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JEE Main 2021 25 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202125 Jul, Evening shift

Physics 24Chemistry 21Mathematics 28

Physics

Q52From the given data, the amount of energy required to break the nucleus of aluminium ₁₃²⁷ Al is _ _ _ _ _ x × 10⁻³ J. Mass of neutron = 1.00866 u Mass of…Atoms and Nuclei
Q53The nuclear activity of a radioactive element becomes (1/8)^(th) of its initial value in 30 years. The half-life of radioactive element is _ _ _ _ _ _ y ears.Atoms and Nuclei
Q55A message signal of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The…Communication Systems
Q56A 16 Ω wire is bend to form a square loop. A 9V supply having internal resistance of 1 Ω is connected across one of its sides. The potential drop across the…Current Electricity
Q59A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted…Dual Nature of Matter and Radiation
Q60In a semiconductor, the number density of intrinsic charge carries at 27° C is 1.5 × 10¹⁶/m³. If the semiconductor is doped with impurity atom, the hole…Electronic Devices
Q63A system consists of two types of gas molecules A and B having same number density 2 × 10²⁵/m³. The diameter of A and B are 10 A^(o) and 5 A^(o) respectively…Thermodynamics
Q70A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through…Rotational Motion
Q74A force of F = (5y + 20) j N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is _ _ _ _ _ J.Work, Energy and Power
Q5896A 10 Ω resistance is connected across 220V - 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is:Electromagnetic Induction and Alternating Currents
Q6156If q f is the free charge on the capacitor plates and q b is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor…Electrostatics
Q6565An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is:Dual Nature of Matter and Radiation
Q6640When radiation of wavelength λ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is…Dual Nature of Matter and Radiation
Q7107A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in…Optics
Q7143Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object…Gravitation
Q7586A force F = (40 i + 10 j)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10 s, will be:Laws of Motion
Q7758Two ions having same mass have charges in the ratio 1: 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2: 3. The…Magnetic Effects of Current and Magnetism
Q7833The instantaneous velocity of a particle moving in a straight line is given as V = α t + β t², where α and β are constants. The distance travelled by the…Kinematics
Q7862A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the…Kinematics
Q7887The relation between time t and distance x for a moving body is given as t = mx² + nx, where m and n are constants. The retardation of the motion is: (When v…Kinematics
Q8017Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:Properties of Solids and Liquids
Q8161In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and…Oscillations and Waves
Q8247The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of AD/B is:Units and Measurements
Q8378Two vectors X and Y have equal magnitude. The magnitude of (X - Y) is n times the magnitude of (X + Y). The angle between X and Y is:Kinematics

Chemistry

Q3Assuming that Ba(OH)₂ is completely ionised in aqueous solution under the given conditions the concentration of H₃O⁺ ions in 0.005 M aqueous solution of…Equilibrium
Q4For a chemical reaction A → B, it was found that concentration of B is increased by 0.2 mol L⁻ⁱn 30 min. The average rate of the reaction is _ _ _ _ _ _ ×…Chemical Kinetics
Q8Number of electrons present in 4f orbital of Ho³⁺ ion is _ _ _ _ _ _. (Given Atomic No. of Ho = 67)d- and f-Block Elements
Q11An LPG cylinder contains gas at a pressure of 300 kPa at 27°. The cylinder can withstand the pressure of 1.2 × 10⁶ Pa. The room in which the cylinder is kept…Gaseous State
Q150.8 g of an organic compound was analyzed by Kjeldahl's method for the estimation of nitrogen. If the percentage of nitrogen in the compound was found to be…Principles Related to Practical Chemistry
Q18When 3.00 g of a substance 'X' is dissolved in 100 g of CCl₄, it raises the boiling point by 0.60 K. The molar mass of the substance 'X' is _ _ _ _ _ _ _ g…Solutions
Q19The number of significant figures in 0.00340 is _ _ _ _ _ _.Some Basic Concepts in Chemistry
Q20An accelerated electron has a speed of 5 × 10⁶ ms⁻¹ with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x × 10⁻⁹ m. The…Atomic Structure
Q22A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change in internal energy is _ _ _ _ _ _ J. (Nearest integer)Chemical Thermodynamics
Q372In the following the correct bond order sequence is:Chemical Bonding and Molecular Structure
Q387Identify the species having one π -bond and maximum number of canonical forms from the following:Chemical Bonding and Molecular Structure
Q593Which one of the following metal complexes is most stable?Coordination Compounds
Q769Which one of the following metals forms interstitial hydride easily?d- and f-Block Elements
Q879The spin only magnetic moments (in BM) for free Ti³⁺, V²⁺ and Sc³⁺ ions respectively are: (At.No. Sc: 21, Ti: 22, V: 23)d- and f-Block Elements
Q1030Given below are two statements: Statement I: Chlorofluoro breakdown by radiation in the visible energy region and release chlorine gas in the atmosphere which…Environmental Chemistry
Q1355Match List I with List II: (Both having metallurgical terms) List - I List - II (a) Concentration of Ag ore (i) Reverberatory furnace (b) Blast furnace (ii)…Isolation of Elements
Q1558The ionic radii of F^(- a)nd O² - respectively are 1.33 A^(o) and 1.4 A^(o), while the covalent radius of N is 0.74 A^(o). The correct statement for the ionic…Classification of Elements and Periodicity in Properties
Q1692A biodegradable polyamide can be made from:Polymers
Q1808Identify the process in which change in the oxidation state is five:Redox Reactions and Electrochemistry
Q1826Match List I with List II: List-I Elements List-II Properties (a) Li (i) Poor water solubility of I^(- s)alt (b) Na (ii) Most abundant element in cell fluid…S Block Elements
Q2260Match List I with List II: List-I Example of colloids List - II Classification (a) Cheese (i) dispersion of liquid in liquid (b) Pumice stone (ii) dispersion…Surface Chemistry

Mathematics

Q23If the lines (x - k)/1 = (y - 2)/2 = (z - 3)/3 and (x + 1)/3 = (y + 2)/2 = (z + 3)/1 are co-planar, then the value of k is _ _ _ _ _ _ _.Three Dimensional Geometry
Q27If the co-efficient of x⁷ and x⁸ in the expansion of (2 + x/3)ⁿ are equal, then the value of n is equal to _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q28Let n N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ⁿ C₀,3.ⁿ C₁,5.ⁿ C₂,7.ⁿ C₃,..... is equal to 2¹⁰⁰. 101, then…Binomial Theorem and Its Simple Applications
Q29The equation of a circle is Re(z²) + 2(Im(z))² + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of…Complex Numbers and Quadratic Equations
Q32Let a curve y = f(x) pass through the point (2, (log e 2)²) and have slope 2y x log e x for all positive real value of x. Then the value of f(e) is equal to _…Differential Equations
Q40A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is _ _ _ _ _ _ _.Statistics and Probability
Q43If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a⁴ + b⁴ + c⁴ is equal to _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q49If (a + 3 b) is perpendicular to (7 a - 5 b) and (a - 4 b) is perpendicular to (7 a - 2 b), then the angle between a and b (in degrees) is _ _ _ _ _ _ _ _.Vector Algebra
Q2887The lowest integer which is greater than (1 + 1/(10¹⁰⁰))^(10¹⁰⁰) is _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q2933The sum of all those terms which are rational numbers in the expansion of (2¹/3 + 3¹/4)¹² is:Binomial Theorem and Its Simple Applications
Q2934If the greatest value of the term independent of 'x' in the expansion of (x sin α + a(cos α)/x)¹⁰ is (10!)/((5!)²), then the value of 'a' is equal to:Binomial Theorem and Its Simple Applications
Q3413If f(x) = \ ∫₀ˣ (5 + | 1 - t |)dt, x > 2 5x + 1, x ≤ 2., thenIntegral Calculus
Q3414The value of the integral ∫₋₁¹ log (x + √(x² + 1))dx is:Integral Calculus
Q3613Let y = y(x) be the solution of the differential equation xdy = (y + x³ cosx)dx with y(π) = 0, then y((π)/2) is equal to:Differential Equations
Q3782If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through…Coordinate Geometry
Q3825Consider function f: A → B and g: B → C (A, B, C R) such that (gof)⁻¹ exists, then:Sets, Relations and Functions
Q4418Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:Mathematical Reasoning
Q4466The number of distinct real roots of | sin x cos x cos x cos x sin x cos x cos x cos x sin x | = 0 in the interval - (π)/4 ≤ x ≤ (π)/4 is:Matrices and Determinants
Q4503If P = [ 1 0 1/2 1 ], then P⁵⁰ is:Matrices and Determinants
Q4830If ⁿ P r = ⁿ P r + 1 and ⁿ C r = ⁿ C r - 1, then the value of r is equal to:Permutations and Combinations
Q4999Let X be a random variable such that the probability function of a distribution is given by P(X = 0) = 1/2,P(X = j) = 1/(3^(j))(j = 1,2,3,...,∞). Then the…Statistics and Probability
Q5062If [x] be the greatest integer less than or equal to x, then Σ n = 8 ¹⁰⁰ [ ((- 1)ⁿn)/2 ] is equal to:Complex Numbers and Quadratic Equations
Q5084The number of real solutions of the equation, x² - |x| - 12 = 0 is:Complex Numbers and Quadratic Equations
Q5466The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard…Statistics and Probability
Q5580Let the equation of the pair of lines, y = px and y = qx, can be written as (y - px) (y - qx) = 0. Then the equation of the pair of the angle bisectors of the…Coordinate Geometry
Q5670The value of cot (π)/24 is:Trigonometry
Q5694Let a, b and c be distinct positive numbers. If the vectors a i + a j + c k, i+ k and c i + c j + b k are co-planar, then c is equal to:Vector Algebra
Q5815If | a | = 2,| b | = 5 and | a × b | = 8, then | a. b | is equal to:Vector Algebra