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

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JEE Main 202131 Aug, Morning shift

Physics 22Chemistry 18Mathematics 30

Physics

Q52If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS…Communication Systems
Q53A square shaped wire with resistance of each side 3 Ω is bent to form a complete circle. The resistance between two diametrically opposite points of the…Current Electricity
Q57The electric field in an electromagnetic wave is given by E = (50 NC⁻¹) sin ω (t - x/c) The energy contained in a cylinder of volume V is 5.5 × 10⁻¹2 J. The…Electromagnetic Waves
Q61A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10 ms⁻² parallel to the plane upward. A bob is suspended by a string from…Laws of Motion
Q65When a rubber ball is taken to a depth of _ _ _ _ _ m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 × 10⁸ Nm⁻², Density of sea…Properties of Solids and Liquids
Q67A particle of mass 1 kg is hanging from a spring of force constant 100 Nm⁻¹. The mass is pulled slightly downward and released so that it executes free simple…Oscillations and Waves
Q70A wire having a linear mass density 9.0 × 10⁻⁴ kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500…Oscillations and Waves
Q71A block moving horizontally on a smooth surface with a speed of 40 ms⁻¹ splits into two equal parts. If one of the parts moves at 60 ms⁻¹ in the same…Work, Energy and Power
Q5900In an ac circuit, an inductor, a capacitor and a resistor are connected in series with X L = R = X C. Impedance of this circuit is:Electromagnetic Induction and Alternating Currents
Q6225A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles θ ₁ and θ ₂ with respect…Rotational Motion
Q6469Consider a galvanometer shunted with 5 Ω resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?Current Electricity
Q6567A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option:Dual Nature of Matter and Radiation
Q6688A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their…Electromagnetic Induction and Alternating Currents
Q7048An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?Optics
Q7200The masses and radii of the earth and moon are (M₁, R₁) and (M₂, R₂) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity…Gravitation
Q7392For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation dp/dv = - ap. If p = p₀ at v =0 is the given boundary…Thermodynamics
Q7684A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a…Magnetic Effects of Current and Magnetism
Q7786A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter…Kinematics
Q7944A uniform heavy rod of weight 10 kg ms⁻², cross-sectional area 100 cm² and length 20 cm is hanging from a fixed support. Young modulus of the material of the…Properties of Solids and Liquids
Q8058Angular momentum of a single particle moving with constant speed along circular path:Rotational Motion
Q8251Match List - I with List - II. List - I List - II (a) Torque (i) MLT ⁻¹ (b) Impulse (ii) MT ⁻² (c) Tension (iii) ML ² T ⁻² (d) Surface Tension (iv) MLT ⁻²…Units and Measurements
Q8252Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g =…Units and Measurements

Chemistry

Q4The number of hydrogen bonded water molecule(s) associated with stoichiometry CuSO₄.5H₂O is _ _ _ _ _ _.Chemical Bonding and Molecular Structure
Q5For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is _ _ _ _ _ _. (Integer answer)Chemical Kinetics
Q6The total number of reagents from those given blow, that can convert nitrobenzene into aniline is _ _ _ _ _ _. (Integer answer) I. Sn - HCl II. Sn - NH₄OH…Organic Compounds Containing Nitrogen
Q10Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Treatment of bromine water with…Organic Compounds Containing Oxygen
Q10Consider the following cell reaction: C d (s) + H g₂ S O 4(s) + 9/5H₂O (l) CdS O₄.9/5H₂O (s) + 2H g (l) The value of E cell ⁰ is 4.315 V at 25° C. If Δ H° =…Redox Reactions and Electrochemistry
Q13A₃B₂ is a sparingly soluble salt of molar mass M (g mol⁻¹) and solubility x g L⁻¹. The solubility product satisfies K sp = a (x/M)⁵. The value of a is _ _ _ _…Equilibrium
Q18The molarity of the solution prepared by dissolving 6.3 g of oxalic acid (H₂C₂O₄.2H₂O) in 250 mL of water in mol L⁻¹ is x × 10⁻². The value of x is _ _ _ _ _…Some Basic Concepts in Chemistry
Q19Ge(Z = 32) in its ground state electronic configuration has x completely filled orbitals with m l = 0. The value of x is _ _ _ _ _ _.Atomic Structure
Q130Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion (A): A simple distillation can be used to…Some Basic Principles of Organic Chemistry
Q175Which one of the following compounds contains β -C₁-C₄ glycosidic linkage?Biomolecules
Q594The denticity of an organic ligand, biuret is:Coordination Compounds
Q772In the structure of the dichromate ion, there is a:d- and f-Block Elements
Q825Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature? (Given Z for Nd = 60, Yb = 70, La = 57, Ce = 58)d- and f-Block Elements
Q1094BOD values (in ppm) for clean water (A) and polluted water (B) are expected respectively:Environmental Chemistry
Q1252Given below are two statements: Statement I: The process of producing syn-gas is called gasification of coal. Statement II: The composition of syn-gas is CO +…Hydrogen
Q1394Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Aluminium is extracted from bauxite…Isolation of Elements
Q1576Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Metallic character decreases and…Classification of Elements and Periodicity in Properties
Q1980Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression?Solutions

Mathematics

Q21The square of the distance of the point of intersection of the line (x - 1)/2 = (y - 2)/3 = (z + 1)/6 and the plane 2x - y + z = 6 from the point (- 1, - 1…Three Dimensional Geometry
Q23If 'R' is the least value of 'a' such that the function f(x) = x² + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function…Limit, Continuity and Differentiability
Q24If ((3⁶)/(4⁴))k is the term, independent of x, in the binomial expansion of (x/4 - 12/(x²))¹², then k is equal to _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q25If the variable line 3x + 4y = α lies between the two circles (x - 1)² + (y - 1)² = 1 and (x - 9)² + (y - 1)² = 4, without intercepting a chord on either…Coordinate Geometry
Q26A point z moves in the complex plane such that arg ((z - 2)/(z + 2)) = (π)/4, then the minimum value of | z - 9 2 - 2i |² is equal to _ _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q28Let [t] denote the greatest integer ≤ t. Then the value of 8.∫ - 1/2 ¹ ([2x] + |x|)dx is _ _ _ _ _ _.Integral Calculus
Q29If xφ (x) = ∫₅ˣ (3t² - 2φ '(t))dt, x > - 2, and φ (0) = 4, then φ (2) is _ _ _ _ _.Integral Calculus
Q41The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together…Permutations and Combinations
Q42An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit…Statistics and Probability
Q47The mean of 10 numbers 7 × 8, 10 × 10, 13 × 12, 16 × 14,....... is _ _ _ _ _ _.Statistics and Probability
Q2438Let the equation of the plane, that passes through the point (1, 4, - 3) and contains the line of intersection of the planes 3x - 2y + 4z - 7 = 0 and x + 5y…Three Dimensional Geometry
Q2661The number of real roots of the equation e⁴ˣ + 2e³ˣ - eˣ - 6 = 0 is:Limit, Continuity and Differentiability
Q3313Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If ∫₀ˣ √(1 - (f'(t))²) dt = ∫₀ˣ f(t)dt, 0 ≤ x ≤ 1 and f(0) = 0, then lim x → 0…Integral Calculus
Q3617If dy/dx = (2^(x + y) - 2ˣ)/(2^(y)), y(0) = 1, then y(1) is equal to:Differential Equations
Q3784The line 12x cos θ + 5y sin θ = 60 is tangent to which of the following curves?Coordinate Geometry
Q3927A vertical pole fixed to the horizontal ground is divided in the ratio 3: 7 by a mark on it with lower part shorter than the upper part. If the two parts…Height and Distance
Q4032The integral ∫ 1/(4 (x - 1)³(x + 2)⁵) dx is equal to: (where C is a constant of integration)Integral Calculus
Q4150If the function f(x) = \ 1/x log e ((1 + x/a)/(1 - x/b)), x < 0 k, x = 0 (cos ²x - sin ²x - 1)/(√(x² + 1) - 1), x > 0. is continuous at x = 0, then 1/a + 1/b…Limit, Continuity and Differentiability
Q4205The function f(x) = | x² - 2x - 3 |. e^(| 9x² - 12x + 4 |) is not differentiable at exactly:Limit, Continuity and Differentiability
Q4287lim x → 0 (sin ²(π cos ⁴x))/(x⁴) is equal to:Limit, Continuity and Differentiability
Q4356Let, ▢, be such that the Boolean expression (p q) ⇒ (p ▢ q) is a tautology. Then:Mathematical Reasoning
Q4468If a r = cos (2rπ)/9 + i sin (2rπ)/9, r = 1, 2, 3,....., i = √(- 1), then the determinant | a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈ a₉ | is equal to:Matrices and Determinants
Q4599If the following system of linear equations 2x + y + z = 5 x - y + z = 3 x + y + az = b has no solution, then:Matrices and Determinants
Q4728The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is:Coordinate Geometry
Q5153cosec18° is a root of the equation:Complex Numbers and Quadratic Equations
Q5263Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic…Sequence and Series
Q5328The sum of 10 terms of the series 3/(1² × 2²) + 5/(2² × 3²) + 7/(3² × 4²) +.... is:Sequence and Series
Q5379Which of the following is not correct for relation R on the set of real numbers ?Sets, Relations and Functions
Q5553If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α - y sec α = k cot 2 α and x sin α + y cos α = k sin2 α respectively…Coordinate Geometry
Q5776Let a and b be two vectors such that | 2 a + 3 b | = | 3 a + b | and the angle between a and b is 60°. If 1/8 a is a unit vector, then | b | is equal to:Vector Algebra