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JEE Main 2021 26 Aug Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202126 Aug, Morning shift

Physics 24Chemistry 19Mathematics 29

Physics

Q53An amplitude modulated wave is represented by C m (t) = 10(1 + 0.2 cos 12560t) sin(111 × 10⁴t) volts. The modulating frequency in kHz will be..................Communication Systems
Q57The electric field in a plane electromagnetic wave is given by E = 200 cos [ ((0.5 × 10³)/m)x - (1.5 × 10¹¹rad/s × t) ]V/m j. If this wave falls normally on a…Electromagnetic Waves
Q65Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same…Kinematics
Q67A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess…Properties of Solids and Liquids
Q70White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet…Optics
Q71A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of…Oscillations and Waves
Q72Two travelling waves produces a standing wave represented by equation, y = 1.0 mm cos(1.57 cm⁻¹) x sin(78.5 s⁻¹)t. The node closest to the origin in the…Oscillations and Waves
Q73A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter lying on the table. If k is the kinetic energy of the chain in joule as…Work, Energy and Power
Q5899A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k Ω, an inductor of inductive reactance X L = 250 π Ω and an unknown…Electromagnetic Induction and Alternating Currents
Q6005A particular hydrogen like ion emits radiation of frequency 2.92 × 10¹⁵ Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation…Atoms and Nuclei
Q6192The material filled between the plates of a parallel plate capacitor has resistivity 200 Ω m. The value of capacitance of the capacitor is 2 pF. If a…Electrostatics
Q6382What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3 Ω ? (Given…Current Electricity
Q6642In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function φ = 2.5 eV. If the wavelength of…Dual Nature of Matter and Radiation
Q6687An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is…Electromagnetic Induction and Alternating Currents
Q6876Statement I: By doping silicon semiconductor with pentavalent material, the electrons density increases. Statement II: The n-type semiconductor has net…Electronic Devices
Q7082Car B overtakes another car A at a relative speed of 40 ms⁻¹. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in…Optics
Q7231Inside a uniform spherical shell: (1) the gravitational field is zero (2) the gravitational potential is zero (3) the gravitational field is same everywhere…Gravitation
Q7387The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are V H, V O and V C respectively then:Kinetic Theory of Gases
Q7534An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by…Thermodynamics
Q7588The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms⁻². The gases…Laws of Motion
Q7682The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field…Magnetic Effects of Current and Magnetism
Q8018Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the…Properties of Solids and Liquids
Q8248If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P =…Units and Measurements
Q8337In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular…Experimental Skills

Chemistry

Q2The total number of negative charge in the tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12.5 will be _ _ _ _ _ _ _. (Integer answer)Biomolecules
Q3AB₃ is an interhalogen T-shaped molecule. The number of lone pairs of electrons on A is _ _ _ _ _. (Integer answer)Chemical Bonding and Molecular Structure
Q4The OH^(- c)oncentration in a mixture of 5.0 mL of 0.0504 M NH₄Cl and 2 mL of 0.0210 M NH₃ solution is x × 10⁻⁶ M. The value of x is _ _ _ _ _ _. (Nearest…Equilibrium
Q5The ratio of number of water molecules in Mohr's salt and potash alum is _ _ _ _ _ _ × 10⁻¹. (Integer answer)Coordination Compounds
Q6The number of 4f electrons in the ground statement electronic configuration of Gd²⁺ is _ _ _ _ _ _. [Atomic number of Gd = 64]d- and f-Block Elements
Q9These are physical properties of an element (A) Sublimation enthalpy (B) Ionisation enthalpy (C) Hydration enthalpy (D) Electron gain enthalpy The total…Redox Reactions and Electrochemistry
Q17Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of 0.10 M C₂H₅OH is _ _ _ _ _ (Integer…Solutions
Q18An aqueous KCl solution of density 1.20 g mL⁻¹ has a molality of 3.30 mol kg⁻¹. The molarity of the solution in mol L⁻¹ is _ _ _ _ _ _ (Nearest integer)…Some Basic Concepts in Chemistry
Q20The Born-Haber cycle for KCl is evaluated with the following data: Δ f H^Θ for KCl = - 436.7 kJ mol⁻¹; Δ sub H^Θ for K = 89.2 kJ mol⁻¹; Δ ionization H^Θ for K…Chemical Thermodynamics
Q880Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere?d- and f-Block Elements
Q945Given below are two statements: Statement I: The limiting molar conductivity of KCl (strong electrolyte) is higher compared to that of CH₃COOH (weak…Redox Reactions and Electrochemistry
Q1093The conversion of hydroxyapatite occurs due to presence of F⁻ⁱons in water. The correct formula of hydroxyapatite is:Environmental Chemistry
Q1200Which one of the following methods is most suitable for preparing deionized water?Hydrogen
Q1309Given below are two statements. Statement I: In the titration between strong acid and weak base methyl orange is suitable as an indicator. Statement II: For…Equilibrium
Q1370Given below are two statements: Statement I: The choice of reducing agents for metals extraction can be made by using Ellingham diagram, a plot of Δ G vs…Isolation of Elements
Q1693The polymer formed on heating Novolac with formaldehyde is:Polymers
Q1731Which one of the following complexes is violet in colour?Principles Related to Practical Chemistry
Q1936Given below are two statements. Statement I: Frenkel defects are vacancy as well as interstitial defects. Statement II: Frenkel defect leads to colour in…Solid State
Q2121Given below are two statements. Statement I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease…Atomic Structure

Mathematics

Q22Let the line L be the projection of the line (x - 1)/2 = (y - 3)/1 = (z - 4)/2 in the plane x - 2y - z = 3. If d is the distance of the point (0, 0, 6) from…Three Dimensional Geometry
Q23A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of…Limit, Continuity and Differentiability
Q24The area of the region S = (x,y):3x² ≤ 4y ≤ 6x + 24 is _ _ _ _ _ _.Integral Calculus
Q26The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of…Coordinate Geometry
Q29Let z = (1 - i 3)/2, i = √(- 1). Then the value of 21 + (z + 1/z)³ + (z² + 1/(z²))³ + (z³ + 1/(z³))³ +.... + (z²¹ + 1/(z²¹))³ is _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q34If y = y(x) is an implicit function of x such that log e (x + y) = 4xy, then d²y d x² at x = 0 is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q36Let a, b R, b 0, Define a function f(x) = \ a sin (π)/2(x - 1), for x ≤ 0 tan 2x - sin 2x b x³, for x > 0.. If f is continuous at x = 0, then 10 - ab is equal…Limit, Continuity and Differentiability
Q40The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is _ _ _ _ _ _ _.Permutations and Combinations
Q41If ¹P₁ + 2.²P₂ + 3.³P₃ +.... + 15.¹⁵P₁₅ = ^(q) P r - s,0 ≤ s ≤ 1, then ^(q + s)C r - s is equal to _ _ _ _ _ _ _.Permutations and Combinations
Q43The sum of all integral values of k (k ≠ 0) for which the equation 2/(x - 1) - 1/(x - 2) = 2/k in x has no real roots, is _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q2434A plane P contains the line x + 2y + 3z + 1 = 0 = x - y - z - 6, and is perpendicular to the plane - 2x + y + z + 8 = 0. Then which of the following points…Three Dimensional Geometry
Q2998If ²⁰C r is the co-efficient of x^(r) in the expansion of (1 + x)²⁰, then the value of Σ r = 0 ²⁰ r².²⁰C r is equal to:Binomial Theorem and Its Simple Applications
Q3051If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point (- 30, 0) and is tangent to the parabola y² = 30x, then the length…Coordinate Geometry
Q3191The equation arg ((z - 1)/(z + 1)) = (π)/4 represents a circle with:Complex Numbers and Quadratic Equations
Q3289The value of lim n → ∞ 1/nΣ r = 0 ²ⁿ⁻¹ (n²)/(n² + 4r²) is:Integral Calculus
Q3416The value of ∫ (- 1)/(2) ^(1/(2)) (((x + 1)/(x - 1))² + ((x - 1)/(x + 1))² - 2)^(1/2) dx is:Integral Calculus
Q3534Let y = y(x) be a solution curve of the differential equation (y + 1) tan ²x dx + tan x dy + y dx = 0, x (0,(π)/2). If lim x → 0 + xy(x) = 1, then the value…Differential Equations
Q3680Let f(x) = cos (2 tan ⁻¹ sin (cot ⁻¹√((1 - x)/x))), 0 < x < 1. Then:Limit, Continuity and Differentiability
Q3783On the ellipse (x²)/8 + (y²)/4 = 1 let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0…Coordinate Geometry
Q4352If the truth value of the Boolean expression ((p q) (q → r) (r)) → (p q) is false, then the truth values of the statements p, q, r respectively can be:Mathematical Reasoning
Q4504If A = (1/(5) 2/(5) (- 2)/(5) 1/(5)), B = (1 0 i 1), i = √(- 1), and Q = A^(T)BA, then the inverse of the matrix A Q²⁰²¹ A^(T) is equal to:Matrices and Determinants
Q4597Let θ (0,(π)/2). If the system of linear equations (1 + cos ²θ)x + sin ²θ y + 4 sin 3 θ z = 0 cos ²θ x + (1 + sin ²θ)y + 4 sin 3 θ z = 0 cos ²θ x + sin ²θ y +…Matrices and Determinants
Q4959Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = 5/9, is:Statistics and Probability
Q5262If the sum of an infinite GP a, ar, ar², ar³,....... is 15 and the sum of the squares of its each term is 150, then the sum of ar², ar⁴, ar⁶,....... is:Sequence and Series
Q5324The sum of the series 1/(x + 1) + 2/(x² + 1) + (2²)/(x⁴ + 1) +...... + (2¹⁰⁰)/(x^(2¹⁰⁰) + 1) when x = 2 is:Sequence and Series
Q5406Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering…Sets, Relations and Functions
Q5468The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25…Statistics and Probability
Q5510Let ABC be a triangle with A(- 3, 1) and ACB = θ, 0 < θ < (π)/2. If the equation of the median through B is 2x + y - 3 = 0 and the equation of angle bisector…Coordinate Geometry
Q5735Let a = i + j + k and b = j - k. If c is a vector such that a × c = b and a. c = 3, then a.(b × c) is equal to:Vector Algebra