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

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JEE Main 202127 Jul, Evening shift

Physics 18Chemistry 22Mathematics 30

Physics

Q56The K_ α X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy of this atom…Atoms and Nuclei
Q59The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to be 3V. The modulation index is 0.6x where x…Communication Systems
Q67The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The…Properties of Solids and Liquids
Q69A particle executes simple harmonic motion represented by displacement function as x(t) = A sin(ω t + φ) If the position and velocity of the particle at t = 0…Oscillations and Waves
Q71The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air…Optics
Q5898A 100 Ω resistance, a 0.1 μ F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance…Electromagnetic Induction and Alternating Currents
Q6112Consider the following statements: A. Atoms of each element emit characteristics spectrum. B. According to Bohr's Postulate, an electron in a hydrogen atom…Atoms and Nuclei
Q6141Match List I with List II. List - I List - II (a) Capacitance, C (i) M¹L¹T⁻³A⁻¹ (b) Permittivity of free space, ε ₀ (ii) M⁻¹L⁻³T⁴A² (c) Permeability of free…Electrostatics
Q6432The resistance of a conductor at 15° C is 16 Ω and at 100° C is 20 Ω. What will be the temperature coefficient of resistance of the conductor?Current Electricity
Q6641An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and…Dual Nature of Matter and Radiation
Q7199The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 × 10³ km. Find the mass of Mars. \ Given (4π ²)/G…Gravitation
Q7269Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each…Gravitation
Q7487One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27° C to 37° C. If the ideal gas is composed of polyatomic…Thermodynamics
Q7587A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F₀[ 1…Laws of Motion
Q7906A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the…Properties of Solids and Liquids
Q8163An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the…Oscillations and Waves
Q8305A physical quantity 'y' is represented by the formula y = m²r⁻⁴gˣ l^(- 3/2) If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p…Units and Measurements
Q8608An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a…Work, Energy and Power

Chemistry

Q2The dihedral angle in staggered form of Newman projection of 1, 1, 1-Trichloro ethane is _ _ _ _ _ d egree. (Round off to the nearest integer)Some Basic Principles of Organic Chemistry
Q4The total number of electrons in all bonding molecular orbitals of O₂²⁻ is _ _ _ _ _ _ _. (Round off to the nearest integer)Chemical Bonding and Molecular Structure
Q5The equilibrium constant for the reaction A(s) M(s) + 1/2 O₂(g) is K p = 4. At equilibrium, the partial pressure of O₂ is _ _ _ _ a tm. (Round off to the…Equilibrium
Q83 moles of metal complex with formula Co(en)₂Cl₃ gives 3 moles of silver chloride on treatment with excess of silver nitrate. The secondary valency of Co in…Coordination Compounds
Q10For the cell Cu(s) | Cu²⁺ (aq) (0.1 M) || Ag⁺(aq) (0.01 M) | Ag(s) the cell potential E₁ = 0.3095 V For the cell Cu(s) | Cu²⁺ (aq) (0.01 M) || Ag⁺(aq) (0.001…Redox Reactions and Electrochemistry
Q1810.0 mL of 0.05 M KMnO₄ solution was consumed in a titration with 10.0 mL of given oxalic acid dihydrate solution. The strength of given oxalic acid solution…Redox Reactions and Electrochemistry
Q21In a solvent 50% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is _ _ _ _ _ × 10⁻². (Round off to the nearest integer)Solutions
Q222SO₂(g) + O₂(g) → 2SO₃(g) The above reaction is carried out in a vessel starting with partial pressure PSO₂ = 250 m bar, PO₂ = 750 m bar and PSO₃ = 0 bar…Some Basic Concepts in Chemistry
Q24When 400 mL of 0.2 M H₂SO₄ solution is mixed with 600 mL of 0.1 M NaOH solution, the increase in temperature of the final solution is _ _ _ _ _ × 10⁻² K…Chemical Thermodynamics
Q83Given below are two statements: Statement I: Hyperconjugation is a permanent effect. Statement II: Hyperconjugation in ethyl cation (C H₃ - C⁺ H₂) involves…Some Basic Principles of Organic Chemistry
Q172Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is:Biomolecules
Q736Given below are two statements: Statement I: [Mn (CN)₆ ]³⁻, [Fe (CN)₆ ]³⁻ and [Co (C₂O₄)₃ ]³⁻ are d²sp³ hybridised. Statement II: [MnCl)₆]³⁻ and [Fe F₆ ]³⁻…Coordination Compounds
Q1250The number of neutrons and electrons, respectively, present in the radioactive isotope of hydrogen is:Hydrogen
Q1392Which one of the following set of elements can be detected using sodium fusion extract?Isolation of Elements
Q1393The addition of silica during the extraction of copper from its sulphide ore:-Isolation of Elements
Q1508Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: SO₂(g) is absorbed to a large extent than…p-Block Elements
Q1509Match List - I with List - II: List - I (compound) List - II (effect/affected species) (a) Carbon monoxide (i) Carcinogenic (b) Sulphur dioxide (ii)…p-Block Elements
Q1611The correct order of first ionisation enthalpy is:Classification of Elements and Periodicity in Properties
Q1772To an aqueous solution containing ions such as Al³⁺, Zn²⁺, Ca²⁺, Fe³⁺, Ni²⁺, Ba²⁺ and Cu²⁺ was added conc. HCl, followed by H₂S. The total number of cations…Principles Related to Practical Chemistry
Q1827Match List - I with List - II: List - I List - II (a) Li (i) photoelectric cell (b) Na (ii) absorbent of C O₂ (c) K (iii) coolant in fast breeder nuclear…S Block Elements
Q1948Select the correct statements (A) Crystalline solids have long range order. (B) Crystalline solids are isotropic (C) Amorphous solid are sometimes called…Solid State
Q2218If the Thompson model of the atom was correct, then the result of Rutherford's gold foil experiment would have been:Atomic Structure

Mathematics

Q26The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points. Q(3, - 4, - 5) and R(2, - 3, 1) and the plane 2x + y + z =…Three Dimensional Geometry
Q30If the real part of the complex number z = (3 + 2i cos θ)/(1 - 3i cos θ),θ (0,(π)/2) is zero, then the value of sin²3 θ + cos² θ is equal to _ _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q33If ∫₀^π (sin ³x)e^(- sin ²x)dx = α - (β)/e∫₀¹ t e^(t)dt, then α + β is equal to _ _ _ _ _ _.Integral Calculus
Q35Let y = y(x) be the solution of the differential equation dy = e^ α x + y dx; α N. If y(log e 2) = log e 2 and y(0) = log e (1/2), then the value of α is…Differential Equations
Q36Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, - 4), one focus at (4, - 4) and one vertex at (5, - 4). If mx…Coordinate Geometry
Q41If A = [ 1 1 1 0 1 1 0 0 1 ] and M = A + A² + A³ +....... + A²⁰, then the sum of all the elements of the matrix M is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q43Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)¹⁰. (11)¹¹. (13)¹³ is equal to _ _ _ _ _.Permutations and Combinations
Q45The number of real roots of the equation e⁴x - e³x - 4e²x - eˣ + 1 = 0 is equal to _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q47Let A = n N | n² ≤ n + 10,000, B = 3k + 1 | k N an dC = 2k | k N, then the sum of all the elements of the set A (B - C) is equal to _ _ _ _ _ _ _.Sets, Relations and Functions
Q54Let a = i - α j + β k, b = 3 i + β j - α k and c = -α i - 2 j + k, where α and β are integers. If a. b = - 1 and b. c = 10, then (a × b). c is equal to _ _ _…Vector Algebra
Q2433For real numbers α and β ≠ 0, if the point of intersection of the straight lines (x - α)/1 = (y - 1)/2 = (z - 1)/3 and (x - 4)/(β) = (y - 6)/3 = (z - 7)/3…Three Dimensional Geometry
Q2835The area of the region bounded by y - x = 2 and x² = y is equal to:Integral Calculus
Q2932A possible value of 'x', for which the ninth term in the expansion of 3^(log ₃√(25ˣ⁻¹ + 7)) + 3^((- 1/8) log ₃(5ˣ⁻¹ + 1)) \¹⁰ in the increasing powers of…Binomial Theorem and Its Simple Applications
Q3084Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6 5 on the x-axis. Then the radius of the circle C is equal to:Coordinate Geometry
Q3189Let C be the set of all complex numbers. Let S₁ = z C: |z - 2| ≤ 1 and S₂ = z C: z(1 + i) + z (1 - i) ≥ 4. Then, the maximum value of | z - 5/2 |² for z S₁ S₂…Complex Numbers and Quadratic Equations
Q3312Let f: (a, b) → R be twice differentiable function such that f(x) = ∫ a ˣ g(t)dt for a differentiable function g(x). If f(x) = 0 has exactly five distinct…Integral Calculus
Q3612Let y = y(x) be the solution of the differential equation (x - x³)dy = (y + yx² - 3x⁴)dx, x > 2. If y(3) = 3, then y(4) is equal to:Differential Equations
Q3867Let f: R → R be defined as f(x + y) + f(x - y) = 2f(x)f(y),f(1/2) = - 1. Then, the value of Σ k = 1 ²⁰ 1/(sin (k) sin (k + f(k))) is equal to:Sets, Relations and Functions
Q4203Let f:[0,∞) → [0,3] be a function defined by f(x) = \ max sin t:0 ≤ t ≤ x, 0 ≤ x ≤ π 2 + cos x, x > π. Then which of the following is true?Limit, Continuity and Differentiability
Q4286The value of lim x → 0 (x/(8 1 - sin x - 8 1 + sin x)) is equal to:Limit, Continuity and Differentiability
Q4417Which of the following is the negation of the statement "for all M > 0, there exists x S such that x ≥ M" ?Mathematical Reasoning
Q4525Let A and B be two 3 × 3 real matrices such that (A² - B²) is invertible matrix. If A⁵ = B⁵ and A³B² = A²B³, then the value of the determinant of the matrix…Matrices and Determinants
Q4885A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. the smallest value of…Statistics and Probability
Q5152Let α = max x R 8^(2 sin 3x).4^(4 cos 3x) and β = min x R 8^(2 sin 3x).4^(4 cos 3x). If 8x² + bx + c = 0 is a quadratic equation whose roots are α ¹/5 and β…Complex Numbers and Quadratic Equations
Q5378Let N be the set of natural numbers and a relation R on N be defined by R = \ (x,y) N × N:x³ - 3x²y - x y² + 3y³ = 0\. Then the relation R is:Sets, Relations and Functions
Q5465Let the mean and variance of the frequency distribution x: x₁ = 2 x₂ = 6 x₃ = 8 x₄ = 9 f: 4 4 α β be 6 and 6.8 respectively. If x₃ is changed from 8 to 7…Statistics and Probability
Q5616The point P (a, b) undergoes the following three transformations successively: (a) reflection about the line y = x. (b) translation through 2 units along the…Coordinate Geometry
Q5617Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9…Coordinate Geometry
Q5637If tan ((π)/9),x, tan ((7π)/18) are in arithmetic progression and tan ((π)/9),y, tan ((5π)/18) are also in arithmetic progression, then |x - 2y| is equal to:Trigonometry
Q5734Let a, b and c be three vectors such that a = b × (b × c). If magnitudes of the vectors a, b and c are 2, 1 and 2 respectively and the angle between b and c…Vector Algebra