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

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JEE Main 202126 Aug, Evening shift

Physics 17Chemistry 20Mathematics 28

Physics

Q55If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to…Electromagnetic Induction and Alternating Currents
Q56A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s⁻¹ in a uniform horizontal magnetic…Electromagnetic Induction and Alternating Currents
Q61A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal…Magnetic Effects of Current and Magnetism
Q63Two simple harmonic motions are represented by the equations x₁ = 5 sin (2π t + (π)/4) and x₂ = 5 2 (sin 2π t + cos 2π t). The amplitude of second motion…Oscillations and Waves
Q65The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake…Units and Measurements
Q66A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids P₁ and P₂ are so placed in between the source of light…Optics
Q67Two waves are simultaneously passing through a string and their equations are: y₁ = A₁ sin k(x - vt), y₂ = A₂ sin k(x - vt + x₀). Given amplitudes A₁ = 12 mm…Oscillations and Waves
Q6273A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = L/(2). The…Kinematics
Q6316A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is range of communication for Line of Sight…Communication Systems
Q6433An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so…Current Electricity
Q6566The de-Broglie wavelength of a particle having kinetic energy E is λ. How much extra energy must be given to this particle so that the de-Broglie wavelength…Dual Nature of Matter and Radiation
Q6780A light beam is described by E = 800 sin ω (t - x/c). An electron is allowed to move normal to the propagation of light beam with a speed of 3 × 10⁷ ms⁻¹…Electromagnetic Waves
Q7017The two thin coaxial rings, each of radius 'a' and having charges +Q and - Q respectively are separated by a distance of 's'. The potential difference between…Electrostatics
Q7388A cylindrical container of volume 4.0 × 10⁻³ m³ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K…Thermodynamics
Q7460The temperature of equal masses of three different liquids x, y and z are 10° C, 20° C and 30° C respectively. The temperature of mixture when x is mixed with…Thermodynamics
Q7784A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:Kinematics
Q8306If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:Units and Measurements

Chemistry

Q4The equilibrium constant K c at 298 K for the reaction A + B C + D is 100. Starting with an equimolar solution with concentrations of A, B, C and D all equal…Equilibrium
Q5The reaction rate for the reaction [PtCl₄]² - + H₂O [Pt(H₂O)Cl₃]⁻⁺ Cl^(- w)as measured as a function of concentrations of different species. It was observed…Equilibrium
Q8The overall stability constant of the complex ion [Cu(NH₃)₄]²⁺ is 2.1 × 10¹³. The overall dissociations constant is y × 10⁻¹4. Then y is _ _ _ _ _. (Nearest…Coordination Compounds
Q9For the galvanic cell, Zn(s) + Cu²⁺ (0.02 M) → Zn²⁺ (0.04 M) + Cu(s), E c ell = _ _ _ _ _ _ _ × 10⁻² V. (Nearest integer) [Use: E_ Cu/C u²⁺ ⁰ = - 0.34 V, E_…Redox Reactions and Electrochemistry
Q12A chloro compound "A". (i) forms aldehydes on ozonolysis followed by the hydrolysis. (ii) when vaporized completely 1.53 g of A, gives 448 mL of vapour at…Organic Compounds Containing Halogens
Q16In the sulphur estimation, 0.471 g of an organic compound gave 1.44 g of barium sulphate. The percentage of sulphur in the compound is _ _ _ _ _ _%. (Nearest…Principles Related to Practical Chemistry
Q1783 g of ethylene glycol dissolved in 625 g of water. The freezing point of the solution is _ _ _ _ _ _ K. (Nearest integer) [Use: Molal Freezing point…Solutions
Q18100 mL of Na₃PO₄ solution contains 3.45 g of sodium. The molarity of the solution is _ _ _ _ _ _ _ × 10⁻² mol L⁻¹. (Nearest integer) [Atomic Masses - Na: 23.0…Some Basic Concepts in Chemistry
Q19A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 × 10¹⁴ Hz. The velocity of ejected…Atomic Structure
Q21For water Δ v ap H = 41 kJ mol⁻¹ at 373 K and 1 bar pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water…Chemical Thermodynamics
Q173Given below are two statements: one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A): Sucrose is a disaccharide and a…Biomolecules
Q373The bond order and magnetic behaviour of O₂⁻ⁱon are respectively:Chemical Bonding and Molecular Structure
Q629Arrange the following Cobalt complexes in the order of increasing Crystal Field Stabilization Energy (CFSE) value. Complexes: [Co F₆ ] ³⁻ A, [Co (H₂O)₆ ] ²⁺…Coordination Compounds
Q688Indicate the complex/complex ion which did not show any geometrical isomerism:Coordination Compounds
Q1031Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Photochemical smog causes cracking of…Environmental Chemistry
Q1105The interaction energy of London forces between two particles is proportional to rˣ, where r is the distance between the particles. The value of x is:Gaseous State
Q1274Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Heavy water is used for the study of…Hydrogen
Q1422Given below are two statements: Statement I: Sphalerite is a sulphide or of zinc and copper glance is a sulphide ore of copper. Statement II: It is possible…Isolation of Elements
Q1559Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Barium carbonate is insoluble in…Classification of Elements and Periodicity in Properties
Q2261The sol given below with negatively charged colloidal particles is:Surface Chemistry

Mathematics

Q22Let Q be the foot of the perpendicular from the point P(7, - 2, 13) on the plane containing the lines (x + 1)/6 = (y - 1)/7 = (z - 3)/8 and (x - 1)/3 = (y…Three Dimensional Geometry
Q25Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x³ - 3x² - 12x. If A is the total area of the region bounded…Integral Calculus
Q26Let (n k) denotes ⁿ C k and [ n k ] = \ (n k), if 0 ≤ k ≤ n 0, otherwise. If A k = Σ i = 0 ⁹ (9 i)[ 12 12 - k + i ] + Σ i = 0 ⁸ (8 i)[ 13 13 - k + i ] and A₄…Binomial Theorem and Its Simple Applications
Q29The least positive integer n such that ((2i)ⁿ)/((1 - i)ⁿ⁻²),i = √(- 1) is a positive integer, is _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q41Let A be a 3 × 3 real matrix. If det(2Adj(2 Adj(Adj(2A)))) = 2⁴¹, then the value of det(A²) equal _ _ _ _ _.Matrices and Determinants
Q44Let λ ≠ 0 be in R. If α and β are the roots of the equation x² - x + 2 λ = 0, and α and γ are the roots of equation 3x² - 10x + 27 λ = 0, then (β γ)/(λ) is…Complex Numbers and Quadratic Equations
Q45The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is _ _ _ _ _ _ _.Sequence and Series
Q46Let a₁, a₂,......., a₁₀ be an AP with common difference - 3 and b₁, b₂,........., b₁₀ be a GP with common ratio 2. Let c k = a k + b k, k = 1, 2,......, 10…Sequence and Series
Q47Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x - y is _ _…Statistics and Probability
Q49If the projection of the vector i + 2 j + k on the sum of the two vectors 2 i + 4 j - 5 k and - λ i + 2 j + 3 k is 1, then λ is equal to _ _ _ _ _.Vector Algebra
Q2587Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes r. (i + j + 4 k) = 16 and r. (- i + j + k) = 6. Then which…Three Dimensional Geometry
Q2658The local maximum value of the function f(x) = (2/x)^(x²), x > 0, isLimit, Continuity and Differentiability
Q3052A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C₁: x² + y² + 2y - 5 = 0 at two points P and Q such that PQ is a diameter of…Coordinate Geometry
Q3243If (3 + i)¹⁰⁰ = 2⁹⁹(p + iq), then p and q are roots of the equation:Complex Numbers and Quadratic Equations
Q3417If the value of the integral ∫₀⁵ (x + [x])/(e^(x - [x]))dx = α e⁻¹ + β, where α, β R, 5 α + 6 β = 0, and [x] denotes the greatest integer less than or equal…Integral Calculus
Q3418The value of ∫ - (π)/2 ^((π)/2) ((1 + sin ²x)/(1 + π ^(sin x))) dx isIntegral Calculus
Q3615Let y(x) be the solution of the differential equation 2x² dy + (e^(y) - 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to:Differential Equations
Q3945The locus of the mid points of the chords of the hyperbola x² - y² = 4, which touch the parabola y² = 8x, is:Coordinate Geometry
Q3953The point P(- 2 6, 3) lies on the hyperbola (x²)/(a²) - (y²)/(b²) = 1 having eccentricity (5)/2. If the tangent and normal at P to the hyperbola intersect its…Coordinate Geometry
Q4063The domain of the function cosec ⁻¹ ((1 + x)/x) is:Trigonometry
Q4123If Σ r = 1 ⁵⁰ tan ⁻¹1/(2r²) = p, then the value of tan p is:Trigonometry
Q4204Let [t] denote the greatest integer less than or equal to t. Let f(x) = x - [x], g(x) = 1 - x + [x], and h(x) = min f(x), g(x), x [ - 2, 2]. Then h is:Limit, Continuity and Differentiability
Q4237lim x → 2 (Σ n = 1 ⁹ x/(n(n + 1)x² + 2(2n + 1)x + 4)) is equal to:Limit, Continuity and Differentiability
Q4353Consider the two statements: (S1): (p → q) (q → p) is a tautology. (S2): (p q) (p q) is a fallacy. Then:Mathematical Reasoning
Q4491Let A = (1 0 0 0 1 1 1 0 0). Then A²⁰²⁵ - A²⁰²⁰ is equal to:Matrices and Determinants
Q4917Two fair dice are thrown. The numbers on them are taken as λ and μ, and a system of linear equations x + y + z = 5 x + 2y + 3z = μ x + 3y + λ z = 1 is…Statistics and Probability
Q4960A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x ≥ 5 | x > 2) is:Statistics and Probability
Q5662The value of 2 sin ((π)/8) sin ((2π)/8) sin ((3π)/8) sin ((5π)/8) sin ((6π)/8) sin ((7π)/8) is:Trigonometry