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JEE Main 2021 1 Sep Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20211 Sep, Evening shift

Physics 20Chemistry 20Mathematics 28

Physics

Q53A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150V. The ratio of minimum amplitude to maximum…Communication Systems
Q56A uniform heating wire of resistance 36 Ω is connected across a potential difference of 240 V. The wire is then cut into half and potential difference of 240V…Current Electricity
Q60Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours…Gravitation
Q61The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0° C without changing the pressure of the gas. The molecules in the gas rotate but do…Thermodynamics
Q62The average translational kinetic energy of N₂ gas molecules at.............° C becomes equal to the K.E. of an electron accelerated from rest through a…Thermodynamics
Q63When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time T. When the same body slides down…Laws of Motion
Q65A steel rod with y = 2.0 × 10¹¹ Nm⁻² and α = 10⁻⁵° C⁻¹ of length 4 m and area of cross-section 10 cm² is heated from 0° C to 400° C without being allowed to…Properties of Solids and Liquids
Q66A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that…Rotational Motion
Q68The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is…Optics
Q69An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh⁻¹ when…Work, Energy and Power
Q6114The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms…Atoms and Nuclei
Q6193A capacitor is connected to a 20 V battery through a resistance of 10 Ω. It is found that the potential difference across the capacitor rises to 2 V in 1 μ s…Electrostatics
Q6384Two resistors R₁ = (4 ± 0.8) Ω and R₂ = (4 ± 0.4) Ω are connected in parallel. The equivalent resistance of their parallel combination will be:Current Electricity
Q6434Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at - 10° C. Resistive heating is used to melt the ice. Current of 0.5A…Current Electricity
Q6569The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is: [m e = mass of…Dual Nature of Matter and Radiation
Q6783Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20cos(2 × 10¹⁰ t - 200x) V/m. The dielectric constant…Electromagnetic Waves
Q7108A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (μ = 4/3) into it while looking at the surface of water from…Optics
Q7787The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are R₁, R₂ and H₁, H₂…Kinematics
Q8307A student determined Young's Modulus of elasticity using the formula Y = Mg L³ 4b d³ δ. The value of g is taken to be 9.8 m/s², without any significant error…Units and Measurements
Q8621A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8 √(gh). The value of workdone by the air-friction is:Work, Energy and Power

Chemistry

Q3A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have _ _ _ _ p eptide linkages.Biomolecules
Q5The spin-only magnetic moment value of B₂⁺ species is _ _ _ _ _ _ _ × 10⁻² BM. (Nearest integer) [Given: 3 = 1.73]Chemical Bonding and Molecular Structure
Q7The sum of oxidation states of two silver ions in [Ag(NH₃)₂] [Ag(CN)₂] complex is _ _ _ _ _ _ _.Coordination Compounds
Q11If the conductivity of mercury at 0° C is 1.07 × 10⁶ S m⁻¹ and the resistance of a cell containing mercury is 0.243 Ω, then the cell constant of the cell is x…Redox Reactions and Electrochemistry
Q13An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm. In the course of use at ambient temperature, the mass of…Gaseous State
Q16The molar solubility of Zn(OH)₂ in 0.1 M NaOH solution is x × 10⁻¹8 M. The value of x is _ _ _ _ _ (Nearest integer) (Given: The solubility product of Zn(OH)₂…Equilibrium
Q19If 80 g of copper sulphate CuSO₄. 5H₂O is dissolved in deionised water to make 5L of solution. The concentration of the copper sulphate solution is x × 10⁻³…Some Basic Concepts in Chemistry
Q20The number of atoms in 8g of sodium is x × 10²³. The value of x is _ _ _ _ _ _. (Nearest integer) [Given: N A = 6.02 × 10²³ mol⁻¹ Atomic mass of Na = 23.0 u]Some Basic Concepts in Chemistry
Q21A 50 watt bulb emits monochromatic red light of wavelength of 795 nm. The number of photons emitted per second by the bulb is x × 10²⁰. The value of x is _ _…Atomic Structure
Q22For the reaction, 2NO₂(g) N₂O₄(g), when Δ S = - 176.0 JK⁻¹ and Δ H = - 57.8 kJ mol⁻¹, the magnitude of Δ G at 298 K for the reaction is _ _ _ _ _ k J mol⁻¹…Chemical Thermodynamics
Q48Experimentally reducing a functional group cannot be done by which one of the following reagents?Organic Compounds Containing Oxygen
Q49Given below are two statements: Statement I: The nucleophilic addition of sodium hydrogen sulphite to an aldehyde or a ketone involves proton transfer to form…Organic Compounds Containing Oxygen
Q375Number of paramagnetic oxides among the following given oxides is _ _ _ _ _ _. Li₂O, CaO, Na₂O₂, KO₂, MgO and K₂OChemical Bonding and Molecular Structure
Q562The potassium ferrocyanide solution gives a Prussian blue colour, when added to:Coordination Compounds
Q630The Crystal Field Stabilization Energy (CFSE) and magnetic moment (spin-only) of an octahedral aqua complex of a metal ion (M^(z)+) are - 0.8 Δ ₀ and 3.87 BM…Coordination Compounds
Q773In the given chemical reaction, colors of the Fe²⁺ and Fe³⁺ ions, are respectively: 5Fe²⁺ + MnO ₄⁻⁺ 8H⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺d- and f-Block Elements
Q882Identify the element for which electronic configuration in +3 oxidation state is [Ar]3d⁵:d- and f-Block Elements
Q1095Water sample is called cleanest on the basis of which one of the BOD values given below:Environmental Chemistry
Q1225Hydrogen peroxide reacts with iodine in basic medium to give:Hydrogen
Q1424Calamine and Malachite, respectively, are the ores of:Isolation of Elements

Mathematics

Q27If the sum of the coefficients in the expansion of (x + y)ⁿ is 4096, then the greatest coefficient in the expansion is _ _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q28If for the complex numbers z satisfying | z - 2 - 2i | ≤ 1, the maximum value of | 3iz + 6 | is attained at a + ib, then a + b is equal to _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q36Let [t] denote the greatest integer ≤ t. The number of points where the function f(x) = [x]| x² - 1 | + sin ((π)/([x] + 3)) - [x + 1],x (- 2,2) is not…Limit, Continuity and Differentiability
Q37Let f(x) = x⁶ + 2x⁴ + x³ + 2x + 3, x R. Then the natural number n for which lim x → 1 (xⁿf(1) - f(x))/(x - 1) = 44 is _ _ _ _ _.Limit, Continuity and Differentiability
Q42All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are…Permutations and Combinations
Q43Let X be a random variable with distribution. x | - 2 | - 1 | 3 | 4 | 6 P(X = x) | 1/5 | a | 1/3 | 1/5 | b If the mean of X is 2.3 and variance of X is σ ²…Statistics and Probability
Q44Let f(x) be a polynomial of degree 3 such that f(k) = - 2/k for k = 2, 3, 4, 5. Then the value of 52 - 10f(10) is equal to:Complex Numbers and Quadratic Equations
Q48Let the points of intersections of the lines x - y + 1 = 0, x - 2y + 3 = 0 and 2x - 5y + 11 = 0 are the mid points of the sides of a triangle Δ ABC. Then, the…Coordinate Geometry
Q49A man starts walking from the point P(- 3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed…Coordinate Geometry
Q50Let a = 2 i - j + 2 k and b = i + 2 j - k. Let a vector v be in the plane containing a and b. If v is perpendicular to the vector 3 i + 2 j - k and its…Vector Algebra
Q2500The distance of line 3y - 2z - 1 = 0 = 3x - z + 4 from the point (2, - 1, 6) is:Three Dimensional Geometry
Q2588Let the acute angle bisector of the two planes x - 2y - 2z + 1 = 0 and 2x - 3y - 6z + 1 = 0 be the plane P. Then which of the following points lies on P?Three Dimensional Geometry
Q2722The function f(x) = x³ - 6x² + ax + b is such that f(2) = f(4) = 0. Consider two statements: Statement 1: there exists x₁, x₂ (2, 4), x₁ < x₂, such that…Limit, Continuity and Differentiability
Q2838The area, enclosed by the curves y = sin x + cos x and y = | cos x - sin x | and the lines x = 0,x = (π)/2, is:Integral Calculus
Q3314Let f: R → R be a continuous function. Then lim x → (π)/4 ((π)/4∫₂^(sec ²x) f(x) dx)/(x² - (π ²)/16) is equal to:Integral Calculus
Q3422Let J n,m = ∫₀^(1/2) (xⁿ)/(x^(m) - 1)dx, n > m and n, m N. Consider a matrix A = [a ij ] 3 × 3 where a ij = \ j 6 + i,3 - j i + 3,3, i ≤ j 0, i > j.. Then |…Integral Calculus
Q3423The function f(x), that satisfies the condition f(x) = x + ∫₀^(π /2) sin x. cos y f(y) dy, is:Integral Calculus
Q3538If y = y(x) is the solution curve of the differential equation x²dy + (y - 1/x)dx = 0; x > 0 and y(1) = 1, then y(1/2) is equal to:Differential Equations
Q3786Let θ be the acute angle between the tangents to the ellipse (x²)/9 + (y²)/1 = 1 and the circle x² + y² = 3 at their point of intersection in the first…Coordinate Geometry
Q3891The range of the function, f(x) = log 5 (3 + cos ((3π)/4 + x) + cos ((π)/4 + x) + cos ((π)/4 - x) - cos ((3π)/4 - x)) is:Sets, Relations and Functions
Q4073cos ⁻¹(cos (- 5)) + sin ⁻¹(sin (6)) - tan ⁻¹(tan (12)) is equal to: (The inverse trigonometric functions take the principal values)Trigonometry
Q4358Which of the following is equivalent to the Boolean expression p q ?Mathematical Reasoning
Q4601Consider the system of linear equations - x + y + 2z = 0 3x - ay + 5z = 1 2x - 2y - az = 7 Let S₁ be the set of all a R for which the system is inconsistent…Matrices and Determinants
Q4712Consider the parabola with vertex (1/2,3/4) and the directrix y = 1/2. Let P be the point where the parabola meets the line x = - 1/2. If the normal to the…Coordinate Geometry
Q4763Let P₁, P₂,......, P₁₅ be 15 points on a circle. The number of distinct triangles formed by points P i, P j, P k such that i +j + k ≠ 15, is:Permutations and Combinations
Q5098The numbers of pairs (a, b) of real numbers, such that whenever α is a root of the equation x² + ax + b = 0, α ² - 2 is also a root of this equation, is:Complex Numbers and Quadratic Equations
Q5223Let a₁, a₂,..........., a₂₁ be an AP such that Σ n = 1 ²⁰ 1 a n a n + 1 = 4/9. If the sum of this AP is 189, then a₆a₁₆ is equal to:Sequence and Series
Q5329Let S n = 1. (n - 1) + 2. (n - 2) + 3. (n - 3) +..... + (n - 1). 1, n ≥ 4. The sum Σ n = 4 ^∞ (2S n /(n!) - 1/((n - 2)!)) is equal to:Sequence and Series