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JEE Main 2022 29 Jun Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202229 Jun, Morning shift

Physics 23Chemistry 22Mathematics 28

Physics

Q53√(d₁) and √(d₂) are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an α particle is approaching a gold nucleus. For…Atoms and Nuclei
Q59The intensity of the light from a bulb incident on a surface is 0.22 W/m². The amplitude of the magnetic field in this light-wave is _ _ _ _ _ _ _ × 10⁻⁹ T…Electromagnetic Waves
Q60A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 μ A, it brings a change of 10 mA in collector current…Electronic Devices
Q62A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the…Optics
Q64Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are…Thermodynamics
Q71A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position…Oscillations and Waves
Q6115The activity of a radioactive material is 2.56 × 10⁻³ Ci. If the half life of the material is 5 days, after how many days the activity will become 2 × 10⁻⁵ Ci ?Atoms and Nuclei
Q6157A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by…Electrostatics
Q6226A body of mass M at rest explodes into three pieces, in the ratio of masses 1: 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of…Rotational Motion
Q6355Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal…Communication Systems
Q6645Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The photoelectric effect does not takes…Dual Nature of Matter and Radiation
Q6968A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 × 10⁵ NC⁻¹. If the charge on the particle is 40…Electrostatics
Q7201The escape velocity of a body on a planet 'A' is 12 kms⁻¹. The escape velocity of the body on another planet 'B', whose density is four times and radius is…Gravitation
Q7394A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of…Thermodynamics
Q7395In van der Waal equation [ P + a/(V²) ] [V - b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a/b…Thermodynamics
Q7625At a certain place the angle of dip is 30° and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that…Magnetic Effects of Current and Magnetism
Q7760A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its…Magnetic Effects of Current and Magnetism
Q7865Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial…Kinematics
Q7946A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when masses 1 kg and 2 kg are suspended respectively from its free end…Properties of Solids and Liquids
Q8380Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of A - B, then the angle between A and B will be:Kinematics
Q8440Using Young's double slit experiment, a monochromatic light of wavelength 5000 A^(o) produces fringes of fringe width 0.5 mm. If another monochromatic light…Optics
Q8504A longitudinal wave is represented by x = 10 sin 2π (nt - x/(λ)) cm. The maximum particle velocity will be four times the wave velocity if the determined…Oscillations and Waves
Q8586A particle of mass 500 gm is moving in a straight line with velocity v = b x⁵/2. The work done by the net force during its displacement from x = 0 to x = 4 m…Work, Energy and Power

Chemistry

Q3C₆H₁₂O₆ Zymase A 0pt _Δ ^(N)aOI B + CHI₃ The number of carbon atoms present in the product B is _ _ _ _ _ _ _ _.Biomolecules
Q5The activation energy of one of the reactions in a biochemical process is 532611 J mol⁻¹. When the temperature falls from 310 K to 300 K, the change in rate…Chemical Kinetics
Q6The number of terminal oxygen atoms present in the product B obtained from the following reaction is _ _ _ _ _ _ _. FeCr₂O₄ + Na₂CO₃ + O₂ → A + Fe₂O₃ + CO₂ A…d- and f-Block Elements
Q7An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation…d- and f-Block Elements
Q9A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases…Redox Reactions and Electrochemistry
Q11Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL⁻¹ at 257° C and 100 mm Hg. The molar mass of geraniol…Gaseous State
Q17Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from 0.55 g of the compound neutralised 12.5 mL of 1 M…Principles Related to Practical Chemistry
Q201.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in freezing point observed for this strength of acid is 0.0198° C. The…Solutions
Q2417.0 g of NH₃ completely vapourises at - 33.42° C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol⁻¹. The enthalpy change for the…Chemical Thermodynamics
Q27Given below are two statements: Statement I: Phenols are weakly acidic. Statement II: Therefore they are freely soluble in NaOH solution and are weaker acids…Organic Compounds Containing Oxygen
Q58Given below are two statements: Statement I: The esterification of carboxylic acid with an alcohol is a nucleophilic acyl substitution. Statement II: Electron…Organic Compounds Containing Oxygen
Q239Sugar moiety in DNA and RNA molecules respectively areBiomolecules
Q883The electronic configuration of Pt (atomic number 78) is:d- and f-Block Elements
Q1035The acid that is believed to be mainly responsible for the damage of Taj Mahal is:Environmental Chemistry
Q1226Which one of the following reactions indicates the reducing ability of hydrogen peroxide in basic medium?Hydrogen
Q1344The solubility of AgCl will be maximum in which of the following?Equilibrium
Q1395In isolation of which one of the following metals from their ores, the use of cyanide salt is not commonly involved?Isolation of Elements
Q1695The polymer, which can be stretched and remains its original status on releasing the force isPolymers
Q1857Arrange the following in the decreasing order of their covalent character: (A) LiCl (B) NaCl (C) KCl (D) CsCl Choose the most appropriate answer from the…S Block Elements
Q2098Production of iron in blast furnace follows the following equation Fe₃O₄(s) + 4CO(g) → 3Fe(l) + 4CO₂(g) when 4.640 kg of Fe₃O₄ and 2.520 kg of CO are allowed…Some Basic Concepts in Chemistry
Q2202Which of the following statements are correct? (A) The electronic configuration of Cr is [Ar] 3d⁵ 4s¹. (B) The magnetic quantum number may have a negative…Atomic Structure
Q2264Which of the following is a correct statement?Surface Chemistry

Mathematics

Q25Let P₁: r. (2 i + j - 3 k) = 4 be a plane. Let P₂ be another plane which passes through the points (2, - 3, 2), (2, - 2, - 3) and (1, - 4, 2). If the…Three Dimensional Geometry
Q27Let d be the distance between the foot of perpendiculars of the points P(1, 2, - 1) and Q(2, - 1, 3) on the plane - x + y + z = 1. Then d² is equal to _ _ _ _…Three Dimensional Geometry
Q33Let S = z C:|z - 2| ≤ 1, z(1 + i) + z (1 - i) ≤ 2. Let |z - 4i| attains minimum and maximum values, respectively, at z₁ S and z₂ S. If 5(|z₁|² + |z₂|²) = α +…Complex Numbers and Quadratic Equations
Q36Let y = y(x) be the solution of the differential equation dy/dx + (2 y)/(2 cos ⁴x - cos ²x) = x e^(tan ⁻¹(2 cot 2x)), 0 < x < (π)/2 with y((π)/4) = (π ²)/32…Differential Equations
Q38Let c, k R. If f(x) = (c + 1)x² + (1 - c²)x + 2k and f(x + y) = f(x) + f(y) - xy, for all x, y R, then the value of |2(f(1) + f(2) + f(3) +...... + f(20))| is…Sets, Relations and Functions
Q39Let H:(x²)/(a²) - (y²)/(b²) = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(2 2 + √(14)). If the…Coordinate Geometry
Q4150 tan (3 tan ⁻¹(1/2) + 2 cos ⁻¹(1/(5))) + 4 2 tan (1/2 tan ⁻¹(2 2)) is equal to _ _ _ _ _ _.Trigonometry
Q46Let b₁b₂b₃b₄ be a 4-element permutation with b i 1, 2, 3,........, 100 for 1 ≤ i ≤ 4 and b i ≠ b j for i ≠ j, such that either b₁, b₂, b₃ are consecutive…Permutations and Combinations
Q2589If the mirror image of the point (2, 4, 7) in the plane 3x - y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to:Three Dimensional Geometry
Q2662A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length…Limit, Continuity and Differentiability
Q2839The area enclosed by y² = 8x and y = 2 x that lies outside the triangle formed by y = 2 x, x = 1, y = 2 2, is equal to:Integral Calculus
Q2957If the constant term in the expansion of (3x³ - 2x² + 5/(x⁵))¹⁰ is 2^(k).l, where l is an odd integer, then the value of k is equal to:Binomial Theorem and Its Simple Applications
Q3133Let the tangent to the circle C₁: x² + y² = 2 at the point M(- 1, 1) intersect the circle C₂: (x - 3)² + (y - 2)² = 5, at two distinct points A and B. If the…Coordinate Geometry
Q3158Let α and β be the roots of the equation x² + (2i - 1) = 0. Then, the value of | α ⁸ + β ⁸| is equal to:Complex Numbers and Quadratic Equations
Q3424Let f:R → R be a function defined by: f(x) = \ max t³ - 3t t ≤ x; x ≤ 2 x² + 2x - 6; 2 < x < 3 [x - 3] + 9; 3 ≤ x ≤ 5 2x + 1; x > 5. where [t] is the greatest…Integral Calculus
Q3425∫₀⁵ cos (π (x - [ x/2 ]))dx, where [t] denotes greatest integer less than or equal to t, is equal to:Integral Calculus
Q3619Let the solution curve of the differential equation xdy/dx - y = √(y² + 16x²), y(1) = 3 be y = y(x). Then y(2) is equal to:Differential Equations
Q4065The domain of the function cos ⁻¹((2 sin ⁻¹(1/(4x² - 1)))/(π)) is:Trigonometry
Q4359Let Δ,, ⇒, be such that (p q) Δ ((p q) ⇒ q) is a tautology. Then Δ is equal to:Mathematical Reasoning
Q4506Let A = [a ij ] be a square matrix of order 3 such that a ij = 2^(j - i), for all i, j = 1, 2, 3. Then, the matrix A² + A³ +...... + A¹⁰ is equal to:Matrices and Determinants
Q4602If the system of linear equations 2x + y - z = 7 x - 3y + 2z = 1 x + 4y + δ z = k, where δ, k R has infinitely many solutions, then δ + k is equal to:Matrices and Determinants
Q4672Let PQ be a focal chord of the parabola y² = 4x such that it subtends an angle of (π)/2 at the point (3, 0). Let the line segment PQ be also a focal chord of…Coordinate Geometry
Q4987The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to:Statistics and Probability
Q5330Let a n n = 0 ^∞ be a sequence such that a₀ = a₁ = 0 and a n + 2 = 2a n + 1 - a n + 1 for all n ≥ 0. Then, Σ n = 2 ^∞ a n /(7ⁿ) is equal to:Sequence and Series
Q5380Let a set A = A₁ A₂..... A k, where A i A j = φ for i ≠ j, 1 ≤ j, j ≤ k. Define the relation R from A to A by R = (x, y): y A i if and only if x A i, 1 ≤ i ≤…Sets, Relations and Functions
Q5470Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be 24/5 and 194/25 respectively. If the mean and variance of the first 4 observation are…Statistics and Probability
Q5548The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle (π)/4…Coordinate Geometry
Q5817Let a = α i + 3 j - k, b = 3 i - β j + 4 k and c = i + 2 j - 2 k where α, β R, be three vectors. If the projection of a on c is 10/3 and b × c = - 6 i + 10 j…Vector Algebra