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JEE Main 2022 27 Jun Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202227 Jun, Morning shift

Physics 26Chemistry 19Mathematics 30

Physics

Q53A beam of monochromatic light is used to excite the electron in Li⁺ + from the first orbit to the third orbit. The wavelength of monochromatic light is found…Atoms and Nuclei
Q54A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the…Electrostatics
Q58A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges…Kinematics
Q59The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory…Communication Systems
Q60The current density in a cylindrical wire of radius 4 mm is 4 × 10⁶ Am⁻². The current through the outer portion of the wire between radial distances R/2 and R…Current Electricity
Q62A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 Ω…Current Electricity
Q72The area of cross-section of a large tank is 0.5 m². It has a narrow opening near the bottom having area of cross-section 1 cm². A load of 25 kg is applied on…Properties of Solids and Liquids
Q75In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits…Optics
Q5951The current flowing through an ac circuit is given by I = 5 sin(120 π t)A How long will the current take to reach the peak value starting from zero?Electromagnetic Induction and Alternating Currents
Q6007A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of: (Given…Atoms and Nuclei
Q6187A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on…Electrostatics
Q6200Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved…Rotational Motion
Q6227What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass?…Rotational Motion
Q6470A 72 Ω galvanometer is shunted by a resistance of 8 Ω. The percentage of the total current which passes through the galvanometer is:Current Electricity
Q6571An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths (λ _α:λ C12) is:Dual Nature of Matter and Radiation
Q6839Match List-I with List-II: List - I List - II (a) Ultraviolet rays (i) Study crystal structure (b) Microwaves (ii) Greenhouse effect (c) Infrared rays (iii)…Electromagnetic Waves
Q7111Consider a light ray travelling in air is incident into a medium of refractive index √(2n). The incident angle is twice that of refracting angle. Then, the…Optics
Q7145Given below are two statements: Statement I: The law of gravitation holds good for any pair of bodies in the universe. Statement II: The weight of any person…Gravitation
Q7398A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number…Thermodynamics
Q7647The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is: [Permeability of free space μ ₀ = 4 π × 10⁻⁷ Wb/A-m]Magnetic Effects of Current and Magnetism
Q7789A projectile is launched at an angle ' α ' with the horizontal with a velocity 20 ms⁻¹. After 10 s, its inclination with horizontal is ' β '. The value of tan…Kinematics
Q7810A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 2 kmh⁻¹…Kinematics
Q7911The velocity of a small ball of mass 'm' and density d₁, when dropped in a container filled with glycerin, becomes constant after some time. If the density of…Properties of Solids and Liquids
Q8207The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic…Oscillations and Waves
Q8308A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04) cm. The maximum percentage error in the measurement of its density…Units and Measurements
Q8532An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency…Oscillations and Waves

Chemistry

Q1Total number of possible stereoisomers of dimethyl cyclopentane is _ _ _ _ _ _.Some Basic Principles of Organic Chemistry
Q32NOCl(g) 2NO(g) + Cl₂(g) In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was…Equilibrium
Q4The rate constant for a first order reaction is given by the following equation: ln k = 33.24 - (2.0 × 10⁴ K)/T The activation energy for the reaction is…Chemical Kinetics
Q7Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the manganese product formed from the above reaction is _ _ _…Coordination Compounds
Q8The number of statements correct from the following for Copper (at. no. 29) is/are _ _ _ _ _ _. (A) Cu(II) complexes are always paramagnetic. (B) Cu(I)…d- and f-Block Elements
Q9The limiting molar conductivities of NaI, NaNO₃ and AgNO₃ are 12.7, 12.0 and 13.3 mS m² mol⁻¹, respectively (all at 25° C). The limiting molar conductivity of…Redox Reactions and Electrochemistry
Q14Metal deficiency defect is shown by Fe₀.93O. In the crystal, some Fe²⁺ cations are missing and loss of positive charge is compensated by the presence of Fe³⁺…Solid State
Q152 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1: 8…Solutions
Q17Two elements A and B which form 0.15 moles of A₂B and AB₃ type compounds. If both A₂B and AB₃ weigh equally, then the atomic weight of A is _ _ _ _ _ _ t imes…Some Basic Concepts in Chemistry
Q18If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10⁻²6 (m s⁻¹) and 10⁻⁷ (m) respectively. The mass of the particle in g is…Atomic Structure
Q535Given below are two statements: Statement I: In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the…Organic Compounds Containing Nitrogen
Q631Which of the following will have maximum stabilization due to crystal field?Coordination Compounds
Q1038Given below are two Statements: Statement I: Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide…Environmental Chemistry
Q1357Match List-I with List-II List - I List - II (A) Concentration of gold ore (I) Aniline (B) Leaching of alumina (II) NaOH (C) Froth stabiliser (III) SO ₂ (D)…Isolation of Elements
Q1562Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The ionic radii of O² - and Mg²⁺ are…Classification of Elements and Periodicity in Properties
Q1719Match List - I with List - II List - I (Polymer) List - II (Used in) (A) Bakelite (I) Radio and television cabinets (B) Glyptal (II) Electrical switches (C)…Polymers
Q1981Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): At 10° C, the density of a 5 M…Solutions
Q2268Match List-I with List-II List - I List - II (A) Lyophilic colloid (I) Liquid-liquid colloid (B) Emulsion (II) Protective colloid (C) Positively charged…Surface Chemistry
Q2328Match List-I with List-II. List - I List - II (A) Spontaneous process (I) Δ H < 0 (B) Process with Δ P = 0, Δ T = 0 (II) Δ G T,P < 0 (C) Δ H reaction (III)…Chemical Thermodynamics

Mathematics

Q22Let the mirror image of the point (a, b, c) with respect to the plane 3x - 4y + 12z + 19 = 0 be (a - 6, β, γ). If a + b + c = 5, then 7 β - 9 γ is equal to _…Three Dimensional Geometry
Q23Let A₁ = (x,y):|x| ≤ y²,|x| + 2y ≤ 8 and A₂ = (x,y):|x| + |y| ≤ k. If 27 (Area A₁) = 5 (Area A₂), then k is equal to:Integral Calculus
Q24If the coefficient of x¹⁰ in the binomial expansion of ((x)/(5^(1/4)) + (5)/(x^(1/3)))⁶⁰ is 5^(k). l, where l, k N and l is co-prime to 5, then k is equal to…Binomial Theorem and Its Simple Applications
Q25A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x - y + 4 =…Coordinate Geometry
Q32Let f: R → R be a function defined by f(x) = (2e²ˣ)/(e²ˣ + e). Then f(1/100) + f(2/100) + f(3/100) +..... + f(99/100) is equal to _ _ _ _ _ _ _.Sets, Relations and Functions
Q37The positive value of the determinant of the matrix A, whose Adj(Adj(A)) = (14 28 - 14 - 14 14 28 28 - 14 14), is _ _ _ _ _ _ _.Matrices and Determinants
Q39A circle of radius 2 unit passes through the vertex and the focus of the parabola y² = 2x and touches the parabola y = (x - 1/4)² + α, where α > 0. Then (4 α…Coordinate Geometry
Q40The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at…Permutations and Combinations
Q44If the sum of all the roots of the equation e²ˣ - 11eˣ - 45e⁻ˣ + 81/2 = 0 is log e p, then p is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q47If the sum of the first ten terms of the series 1/5 + 2/65 + 3/325 + 4/1025 + 5/2501 +.... is m/n, where m and n are co-prime numbers, then m + n is equal to…Sequence and Series
Q2380If two straight lines whose direction cosines are given by the relations l + m - n = 0, 3l² + m² + cnl = 0 are parallel, then the positive value of c is:Three Dimensional Geometry
Q3224The area of the polygon, whose vertices are the non-real roots of the equation z = i z² is:Complex Numbers and Quadratic Equations
Q3432The value of the integral ∫₋₂² (|x³ + x|)/((e^(x|x|) + 1))dx is equal to:Integral Calculus
Q3498Let dy/dx = (ax - by + a)/(bx + cy + a), where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the…Differential Equations
Q3623If dy/dx + (2^(x - y)(2^(y) - 1))/(2ˣ - 1) = 0, x, y > 0, y(1) = 1, then y(2) is equal to:Differential Equations
Q3689If cos ⁻¹(y/2) = log e (x/5)⁵, |y| < 2, then:Limit, Continuity and Differentiability
Q3760Let the eccentricity of an ellipse (x²)/(a²) + (y²)/(b²) = 1, a > b, be 1/4. If this ellipse passes through the point (- 4√(2/5),3), then a² + b² is equal to:Coordinate Geometry
Q4053If ∫ ((x² + 1)eˣ)/((x + 1)²)dx = f(x)eˣ + C, where C is a constant, then d³f d x³ at x = 1 is equal to:Integral Calculus
Q4074sin ¹(sin (2π)/3) + cos ⁻¹(cos (7π)/6) + tan ⁻¹(tan (3π)/4) is equal to:Trigonometry
Q4239Let a be an integer such that lim x → 7 (18 - [1 - x])/([x - 3a]) exists, where [t] is greatest integer ≤ t. Then a is equal to:Limit, Continuity and Differentiability
Q4363The boolean expression ((p q)) q is equivalent to:Mathematical Reasoning
Q4604Let the system of linear equations x + 2y + z = 2, α x + 3y - z = α, - α x + y + 2z = - α be inconsistent. Then α is equal to:Matrices and Determinants
Q4887Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is:Statistics and Probability
Q4989Five numbers x₁,x₂,x₃,x₄,x₅ are randomly selected from the numbers 1, 2, 3,......., 18 and are arranged in the increasing order (x₁ < x₂ < x₃ < x₄ < x₅). The…Statistics and Probability
Q5029The lengths of the sides of a triangle are 10 + x², 10 + x² and 20 - 2x². If for x = k, the area of the triangle is maximum, then 3k² is equal to:Properties of Triangle
Q5099The number of distinct real roots of x⁴ - 4x + 1 = 0 is:Complex Numbers and Quadratic Equations
Q5280x = Σ n = 0 ^∞ aⁿ,y = Σ n = 0 ^∞ bⁿ,z = Σ n = 0 ^∞ cⁿ, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc ≠ 0, then:Sequence and Series
Q5539In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If (α, β) is…Coordinate Geometry
Q5677The value of cos ((2π)/7) + cos ((4π)/7) + cos ((6π)/7) is equal to:Trigonometry
Q5821Let a = i + j - k and c = 2 i - 3 j + 2 k. Then the number of vectors b such that b × c = a and | b | 1, 2,........, 10 is:Vector Algebra