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JEE Main 2021 27 Jul Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202127 Jul, Morning shift

Physics 18Chemistry 22Mathematics 30

Physics

Q55In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 A^(o). If the speed of electron is 2.2 × 16⁶ m/s, then the…Atoms and Nuclei
Q57A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 μ F is first charged and later connected with resistor 'R'…Atoms and Nuclei
Q59The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulated by a 7.7…Communication Systems
Q60A particle of mass 9.1 × 10⁻³1 kg travels in a medium with a speed of 10⁶ m/s and a photon of a radiation of linear momentum 10⁻²7 kg m/s travels in vacuum…Dual Nature of Matter and Radiation
Q62A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop across a resistor of 1000 Ω in…Electronic Devices
Q65In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 × 10⁻² A/m² and moment of inertia 5 × 10⁻⁶ kg m². If it performs 10 complete…Magnetic Effects of Current and Magnetism
Q68A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10⁻⁶ m² stretched by an amount 0.04 m. The velocity of the…Properties of Solids and Liquids
Q5897A 0.07 H inductor and a 12 Ω resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between…Electromagnetic Induction and Alternating Currents
Q6111If 'f' denotes the ratio of the number of nuclei decayed (N d) to the number of nuclei at t = 0 (N₀) then for a collection of radioactive nuclei, the rate of…Atoms and Nuclei
Q6145Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled…Electrostatics
Q6779The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given μ r = 1)Electromagnetic Waves
Q6924Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation…Electrostatics
Q7386The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 × 10⁻⁹ J per molecules is:Thermodynamics
Q7863A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching h/3 in both the…Kinematics
Q7973A body takes 4 min. to cool from 61° C to 59° C. If the temperature of the surroundings is 30° C, the time taken by the body to cool from 51° C to 49° C is:Properties of Solids and Liquids
Q8162A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is 3E/4 then its displacement…Oscillations and Waves
Q8336Assertion A: If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total…Experimental Skills
Q8438In Young's double slit experiment, if the source of light changes from orange to blue then:Optics

Chemistry

Q3The difference between bond orders of CO and NO ^ is x/2 where x = _ _ _ _ _ _ _. (Round off to the Nearest Integer)Chemical Bonding and Molecular Structure
Q4PCl₅ PCl₃ + Cl₂ K c = 1.844 3.0 moles of PCl₅ is introduced in a 1 L closed reaction vessel at 380 K. The number of moles of PCl₅ at equilibrium is _ _ _ _ _…Equilibrium
Q6In gaseous triethyl amine the " - C - N - C - " bond angle is _ _ _ _ d egree.Organic Compounds Containing Nitrogen
Q9The number of geometrical isomers possible in triamminetrinitrocobalt (III) is X and in trioxalatochromate (III) is Y. Then the value of X + Y is _ _ _ _ _ _…Coordination Compounds
Q11The conductivity of a weak acid HA of concentration 0.001 mol L⁻¹ is 2.0 × 10⁻⁵ S cm⁻¹. If Λ m ^(o) (HA) = 190 S cm² mol⁻¹, the ionization constant (K a) of…Redox Reactions and Electrochemistry
Q16An organic compound is subjected to chlorination to get compound A using 5.0 g of chlorine. When 0.5 g of compound A is reacted with AgNO₃ [Carius Method]…Principles Related to Practical Chemistry
Q201.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure of 2.42 × 10⁻³ bar. The molar mass of the biopolymer is _ _ _ _ _ _ _…Solutions
Q21The density of NaOH solution is 1.2 g cm⁻³. The molality of this solution is _ _ _ _ _ _ m. (Round off to the Nearest Integer) [Use: Atomic mass: Na: 23.0 u…Some Basic Concepts in Chemistry
Q23For water at 100° C and 1 bar, Δ v ap H - Δ v ap U = _ _ _ _ _ _ _ × 10² J mol⁻¹. (Round off to the Nearest Integer) [Use: R = 8.31 J mol⁻¹ K⁻¹] [Assume…Chemical Thermodynamics
Q105Staggered and eclipsed conformers of ethane are:Some Basic Principles of Organic Chemistry
Q171Which one among the following chemical tests is used to distinguish monosaccharide from disaccharide?Biomolecules
Q501For a reaction of order n, the unit of the rate constant is:Chemical Kinetics
Q540Given below are two statements: Statement I: Aniline is less basic than acetamide. Statement II: In aniline, the lone pair of electrons on nitrogen atom is…Organic Compounds Containing Nitrogen
Q735The type of hybridisation and magnetic property of the complex [MnCl₆]³ -, respectively, are:Coordination Compounds
Q1092Which one of the following statements is NOT correct?Environmental Chemistry
Q1180Presence of which reagent will affect the reversibility of the following reaction, and change it to a irreversible reaction: CH₄ + I₂ 0pt _ Re versible ^(hv)…Hydrocarbons
Q1369The statement is incorrect about Ellingham diagram isIsolation of Elements
Q1636Match List - I with List - II: List - I List - II (a) NaOH (i) Acidic (b) Be (OH)₂ (ii) Basic (c) Ca (OH)₂ (iii) Amphoteric (d) B (OH)₃ (e) Al (OH)₃ Choose…Classification of Elements and Periodicity in Properties
Q1809The oxidation states of 'P' in H₄P₂O₇, H₄P₂O₅ and H₄P₂O₆, respectively, are:Redox Reactions and Electrochemistry
Q1855Given below are two statements: One is labelled as Assertion A and the other labelled as Reason R. Assertion A: Lithium halides are some what covalent in…S Block Elements
Q1929The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, α = 90°, β = 120°, γ = 90°. The crystal system of the substance is:Solid State
Q2217Given below are two statements: Statement I: Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom. Statement II: Bohr's model…Atomic Structure

Mathematics

Q24Let a plane P pass through the point (3, 7, - 7) and contain the line, (x - 2)/(- 3) = (y - 3)/2 = (z + 2)/1. If distance of the plane P from the origin is d…Three Dimensional Geometry
Q33Let F:[3,5] → R be a twice differentiable function on (3, 5) such that F(x) = e⁻ˣ∫₃ˣ (3t² + 2t + 4F'(t))dt. If F'(4) = (α e^β - 224)/((e^β - 4)²), then α + β…Integral Calculus
Q35Let the domain of the function f(x) = log ₄(log ₅(log ₃(18x - x² - 77))) be (a, b). Then the value of the integral ∫ a ^(b) (sin ³x)/((sin ³x + sin ³(a + b…Integral Calculus
Q37If y = y(x),y [ 0,(π)/2) is the solution of the differential equation sec ydy/dx - sin (x + y) - sin (x - y) = 0, with y(0) = 0, then 5y'((π)/2) is equal to _…Differential Equations
Q39Let S = 1, 2, 3, 4, 5, 6, 7. Then the number of possible functions f: S → S such that f(m. n) = f(m). f(n) for every m, n S and m. n S is equal to _ _ _ _ _ _…Sets, Relations and Functions
Q41Let f:[0,3] → R be defined by f(x) = min x - [x],1 + [x] - x where [x] is the greatest integer less than or equal to x. Let P denote the set containing all x…Limit, Continuity and Differentiability
Q44Let f(x) = | sin ²x - 2 + cos ²x cos 2x 2 + sin ²x cos ²x cos 2x sin ²x cos ²x 1 + cos 2x |,x [0,π ]. Then the maximum value of f(x) is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q46For real numbers α and β, consider the following system of linear equations: x + y - z = 2, x + 2y + α z = 1, 2x - y + z = β. If the system has infinite…Matrices and Determinants
Q49If log ₃2, log ₃(2ˣ - 5), log ₃(2ˣ - 7/2) are in an arithmetic progression, then the value of x is equal to _ _ _ _ _ _ _.Sequence and Series
Q53Let a = i + j + k, b and c = j - k be three vectors such that a × b = c and a. b = 1. If the length of projection vector of the vector b on the vector a × c…Vector Algebra
Q2586Let the plane passing through the point (- 1, 0, - 2) and perpendicular to each of the planes 2x + y - z = 2 and x - y - z = 3 be ax + by + cz + 8 = 0. Then…Three Dimensional Geometry
Q2836If the area of the bounded region R = (x,y): max 0, log e x ≤ y ≤ 2ˣ,1/2 ≤ x ≤ 2 is, α (log e 2)⁻¹ + β (log e 2) + γ, then the value of (α + β - 2λ)² is equal…Integral Calculus
Q2935If the coefficients of x⁷ in (x² + 1/bx)¹¹ and x⁻⁷ in (x - 1/(bx²))¹¹, b ≠ 0, are equal, then the value of b is equal to:Binomial Theorem and Its Simple Applications
Q3023Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments…Coordinate Geometry
Q3024Let A = (x,y) R × R|2x² + 2y² - 2x - 2y = 1, B = (x,y) R × R|4x² + 4y² - 16y + 7 = 0 and C = (x,y) R × R|x² + y² - 4x - 2y + 5 ≤ r². Then the minimum value of…Coordinate Geometry
Q3132Two tangents are drawn from the point P(- 1, 1) to the circle x² + y² - 2x - 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a…Coordinate Geometry
Q3190Let C be the set of all complex numbers. Let S₁ = \ z C||z - 3 - 2i |² = 8\ S₂ = \ z C| Re (z) ≥ 5\ and S₃ = z C||z - z | ≥ 8. Then the number of elements in…Complex Numbers and Quadratic Equations
Q3288The value of lim n → ∞ 1/nΣ j = 1 ⁿ ((2j - 1) + 8n)/((2j - 1) + 4n) is equal to:Integral Calculus
Q3415The value of the definite integral ∫ - (π)/4 ^((π)/4) dx/((1 + e^(x cos x))(sin ⁴x + cos ⁴x)) is equal to:Integral Calculus
Q3614Let y = y(x) be solution of the differential equation log (dy/dx) = 3x + 4y, with y(0) = 0. If y(- 2/3 log e 2) = α log e 2, then the value of α is equal to:Differential Equations
Q3758A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an…Coordinate Geometry
Q4149Let f:(- (π)/4,(π)/4) → R be defined as f(x) = \ (1 + | sin x|)^(3a/(| sin x|)), - (π)/4 < x < 0 b, x = 0 e^(cot 4x/ cot 2x), 0 < x < (π)/4. If f is…Limit, Continuity and Differentiability
Q4236Let f: R → R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of lim x → 2 (x²f(2) - 4f(x))/(x - 2) is equal to:Limit, Continuity and Differentiability
Q4351The compound statement (P Q) (P) ⇒ Q is equivalent to:Mathematical Reasoning
Q4482Let A = [ 1 2 - 1 4 ]. If A⁻¹ = α I + β A, α, β R, I is a 2 × 2 identity matrix then 4(α - β) is equal to:Matrices and Determinants
Q4916The probability that a randomly selected 2-digit number belongs to the set n N: (2ⁿ - 2) is a multiple of 3 is equal to:Statistics and Probability
Q5046Let α, β be two roots of the equation x² + (20)¹/4x + (5)¹/2 = 0. Then α ⁸ + β ⁸ is equal toComplex Numbers and Quadratic Equations
Q5467If the mean and variance of the following data: 6, 10, 7, 13, a, 12, b, 12 are 9 and 37/4 respectively, then (a - b)² is equal to:Statistics and Probability
Q5655If sin θ + cos θ = 1/2, then 16(sin(2 θ) + cos(4 θ) + sin(6 θ)) is equal to:Trigonometry
Q5816Let a = i + j + 2 k and b = - i + 2 j + 3 k. Then the vector product (a + b) × ((a × ((a - b) × b)) × b) is equal to:Vector Algebra