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JEE Main 2022 27 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202227 Jul, Evening shift

Physics 22Chemistry 20Mathematics 28

Physics

Q53A parallel plate capacitor with width 4 ~cm, length 8 ~cm and separation between the plates of 4 ~mm is connected to a battery of 20 ~V. A dielectric slab of…Electrostatics
Q57A conducting circular loop is placed in X-Y plane in presence of magnetic field B=(3 t³ j+3 t² k) in SI unit. If the radius of the loop is 1 ~m, the induced…Electromagnetic Induction and Alternating Currents
Q69A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius…Properties of Solids and Liquids
Q72A wire of length 30 cm, stretched between rigid supports, has it's n^(t)h and (n + 1)^(t)h harmonics at 400 Hz and 450 Hz, respectively. If tension in the…Oscillations and Waves
Q5910A series LCR circuit has L=0.01 H, R=10 Ω and C=1 μ F and it is connected to ac voltage of amplitude (V m) 50 ~V. At frequency 60% lower than resonant…Electromagnetic Induction and Alternating Currents
Q6123The activity of a radioactive material is 6.4 × 10⁻⁴ curie. Its half life is 5 days. The activity will become 5 × 10⁻⁶ curie after:Atoms and Nuclei
Q6245A body of mass 10 ~kg is projected at an angle of 45^(°) with the horizontal. The trajectory of the body is observed to pass through a point (20,10). If T is…Rotational Motion
Q6402(A) The drift velocity of electrons decreases with the increase in the temperature of conductor. (B) The drift velocity is inversely proportional to the area…Current Electricity
Q6651With reference to the observations in photo-electric effect, identify the correct statements from below: (A) The square of maximum velocity of photoelectrons…Dual Nature of Matter and Radiation
Q6800Identify the correct statements from the following descriptions of various properties of electromagnetic waves. (A) In a plane electromagnetic wave electric…Electromagnetic Waves
Q6911For a constant collector-emitter voltage of 8 ~V, the collector current of a transistor reached to the value of 6 ~mA from 4 ~mA, whereas base current changed…Electronic Devices
Q6929A charge of 4 μ C is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force…Electrostatics
Q7204A body of mass m is projected with velocity λ v e in vertically upward direction from the surface of the earth into space. It is given that v e is escape…Gravitation
Q7313Which statements are correct about degrees of freedom ? (A) A molecule with n degrees of freedom has n ² different ways of storing energy. (B) Each degree of…Kinetic Theory of Gases
Q7569A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the…Laws of Motion
Q7570A block 'A' takes 2 s to slide down a frictionless incline of 30° and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is…Laws of Motion
Q7629A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30^(°). The number of oscillations per minute become 10 at…Magnetic Effects of Current and Magnetism
Q7713A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 ~T and the radius of the cyclotron 'dees' is 60 ~cm, the kinetic energy of…Magnetic Effects of Current and Magnetism
Q7849The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its…Kinematics
Q7950A steel wire of length 3.2 ~m(Y s =2.0 × 10¹¹ Nm⁻²) and a copper wire of length 4.4 ~m(Y c =1.1 × 10¹¹ Nm⁻²), both of radius 1.4 ~mm are connected end to end…Properties of Solids and Liquids
Q8260An expression of energy density is given by u=(α)/(β) sin ((α x)/(k t)), where α, β are constants, x is displacement, k is Boltzmann constant and t is the…Units and Measurements
Q8448Two coherent sources of light interfere. The intensity ratio of two sources is 1: 4. For this interference pattern if the value of (I max +I min)/(I max -I…Optics

Chemistry

Q1The spin only magnetic moment of the complex present in Fehling's reagent is _ _ _ _ _ B.M. (Nearest integer).Organic Compounds Containing Oxygen
Q5The number of molecule(s) or ion(s) from the following having non-planar structure is _ _ _ _ _ _. NO₃⁻, H₂ O₂, BF₃, PCl₃, XeF₄, SF₄, XeO₃, PH₄⁺, SO₃,[Al(OH)₄]⁻Chemical Bonding and Molecular Structure
Q6[A] → [B] Reactant Product If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half…Chemical Kinetics
Q12For a real gas at 25^(°) C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant 'b' should…Gaseous State
Q13The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic medium is _ _ _ _ _ _.Hydrogen
Q14Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of…Isolation of Elements
Q16The normality of H₂ SO₄ in the solution obtained on mixing 100 ~mL of 0.1 M H₂ SO₄ with 50 ~mL of 0.1 M NaOH is _ _ _ _ _ _ _ _ × 10⁻¹ ~N. (Nearest Integer)Redox Reactions and Electrochemistry
Q18When a certain amount of solid A is dissolved in 100 ~g of water at 25^(°) C to make a dilute solution, the vapour pressure of the solution is reduced to…Solutions
Q22A gas (Molar mass = 280 ~g ~mol⁻¹) was burnt in excess O₂ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from…Chemical Thermodynamics
Q135Match List - I with List - II. List - I (Mixture) List - II (Purification Process) (A) Chloroform Aniline (I) Steam distillation (B) Benzoic acid Napthalene…Some Basic Principles of Organic Chemistry
Q268Match List - I with List - II. List - I List - II (A) ψ MO =ψ A -ψ B (I) Dipole moment (B) μ=Q × r (II) Bonding molecular orbital (C) (N b -N a)/2 (III)…Chemical Bonding and Molecular Structure
Q565Fe³⁺ cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of:Coordination Compounds
Q596Low oxidation state of metals in their complexes are common when ligands:Coordination Compounds
Q777In neutral or alkaline solution, MnO₄⁻ oxidises thiosulphate to:d- and f-Block Elements
Q948Given below are two statements: Statement I: For KI, molar conductivity increases steeply with dilution Statement II: For carbonic acid, molar conductivity…Redox Reactions and Electrochemistry
Q1073Given below are two statements: Statement I: The non bio-degradable fly ash and slag from steel industry can be used by cement industry. Statement II: The…Environmental Chemistry
Q1893An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is:S Block Elements
Q2147Outermost electronic configurations of four elements A, B, C, D are given below: (A) 3 s² (B) 3 s² 3 p¹ (C) 3 s² 3 p³ (D) 3 s² 3 p⁴ The correct order of first…Atomic Structure
Q2207The correct decreasing order of energy for the orbitals having, following set of quantum numbers: (A) n = 3, l = 0, m = 0 (B) n = 4, l = 0, m = 0 (C) n = 3, l…Atomic Structure
Q2275Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Dissolved substances can be removed…Surface Chemistry

Mathematics

Q25A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan ⁻¹ 3/4. Water is poured in it at a…Limit, Continuity and Differentiability
Q27Let for the 9^(th) term in the binomial expansion of (3+6 x)ⁿ, in the increasing powers of 6 x, to be the greatest for x=3/2, the least value of n is n₀. If k…Binomial Theorem and Its Simple Applications
Q30Let f be a differentiable function satisfying f(x)=2/(√(3)) ∫₀^(√(3)) f((λ² x)/3) d λ, x>0 and f(1)=√(3). If y=f(x) passes through the point (α, 6), then α is…Integral Calculus
Q33Let f(x)= min \[x-1],[x-2],,[x-10] where [t] denotes the greatest integer ≤ t. Then ∫₀¹⁰ f(x) d x+∫₀¹⁰(f(x))² ~d x+∫₀¹⁰|f(x)| d x is equal to _ _ _ _ _ _ _ _.Integral Calculus
Q34For the curve C:(x²+y²-3)+(x²-y²-1)⁵=0, the value of 3 y^()-y³ y^(), at the point (α, α), α>0, on C, is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q35The number of functions f, from the set A= N: x²-10 x+9 ≤ 0 to the set B= ²: n N such that f(x) ≤(x-3)²+1, for every x A, is _ _ _ _ _ _.Sets, Relations and Functions
Q37A common tangent T to the curves C₁: (x²)/4+(y²)/9=1 and C₂: (x²)/42-(y²)/143=1 does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂…Coordinate Geometry
Q42Consider a matrix A=[ cccα β γ α² β² γ² β+γ γ+α α+β ], where α, β, γ are three distinct natural numbers. If (det(adj(adj(adj(adj…Matrices and Determinants
Q48(2³-1³)/(1 × 7)+(4³-3³+2³-1³)/(2 × 11)+(6³-5³+4³-3³+2³-1³)/(3 × 15)+ + (30³-29³+28³-27³+ +2³-1³)/(15 × 63) is equal to _ _ _ _ _ _ _.Sequence and Series
Q50Let a, b, c be three non-coplanar vectors such that a × b = 4 c, b × c = 9 a and c × a = α b, α > 0. If | a | + | b | + | c | = 1/36, then α is equal to _ _ _…Vector Algebra
Q2450If the line of intersection of the planes a x+b y=3 and a x+b y+c z=0, a >0 makes an angle 30^(°) with the plane y-z+2=0, then the direction cosines of the…Three Dimensional Geometry
Q2507If the length of the perpendicular drawn from the point P(a, 4,2), a >0 on the line (x+1)/2=(y-3)/3=(z-1)/(-1) is 2 √(6) units and Q(α₁, α₂, α₃) is the image…Three Dimensional Geometry
Q2849The area of the region enclosed by y ≤ 4 x², x² ≤ 9 y and y ≤ 4, is equal to:Integral Calculus
Q3137A circle C₁ passes through the origin O and has diameter 4 on the positive x -axis. The line y=2 x gives a chord OA of circle C₁. Let C₂ be the circle with OA…Coordinate Geometry
Q3159Let S be the set of all (α, β), π<α, β<2 π, for which the complex number (1-i sin α)/(1+2 i sin α) is purely imaginary and (1+i cos β)/(1-2 i cos β) is purely…Complex Numbers and Quadratic Equations
Q3442Let f(x)=2+|x|-|x-1|+|x+1|, x R. Consider (S 1): f^()(-3/2)+f^()(-1/2)+f^()(1/2)+f^()(3/2)=2 (S 2): ∫₋₂² f(x) d x=12 Then,Integral Calculus
Q3443∫₀²(|2 x²-3 x|+[x-1/2]) d x, where [t] is the greatest integer function, is equal to:Integral Calculus
Q3932The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45^(°). Let R be a point on AQ and from a…Height and Distance
Q4067The domain of the function f(x)= sin ⁻¹[2 x²-3]+ log ₂(log 1/2 (x²-5 x+5)), where [t] is the greatest integer function, is:Trigonometry
Q4156If for p ≠ q ≠ 0, the function f(x)=(7√(p(729+x))-3)/(3√(729+q x)-9) is continuous at x=0, then:Limit, Continuity and Differentiability
Q4374If the truth value of the statement (P (R)) →((R) Q) is F, then the truth value of which of the following is F ?Mathematical Reasoning
Q4535Let A=(rr4 -2 α β). If A²+γ A+18 I=O, then det(A) is equal to _ _ _ _ _ _ _.Matrices and Determinants
Q4752If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x+y=a, is 16, then |a| is equal to:Coordinate Geometry
Q4894Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If P(X>n-3)=k/(2ⁿ)…Statistics and Probability
Q5002A six faced die is biased such that 3 × P(a prime number) =6 × P(a composite number) =2 × P(1). Let X be a random variable that counts the number of times one…Statistics and Probability
Q5157If α, β are the roots of the equation x²-(5+3^(√(log ₃ 5))-5^(√(log ₅ 3)))x+3(3^(log ₃ 5)^(1/3)-5^(log ₅ 3)^(2/3)-1)=0, then the equation, whose roots are…Complex Numbers and Quadratic Equations
Q5265Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the…Sequence and Series
Q5540The equations of the sides AB, BC and CA of a triangle ABC are 2 x+y=0, x+p y=39 and x-y=3 respectively and P(2,3) is its circumcentre. Then which of the…Coordinate Geometry