing S.H.M.: (1) Potential energy is always equal to its K.E. (2) Average potential and kinetic energy over any given time interval are always…Oscillations and Waves
Q8206A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has…Oscillations and Waves
Q8253If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be:Units and Measurements
Q8379Statement I: Two forces (P + Q) and (P - Q) where P Q, when act at an angle θ ₁ to each other, the magnitude of their resultant is √(3(P² + Q²)), when they…Laws of Motion
Q8585A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1: 2. If the smaller part moves at 60…Work, Energy and Power

Chemistry

Q2According to molecular orbital theory, the number of unpaired electron(s) in O₂²⁻ is:Chemical Bonding and Molecular Structure
Q3For the reaction A → B, the rate constant k(in s⁻¹) is given by log ₁₀k = 20.35 - ((2.47 × 10³))/T The energy of activation in kJ mol⁻¹ is _ _ _ _ _ _…Chemical Kinetics
Q6The value of magnetic quantum number of the outermost electron of Zn⁺ ion is _ _ _ _ _ _ _.d- and f-Block Elements
Q10The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M NaOH is x × 10⁻⁴. The value of x is _ _ _ _ _ _. (Nearest integer) [log 2.5 = 0.3979]Equilibrium
Q11In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anode mud is _ _ _ _ _ _ _ Pb, Sb, Se, Te…Isolation of Elements
Q14The transformation occurring in Duma's method is given below: C₂H₇N + (2x + y/2)CuO → xC O₂ + y/2H₂O + z/2N₂ + (2x + y/2)Cu The value of y is _ _ _ _ _ _ _…Principles Related to Practical Chemistry
Q16The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the octahedral sites in A x B. The value…Solid State
Q171.22 g of an organic acid is separately dissolved in 100 g of benzene (K b = 2.6 K kg mol⁻¹) and 100 g of acetone (K b = 1.7 K kg mol⁻¹). The acid is known to…Solutions
Q18Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is dissolved in 500 mL of water. Neglecting the change in volume, the…Some Basic Concepts in Chemistry
Q208Which of the following is not an example of fibrous protein?Biomolecules
Q737Spin only magnetic moment in BM of [Fe(CO)₄(C₂O₄)]⁺ is:Coordination Compounds
Q826The Eu²⁺ ion is a strong reducing agent in spite of its ground state electronic configuration (outermost): [Atomic number of Eu = 63]d- and f-Block Elements
Q946Match List - I with List - II List - I (Parmeter) List - II (Unit) (a) Cell constant (i) S c m² mo l⁻¹ (b) Molar conductivity (ii) Dimensionless (c)…Redox Reactions and Electrochemistry
Q1034The deposition of X and Y on ground surfaces is referred as wet and dry depositions, respectively. X and Y are:Environmental Chemistry
Q1253Which one of the following statements is incorrect?Hydrogen
Q1655Match List - I with List - II: List - I (Metal Ion) List - II (Group of Qualitative analysis) (a) M n²⁺ (i) Group - III (b) A s³⁺ (ii) Group - IIA (c) C u²⁺…Classification of Elements and Periodicity in Properties
Q1694Which among the following is not a polyester?Polymers
Q1856Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Lithium salts are hydrated. Reason…S Block Elements

Mathematics

Q21Suppose, the line (x - 2)/(α) = (y - 2)/(- 5) = (z + 2)/2 lies on the plane x + 3y - 2z + β = 0. Then (α + β) is equal to _ _ _ _.Three Dimensional Geometry
Q22Let f(x) be a cubic polynomial with f(1) = - 10, f(- 1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = - 1. Then f(3) is equal to _…Limit, Continuity and Differentiability
Q23If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3/2 and the curve y = 1 + 4x - x², then 12 m is equal to _ _ _ _ _ _ _.Integral Calculus
Q24If the coefficient of a⁷b⁸ in the expansion of (a + 2b + 4ab)¹⁰ is K.2¹⁶, then K is equal to _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q25Let B be the centre of the circle x² + y² - 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8…Coordinate Geometry
Q33If ∫ (sin x)/(sin ³x + cos ³x)dx = α log e |1 + tan x| + β log e |1 - tan x + tan ²x| + γ tan ⁻¹((2 tan x - 1)/(3)) + C, when C is constant of integration…Integral Calculus
Q38The number of elements in the set \ A = (a b 0 d):a,b,d - 1,0,1 and (I - A)³ = I - A³ \, where I is 2 × 2 identity matrix, is:Matrices and Determinants
Q40A tangent line L is drawn at the point (2, - 4) on the parabola y² = 8x. If the line L is also tangent to the circle x² + y² = a, then 'a' is equal to _ _ _ _…Coordinate Geometry
Q44The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is _ _ _ _ _ _.Sequence and Series
Q45If S = 7/5 + 9/(5²) + 13/(5³) + 19/(5⁴) +...., then 160 S is equal to _ _ _ _.Sequence and Series
Q2439The distance of the point (- 1, 2, - 2) from the line of intersection of the planes 2x + 3y + 2z = 0 and x - 2y + z = 0 is:Three Dimensional Geometry
Q3260If z is a complex number such that (z - i)/(z - 1) is purely imaginary, then the minimum value of | z - (3 + 3i) | is:Complex Numbers and Quadratic Equations
Q3421If [x] is the greatest integer ≤ x, then π ²∫₀² (sin (π x)/2)(x - [x])^([x])dx is equal to:Integral Calculus
Q3537If dy/dx = 2ˣy + 2^(y).2ˣ 2ˣ + 2^(x + y) log e 2, y(0) = 0, then for y = 1, the value of x lies in the interval:Differential Equations
Q3618If ydy/dx = x[ (y²)/(x²) + (φ ((y²)/(x²)))/(φ '((y²)/(x²))) ], x > 0, φ > 0, and y(1) = - 1, then φ ((y²)/4) is equal to:Differential Equations
Q3724The locus of mid-points of the line segments joining (- 3, - 5) and the points on the ellipse (x²)/4 + (y²)/9 = 1 is:Coordinate Geometry
Q3785An angle of intersection of the curves, (x²)/(a²) + (y²)/(b²) = 1 and x² + y² = ab, a > b, is:Coordinate Geometry
Q3868Let f: N → N be a function such that f(m + n) = f(m) + f(n) for every m, n N. If f(6) = 18, then f(2). f(3) is equal to:Sets, Relations and Functions
Q4064The domain of the function f(x) = sin ⁻¹((3x² + x - 1)/((x - 1)²)) + cos ⁻¹((x - 1)/(x + 1)) is:Trigonometry
Q4206Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, thenLimit, Continuity and Differentiability
Q4288If α = lim x → (π)/4 (tan ³x - tan x)/(cos (x + (π)/4)) and β = lim x → 0 (cos x)^(cot x) are the roots of the equation, ax² + bx - 4 = 0, then the ordered…Limit, Continuity and Differentiability
Q4357Negation of the statement (p r) ⇒ (q r) is:Mathematical Reasoning
Q4600If α + β + γ = 2 π, then the system of equations x + (cos γ)y + (cos β)z = 0 (cos γ)x + y + (cos α)z = 0 (cos β)x + (cos α)y + z = 0 has:Matrices and Determinants
Q4986Let S = 1, 2, 3, 4, 5, 6. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is:Statistics and Probability
Q5047The sum of the roots of the equation x + 1 - 2 log ₂(3 + 2ˣ) + 2 log ₄(10 - 2⁻ˣ) = 0, is:Complex Numbers and Quadratic Equations
Q5222Let a₁, a₂, a₃,..... be an A.P. If (a₁ + a₂ +.... + a₁₀)/(a₁ + a₂ +.... + a p) = 100/(p²), p ≠ 10, then (a₁₁)/(a₁₀) is equal to:Sequence and Series
Q5469The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is:Statistics and Probability
Q5519Let A be the set of all points (α, β) such that the area of triangle formed by the points (5, 6), (3, 2) and (α, β) is 12 square units. Then the least…Coordinate Geometry
Q5736Let a, b, c three vectors mutually perpendicular to each other and have same magnitude. If a vector r satisfies. a × (r - b) × a + b × (r - c) × b + c × (r…Vector Algebra