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

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JEE Main 202127 Aug, Evening shift

Physics 19Chemistry 22Mathematics 28

Physics

Q52An ac circuit has an inductor and a resistor resistance R in series, such that X L = 3R. Now, a capacitor is added in series such that X C = 2R. The ratio of…Electromagnetic Induction and Alternating Currents
Q53X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The…Atoms and Nuclei
Q57A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic…Electromagnetic Waves
Q66Two simple harmonic motion, are represented by the equations y₁ = 10 sin (3π t + (π)/3) y₂ = 5(sin 3π t + 3 cos 3π t) Ratio of amplitude of y₁ to y₂ = x: 1…Oscillations and Waves
Q70A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _ _ _ _ _ cm. (Take speed…Oscillations and Waves
Q6317An antenna is mounted on a 400 m tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range…Communication Systems
Q6468For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2…Current Electricity
Q6644A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping…Dual Nature of Matter and Radiation
Q6907For a transistor α and β are given as α = I C /I E and β = I C /I B. Then the correct relation between α and β will be:Electronic Devices
Q7232A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the…Gravitation
Q7391if the rms speed of oxygen molecules at 0° C is 160 m/s, find the rms speed of hydrogen molecules at 0° C.Kinetic Theory of Gases
Q7461The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall? [Given 1 cal = 4.2 J and specific…Thermodynamics
Q7683A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries…Magnetic Effects of Current and Magnetism
Q7785A player kicks a football with an initial speed of 25 ms⁻¹ at an angle of 45° from the ground. What are the maximum height and the time taken by the football…Kinematics
Q7864Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop…Kinematics
Q8057Two discs have moments of inertia I₁ and I₂ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with…Rotational Motion
Q8250If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:Units and Measurements
Q8343Match List - I with List - II. List - I List - II (a) R H (Rydberg constant) (i) kg m⁻¹s⁻¹ (b) h (Planck's constant) (ii) kg m²s⁻¹ (c) μ B (Magnetic field…Units and Measurements
Q8439The light waves from two coherent sources have same intensity I₁ = I₂ = I₀. In interference pattern the intensity of light at minima is zero. What will be the…Optics

Chemistry

Q4The number of species having non-pyramidal shape among the following is _ _ _ _ _ _. (A) SO₃ (B) NO ₃^ - (C) PCl₃ (D) CO ₃²⁻Chemical Bonding and Molecular Structure
Q5When 5.1 g of solid NH₄HS is introduced into a two litre evacuated flask at 27° C, 20% of the solid decomposes into gaseous ammonia and hydrogen sulphide. The…Equilibrium
Q6The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 × 10⁻³s⁻¹ and activation energy is 209 kJ mol⁻¹. Its rate constant (in s⁻¹) at…Chemical Kinetics
Q7The number of optical isomers possible for [Cr(C₂O₄)₃]³ - is _ _ _ _ _ _.Coordination Compounds
Q10The resistance of a conductivity cell with cell constant 1.14 cm⁻¹, containing 0.001 M KCl at 298 K is 1500 Ω. The molar conductivity of 0.001 M KCl solution…Redox Reactions and Electrochemistry
Q1840 g of glucose (Molar mass = 180) is mixed with 200 mL of water. The freezing point of solution is _ _ _ _ _ K. (Nearest integer) [Given: K f = 1.86 K kg…Solutions
Q19100 g of propane is completely reacted with 1000 g of oxygen. The mole fraction of carbon dioxide in the resulting mixture is x × 10⁻². The value of x is _ _…Some Basic Concepts in Chemistry
Q20The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength of 1000 nm, in 0.1 second is x × 10¹³…Atomic Structure
Q22Data given for the following reaction is as follows: FeO_(s) + C_(graphite) → Fe_(s) + CO_(g) Substance | Δ H° (kJ mol ⁻¹) | Δ S° (J mol ⁻¹ K ⁻¹) Fe O (s) |…Chemical Thermodynamics
Q56Given below are two statements: Statement I: Ethyl pent-4-yn-oate on reaction with CH₃MgBr gives a 3° -alcohol. Statement II: In this reaction one mole of…Organic Compounds Containing Oxygen
Q57Which one of the following reactions will not yield propionic acid?Organic Compounds Containing Oxygen
Q174Hydrolysis of sucrose gives:Biomolecules
Q770The addition of dilute NaOH to Cr³⁺ salt solution will give:d- and f-Block Elements
Q771Potassium permanganate on heating at 513 K gives a product which is:d- and f-Block Elements
Q1033In stratosphere most of the ozone formation is assisted by:Environmental Chemistry
Q1070Which one of the following is used to remove most of plutonium from spent nuclear fuel?Environmental Chemistry
Q1224The oxide that gives H₂O₂ most readily on treatment with H₂O is:Hydrogen
Q1423Match List-I with List-II: List - I (Name of ore/mineral) List - II (Chemical formula) (a) Calmine (i) Zns (b) Malachite (ii) FeC O₃ (c) Siderite (iii) ZnC O₃…Isolation of Elements
Q1560The correct order of ionic radii for the ions, P³ -, S² -, Ca²⁺, K⁺, Cl⁻ⁱs:Classification of Elements and Periodicity in Properties
Q1751Which one of the following tests used for the identification of functional groups in organic compounds does not use copper reagent?Principles Related to Practical Chemistry
Q1828Choose the correct statement from the following:S Block Elements
Q2263Lyophilic sols are more stable than lyophobic sols because:Surface Chemistry

Mathematics

Q25Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x - y + z + 3 = 0 and let R(3, 5, γ) be a point of this plane. Then the square of…Three Dimensional Geometry
Q283 × 7²² + 2 × 10²² - 44 when divided by 18 leaves the remainder _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q30Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C₁(α, β) and C₂(γ, δ)…Coordinate Geometry
Q31Let z₁ and z₂ be two complex numbers such that arg (z₁ - z₂) = (π)/4 and z₁, z₂ satisfy the equation | z - 3 | = Re(z). Then the imaginary part of z₁ + z₂ is…Complex Numbers and Quadratic Equations
Q38If ∫ (2eˣ + 3e⁻ˣ)/(4eˣ + 7e⁻ˣ)dx = 1/14(ux + v log e (4eˣ + 7e⁻ˣ)) + C, where C is a constant of integration, then u + v is equal to _ _ _ _ _ _ _.Integral Calculus
Q46Let S = 1, 2, 3, 4, 5, 6, 9. Then the number of elements in the set T = A S: A ≠ φ and the sum of all the elements of A is not a multiple of 3 is _ _ _ _ _ _…Permutations and Combinations
Q48The probability distribution of random variable X is given by: X | 1 | 2 | 3 | 4 | 5 P(X) | K | 2K | 2K | 3K | K Let p = P(1 < X < 4 | X < 3). If 5p = λ K…Statistics and Probability
Q51An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks…Statistics and Probability
Q2379The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is:Three Dimensional Geometry
Q2437The equation of the plane passing through the line of intersection of the planes r.(i + j + k) = 1 and r.(2 i + 3 j - k) + 4 = 0 and parallel to the x-axis is:Three Dimensional Geometry
Q2660A box open from top is made from a rectangular sheet of dimension a × b by cutting squares each of side x from each of the four corners and folding up the…Limit, Continuity and Differentiability
Q2837The area of the region bounded by the parabola (y - 2)² = (x - 1), the tangent to it at the point whose ordinate is 3 and the x-axis is:Integral Calculus
Q3025Let Z be the set of all integers, A = (x,y) Z × Z:(x - 2)² + y² ≤ 4 B = (x,y) Z × Z:x² + y² ≤ 4 C = (x,y) Z × Z:(x - 2)² + (y - 2)² ≤ 4 If the total number of…Coordinate Geometry
Q3420The value of the integral ∫₀¹ (x dx)/((1 + x)(1 + 3x)(3 + x)) is:Integral Calculus
Q3497A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2…Differential Equations
Q3536If the solution curve of the differential equation (2x - 10y³)dy + ydx = 0, passes through the points (0, 1) and (2, β), then β is a root of the equation:Differential Equations
Q3681If y(x) = cot ⁻¹((√(1 + sin x) + √(1 - sin x))/(√(1 + sin x) - √(1 - sin x))),x ((π)/2,π), then dy/dx at x = (5π)/6 is:Limit, Continuity and Differentiability
Q3926Two poles, AB of length a metres and CD of length a + b (b ≠ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan ACB =…Height and Distance
Q4105Let M and m respectively be the maximum and minimum values of the function f(x) = tan⁻¹ (sin x + cos x) in [ 0,(π)/2 ], then the value of tan(M - m) is equal…Trigonometry
Q4238If lim x → ∞ (√(x² - x + 1) - ax) = b, then the ordered pair (a, b) is:Limit, Continuity and Differentiability
Q4355The Boolean expression (p q) ⇒ ((r q) p) is equivalent to:Mathematical Reasoning
Q4467Let A = ([x + 1] [x + 2] [x + 3] [x] [x + 3] [x + 3] [x] [x + 2] [x + 4]), where [t] denotes the greatest integer less than or equal to t. If det(A) = 192…Matrices and Determinants
Q4526Let A(a, 0), B(b, 2b + 1) and C(0, b), b ≠ 0, |b| ≠ 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is:Matrices and Determinants
Q4598Let [ λ ] be the greatest integer less than or equal to λ. The set of all values of λ for which the system of linear equations x + y + z = 4, 3x + 2y + 5z =…Matrices and Determinants
Q4699If two tangents drawn from a point P to the parabola y² = 16(x - 3) are at right angles, then the locus of point P is:Coordinate Geometry
Q4886Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is:Statistics and Probability
Q5097The set of all values of K > - 1, for which the equation (3x² + 4x + 3)² - (k + 1)(3x² + 4x + 3)(3x² + 4x + 2) + k (3x² + 4x + 2)² = 0 has real roots, is:Complex Numbers and Quadratic Equations
Q5327If 0 < x < 1 and y = 1/2x² + 2/3x³ + 3/4x⁴ +...., then the value of e¹ + y at x = 1/2 is:Sequence and Series