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JEE Main 2021 20 Jul Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202120 Jul, Morning shift

Physics 21Chemistry 23Mathematics 30

Physics

Q56In an LCR series circuit, an inductor 30 mH and a resistor 1 Ω are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for…Electromagnetic Induction and Alternating Currents
Q59A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod…Rotational Motion
Q61A carrier wave V c (t) = 160 sin(2 π × 10⁶t) volts is made to vary between V m ax = 200 V and V m in = 120 V by a message signal V m (t) = A m sin(2 π × 10³t)…Communication Systems
Q65An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed…Optics
Q72A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't₁'. When it rolls down the plane…Rotational Motion
Q74The amplitude of wave disturbance propagating in the positive x-direction is given by y = 1/((1 + x)²) at time t = 0 and y = 1/(1 + (x - 2)²) at t = 1 s…Oscillations and Waves
Q75The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the…Oscillations and Waves
Q5893AC voltage V(t) = 20 sin ω t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m². The…Electromagnetic Induction and Alternating Currents
Q6050A nucleus of mass M emits γ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is: [Take 'c' as the speed of electromagnetic wave]Atoms and Nuclei
Q6108A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after…Atoms and Nuclei
Q6272The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is _ _ _ _ _ _ × 10³…Kinematics
Q6400A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m². At every point the direction of current density is at an angle of…Current Electricity
Q6639The radiation corresponding to 3 → 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a…Dual Nature of Matter and Radiation
Q6923A certain charge Q is divided into two parts q and (Q - q). How should the charges Q and q be divided so that q and (Q - q) placed at a certain distance apart…Electrostatics
Q7332The entropy of any system is given by S = α ²β ln [ μ kR J β ² + 3 ] where α and β are the constants. μ, J, k and R are no. of moles, mechanical equivalent of…Thermodynamics
Q7384Consider a mixture of gas molecule of types A, B and C having masses m A < m B < m C. The ratio of their root mean square speeds at normal temperature and…Kinetic Theory of Gases
Q7459The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0° C to 50° C when no work is done is _ _ _ _ _ _. (R is the…Thermodynamics
Q7757A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r d and r_ α be their respective radii of…Magnetic Effects of Current and Magnetism
Q7821A butterfly is flying with a velocity 4 2 m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the…Kinematics
Q7941The value of tension in a long thin metal wire has been changed from T₁ to T₂. The lengths of the metal wire at two different values of tension T₁ and T₂ are…Properties of Solids and Liquids
Q8373If A and B are two vectors satisfying the relation A. B = | A × B |. Then the value of | A - B | will be:Kinematics

Chemistry

Q2To synthesize 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate _ _ _ _ _ e quivalents of CH₃MgBr Reagent will be required. (Integer value)Organic Compounds Containing Oxygen
Q4The number of lone pairs of electrons on the central I atom in I ₃⁻ⁱs _ _ _ _ _ _.Chemical Bonding and Molecular Structure
Q52SO₂(g) + O₂(g) 2SO₃(g) In an equilibrium mixture, the partial pressures are PSO₃ = 43 kPa; PO₂ = 530 Pa and PSO₂ = 45 kPa. The equilibrium constant K P = _ _…Equilibrium
Q6The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation, 10% of the virus is inactivated…Chemical Kinetics
Q8The number of nitrogen atoms in a semicarbazone molecule of acetone is _ _ _ _ _ _ _.Organic Compounds Containing Nitrogen
Q11The spin-only magnetic moment value for the complex [Co(CN)₆]⁴ - is _ _ _ _ _ BM. [At. no. of Co = 27]Coordination Compounds
Q20At 20° C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The mole fraction of benzene in the vapour phase at 20° above an…Solutions
Q21250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl. The number of unreacted HCl molecules in the solution after complete reaction is _ _ _ _ _ _ × 10²¹…Some Basic Concepts in Chemistry
Q22An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol⁻¹) needed to meet this energy requirement is _ _ _ _ _…Some Basic Concepts in Chemistry
Q23The Azimuthal quantum number for the valence electrons of Ga⁺ ion is _ _ _ _ _ _. (Atomic number of Ga = 31)Atomic Structure
Q170Identify the incorrect statement from the followingBiomolecules
Q533Compound A is converted to B on reaction with CHCl₃ and KOH. The compound B is toxic and can be decomposed by C. A, B and C respectively are:Organic Compounds Containing Nitrogen
Q628The correct order of intensity of colors of the compounds is:Coordination Compounds
Q731According to the valence bond theory the hybridization of central metal atom is dsp² for which one of the following compounds?Coordination Compounds
Q1223Given below are two statements: One is labelled as Assertion A and other is labelled as Reason R. Assertion A: The dihedral angles in H₂O₂ in gaseous phase is…Hydrogen
Q1441The metal that can be purified economically by fractional distillation method is:Isolation of Elements
Q1529The species given below that does NOT show disproportionation reaction is:p-Block Elements
Q1690Orlon fibres are made up of:Polymers
Q1769An inorganic Compound 'X' on treatment with concentrated H₂SO₄ produces brown fumes and gives dark brown ring with FeSO₄ in presence of concentrated H₂SO₄…Principles Related to Practical Chemistry
Q1825A s-block element (M) reacts with oxygen to form an oxide of the formula MO₂. The oxide is pale yellow in colour and paramagnetic. The element (M) is:S Block Elements
Q1886The set in which compounds have different nature is:S Block Elements
Q1947Given below are two statements. One is labelled as Assertion A nd the other is labelled as Reason R. Assertion A: Sharp glass edge becomes smooth on heating…Solid State
Q2259The conditions given below are in the context of observing Tyndall effect in colloidal solutions: (A) The diameter of the colloidal particles is comparable to…Surface Chemistry

Mathematics

Q25Let P be a plane passing through the points (1, 0, 1), (1, - 2, 1) and (0, 1, - 2). Let a vector a = α i + β j + γ k be such that a is parallel to the plane…Three Dimensional Geometry
Q28Let T be the tangent to the ellipse E: x² + 4y² = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = 5…Integral Calculus
Q29The number of rational terms in the binomial expansion of (4^(1/4) + 5^(1/6))¹²⁰ is _ _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q39If the value of lim x → 0 (2 - cos x√(cos 2x))^(((x + 2)/(x²))) is equal to e^(a), then a is equal to _ _ _ _ _.Limit, Continuity and Differentiability
Q41Let a, b, c, d in arithmetic progression with common difference λ. If | x + a - c x + b x + a x - 1 x + c x + b x - b + d x + d x + c | = 2, then value of λ ²…Matrices and Determinants
Q42Let A = (1 - 1 0 0 1 - 1 0 0 1) and B = 7A²⁰ - 20A⁷ + 2I, where I is an identity matrix of order 3 × 3. If B = [b i j], then b₁₃is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q45Let y = mx + c, m > 0 be the focal chord of y² = - 64x, which is tangent to (x + 10)² + y² = 4. Then, the value of 4 2 (m + c) is equal to _ _ _ _ _ _ _.Coordinate Geometry
Q46There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be…Permutations and Combinations
Q53Let a, b, c be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector a + b + c. Then 36cos²2 θ is…Vector Algebra
Q54If the shortest distance between the lines r₁ = α i + 2 j + 2 k + λ (i - 2 j + 2 k), λ R, α > 0 and r₂ = - 4 i - k + μ (3 i - 2 j - 2 k), μ R is 9, then α is…Vector Algebra
Q2655Let A = [a ij ] be a 3 × 3 matrix, where a ij = \ 1, if i = j - x, if | i - j | = 1 2x + 1, otherwise.. Let a function f: R → R be defined as f(x) = det(A)…Limit, Continuity and Differentiability
Q2656Let 'a' be a real number such that the function f(x) = ax² + 6x - 15, x R is increasing in (- ∞,3/4) and decreasing in (3/4,∞). Then the function g(x) = ax²…Limit, Continuity and Differentiability
Q2996The coefficient of x²⁵⁶ in the expansion of (1 - x)¹⁰¹ (x² + x + 1)¹⁰⁰ is:Binomial Theorem and Its Simple Applications
Q3213If z and ω are two complex numbers such that | zω | = 1 and arg (z) - arg (ω) = (3π)/2, then arg ((1 - 2 z ω)/(1 + 3 z ω)) is: (Here arg(z) denotes the…Complex Numbers and Quadratic Equations
Q3405Let a be a positive real number such that ∫₀^(a) e^(x - [x]) dx = 10e - 9 where [ x ] is the greatest integer less than or equal to x. Then a is equal to:Integral Calculus
Q3406The value of the integral ∫₋₁¹ log e (√(1 - x) + √(1 + x))dx is equal to:Integral Calculus
Q3609Let y = y(x) be the solution of the differential equation x tan (y/x)dy = (y tan (y/x) - x)dx, - 1 ≤ x ≤ 1, y(1/2) = (π)/6. Then the area of the region…Differential Equations
Q3610Let y = y(x) be the solution of the differential equation eˣ√(1 - y²) dx + (y/x)dy = 0, y(1) = - 1. Then the value of (y(3))² is equal to:Differential Equations
Q3844Let [ x ] denote the greatest integer ≤ x, where x R. If the domain of the real valued function f(x) = √((| [x] | - 2)/(| [x] | - 3)) is (- ∞, a) ] [b, c) [4…Sets, Relations and Functions
Q4061The number of real roots of the equation tan ⁻¹√(x(x + 1)) + sin ⁻¹√(x² + x + 1) = (π)/4 is:Trigonometry
Q4146Let a function f: R → R be defined as f(x) = \ sin x - eˣ if x ≤ 0 a + [ - x] if 0 < x < 1 2x - b if x ≥ 1. where [ x ] is the greatest integer less than or…Limit, Continuity and Differentiability
Q4348The Boolean expression (p q) ⇒ (q p) is equivalent to:Mathematical Reasoning
Q4646Let A = [ 2 3 a 0 ], a R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all…Matrices and Determinants
Q4710Let the tangent to the parabola S: y² = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in…Coordinate Geometry
Q4915The probability of selecting integers a [ - 5, 30] such that x² + 2(a + 4)x - 5a + 64 > 0, for all x R, is:Statistics and Probability
Q4983Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position…Statistics and Probability
Q5042If in a triangle ABC, AB = 5 units, B = cos ⁻¹(3/5) and radius of circumcircle of Δ ABC is 5 units, then the area (in sq. units) of Δ ABC is:Properties of Triangle
Q5151If α and β are the distinct roots of the equation x² + (3)^(1/4)x + 3^(1/2) = 0, then the value of α ⁹⁶(α ¹² - 1) + β ⁹⁶(β ¹² - 1) is equal to:Complex Numbers and Quadratic Equations
Q5463The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:Statistics and Probability
Q5730Let a = 2 i + j - 2 k and b = i + j. If c is a vector such that a. c = | c |,| c - a | = 2 2 and the angle between (a × b) and c is (π)/6, then the value of |…Vector Algebra