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JEE Main 2022 28 Jun Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202228 Jun, Evening shift

Physics 21Chemistry 20Mathematics 30

Physics

Q66A liquid of density 750 kgm⁻³ flows smoothly through a horizontal pipe that tapers in cross-sectional area from A₁ = 1.2 × 10⁻² m² to A₂ = A₁/2. The pressure…Properties of Solids and Liquids
Q68A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is…Units and Measurements
Q71In a Young's double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular…Optics
Q72A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water…Oscillations and Waves
Q6117Following statements related to radioactivity are given below: (A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical…Atoms and Nuclei
Q6356Amplitude modulated wave is represented by V AM = 10 [1 + 0.4 cos (2π × 10⁴t)] cos (2π × 10⁷t). The total bandwidth of the amplitude modulated wave is:Communication Systems
Q6435Resistance of the wire is measured as 2 Ω and 3 Ω at 10° C and 30° C respectively. Temperature co-efficient of resistance of the material of the wire is:Current Electricity
Q6647Let K₁ and K₂ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ ₁ and λ ₂, respectively are incident on…Dual Nature of Matter and Radiation
Q6706A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power…Electromagnetic Induction and Alternating Currents
Q6784An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm⁻¹. Choose the correct…Electromagnetic Waves
Q6969Two point charges A and B of magnitude +8 × 10⁻⁶ C and - 8 × 10⁻⁶ C respectively are placed at a distance d apart. The electric field at the middle point O…Electrostatics
Q7233Water falls from a 40 m high dam at the rate of 9 × 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical…Gravitation
Q7271Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred…Gravitation
Q7397What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?Kinetic Theory of Gases
Q7590A block of mass 2 kg moving on a horizontal surface with speed of 4 ms⁻¹ enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in…Laws of Motion
Q7646The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10⁻⁵. What is…Magnetic Effects of Current and Magnetism
Q7708Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each…Magnetic Effects of Current and Magnetism
Q7908A water drop of radius 1 μ m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10⁻⁵ Nsm⁻² and…Properties of Solids and Liquids
Q8073A ball is spun with angular acceleration α = 6t² - 2t where t is in second and α is in rads⁻². At t = 0, the ball has angular velocity of 10 rads⁻¹ and…Rotational Motion
Q8344Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as v₂ = n/(m²)v₁ and a₂ = a₁/mn respectively. Here m and n are constants. The…Units and Measurements
Q8441In Young's double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness x λ is introduced in the…Optics

Chemistry

Q3A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is _ _ _ _ _ _. (Nearest integer) (Given…Chemical Kinetics
Q4(a) CoCl₃.4NH₃, (b) CoCl₃.5NH₃, (c) CoCl₃.6NH₃ and (d) CoCl(NO₃)₂.5NH₃. Number of complex(es) which will exist in cis-trans form is/are _ _ _ _ _ _ _ _.Coordination Compounds
Q5[Fe (CN)₆ ]⁴⁻ [Fe (CN)₆ ]³⁻ [Ti (CN)₆ ]³⁻ [Ni (CN)₄ ]²⁻ [Co (CN)₆ ]³⁻ Among the given complexes, number of paramagnetic complexes is _ _ _ _ _ _.Coordination Compounds
Q6For the given reactions Sn²⁺ + 2e^ - → Sn Sn⁴⁺ + 4e^ - → Sn the electrode potentials are; E_ S n²⁺ /Sn ^(o) = - 0.140 V and E_ S n⁴⁺ /Sn ^(o) = + 0.010 V. The…Redox Reactions and Electrochemistry
Q8100 g of an ideal gas is kept in a cylinder of 416 L volume at 27° C under 1.5 bar pressure. The molar mass of the gas is _ _ _ _ _ g mol⁻¹. (Nearest integer)…Gaseous State
Q150.01 M KMnO₄ solution was added to 20.0 mL of 0.05 M Mohr's salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO₄…Redox Reactions and Electrochemistry
Q162.5 g of protein containing only glycine (C₂H₅NO₂) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found…Solutions
Q18The complete combustion of 0.492 g of an organic compound containing 'C', 'H' and 'O' gives 0.793 g of CO₂ and 0.442 g of H₂O. The percentage of oxygen…Some Basic Concepts in Chemistry
Q21For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, Δ C H^ Θ = - 601.70 kJ mol⁻¹, the magnitude of change in internal…Chemical Thermodynamics
Q308In the structure of SF₄, the lone pair of electrons on S is in.Chemical Bonding and Molecular Structure
Q1036Correct statement about photo-chemical smog is:Environmental Chemistry
Q1254Hydrogen has three isotopes: protium (¹H), deuterium (²H or D) and tritium (³H or T). They have nearly same chemical properties but different physical…Hydrogen
Q1310A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of [C H₃ C H₂ CO O^ - ] [C H₃ C H₂ COOH] required to…Equilibrium
Q1396In the metallurgical extraction of copper, following reaction is used: FeO + SiO₂ → FeSiO₃ FeO and FeSiO₃ respectively are.Isolation of Elements
Q1637Match List - I with List - II: List-I (Oxide) List-II (Nature) (A) C l₂ O₇ (I) Amphoteric (B) N a₂ O (II) Basic (C) A l₂ O₃ (III) Neutral (D) N₂O (IV) Acidic…Classification of Elements and Periodicity in Properties
Q1638Among the following, basic oxide is:Classification of Elements and Periodicity in Properties
Q1696Given below are two statements, one is Assertion (A) and other is Reason (R). Assertion (A): Natural rubber is a linear polymer of isoprene called…Polymers
Q2099Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is, Given: Atomic masses of C, H and N are 12, 1 and…Some Basic Concepts in Chemistry
Q2203Consider the following statements: (A) The principal quantum number 'n' is a positive integer with values of 'n' = 1, 2, 3,... (B) The azimuthal quantum…Atomic Structure
Q2266Match List - I with List - II: List-I List-II (A) negatively charged sol (I) F e₂ O₃. x H₂ O (B) macromolecular colloid (II) CdS sol (C) positively charged…Surface Chemistry

Mathematics

Q22Let the image of the point P(1, 2, 3) in the line L:(x - 6)/3 = (y - 1)/2 = (z - 2)/3 be Q. Let R (α, β, γ) be a point that divides internally the line…Three Dimensional Geometry
Q26If one of the diameters of the circle x² + y² - 2 2 x - 6 2 y + 14 = 0 is a chord of the circle (x - 2 2)² + (y - 2 2)² = r², then the value of r² is equal to…Coordinate Geometry
Q27Sum of squares of modulus of all the complex numbers z satisfying z = i z² + z² - z is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q32Let S = 1, 2, 3, 4. Then the number of elements in the set f: S × S → S: f is onto and f (a, b) = f (b, a) ≥ a (a, b) S × S is _ _ _ _ _ _ _.Sets, Relations and Functions
Q36If lim x → 1 (sin (3x² - 4x + 1) - x² + 1)/(2x³ - 7x² + ax + b) = - 2, then the value of (a - b) is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q37The maximum number of compound propositions, out of p r s, p r s, p q s, p r s, p r s, p q s, q r s, q r s, p q s that can be made simultaneously true by an…Mathematical Reasoning
Q38Let A = (1 + i 1 - i 0) where i = √(- 1). Then, the number of elements in the set n 1, 2,......, 100: Aⁿ = A is _ _ _ _ _ _.Matrices and Determinants
Q39If the system of linear equations 2x - 3y = γ + 5, α x + 5y = β + 1, where α, β, γ R has infinitely many solutions then the value of | 9 α + 3 β + 5 γ | is…Matrices and Determinants
Q45Let for n = 1, 2,......, 50, S n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is 1/((n + 1)²). Then the…Sequence and Series
Q47Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the…Statistics and Probability
Q2590Let the plane ax + by + cz = d pass through (2, 3, - 5) and is perpendicular to the planes 2x + y - 5z = 10 and 3x + 5y - 7z = 12. If a, b, c, d are integers…Three Dimensional Geometry
Q2885The area of the bounded region enclosed by the curve y = 3 - | x - 1/2 | - |x + 1| and the x-axis is:Integral Calculus
Q2936The term independent of x in the expansion of (1 - x² + 3x³)(5/2x³ - 1/(5x²))¹¹, x ≠ 0 is:Binomial Theorem and Its Simple Applications
Q3428Let f: R → R be a differentiable function such that f((π)/4) = 2, f((π)/2) = 0 and f'((π)/2) = 1 and let g(x) = ∫ x ^(π /4) (f'(t) sec t + tan t sec t f(t))…Integral Calculus
Q3429Let f: R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x R where k > 0 and n is a positive integer. If I₁ = ∫₀^(4nk) f(x)dx and I₂ = ∫…Integral Calculus
Q3539Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 tan x(cos x - y). If the curve passes through the point ((π)/4,0), then the value of…Differential Equations
Q3621Let x = x(y) be the solution of the differential equation 2y e^(x/y²)dx + (y² - 4x e^(x/y²))dy = 0 such that x(1) = 0. Then, x(e) is equal to:Differential Equations
Q3973Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola (x²)/(a²) - (y²)/(b²) = 1. Let e' and l'…Coordinate Geometry
Q4151Let f, g: R → R be functions defined by f(x) = \ [x], x < 0 |1 - x|, x ≥ 0. and g(x) = \ eˣ - x, x < 0 (x - 1)² - 1, x ≥ 0. where [x] denote the greatest…Limit, Continuity and Differentiability
Q4290The value of lim n → ∞ 6 tan Σ r = 1 ⁿ tan ⁻¹(1/(r² + 3r + 3)) is equal to:Limit, Continuity and Differentiability
Q4729If vertex of a parabola is (2, - 1) and the equation of its directrix is 4x - 3y = 21, then the length of its latus rectum is:Coordinate Geometry
Q4777The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives at least 4 and at most 7 candies, C₃ receives…Permutations and Combinations
Q4988The probability that a randomly chosen one-one function from the set a, b, c, d to the set 1, 2, 3, 4, 5 satisfies f(a) + 2f(b) - f(c) = f(d) is:Statistics and Probability
Q5154Let f(x) be a quadratic polynomial such that f(- 2) + f(3) = 0. If one of the roots of f(x) = 0 is - 1, then the sum of the roots of f(x) = 0 is equal to:Complex Numbers and Quadratic Equations
Q5181If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1: 7 and a + n = 33, then the value of n is:Sequence and Series
Q5381Let R₁ = (a, b) N × N: |a - b| ≤ 13 and R₂ = (a, b) N × N: |a - b| ≠ 13. Then on N:Sets, Relations and Functions
Q5520Let a triangle be bounded by the lines L₁: 2x + 5y = 10; L₂: - 4x + 3y = 12 and the line L₃, which passes through the point P(2, 3), intersects L₂ at A and L₁…Coordinate Geometry
Q5638If cot α = 1 and sec β = - 5/3, where π < α < (3π)/2 and (π)/2 < β < π, then the value of tan (α + β) and the quadrant in which α + β lies, respectively are:Trigonometry
Q5818Let a = α i + 2 j - k and b = - 2 i + α j + k, where α R. If the area of the parallelogram whose adjacent sides are represented by the vectors a and b is…Vector Algebra
Q5819Let a be a vector which is perpendicular to the vector 3 i + 1/2 j + 2 k. If a × (2 i + k) = 2 i - 13 j - 4 k, then the projection of the vector a on the…Vector Algebra