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JEE Main 2021 24 Feb Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202124 Feb, Morning shift

Physics 23Chemistry 18Mathematics 30

Physics

Q50A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are…Electromagnetic Induction and Alternating Currents
Q51A resonance circuit having inductance and resistance 2 × 10⁻⁴ H and 6.28 Ω respectively oscillates at 10 MHz frequency. The value of quality factor of this…Electromagnetic Induction and Alternating Currents
Q53A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the…Rotational Motion
Q54An audio signal v m = 20 sin 2 π (1500t) amplitude modulates a carrier v c = 80 sin 2 π (100,000t). The value of percent modulation is _ _ _ _ _.Communication Systems
Q57An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its…Electromagnetic Waves
Q65An inclined plane is bent in such a way that the vertical cross-section is given by y = (x²)/4 where y is in vertical and x in horizontal direction. If the…Laws of Motion
Q66The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be…Laws of Motion
Q68A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift _ _ _ _ _ k g when the diameter of the larger piston is…Properties of Solids and Liquids
Q72An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as…Optics
Q6170Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:Electrostatics
Q6398A current through a wire depends on time as i = α ₀t + β t² where α ₀ = 20 A/s and β = 8 As⁻². Find the charge crossed through a section of the wire in 15 s.Current Electricity
Q6600Given below are two statements: Statement I: Two photons having equal linear momenta have equal wavelengths. Statement II: If the wavelength of photon is…Dual Nature of Matter and Radiation
Q6903If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of β will be:Electronic Devices
Q7079The focal length f is related to the radius of curvature r of the spherical convex mirror by:Optics
Q7195Consider two satellites S₁ and S₂ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular…Gravitation
Q7261Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual…Gravitation
Q7262Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is:Gravitation
Q7484Match List I with List II. List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d)…Thermodynamics
Q7520Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' α '. The…Properties of Solids and Liquids
Q7938If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these…Properties of Solids and Liquids
Q8098Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I₁ = M.I. of thin circular ring about its diameter, I₂ = M.I. of…Rotational Motion
Q8241The work done by a gas molecule in an isolated system is given by, W = α β ²e^(- (x²)/(α kT)), where x is the displacement, k is the Boltzmann constant and T…Units and Measurements
Q8432In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is…Optics

Chemistry

Q4At 1990 K and 1 atm pressure, there are equal number of Cl₂, molecules and Cl atoms in the reaction mixture. The value of K p for the reaction Cl₂ (g) 2Cl_(g)…Equilibrium
Q5For the reaction A_(g) → B_(g) the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The value of Δ r G for the reaction at 300 K and 1…Equilibrium
Q6Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k' value of 3.3 × 10⁻⁴ s⁻¹ at 153°C. The time in minutes it takes for the…Chemical Kinetics
Q14Number of amphoteric compounds among the following is _ _ _ _. (A) BeO (B) BaO (C) Be(OH)₂ (D) Sr(OH)₂Classification of Elements and Periodicity in Properties
Q16The coordination number of an atom in a body-centered cubic structure is _ _ _ _. [Assume that the lattice is made up of atoms.]Solid State
Q17When 9.45 g of CICH₂COOH is added to 500 mL of water, its freezing point drops by 0.5°C. The dissociation constant of CICH₂COOH is x × 10⁻³. The value of x is…Solutions
Q184.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the solution in M is x × 10⁻¹. The value of x is _ _ _ _…Some Basic Concepts in Chemistry
Q19A proton and a Li³⁺ nucleus are accelerated by the same potential. If λ Li and λ p denote the de Broglie wavelengths of Li³⁺ and proton respectively, then the…Atomic Structure
Q53Which of the following reagent is used for the following reaction ? CH₃ CH₂ CH₃ ? CH₃ CH₂ CHOOrganic Compounds Containing Oxygen
Q204Out of the following, which type of interaction is reponsible for the stabilisation of α -helix structure of proteins ?Biomolecules
Q300Which of the following are isostructural pairs ? A. SO₄²⁻ and CrO₄²⁻ B. SiCl₄, and TiCl₄ C. NH₃ and NO₃⁻ D. BCl₃ and BrCl₃Chemical Bonding and Molecular Structure
Q873Given below are two statements: Statement I: Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame. Statement II: Cuprous…d- and f-Block Elements
Q998The electrode potential of M²⁺/M of 3d-series elements shows positive value for:Redox Reactions and Electrochemistry
Q1064The gas released during anaerobic degradation of vegetation may lead to:Environmental Chemistry
Q1218(A) HOCI + H₂O₂ → H₃O⁺ + Cl⁻ + O₂ (B) I₂ + H₂O₂ + 2OH⁻ → 2I⁻ + 2H₂O + O₂ Choose the correct option.Hydrogen
Q1414The major components in "Gun Metal” are:Isolation of Elements
Q1415Which of the following ore is concentrated using group 1 cyanide salt ?Isolation of Elements
Q1607Consider the elements Mg, Al, S, P and Si, the correct increasing order of their first ionization enthalpy is:Classification of Elements and Periodicity in Properties

Mathematics

Q22The minimum value of α for which the equation 4/(sin x) + 1/(1 - sin x) = α has at least one solution in (0,(π)/2) is.......Limit, Continuity and Differentiability
Q27If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is _ _ _ _.Coordinate Geometry
Q28If the least and the largest real values of a, for which the equation z + α |z – 1| + 2i = 0 (z C and i = √(- 1)) has a solution, are p and q respectively…Complex Numbers and Quadratic Equations
Q30If ∫ - a ^(a) (| x | + | x - 2 |) dx = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then ∫ - a ^(a) (x + [ x ]) dx is equal to _ _ _ _ _.Integral Calculus
Q36lim n → ∞ tan Σ r = 1 ⁿ tan ⁻¹(1/(1 + r + r²)) is equal to _ _ _.Limit, Continuity and Differentiability
Q38Let P = [ 3 - 1 - 2 2 0 α 3 - 5 0 ], where α R. Suppose Q = [ q i j] is a matrix satisfying PQ = kl₃ for some non-zero k R. If q₂₃ = - k/8 and |Q| = (k²)/2…Matrices and Determinants
Q40Let M be any 3 × 3 matrix with entries from the set 0, 1, 2. The maximum number of such matrices, for which the sum of diagonal elements of M^(T)M is seven…Matrices and Determinants
Q44Let B i (i = 1, 2, 3) be three independent events in a sample space. The probability that only B₁ occur is α, only B₂ occurs is β and only B₃ occurs is γ. Let…Statistics and Probability
Q46Let A = n N: n is a 3-digit number B = 9k + 2: k N and C = 9k + l: k N for some l (0 < l < 9) If the sum of all the elements of the set A (B C) is 274 × 400…Sets, Relations and Functions
Q49Let three vectors a, b and c be such that c is coplanar with a and b, a. c = 7 and b is perpendicular to c, where a = - i + j + k and b = 2 i + k, then the…Vector Algebra
Q2425The distance of the point (1, 1, 9) from the point of intersection of the line (x - 3)/1 = (y - 4)/2 = (z - 5)/2 and the plane x + y + z = 17 is:Three Dimensional Geometry
Q2578The equation of the plane passing through the point (1, 2, -3) and perpendicular to the planes 3x + y - 2z = 5 and 2x - 5y - z = 7, is:Three Dimensional Geometry
Q2716The function f(x) = (4x³ - 3x²)/6 - 2 sin x + (2x - 1) cos x:Limit, Continuity and Differentiability
Q2779If the tangent to the curve y = x³ at the point P(t, t³) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio…Limit, Continuity and Differentiability
Q2832The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the parabola y² = 9x, is:Integral Calculus
Q2991The value of -¹⁵C₁ + 2.¹⁵C₂ – 3.¹⁵C₃ +... - 15.¹⁵C₁₅ + ¹⁴C₁ + ¹⁴C₃ + ¹⁴C₅ +...+ ¹⁴C₁₁ is:Binomial Theorem and Its Simple Applications
Q3309lim x → 0 (∫₀^(x²) (sin t)dt)/(x³) is equal to:Integral Calculus
Q3605The population P = P(t) at time 't' of a certain species follows the differential equation dP/dt = 0.5P – 450. If P(0) = 850, then the time at which…Differential Equations
Q3822Let f: R → R be defined as f (x) = 2x – 1 and g: R - 1 → R be defined as g(x) = (x - 1/2)/(x - 1). Then the composition function f(g(x)) is:Sets, Relations and Functions
Q3920Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an…Height and Distance
Q4028If ∫ (cos x - sin x)/(√(8 - sin 2x)) dx = a sin ⁻¹ ((sin x + cos x)/b) + c, where c is a constant of integration, then the ordered pair (a, b) is equal to:Integral Calculus
Q4142If f: R → R is a function defined by f(x)= [x - 1] cos ((2x - 1)/2)π, where [.] denotes the greatest integer function, then f is:Limit, Continuity and Differentiability
Q4339The statement among the following that is a tautology is:Mathematical Reasoning
Q4586The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is inconsistent if:Matrices and Determinants
Q4697The locus of the mid-point of the line segment joining the focus of the parabola y² = 4ax to a moving point of the parabola, is another parabola whose…Coordinate Geometry
Q4774A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then…Permutations and Combinations
Q4882An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even…Statistics and Probability
Q5068Let p and q be two positive numbers such that p + q = 2 and p⁴+q⁴ = 272. Then p and q are roots of the equation:Complex Numbers and Quadratic Equations
Q5613A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1/4. Three stones A, B…Coordinate Geometry
Q5664If e^((cos ²x + cos ⁴x + cos ⁶x +...∞) log e 2) satisfies the equation t² - 9t + 8 = 0, then the value of (2 sin x)/(sin x + 3 cos x)(0 < x < (π)/2) is:Trigonometry