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JEE Main 2021 22 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202122 Jul, Evening shift

Physics 25Chemistry 21Mathematics 29

Physics

Q54The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its…Rotational Motion
Q57In an electric circuit, a cell of certain emf provides a potential difference of 1.25 V across a load resistance of 5 Ω. However, it provides a potential…Current Electricity
Q62The total charge enclosed in an incremental volume of 2 × 10⁻⁹ m³ located at the origin is _ _ _ _ _ n C, if electric flux density of its field is found as D…Electrostatics
Q63A ray of light passing through a prism (μ = 3) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the…Optics
Q66The area of cross-section of a railway track is 0.01 m². The temperature variation is 10° C. Coefficient of liner expansion of material of track is 10⁻⁵/° C…Thermodynamics
Q69In 5 minutes, a body cools from 75° C to 65° C at room temperature of 25° C. The temperature of body at the end of next 5 minutes is _ _ _ _ _° C.Properties of Solids and Liquids
Q71The centre of a wheel rolling on a plane surface moves with a speed v₀. A particle on the rim of the wheel at the same level as the centre will be moving at a…Rotational Motion
Q73Three students S₁, S₂ and S₃ perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of…Units and Measurements
Q74Three particles P, Q and R are moving along the vectors A = i + j, B = j + k and C = - i + j respectively. They strike on a point and start to move in…Kinematics
Q5895Match List - I with List - II List - I List - II (a) ω L > 1/(ω C) (i) Current is in phase with emf (b) ω L = 1/(ω C) (ii) Current lags behind the applied emf…Electromagnetic Induction and Alternating Currents
Q6051A nucleus with mass number 184 initially at rest emits an α -particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α…Atoms and Nuclei
Q6240A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms⁻¹, the impulse imparted to the gun and velocity of…Rotational Motion
Q6315What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km? The average population…Communication Systems
Q6562An electron of mass m e and a proton of mass m p are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with…Dual Nature of Matter and Radiation
Q6777Intensity of sunlight is observed as 0.092 Wm⁻² at a point in free space. What will be the peak value of magnetic field at the point? (ε ₀ = 8.85 ×…Electromagnetic Waves
Q6875Consider a situation in which reserve biased current of a particular P-N junction increases when it is exposed to a light of wavelength ≤ 621 nm. During this…Electronic Devices
Q6946An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 × 10⁻⁶ C/m. Line charge is placed on z-axis and positive and…Electrostatics
Q7230A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach…Gravitation
Q7309What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?Thermodynamics
Q7624Choose the correct optionMagnetic Effects of Current and Magnetism
Q7645Statement I: The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II: At high temperature, the…Magnetic Effects of Current and Magnetism
Q8072Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start…Rotational Motion
Q8205T₀ is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to 1/16 times of its initial value, the modified time period is:Oscillations and Waves
Q8386What will be the projection of vector A = i + j + k on vector B = i + j ?Kinematics
Q8620A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done…Work, Energy and Power

Chemistry

Q2The number of acyclic structural isomers (including geometrical isomers) for pentene are _ _ _ _ _ _Some Basic Principles of Organic Chemistry
Q6Value of K P for the equilibrium reaction N₂O₄(g) 2NO₂(g) at 288 K is 47.9. The K C for this reaction at same temperature is _ _ _ _ _ _. (Nearest integer) (R…Equilibrium
Q7N₂O 5(g) → 2N O 2(g) + 1/2O 2(g) In the above first order reaction the initial concentration of N₂O₅ is 2.40 × 10⁻² mol L⁻¹ at 318 K. The concentration of…Chemical Kinetics
Q9The total number of unpaired electrons present in [Co(NH₃)₆]Cl₂ and [Co(NH₃)₆]Cl₃ is:Coordination Compounds
Q11Number of electrons that Vanadium (Z = 23) has in p-orbitals is equal to _ _ _ _ _ _ _d- and f-Block Elements
Q12Assume a cell with the following reaction C u (s) + 2A g⁺ (1 × 10⁻³M) → C u²⁺ (0.250M) + 2A g (s) E cell ^Θ = 2.97 V E c ell for the above reaction is _ _ _ _…Redox Reactions and Electrochemistry
Q17Methylation of 10 g of benzene gave 9.2 g of toluene. Calculate the percentage yield of toluene _ _ _ _ _. (Nearest integer)Principles Related to Practical Chemistry
Q19A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a…Solid State
Q21If the concentration of glucose (C₆H₁₂O₆) in blood is 0.72 g L⁻¹, the molarity of glucose in blood is _ _ _ _ _ _ × 10⁻³ M. (Nearest integer) [Given: Atomic…Some Basic Concepts in Chemistry
Q22If the standard molar enthalpy change for combustion of graphite powder is - 2.48 × 10² kJ mol⁻¹, the amount of heat generated on combustion of 1 g of…Chemical Thermodynamics
Q129Which purification technique is used for high boiling organic liquid compound (decomposes near its boiling point)?Some Basic Principles of Organic Chemistry
Q238Thiamine and pyridoxine are also known respectively as:Biomolecules
Q305Match List-I with List-II: List-I (Species) List-II (Hybrid Orbitals) (a) S F₄ (i) s p³ d² (b) I F₅ (ii) d²s p³ (c) NO₂⁺ (iii) s p³ d (d) NH₄⁺ (iv) s p³ (v)…Chemical Bonding and Molecular Structure
Q489Isotope(s) of hydrogen which emits low energy β ^(- p)articles with t₁/2 value > 12 years is/areNuclear Chemistry (historical)
Q878The set having ions which are coloured and paramagnetic both is:d- and f-Block Elements
Q1273The water having more dissolved O₂ is:Hydrogen
Q1421Sulphide ion is soft base and its ores are common for metals. (a) Pb (b) Al (c) Ag (d) MgIsolation of Elements
Q1488Which one of the following group-15 hydride is the strongest reducing agent?p-Block Elements
Q1654Which one of the following statements for D.I. Mendeleeff, is incorrect?Classification of Elements and Periodicity in Properties
Q1771When silver nitrate solution is added to potassium iodide solution then the sol produced is:Principles Related to Practical Chemistry
Q1967Which one of the following 0.06 M aqueous solutions has lowest freezing point?Solutions

Mathematics

Q26The area (in sq. units) of the region bounded by the curves x² + 2y - 1 = 0, y² + 4x - 4 = 0 and y² - 4x - 4 = 0, in the upper half plane is _ _ _ _ _ _ _ _.Integral Calculus
Q27If the constant term, in binomial expansion of (2x^(r) + 1/(x²))¹⁰ is 180, then r is equal to _ _ _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q28The number of elements in the set n 1, 2, 3,......., 100 | (11)ⁿ > (10)ⁿ + (9)ⁿ is _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q33Let y = y(x) be the solution of the differential equation ((x + 2)e^(((y + 1)/(x + 2))) + (y + 1))dx = (x + 2)dy, y(1) = 1. If the domain of y = y(x) is an…Differential Equations
Q35Let A = 0, 1, 2, 3, 4, 5, 6, 7. Then the number of bijective functions f: A → A such that f(1) + f(2) = 3 - f(3) is equal toSets, Relations and Functions
Q39Let f: R → R be a function defined as f(x) = \ 3(1 - (|x|)/2) if |x| ≤ 2 0 if |x| > 2. Let g: R → R be given by g(x) = f(x + 2) - f(x - 2). If n and m denote…Limit, Continuity and Differentiability
Q41Let A = [ 0 1 0 1 0 0 0 0 1 ]. Then the number of 3 × 3 matrices B with entries from the set 1, 2, 3, 4, 5 and satisfying AB = BA is _ _ _ _ _ _.Matrices and Determinants
Q44If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to…Permutations and Combinations
Q48The sum of all the elements in the set n 1, 2,....., 100 | H.C.F. of n and 2040 is 1 is equal to _ _ _ _ _ _ _.Sequence and Series
Q49Consider the following frequency distribution: Class: | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 Frequency: | a | b | 12 | 9 | 5 If mean = 309/22 and median = 14…Statistics and Probability
Q2431Let L be the line of intersection of planes r.(i - j + 2 k) = 2 and r.(2 i + j - k) = 2. If P(α,β,γ) is the foot of perpendicular on L from the point (1, 2…Three Dimensional Geometry
Q2499If the shortest distance between the straight lines 3(x - 1) = 6(y - 2) = 2(z - 1) and 4(x - 2) = 2(y - λ) = (z - 3),λ R is 1/(√(38)), then the integral value…Three Dimensional Geometry
Q2720Let f: R → R be defined as f(x) = \ - 4/3x³ + 2x² + 3x, x > 0 3x eˣ, x ≤ 0.. Then f is increasing function in the intervalLimit, Continuity and Differentiability
Q3111Let the circle S: 36x² + 36y² - 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the…Coordinate Geometry
Q3223Let n denote the number of solutions of the equation z² + 3 z = 0, where z is a complex number. Then the value of Σ k = 0 ^∞ 1/(n^(k)) is equal to:Complex Numbers and Quadratic Equations
Q3410If ∫₀^(100π) (sin ²x)/(e^((x/(π) - [ x/(π) ])))dx = (α π ³)/(1 + 4π ²),α R where [x] is the greatest integer less than or equal to x, then the value of α is:Integral Calculus
Q3533Let y = y(x) be the solution of the differential equation cos e c² xdy + 2dx = (1 + y cos 2x) cos e c² xdx, with y((π)/4) = 0. Then, the value of (y(0) + 1)²…Differential Equations
Q3757Let E₁:(x²)/(a²) + (y²)/(b²) = 1,a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end…Coordinate Geometry
Q3990Let a line L: 2x + y = k, k > 0 be a tangent to the hyperbola x² - y² = 3. If L is also a tangent to the parabola y² = α x, then α is equal to:Coordinate Geometry
Q4062If the domain of the function f(x) = (cos ⁻¹√(x² - x + 1))/(√(sin ⁻¹((2x - 1)/2))) is the interval (α, β ], then α + β is equal to:Trigonometry
Q4147Let f: R → R be defined as f(x) = \ (x³)/((1 - cos 2x)²) log e (1 + 2x e⁻²ˣ (1 - x e⁻ˣ) ²), x ≠ 0 α, x = 0. If f is continuous at x = 0, then α is equal to:Limit, Continuity and Differentiability
Q4349Which of the following Boolean expressions is not a tautology?Mathematical Reasoning
Q4502Let A = [a i j] be a real matrix of order 3 × 3, such that a i 1 + a i 2 + a i 3 = 1, for i = 1, 2, 3. Then, the sum of all the entries of the matrix A³ is…Matrices and Determinants
Q4595The values of λ and μ such that the system of equations x + y + z = 6, 3x + 5y + 5z = 26, x + 2y + λ z = μ has no solution, are:Matrices and Determinants
Q4984Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrix have all…Statistics and Probability
Q5061Let [x] denote the greatest integer less than or equal to x. Then, the values of x R satisfying the equation [eˣ]² + [eˣ + 1] - 3 = 0 lie in the interval:Complex Numbers and Quadratic Equations
Q5220Let S n denote the sum of first n-terms of an arithmetic progression. If S₁₀ = 530, S₅ = 140, then S₂₀ - S₆ is equal to:Sequence and Series
Q5731Let a vector a be coplanar with vectors b = 2 i + j + k and c = i - j + k. If a is perpendicular to d = 3 i + 2 j + 6 k, and | a | = √(10). Then a possible…Vector Algebra
Q5732Let three vectors a, b and c be such that a × b = c, b × c = a and | a | = 2. Then which one of the following is not true?Vector Algebra