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

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JEE Main 202227 Jul, Morning shift

Physics 25Chemistry 22Mathematics 30

Physics

Q56To light, a 50 ~W, 100 ~V lamp is connected, in series with a capacitor of capacitance 50/(π √(x)) μ F, with 200 ~V, 50 ~Hz AC source. The value of x will be…Electromagnetic Induction and Alternating Currents
Q60A 1 ~m long copper wire carries a current of 1 ~A. If the cross section of the wire is 2.0 ~mm² and the resistivity of copper is 1.7 × 10⁻⁸ Ω m, the force…Current Electricity
Q71A ball of mass m is thrown vertically upward. Another ball of mass 2 ~m is thrown at an angle θ with the vertical. Both the balls stay in air for the same…Kinematics
Q73A square aluminum (shear modulus is 25 × 10⁹ Nm⁻²) slab of side 60 ~cm and thickness 15 ~cm is subjected to a shearing force (on its narrow face) of 18.0 ×…Properties of Solids and Liquids
Q74A pulley of radius 1.5 ~m is rotated about its axis by a force F=(12 t-3 t²) N applied tangentially (while t is measured in seconds). If moment of inertia of…Rotational Motion
Q75A mass 0.9 ~kg, attached to a horizontal spring, executes SHM with an amplitude A₁. When this mass passes through its mean position, then a smaller mass of…Oscillations and Waves
Q77The one division of main scale of Vernier callipers reads 1 ~mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws…Units and Measurements
Q78Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π / 2 and π /…Optics
Q5909A direct current of 4 ~A and an alternating current of peak value 4 ~A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the…Electromagnetic Induction and Alternating Currents
Q6122What is the half-life period of a radioactive material if its activity drops to 1 / 16^(th) of its initial value in 30 years?Atoms and Nuclei
Q6322At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased toCommunication Systems
Q6394Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are…Current Electricity
Q6575An electron (mass m) with an initial velocity v=v₀ i(v₀>0) is moving in an electric field E=-E₀ i(E₀>0) where E₀ is constant. If at t=0 de Broglie wavelength…Dual Nature of Matter and Radiation
Q6799A beam of light travelling along X -axis is described by the electric field E y =900 sin ω(t-x / c). The ratio of electric force to magnetic force on a charge…Electromagnetic Waves
Q6928Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge q₀ with mass 'm' is placed at midpoint…Electrostatics
Q7069A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is λ…Optics
Q7203Two satellites A and B, having masses in the ratio 4: 3, are revolving in circular orbits of radii 3 r and 4 r respectively around the earth. The ratio of…Gravitation
Q7346Read the following statements: A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid…Thermodynamics
Q7405Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1: 4, then A. The r.m.s. velocity of…Kinetic Theory of Gases
Q7556A bag is gently dropped on a conveyor belt moving at a speed of 2 ~m / s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the…Laws of Motion
Q7627Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 ~s and 4 ~s respectively. If their moments of inertia are in…Magnetic Effects of Current and Magnetism
Q7628A magnet hung at 45^(°) with magnetic meridian makes an angle of 60^(°) with the horizontal. The actual value of the angle of dip is -Magnetic Effects of Current and Magnetism
Q7994Two cylindrical vessels of equal cross-sectional area 16 ~cm² contain water upto heights 100 ~cm and 150 ~cm respectively. The vessels are interconnected so…Properties of Solids and Liquids
Q8311A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque…Units and Measurements
Q8609Sand is being dropped from a stationary dropper at a rate of 0.5 kgs⁻¹ on a conveyor belt moving with a velocity of 5 ~ms⁻¹. The power needed to keep the belt…Work, Energy and Power

Chemistry

Q1Optical activity of an enantiomeric mixture is +12.6^(°) and the specific rotation of (+) isomer is +30^(°). The optical purity is _ _ _ _ _%.Some Basic Principles of Organic Chemistry
Q4Amongst the following, the number of oxide(s) which are paramagnetic in nature is Na₂ O, KO₂, NO₂, ~N₂ O, ClO₂, NO, SO₂, Cl₂ OChemical Bonding and Molecular Structure
Q5According to MO theory, number of species/ions from the following having identical bond order is _ _ _ _. CN⁻, NO⁺, O₂, O₂⁺, O₂²⁺Chemical Bonding and Molecular Structure
Q62 NO+2 H₂ → N₂+2 H₂ O The above reaction has been studied at 800^(°) C. The related data are given in the table below Reaction serial number | Initial…Chemical Kinetics
Q8The conductivity of a solution of complex with formula CoCl₃(NH₃)₄ corresponds to 1: 1 electrolyte, then the primary valency of central metal ion is _ _ _ _ _.Coordination Compounds
Q13In the titration of KMnO₄ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is _ _ _ _ _ _.Equilibrium
Q14At 310 ~K, the solubility of CaF₂ in water is 2.34 × 10⁻³ ~g / 100 ~mL. The solubility product of CaF₂ is _ _ _ _ _ _ × 10⁻⁸(~mol / L)³. (Give molar mass…Equilibrium
Q2120 ~mL of 0.02 M K₂ Cr₂ O₇ solution is used for the titration of 10 ~mL of Fe²⁺ solution in the acidic medium. The molarity of Fe²⁺ solution is _ _ _ _ _ ×…Some Basic Concepts in Chemistry
Q24The molar heat capacity for an ideal gas at constant pressure is 20.785 ~J ~K⁻¹ ~mol⁻¹. The change in internal energy is 5000 ~J upon heating it from 300 ~K…Chemical Thermodynamics
Q263Given below are two statements. Statement I: O₂, Cu²⁺, and Fe³⁺ are weakly attracted by magnetic field and are magnetized in the same direction as magnetic…Chemical Bonding and Molecular Structure
Q536Match List I with List II. List I List II (A) Benzenesulphonyl chloride (I) Test for primary amines (B) Hoffmann bromamide reaction (II) Anti Saytzeff (C)…Organic Compounds Containing Nitrogen
Q775Given below are two statements. Statement I: Iron (III) catalyst, acidified K₂ Cr₂ O₇ and neutral KMnO₄ have the ability to oxidise I⁻ to I₂ independently…d- and f-Block Elements
Q776The total number of Mn=O bonds in Mn₂ O₇ is _ _ _ _ _.d- and f-Block Elements
Q1099Match List I with List II. List I Pollutant List II Disease/sickness (A) Sulphate (>500 ppm) (I) Methemoglobinemia (B) Nitrate (>50 ppm) (II) Brown mottling…Environmental Chemistry
Q1231Given below are two statements. Statement I: Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions. Statement II: Density of…Hydrogen
Q1444Which of the following methods are not used to refine any metal? A. Liquation B. Calcination C. Electrolysis D. Leaching E. Distillation Choose the correct…Isolation of Elements
Q1514Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Activated charcoal adsorbs SO₂ more…p-Block Elements
Q1614The incorrect statement isClassification of Elements and Periodicity in Properties
Q1987Boiling point of a 2% aqueous solution of a non-volatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The…Solutions
Q2043250 ~g solution of D -glucose in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, H, 1 u; C…Some Basic Concepts in Chemistry
Q2077In Carius method of estimation of halogen, 0.45 ~g of an organic compound gave 0.36 ~g of AgBr. Find out the percentage of bromine in the compound. (Molar…Some Basic Concepts in Chemistry
Q2123Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Energy of 2 s orbital of hydrogen atom is…Atomic Structure

Mathematics

Q25Let the line (x-3)/7=(y-2)/(-1)=(z-3)/(-4) intersect the plane containing the lines (x-4)/1=(y+1)/(-2)=z/1 and 4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a R at the point…Three Dimensional Geometry
Q27Let M and N be the number of points on the curve y⁵-9 x y+2 x=0, where the tangents to the curve are parallel to x -axis and y -axis, respectively. Then the…Limit, Continuity and Differentiability
Q31Let S= C: z²+z=0. Then Σ z S (Re(z)+Im(z)) is equal to _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q37Let y=y(x) be the solution curve of the differential equation sin (2x²) log e (tan x²)dy + (4xy - 4 2 x sin (x² - (π)/4))dx = 0, 0 < x < √((π)/2), which…Differential Equations
Q38If the length of the latus rectum of the ellipse x²+4 y²+2 x+8 y-λ=0 is 4, and l is the length of its major axis, then λ+l is equal to _ _ _ _ _ _.Coordinate Geometry
Q40Let f(x)=2 x²-x-1 and S= Z:|f(n)| ≤ 800. Then, the value of Σ n S f(n) is equal to _ _ _ _ _ _.Sets, Relations and Functions
Q42An ellipse E: (x²)/(a²)+(y²)/(b²)=1 passes through the vertices of the hyperbola H: (x²)/49-(y²)/64=-1. Let the major and minor axes of the ellipse E coincide…Coordinate Geometry
Q43For k R, let the solutions of the equation cos (sin ⁻¹(x cot (tan ⁻¹(cos (sin ⁻¹ x)))))=k, 0<|x|<1/(√(2)) be α and β, where the inverse trigonometric…Trigonometry
Q46Let S be the set containing all 3 × 3 matrices with entries from \-1,0,1. The total number of matrices A S such that the sum of all the diagonal elements of…Matrices and Determinants
Q51The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation…Statistics and Probability
Q2597If the plane P passes through the intersection of two mutually perpendicular planes 2 x+k y-5 z=1 and 3 k x-k y+z=5, k<3 and intercepts a unit length on…Three Dimensional Geometry
Q2848The area of the smaller region enclosed by the curves y²=8 x+4 and x²+y²+4 √(3) x-4=0 is equal toIntegral Calculus
Q2897The remainder when (2021)²⁰²²+(2022)²⁰²¹ is divided by 7 isBinomial Theorem and Its Simple Applications
Q3085If the circle x²+y²-2 g x+6 y-19 c=0, g, c R passes through the point (6,1) and its centre lies on the line x-2 c y=8, then the length of intercept made by…Coordinate Geometry
Q3265Let the minimum value v₀ of v=|z|²+|z-3|²+|z-6 i|², z C is attained at z=z₀. Then |2 z₀²-z₀³+3|²+v₀² is equal to:Complex Numbers and Quadratic Equations
Q3439Let f: R → R be a function defined as f(x)=a sin ((π[x])/2)+[2-x], a R where [t] is the greatest integer less than or equal to t. If lim x → -1 f(x) exists…Integral Calculus
Q3440Let I=∫ π / 4 ^(π / 3)((8 sin x- sin 2 x)/x) d x. ThenIntegral Calculus
Q3441Let a function f: R → R be defined as: f(x)= ∫₀ˣ(5-|t-3|) d t, x>4 x²+b x, x ≤ 4 where b R. If f is continuous at x=4, then which of the following statements…Integral Calculus
Q3549Let y=y₁(x) and y=y₂(x) be two distinct solutions of the differential equation (d y)/(d x)=x+y, with y₁(0)=0 and y₂(0)=1 respectively. Then, the number of…Differential Equations
Q3829Let f, g: N-\1 → N be functions defined by f(a)=α, where α is the maximum of the powers of those primes p such that p^(α) divides a, and g(a)=a+1, for all a…Sets, Relations and Functions
Q3931Let a vertical tower A B of height 2 h stands on a horizontal ground. Let from a point P% on the ground a man can see upto height h of the tower with an angle…Height and Distance
Q4373(p r) (p (q)) is equivalent to (p) when r isMathematical Reasoning
Q4493Let A=(cc1 2 -2 -5). Let α, β R be such that α A²+β A=2 I. Then α+β is equal toMatrices and Determinants
Q4751Let P(a, b) be a point on the parabola y²=8 x such that the tangent at P passes through the centre of the circle x²+y²-10 x-14 y+65=0. Let A be the product of…Coordinate Geometry
Q4921Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is a multiple of 7 but not divisible by…Statistics and Probability
Q5226Suppose a₁, a₂,, a n,.. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the…Sequence and Series
Q5382Let R₁ and R₂ be two relations defined on R by a R₁ b a b ≥ 0 and a R₂ b a ≥ b Then,Sets, Relations and Functions
Q5524Let A(1,1), B(-4,3), C(-2,-5) be vertices of a triangle A B C, P be a point on side B C, and Δ₁ and Δ₂ be the areas of triangles A P B and A B C…Coordinate Geometry
Q5739Let a=2 i-j+5 k and b=α i+β j+2 k. If ((a × b) × i) · k=23/2, then |b × 2 j| is equal to:Vector Algebra
Q5827Let a=α i+j+β k and b=3 i-5 j+4 k be two vectors, such that a × b=-i+9 j+12 k. Then the projection of b-2 a on b+a is equal to:Vector Algebra