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JEE Main 2021 27 Aug Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202127 Aug, Morning shift

Physics 22Chemistry 19Mathematics 30

Physics

Q52The alternating current is given by i = √(42) sin ((2π)/Tt) + 10 The r.m.s. value of of this current is................. A.Electromagnetic Induction and Alternating Currents
Q55A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line…Communication Systems
Q57First, a set of n equal resistors of 10 Ω each are connected in series to a battery of emf 20V and internal resistance 10 Ω. A current I is observed to flow…Current Electricity
Q65A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and…Magnetic Effects of Current and Magnetism
Q67If the velocity of a body related to displacement x is given by = √(5000 + 24x) m/s, then the acceleration of the body is.................... m/s².Kinematics
Q72Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in…Oscillations and Waves
Q73Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45° and 60° with the…Work, Energy and Power
Q6113There are 10¹⁰ radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? (2 = 1.414)Atoms and Nuclei
Q6274A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its…Kinematics
Q6383Five identical cells each of internal resistance 1 Ω and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of…Current Electricity
Q6643In a photoelectric experiment, increasing the intensity of incident light:Dual Nature of Matter and Radiation
Q6781Electric field in a plane electromagnetic wave is given by E = 50 sin(500x - 10 × 10¹⁰ t) V/m The velocity of electromagnetic wave in this medium is: (Given C…Electromagnetic Waves
Q6906For a transistor in CE mode to be used as an amplifier, it must be operated in:Electronic Devices
Q6967A uniformly charged disc of radius R having surface charge density σ is placed in the xy plane with its center at the origin. Find the electric field…Electrostatics
Q7083An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d₁ from C and the distance of the image…Optics
Q7389A balloon carries a total load of 185 kg at normal pressure and temperature of 27° C. What load will the balloon carry on rising to a height at which the…Thermodynamics
Q7390An ideal gas is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is:Properties of Solids and Liquids
Q7759Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The…Magnetic Effects of Current and Magnetism
Q7907In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 × 10⁻⁵ m and density 1.2 × 10³ kgm⁻³ ? Take viscosity of…Properties of Solids and Liquids
Q8102Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:Rotational Motion
Q8249Which of the following is not a dimensionless quantity?Units and Measurements
Q8342If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be:Units and Measurements

Chemistry

Q3The number of moles of NH₃, that must be added to 2L of 0.80 M AgNO₃ in order to reduce the concentration of Ag⁺ ions to 5.0 × 10⁻⁸ M (K f ormation for…Equilibrium
Q4The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is 2K₂C r₂ O₇ + 8H₂S O₄ + 3C₂H₆O → 2C…Chemical Kinetics
Q61 mol of an octahedral metal complex with formula MCl₃. 2L on reaction with excess of AgNO₃ gives 1 mol of AgCl. The denticity of Ligand L is _ _ _ _ _ _…Coordination Compounds
Q7The number of f electrons in the ground state electronic configuration of Np (Z = 93) is _ _ _ _ _ _. (Nearest integer)d- and f-Block Elements
Q15When 10 mL of an aqueous solution of KMnO₄ was titrated in acidic medium, equal volume of 0.1 M of an aqueous solution of ferrous sulphate was required for…Principles Related to Practical Chemistry
Q16The number of moles of CuO, that will be utilized in Dumas method for estimation nitrogen in a sample of 57.5 g of N, N-dimethylaminopentane is _ _ _ _ _ _ _…Principles Related to Practical Chemistry
Q171 kg of 0.75 molal aqueous solution of sucrose can be cooled up to - 4° C before freezing. The amount of ice (in g) that will be separated out is _ _ _ _ _…Solutions
Q18In Carius method for estimation of halogens, 0.2 g of an organic compound gave 0.188 g of AgBr. The percentage of bromine in the compound is _ _ _ _ _ _ _…Some Basic Concepts in Chemistry
Q19The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to (h²)/(xma₀²). The value of 10x is _ _ _ _ _ _. (a₀ is radius of…Atomic Structure
Q21200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH. The molar heat of neutralization of this reaction is - 57.1 kJ. The increase in temperature in° C of…Chemical Thermodynamics
Q374Match items of List-I with those of List-II: List - I (Property) List - II (Example) (a) Diamagnetism (i) MnO (b) Ferrimagnetism (ii) O₂ (c) Paramagnetism…Chemical Bonding and Molecular Structure
Q534Which of the following is not a correct statement for primary aliphatic amines?Organic Compounds Containing Nitrogen
Q881The nature of oxides V₂O₃ and CrO is indexed as 'X' and 'Y' type respectively. The correct set of X and Y is:d- and f-Block Elements
Q1032The gas 'A' is having very low reactivity reaches to stratosphere. It is non-toxic and non-flammable but dissociated by UV-radiations in stratosphere. The…Environmental Chemistry
Q1131The unit of the van der Waals gas equation parameter 'a' in (P + a n² V²)(V - nb) = nRT is:Gaseous State
Q1251Deuterium resembles hydrogen in properties but:Hydrogen
Q1442Which refining process is generally used in the purification of low melting metals?Isolation of Elements
Q1732Acidic ferric chloride solution on treatment with excess of potassium ferrocyanide gives a Prussian blue coloured colloidal species. It is:Principles Related to Practical Chemistry
Q2262Tyndall effect is more effectively shown by:Surface Chemistry

Mathematics

Q25The number of distinct real roots of the equation 3x⁴ + 4x³ - 12x² + 4 = 0 is _ _ _ _ _ _ _.Limit, Continuity and Differentiability
Q27Let the equation x² + y² + px + (1 - p)y + 5 = 0 represent circles of varying radius r (0, 5]. Then the number of elements in the set S = q: q = p² and q is…Coordinate Geometry
Q31If y^(1/4) + y^(- 1/4) = 2x, and (x² - 1) d²y d x² + α xdy/dx + β y = 0, then | α - β | is equal to _ _ _ _ _.Differential Equations
Q35If the minimum area of the triangle formed by a tangent to the ellipse (x²)/(b²) + (y²)/(4a²) = 1 and the co-ordinate axis is kab, then k is equal to _ _ _ _…Coordinate Geometry
Q36If ∫ dx/((x² + x + 1)²) = a tan ⁻¹ ((2x + 1)/(3)) + b((2x + 1)/(x² + x + 1)) + C, x > 0 where C is the constant of integration, then the value of 9(3 a + b)…Integral Calculus
Q41If the system of linear equations 2x + y - z = 3 x - y - z = α 3x + 3y + β z = 3 has infinitely many solution, then α + β - α β is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q43A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit…Permutations and Combinations
Q48If A = x R: |x - 2| > 1, B = x R: √(x² - 3) > 1, C = x R: |x - 4| ≥ 2 and Z is the set of all integers, then the number of subsets of the set (A B C)^(c) Z is…Sets, Relations and Functions
Q49Let n be an odd natural number such that the variance of 1, 2, 3, 4,......, n is 14. Then n is equal to _ _ _ _ _ _ _.Statistics and Probability
Q51Let a = i + 5 j + α k, b = i + 3 j + β k and c = - i + 2 j - 3 k be three vectors such that, | b × c | = 5 3 and a is perpendicular to b. Then the greatest…Vector Algebra
Q2435The distance of the point (1, - 2, 3) from the plane x - y + z = 5 measured parallel to a line, whose direction ratios are 2, 3, - 6 is:Three Dimensional Geometry
Q2436Equation of a plane at a distance √(2/21) from the origin, which contains the line of intersection of the planes x - y - z - 1 = 0 and 2x + y - 3z + 4 = 0, is:Three Dimensional Geometry
Q2659A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the…Limit, Continuity and Differentiability
Q2999Σ k = 0 ²⁰ (²⁰C k)² is equal to:Binomial Theorem and Its Simple Applications
Q3157If S = z C:(z - i)/(z + 2i) R, then:Complex Numbers and Quadratic Equations
Q3290If U n = (1 + 1/(n²))(1 + (2²)/(n²))².....(1 + (n²)/(n²))ⁿ, then lim n → ∞ (U n)^((- 4)/(n²)) is equal to:Integral Calculus
Q3419∫₆¹⁶ log e x² log e x² + log e (x² - 44x + 484) dx is equal to:Integral Calculus
Q3535Let us consider a curve, y = f(x) passing through the point (- 2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) +…Differential Equations
Q3616Let y = y(x) be the solution of the differential equation dy/dx = 2(y + 2 sin x - 5)x - 2 cos x such that y(0) = 7. Then y(π) is equal to:Differential Equations
Q3759If x² + 9y² - 4x + 3 = 0, x, y R, then x and y respectively lie in the intervals:Coordinate Geometry
Q4104If (sin ⁻¹x)² - (cos ⁻¹x)² = a; 0 < x < 1, a ≠ 0, then the value of 2x² - 1 is:Trigonometry
Q4255If α, β are the distinct roots of x² + bx + c = 0, then lim x → β (e^(2(x² + bx + c)) - 1 - 2(x² + bx + c))/((x - β)²) is equal to:Limit, Continuity and Differentiability
Q4354The statement (p (p → q) (q → r)) → r is:Mathematical Reasoning
Q4505If the matrix A = (0 2 K - 1) satisfies A(A³ + 3I) = 2I, then the value of K is:Matrices and Determinants
Q4711A tangent and a normal are drawn at the point P(2, - 4) on the parabola y² = 8x, which meet the directrix of the parabola at the points A and B respectively…Coordinate Geometry
Q4961When a certain biased die is rolled, a particular face occurs with probability 1/6 - x and its opposite face occurs with probability 1/6 + x. All other faces…Statistics and Probability
Q5043Let (sin A)/(sin B) = (sin (A - C))/(sin (C - B)), where A, B, C are angles of triangle ABC. If the lengths of the sides opposite these angles are a, b, c…Properties of Triangle
Q5325If 0 < x < 1, then 3/2x² + 5/3x³ + 7/4x⁴ +....., is equal to:Sequence and Series
Q5326If for x, y R, x > 0, y = log₁₀x + log₁₀x¹/3 + log₁₀x¹/9 +...... upto ∞ terms and (2 + 4 + 6 +.... + 2y)/(3 + 6 + 9 +..... + 3y) = 4/(log ₁₀x), then the…Sequence and Series
Q5569Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The…Coordinate Geometry