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

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JEE Main 202125 Jul, Morning shift

Physics 23Chemistry 18Mathematics 29

Physics

Q49An inductor of 10 mH is connected to a 20V battery through a resistor of 10 k Ω and a switch. After a long time, when maximum current is set up in the…Electromagnetic Induction and Alternating Currents
Q53A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but…Rotational Motion
Q55An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the…Current Electricity
Q58A circular conducting coil of radius 1 m is being heated by the change of magnetic field B passing perpendicular to the plane in which the coil is laid. The…Electromagnetic Induction and Alternating Currents
Q60A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If…Electrostatics
Q65The value of aluminium susceptibility is 2.2 × 10⁻⁵. The percentage increase in the magnetic field if space within a current carrying toroid is filled with…Magnetic Effects of Current and Magnetism
Q68A particle of mass 'm' is moving in time 't' on a trajectory given by r = 10α t² i + 5β (t - 5) j Where α and β are dimensional constants. The angular…Rotational Motion
Q70A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the…Oscillations and Waves
Q6109Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when…Atoms and Nuclei
Q6110The half-life of ¹⁹⁸Au is 3 days. If atomic weight of ¹⁹⁸Au is 198 g/mol then the activity of 2 mg of ¹⁹⁸Au is [in disintegration/second]:Atoms and Nuclei
Q6155A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when…Electrostatics
Q6354In amplitude modulation, the message signal V m (t) = 10 sin (2 π × 10⁵t) volts and Carrier signal V C (t) = 20 sin(2 π × 10⁷ t) volts The modulated signal…Communication Systems
Q6563What should be the order of arrangement of de-Broglie wavelength of electron (λ e), an α -particle (λ a) and proton (λ p) given that all have the same kinetic…Dual Nature of Matter and Radiation
Q6564A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of…Dual Nature of Matter and Radiation
Q6778A linearly polarized electromagnetic wave in vacuum is E = 3.1 cos [ (1.8)z - (5.4 × 10⁶)t ] iN/C is incident normally on a perfectly reflecting wall at z =…Electromagnetic Waves
Q7106A ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond-air interface. It is going from diamond to air. The refractive index of…Optics
Q7268The minimum and maximum distances of a planet revolving around the sun are x₁ and x₂. If the minimum speed of the planet on its trajectory is v₀ then its…Gravitation
Q7385For a gas C P - C V = R in a state P and C P - C V = 1.10 R in a state Q, T P and T Q are the temperatures in two different states P and Q respectively. ThenThermodynamics
Q7486A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to…Thermodynamics
Q7861Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4^(t)h second after its fall to the next droplet is…Kinematics
Q7943Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y₁ and Y₂. The combination…Properties of Solids and Liquids
Q8101Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Moment of inertia of a circular disc of…Rotational Motion
Q8437In the Young's double slit experiment, the distance between the slits varies in time as d(t) = d₀ + a₀ sin ω t; where d₀, ω and a₀ are constants. The…Optics

Chemistry

Q2For the reaction A + B 2C the value of equilibrium constant is 100 at 298 K. If the initial concentration of all the three species is 1 M each, then the…Equilibrium
Q4Three moles of AgCl get precipitated when one mole of an octahedral co-ordination compound with empirical formula CrCl₃.3NH₃.3H₂O reacts with excess of silver…Coordination Compounds
Q7Consider the cell at 25° C Zn | Zn²⁺ (aq), (1M) || Fe³⁺ (aq), Fe²⁺ (aq) | Pt(s) The fraction of total iron present as Fe³⁺ ion at the cell potential of 1.500…Redox Reactions and Electrochemistry
Q8A home owner uses 4.00 × 10³ m³ of methane (CH₄) gas, (assume CH₄ is an ideal gas) in a year to heat his home. Under the pressure of 1.0 atm and 300 K, mass…Gaseous State
Q15CO₂ gas is bubbled through water during a soft drink manufacturing process at 298 K. If CO₂ exerts a partial pressure of 0.835 bar then x m mol of CO₂ would…Solutions
Q16When 10 mL of an aqueous solution of Fe²⁺ ions was titrated in the presence of dil H₂SO₄ using diphenylamine indicator, 15 mL of 0.02 M solution of K₂Cr₂O₇…Some Basic Concepts in Chemistry
Q17Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is _ _ _ _ _ _ × 10⁻¹ g. (in nearest integer)Some Basic Concepts in Chemistry
Q18A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, x × 10²⁰…Atomic Structure
Q19At 298 K, the enthalpy of fusion of a solid (X) is 2.8 kJ mol⁻¹ and the enthalpy of vaporisation of the liquid (X) is 98.2 kJ mol⁻¹. The enthalpy of…Chemical Thermodynamics
Q207The water soluble protein is:Biomolecules
Q539Given below are two statements, one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A): Gabriel phthalimide synthesis cannot be…Organic Compounds Containing Nitrogen
Q734Which one of the following species responds to an external magnetic field?Coordination Compounds
Q768The correct order of following 3d metal oxides, according to their oxidation numbers is: (a) CrO₃, (b) Fe₂O₃, (c) MnO₂, (d) V₂O₅, (e) Cu₂Od- and f-Block Elements
Q1249At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol⁻¹) for hydrogen (E H) and its isotope, deuterium (E D), is best described by:Hydrogen
Q1354In the leaching of alumina from bauxite, the ore expected to leach out in the process by reacting with NaOH is:Isolation of Elements
Q1472Which one of the following compounds of Group-14 elements is not known?p-Block Elements
Q1557The ionic radii of K⁺, Na⁺, Al³⁺ and Mg²⁺ are in the order:Classification of Elements and Periodicity in Properties
Q1887Given below are two statements: Statement I: None of the alkaline earth metal hydroxides dissolve in alkali. Statement II: Solubility of alkaline earth metal…S Block Elements

Mathematics

Q23The term independent of 'x' in the expansion of ((x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2)))¹⁰, where x ≠ 0, 1 is equal to _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q24The ratio of the coefficient of the middle term in the expansion of (1 + x)²⁰ and the sum of the coefficients of two middle terms in expansion of (1 + x)¹⁹ is…Binomial Theorem and Its Simple Applications
Q26Let S = \ n N| (0 i 1 0) ⁿ (a b c d) = (a b c d) a,b,c,d R. \, where i = √(- 1). Then the number of 2-digit numbers in the set S is _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q29Let y = y(x) be solution of the following differential equation e^(y)dy/dx - 2e^(y) sin x + sin x cos ² x = 0,y((π)/2) = 0 If y(0) = log e (α + β e⁻²), then…Differential Equations
Q37Let M = \ A = (a b c d):a,b,c,d ± 3, ± 2, ± 1,0 \. Define f: M → Z, as f(A) = det(A), for all A M, where z is set of all integers. Then the number of A M such…Matrices and Determinants
Q40There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so…Permutations and Combinations
Q43If α, β are roots of the equation x² + 5(2)x + 10 = 0, α > β and P n = α ⁿ - β ⁿ for each positive integer n, then the value of ((P₁₇P₂₀ + 5 2 P₁₇P₁₉)/(P₁₈P₁₉…Complex Numbers and Quadratic Equations
Q45If the value of (1 + 2/3 + 6/(3²) + 10/(3³) +....upto ∞)^(log (0.25) (1/3 + 1/(3²) + 1/(3³) +....upto ∞)) is l, then l ² is equal to _ _ _ _ _ _ _ _.Sequence and Series
Q46Consider the following frequency distribution: Class: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 Frequency: | α | 110 | 54 | 30 | β If the sum of all frequencies…Statistics and Probability
Q48Let p = 2 i + 3 j + k and q = i + 2 j + k be two vectors. If a vector r = (α i + β j + γ k) is perpendicular to each of the vectors ((p + q) and (p - q), and…Vector Algebra
Q2432Let the foot of perpendicular from a point P(1, 2, - 1) to the straight line L:x/1 = y/0 = z/(- 1) be N. Let a line be drawn from P parallel to the plane x +…Three Dimensional Geometry
Q2721Let f(x) = 3 sin ⁴x + 10 sin ³x + 6 sin ²x - 3, x [ - (π)/6,(π)/2 ]. Then, f is:Limit, Continuity and Differentiability
Q2834The area (in sq. units) of the region, given by the set (x,y) R × R|x ≥ 0,2x² ≤ y ≤ 4 - 2x is:Integral Calculus
Q2963If b is very small as compared to the value of a, so that the cube and other higher powers of b/a can be neglected in the identity 1/(a - b) + 1/(a - 2b) +…Binomial Theorem and Its Simple Applications
Q3411The value of the definite integral ∫ π /24 ^(5π /24) dx/(1 + 3 tan 2x) is:Integral Calculus
Q3412Let f:[0,∞) → [0,∞) be defined as f(x) = ∫₀ˣ [y]dy where [x] is the greatest integer less than or equal to x. Which of the following is true?Integral Calculus
Q3611Let y = y(x) be the solution of the differential equation dy/dx = 1 + x e^(y - x), - 2 < x < 2,y(0) = 0 then, the minimum value of y(x),x (- 2, 2) is equal to:Differential Equations
Q3715Let an ellipse E:(x²)/(a²) + (y²)/(b²) = 1, a² > b², passes through (√(3/2),1) and has eccentricity 1/(3). If a circle, centered at focus F(α, 0), α > 0, of E…Coordinate Geometry
Q3804Let g: N → N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n ≥ 0. Then which of the following statements is true?Sets, Relations and Functions
Q3925A spherical gas balloon of radius 16 meter subtends an angle 60° at the eye of the observer A while the angle of elevation of its center from the eye of A is…Height and Distance
Q3944The locus of the centroid of the triangle formed by any point P on the hyperbola 16x² - 9y² + 32x + 36y - 164 = 0, and its foci is:Coordinate Geometry
Q4148Let f: R → R be defined as f(x) = \ (λ | x² - 5x + 6 |)/(μ (5x - x² - 6)), x < 2 e^((tan (x - 2))/(x - [x])), x > 2 μ, x = 2. where [x] is the greatest…Limit, Continuity and Differentiability
Q4350The Boolean expression (p ⇒ q) (q ⇒ p) is equivalent to:Mathematical Reasoning
Q4596The values of a and b, for which the system of equations 2x + 3y + 6z = 8 x + 2y + az = 5 3x + 5y + 9z = b has no solution, are:Matrices and Determinants
Q4747Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn…Coordinate Geometry
Q4985Let 9 distinct balls be distributed among 4 boxes, B₁, B₂, B₃ and B₄. If the probability than B₃ contains exactly 3 balls is k (3/4)⁹ then k lies in the set:Statistics and Probability
Q5045The number of real roots of the equation e⁶ˣ - e⁴ˣ - 2e³ˣ - 12e²ˣ + eˣ + 1 = 0 is:Complex Numbers and Quadratic Equations
Q5221Let S n be the sum of the first n terms of an arithmetic progression. If S₃n = 3S₂n, then the value of (S 4n)/(S 2n) is:Sequence and Series
Q5733Let the vectors (2 + a + b) i + (a + 2b + c) j - (b + c) k,(1 + b) i + 2b j - b k and (2 + b) i + 2b j + (1 - b) k, a,b,c, R be co-planar. Then which of the…Vector Algebra