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

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JEE Main 202228 Jun, Morning shift

Physics 22Chemistry 24Mathematics 30

Physics

Q55A telegraph line of length 100 km has a capacity of 0.01 μ F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is…Electromagnetic Induction and Alternating Currents
Q57A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms⁻¹…Rotational Motion
Q68The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _ _ _ _ _ _ J. (Given R = 8.31 J/mol.K)Thermodynamics
Q70A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude…Magnetic Effects of Current and Magnetism
Q73The position vector of 1 kg object is r = (3 i - j)m and its velocity v = (3 j + k)m s⁻¹. The magnitude of its angular momentum is x Nm where x is _ _ _ _ _ _.Rotational Motion
Q6052The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K p are related as:Atoms and Nuclei
Q6258A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k²rt², where k…Kinematics
Q6319Match List-I with List-II List-I List-II (A) Television signal (I) 03 KHz (B) Radio signal (II) 20 KHz (C) High Quality Music (III) 02 MHz (D) Human speech…Communication Systems
Q6570The de Broglie wavelengths for an electron and a photon are λ e and λ p respectively. For the same kinetic energy of electron and photon, which of the…Dual Nature of Matter and Radiation
Q6785A radar sends an electromagnetic signal of electric field (E₀) = 2.25 V/m and magnetic field (B₀) = 1.5 × 10⁻⁸ T which strikes a target on line of sight at a…Electromagnetic Waves
Q6878For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:Electronic Devices
Q6908Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: n-p-n transistor permits more current than…Electronic Devices
Q6970Given below are two statements: Statement I: A point charge is brought in an electric field. The value of electric field at a point near to the charge may…Electrostatics
Q7068The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 A^(o) is used to see th object will be:Optics
Q7110The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -Optics
Q7272Two planets A and B of equal mass are having their period of revolutions T A and T B such that T A = 2T B. These planets are revolving in the circular orbits…Gravitation
Q7489Given below are two statements: Statement I: When μ amount of an ideal gas undergoes adiabatic change from state (P₁, V₁, T₁) to state (P₂, V₂, T₂), then work…Thermodynamics
Q7909Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Product of Pressure (P) and time (t) has…Properties of Solids and Liquids
Q8019A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be:Properties of Solids and Liquids
Q8104Match List-I with List-II List-I List-II (A) Moment of inertia of solid sphere of radius R about any tangent. (I) 5/3M R² (B) Moment of inertia of hollow…Rotational Motion
Q8166Motion of a particle in x-y plane is described by a set of following equations x = 4 sin ((π)/2 - ω t) m and y = 4 sin (ω t) m. The path of the particle will…Oscillations and Waves
Q8555The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be:Oscillations and Waves

Chemistry

Q3The hybridization of P exhibited in PF₅ is spˣd^(y). The value of y is _ _ _ _ _.Chemical Bonding and Molecular Structure
Q4For a first order reaction A → B, the rate constant, k = 5.5 × 10⁻¹4 s⁻¹. The time required for 67% completion of reaction is x × 10⁻¹ times the half life of…Chemical Kinetics
Q7Number of complexes which will exhibit synergic bonding amongst, [Cr (CO)₆ ], [Mn (CO)₅ ] and [M n₂ (CO)₁₀ ] is _ _ _ _ _ _.Coordination Compounds
Q10The quantity of electricity in Faraday needed to reduce 1 mol of Cr₂O ₇²⁻ to Cr³⁺ is _ _ _ _ _ _.Redox Reactions and Electrochemistry
Q12The solubility product of a sparingly soluble salt A₂X₃ is 1.1 × 10⁻²3. If specific conductance of the solution is 3 × 10⁻⁵ S m⁻¹, the limiting molar…Equilibrium
Q17In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _ _ _ _ _%…Principles Related to Practical Chemistry
Q18A 2.0 g sample containing MnO₂ is treated with HCl liberating Cl₂. The Cl₂ gas is passed into a solution of KI and 60.0 mL of 0.1 M Na₂S₂O₃ is required to…Principles Related to Practical Chemistry
Q21The vapour pressures of two volatile liquids A and B at 25° C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A…Solutions
Q22If the work function of a metal is 6.63 × 10⁻¹9J, the maximum wavelength of the photon required to remove a photoelectron from the metal is _ _ _ _ _ _ nm…Atomic Structure
Q244.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat absorbed in this expansion is _ _ _ _…Chemical Thermodynamics
Q131Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?Some Basic Principles of Organic Chemistry
Q210Stability of α -Helix structure of proteins depends uponBiomolecules
Q513Which amongst the following is not a pesticide?Chemistry in Everyday Life
Q551A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K)…Organic Compounds Containing Nitrogen
Q738Given below are two statements: Statement I: [Ni(CN)₄]² - is square planar and diamagnetic complex, with dsp² hybridization for Ni but [Ni(CO)₄] is…Coordination Compounds
Q827Which one of the lanthanoids given below is the most stable in divalent form?d- and f-Block Elements
Q1255Dihydrogen reacts with CuO to give:Hydrogen
Q1397Given are two statements one is labelled as Assertion A and other is labelled as Reason R. Assertion A: Magnesium can reduce Al₂O₃ at a temperature below…Isolation of Elements
Q1489Nitrogen gas is obtained by thermal decomposition of:p-Block Elements
Q1656Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above "E" in…Classification of Elements and Periodicity in Properties
Q1697Which one of the following is NOT a copolymer?Polymers
Q1752The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is:Principles Related to Practical Chemistry
Q1937The incorrect statement about the imperfections in solids is:Solid State
Q2267The Zeta potential is related to which property of colloids?Surface Chemistry

Mathematics

Q29Let l be a line which is normal to the curve y = 2x² + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area…Limit, Continuity and Differentiability
Q31The number of positive integers k such that the constant term in the binomial expansion of (2x³ + 3/(x^(k)))¹², x ≠ 0 is 2⁸. l, where l is an odd integer, is…Binomial Theorem and Its Simple Applications
Q34Let the lines y + 2x = √(11) + 7 7 and 2y + x = 2√(11) + 6 7 be normal to a circle C:(x - h)² + (y - k)² = r². If the line √(11) y - 3x = (5√(77))/3 + 11 is…Coordinate Geometry
Q35The number of elements in the set z = a + ib C: a, b Z and 1 < | z - 3 + 2i | < 4 is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q48The number of real solutions of the equation e⁴ˣ + 4e³ˣ - 58e²ˣ + 4eˣ + 1 = 0 is _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q49Let A = 1, a₁, a₂....... a₁₈, 77 be a set of integers with 1 < a₁ < a₂ <....... < a₁₈ < 77. Let the set A + A = x + y: x, y A contain exactly 39 elements…Sequence and Series
Q51Let R₁ and R₂ be relations on the set 1, 2,......., 50 such that R₁ = (p, pⁿ): p is a prime and n ≥ 0 is an integer and R₂ = (p, pⁿ): p is a prime and n = 0…Sets, Relations and Functions
Q52The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread…Statistics and Probability
Q53A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point…Coordinate Geometry
Q54If a = 2 i + j + 3 k, b = 3 i + 3 j + k and c = c₁ i + c₂ j + c₃ k are coplanar vectors and a. c = 5, b c, then 122(c₁ + c₂ + c₃) is equal to _ _ _ _ _ _.Vector Algebra
Q2442If two distinct point Q, R lie on the line of intersection of the planes - x + 2y - z = 0 and 3x - 5y + 2z = 0 and PQ = PR = √(18) where the point P is (1…Three Dimensional Geometry
Q2443Let the plane P: r. a = d contain the line of intersection of two planes r. (i + 3 j - k) = 6 and r. (- 6 i + 5 j - k) = 7. If the plane P passes through the…Three Dimensional Geometry
Q2591The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z - 29 = 0 and 8x - 7y…Three Dimensional Geometry
Q2723The number of real solutions of x⁷ + 5x³ + 3x + 1 = 0 is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q2840The area of the region S = (x, y): y² ≤ 8x, y ≥ 2 x, x ≥ 1 isIntegral Calculus
Q3001If Σ k = 1 ³¹ (³¹C k)(³¹C k - 1) - Σ k = 1 ³⁰ (³⁰C k)(³⁰C k - 1) = (α (60!))/((30!)(31!)), where α R, then the value of 16 α is equal toBinomial Theorem and Its Simple Applications
Q3134If the tangents drawn at the points O(0,0) and P(1 + 5,2) on the circle x² + y² - 2x - 4y = 0 intersect at the point Q, then the area of the triangle OPQ is…Coordinate Geometry
Q3430Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral ∫₀¹ [ - 8x² + 6x - 1]dx is equal to:Integral Calculus
Q3540Let y = y(x) be the solution of the differential equation x(1 - x²)dy/dx + (3x²y - y - 4x³) = 0, x > 1, with y(2) = - 2. Then y(3) is equal to:Differential Equations
Q3622Let the solution curve y = y(x) of the differential equation [ x/(√(x² - y²)) + e^(y/x) ]xdy/dx = x + [ x/(√(x² - y²)) + e^(y/x) ]y pass through the points…Differential Equations
Q3805Let a function f: N → N be defined by f(n) = [ 2n, n = 2,4,6,8,...... n - 1, n = 3,7,11,15,...... (n + 1)/2, n = 1,5,9,13,....... then, f isSets, Relations and Functions
Q3929Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let (π)/8 and θ be…Height and Distance
Q3991Let the eccentricity of the hyperbola H:(x²)/(a²) - (y²)/(b²) = 1 be √(5/2) and length of its latus rectum be 6 2. If y = 2x + c is a tangent to the hyperbola…Coordinate Geometry
Q4152Let f: R → R be defined as f(x) = [ [eˣ], x < 0 a eˣ + [x - 1], 0 ≤ x < 1 b + [ sin (π x)], 1 ≤ x < 2 [e⁻ˣ] - c, x ≥ 2. where a, b, c R and [t] denotes…Limit, Continuity and Differentiability
Q4361Let p, q, r be three logical statements. Consider the compound statements S₁:((p) q) ((p) r) and S₂:p → (q r) Then, which of the following is NOT true?Mathematical Reasoning
Q4528Let A be a matrix of order 3 × 3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q4603If the system of linear equations 2x + 3y - z = - 2 x + y + z = 4 x - y + |λ |z = 4λ - 4 where, λ R, has no solution, thenMatrices and Determinants
Q4797The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is:Permutations and Combinations
Q4918The probability, that in a randomly selected 3-digit number at least two digits are odd, is:Statistics and Probability
Q5264Let A₁, A₂, A₃,....... be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = 1/1296 and A₂ + A₄ = 7/36, then the value of A₆ + A₈ +…Sequence and Series