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JEE Main 2021 17 Mar Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202117 Mar, Morning shift

Physics 21Chemistry 19Mathematics 29

Physics

Q53A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is…Electrostatics
Q54For VHF signal broadcasting, _ _ _ _ _ k m² of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at…Communication Systems
Q55The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np…Current Electricity
Q58If 2.5 × 10⁻⁶ N average force is exerted by a light wave on a non-reflecting surface of 30 cm² area during 40 minutes of time span, the energy flux of light…Electromagnetic Waves
Q60The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is _ _ _ _ _ _.Gravitation
Q67The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _ _ _…Rotational Motion
Q5887An AC current is given by I = I₁ sin ω t + I₂ cos ω t. A hot wire ammeter will give a reading:Electromagnetic Induction and Alternating Currents
Q6001If an electron is moving in the n^(t)h orbit of the hydrogen atom, then its velocity (v n) for the n^(t)h orbit is given as:Atoms and Nuclei
Q6002Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?Atoms and Nuclei
Q6399A current of 10A exists in a wire of cross-sectional area of 5 mm² with a drift velocity of 2 × 10⁻³ ms⁻¹. The number of free electrons in each cubic meter of…Current Electricity
Q6559An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)Dual Nature of Matter and Radiation
Q7047The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 10⁸ ms⁻¹. The…Optics
Q7304A polyatomic ideal gas has 24 vibrational modes. What is the value of γ ?Thermodynamics
Q7305Two ideal polyatomic gases at temperatures T₁ and T₂ are mixed so that there is no loss of energy. If F₁ and F₂, m₁ and m₂, n₁ and n₂ be the degrees of…Kinetic Theory of Gases
Q7343Two identical metal wires of thermal conductivities K₁ and K₂ respectively are connected in series. The effective thermal conductivity of the combination is:Properties of Solids and Liquids
Q7681A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic…Magnetic Effects of Current and Magnetism
Q7847A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t…Kinematics
Q8015When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is:Properties of Solids and Liquids
Q8157For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?Oscillations and Waves
Q8356The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies…Experimental Skills
Q8584A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms⁻¹. The ball gets deflected by an obstacle on the way. After deflection it…Work, Energy and Power

Chemistry

Q40.01 moles of a weak acid HA (K a = 2.0 × 10⁻⁶) is dissolved in 1.0 L of 0.1 M HCl solution. The degree of dissociation of HA is _ _ _ _ _ × 10⁻⁵ (Round off…Equilibrium
Q5For a certain first order reaction 32% of the reactant is left after 570s. The rate constant of this reaction is _ _ _ _ _ × 10⁻³ s⁻¹. (Round off to the…Chemical Kinetics
Q9The pressure exerted by a non-reactive gaseous mixture of 6.4g of methane and 8.8 g of carbon dioxide in a 10L vessel at 27° C is _ _ _ _ _ kPa. (Round off to…Gaseous State
Q15The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility of oxygen in water is _ _ _ _ _ × 10⁻⁵ mol…Solutions
Q1615 mL of aqueous solution of Fe²⁺ in acidic medium completely reacted with 20 mL of 0.03 M aqueous Cr₂O ₇²⁻. The molarity of the Fe²⁺ solution is _ _ _ _ _ ×…Some Basic Concepts in Chemistry
Q17The mole fraction of a solute in a 100 molal aqueous solution is _ _ _ _ _ _ × 10⁻². (Round off to the Nearest Integer). [Given: Atomic masses: H: 1.0 u, O…Some Basic Concepts in Chemistry
Q18A certain orbital has n = 4 and m L = - 3. The number of radial nodes in this orbital is _ _ _ _ _ _. (Round off to the Nearest Integer).Atomic Structure
Q20The standard enthalpies of formation of Al₂O₃ and CaO are - 1675 kJ mol⁻¹ and - 635 kJ mol⁻¹ respectively. For the reaction 3CaO + 2Al → 3Ca + Al₂O₃ the…Chemical Thermodynamics
Q128Given below are two statements: Statement I: Retardation factor (R f) can be measured in meter/centimeter. Statement II: R f value of a compound remains…Some Basic Principles of Organic Chemistry
Q303A central atom in a molecule has two lone pairs of electrons and forms three single bonds. The shape of this molecule is:Chemical Bonding and Molecular Structure
Q765Given below are two statements: Statement I: Potassium permanganate on heating at 573K forms potassium manganate. Statement II: Both potassium permanganate…d- and f-Block Elements
Q876What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous solution?d- and f-Block Elements
Q1029Reducing smog is a mixture of:Environmental Chemistry
Q1157Which of the following reaction is an example of ammonolysis?Organic Compounds Containing Halogens
Q1272The INCORRECT statement(s) about heavy water is (are) (A) used as a moderator in nuclear reactor (B) obtained as a by-product in fertilizer industry (C) used…Hydrogen
Q1285Which of the following compound CANNOT act as a Lewis base?Equilibrium
Q1575The absolute value of the electron gain enthalpy of halogens satisfies:Classification of Elements and Periodicity in Properties
Q1854The correct order of conductivity of ions in water is:S Block Elements
Q2256A colloidal system consisting of a gas dispersed in a solid is called a/an:Surface Chemistry

Mathematics

Q21If the equation of the plane passing through the line of intersection of the planes 2x - 7y + 4z - 3 = 0, 3x - 5y + 4z + 11 = 0 and the point (- 2, 1, 3) is…Three Dimensional Geometry
Q23If (2021)³⁷⁶² is divided by 17, then the remainder is _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q26The minimum distance between any two points P₁ and P₂ while considering point P₁ on one circle and point P₂ on the other circle for the given circles'…Coordinate Geometry
Q30If [. ] represents the greatest integer function, then the value of | ∫₀^(√((π)/2)) [ [x²] - cos x ]dx | is _ _ _ _ _ _.Integral Calculus
Q32If f(x) = sin (cos ⁻¹((1 - 2²ˣ)/(1 + 2²ˣ))) and its first derivative with respect to x is - b/a log e 2 when x = 1, where a and b are integers, then the…Limit, Continuity and Differentiability
Q36If the function f(x) = (cos (sin x) - cos x)/(x⁴) is continuous at each point in its domain and f(0) = 1/k, then k is _ _ _ _ _ _.Limit, Continuity and Differentiability
Q40If A = [ 2 3 0 - 1 ], then the value of det(A⁴) + det(A¹⁰ - (Adj(2A))¹⁰) is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q44Let there be three independent events E₁, E₂ and E₃. The probability that only E₁ occurs is α, only E₂ occurs is β and only E₃ occurs is γ. Let 'p' denote the…Statistics and Probability
Q47The maximum value of z in the following equation z = 6xy + y², where 3x + 4y ≤ 100 and 4x + 3y ≤ 75 for x ≥ 0 and y ≥ 0 is _ _ _ _ _.Coordinate Geometry
Q49If a = α i + β j + 3 k, b = - β i - α j - k and c = i - 2 j - k such that a. b = 1 and b. c = - 3, then 1/3((a × b). c) is equal to _ _ _ _ _ _ _.Vector Algebra
Q2585The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is:Three Dimensional Geometry
Q2931If the fourth term in the expansion of (x + x^(log ₂x))⁷ is 4480, then the value of x where x N is equal to:Binomial Theorem and Its Simple Applications
Q3098Choose the incorrect statement about the two circles whose equations are given below: x² + y² - 10x - 10y + 41 = 0 and x² + y² - 16x - 10y + 80 = 0Coordinate Geometry
Q3129The line 2x - y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x - 2y = 4. Then, the radius of the circle is:Coordinate Geometry
Q3185The area of the triangle with vertices A(z), B(iz) and C(z + iz) is:Complex Numbers and Quadratic Equations
Q3402Which of the following statements is correct for the function g(α) for α R such that g(α) = ∫ (π)/6 ^((π)/3) (sin ^α x)/(cos ^α x + sin ^α x)dxIntegral Calculus
Q3608Which of the following is true for y(x) that satisfies the differential equation dy/dx = xy - 1 + x - y; y(0) = 0:Differential Equations
Q3882The inverse of y = 5^(log x) is:Sets, Relations and Functions
Q4102The sum of possible values of x for tan⁻¹(x + 1) + cot⁻¹ (1/(x - 1)) = tan⁻¹ (8/31) is:Trigonometry
Q4122If cot⁻¹(α) = cot⁻¹ 2 + cot⁻¹ 8 + cot⁻¹ 18 + cot⁻¹ 32 +...... upto 100 terms, then α is:Trigonometry
Q4283The value of lim x → 0⁺ (cos ⁻¹(x - [x]²). sin ⁻¹(x - [x]²))/(x - x³), where [ x ] denotes the greatest integer ≤ x is:Limit, Continuity and Differentiability
Q4345If the Boolean expression (p ⇒ q) (q (p) is a tautology, then the boolean expression (p (q)) is equivalent to:Mathematical Reasoning
Q4524If A = (0 sin α sin α 0) and det (A² - 1/2I) = 0, then a possible value of α is:Matrices and Determinants
Q4591The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to:Matrices and Determinants
Q4829Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a…Permutations and Combinations
Q4913Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less…Statistics and Probability
Q5149The value of 4 + 1/(5 + 1/(4 + 1/(5 + 1/(4 +......∞)))) is:Complex Numbers and Quadratic Equations
Q5536In a triangle PQR, the co-ordinates of the points P and Q are (- 2, 4) and (4, - 2) respectively. If the equation of the perpendicular bisector of PR is 2x…Coordinate Geometry
Q5728Let a = 2 i - 3 j + 4 k and b = 7 i + j - 6 k. If r × a = r × b, r. (i + 2 j + k) = - 3, then r. (2 i - 3 j + k) is equal to:Vector Algebra