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JEE Main 2022 29 Jun Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202229 Jun, Evening shift

Physics 27Chemistry 20Mathematics 28

Physics

Q52An inductor of 0.5 mH, a capacitor of 200 μ F and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf…Electromagnetic Induction and Alternating Currents
Q54The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The…Atoms and Nuclei
Q59The displacement current of 4.425 μ A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 10⁶ Vs⁻¹…Electromagnetic Waves
Q60A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ ms⁻¹. The speed with…Electronic Devices
Q73A small spherical ball of radius 0.1 mm and density 10⁴ kg m⁻³ falls freely under gravity through a distance h before entering a tank of water. If, after…Properties of Solids and Liquids
Q74The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I₁. The same rod is bent into a ring and its moment of…Rotational Motion
Q76The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of (- 0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7…Units and Measurements
Q77In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved…Optics
Q78In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has…Oscillations and Waves
Q6116In the following nuclear reaction, D α D₁ β ^ - D₂ α D₃ γ D₄ Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D₄ respectively…Atoms and Nuclei
Q6194A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂…Electrostatics
Q6318The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased byCommunication Systems
Q6392The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 Ω…Current Electricity
Q6646The electric field at a point associated with a light wave is given by E = 200 [sin (6 × 10¹⁵)t + sin (9 × 10¹⁵)t] Vm⁻¹ Given: h = 4.14 × 10⁻¹5 eVs If this…Dual Nature of Matter and Radiation
Q6925Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The…Electrostatics
Q7018If the electric potential at any point (x, y, z) m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3) m will be:Electrostatics
Q7109The speed of light in media 'A' and 'B' are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s respectively. A ray of light enters from the medium B to A at an incident…Optics
Q7270The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then…Gravitation
Q7396A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm³ is:Thermodynamics
Q7488Starting with the same initial conditions, an ideal gas expands from volume V₁ to V₂ in three different ways. The work done by the gas is W₁ if the process is…Thermodynamics
Q7522At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been…Properties of Solids and Liquids
Q7589A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of…Laws of Motion
Q7707Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point…Magnetic Effects of Current and Magnetism
Q7761Given below are two statements: Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the…Magnetic Effects of Current and Magnetism
Q7788A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?Kinematics
Q7848A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy…Kinematics
Q8165The motion of a simple pendulum executing S.H.M. is represented by the following equation. y = A sin (π t + φ), where time is measured in second. The length…Oscillations and Waves

Chemistry

Q1The number of chiral alcohol(s) with molecular formula C₄H₁₀O is _ _ _ _.Organic Compounds Containing Oxygen
Q6A box contains 0.90 g of liquid water in equilibrium with water vapour at 27° C. The equilibrium vapour pressure of water at 27° C is 32.0 Torr. When the…Equilibrium
Q7The equation k = (6.5 × 10¹²s⁻¹)e⁻²6000K/T is followed for the decomposition of compound A. The activation energy for the reaction is _ _ _ _ kJ mol⁻¹…Chemical Kinetics
Q10Spin only magnetic moment of [MnBr₆]⁴ - is _ _ _ _ B.M. (round off to the closest integer)d- and f-Block Elements
Q11For the reaction given below: CoCl₃. xNH₃ + AgNO₃ (aq) → If two equivalents of AgCl precipitate out, then the value of x will be _ _ _ _ _ _ _.d- and f-Block Elements
Q12The cell potential for the given cell at 298 K Pt| H₂ (g, 1 bar) | H⁺ (aq) || Cu²⁺ (aq) | Cu(s) is 0.31 V. The pH of the acidic solution is found to be 3…Redox Reactions and Electrochemistry
Q19Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4…Solutions
Q222.2 g of nitrous oxide (N₂O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL…Chemical Thermodynamics
Q209The structure of protein that is unaffected by heating isBiomolecules
Q306Consider the species CH₄, NH ₄⁺ and BH ₄^ -. Choose the correct option with respect to the these species.Chemical Bonding and Molecular Structure
Q307Number of lone pair(s) of electrons on central atom and the shape BrF₃ molecule respectively, areChemical Bonding and Molecular Structure
Q4194.0 moles of argon and 5.0 moles of PCl₅ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At…Equilibrium
Q595Given below are two statements. Statement I: In CuSO₄. 5H₂O, Cu-O bonds are present. Statement II: In CuSO₄. 5H₂O, ligands coordinating with Cu(II) ion are…Coordination Compounds
Q1425Match List I with List II. List-I Ore List-II Composition (A) Siderite (I) FeCO ₃ (B) Malachite (II) CuCO ₃. Cu(OH) ₂ (C) Sphalerite (III) ZnS (D) Calamine…Isolation of Elements
Q1510Sulphur dioxide is one of the components of polluted air. SO₂ is also a major contributor to acid rain. The correct and complete reaction to represent acid…p-Block Elements
Q1612Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The first ionization enthalpy for oxygen is…Classification of Elements and Periodicity in Properties
Q1773A white precipitate was formed when BaCl₂ was added to water extract of an inorganic salt. Further, a gas 'X' with characteristic odour was released when the…Principles Related to Practical Chemistry
Q1829Amongst baking soda, caustic soda and washing soda, carbonate anion is present in:S Block Elements
Q2106Using the rules for significant figures, the correct answer for the expression (0.02858 × 0.112)/0.5702 will beSome Basic Concepts in Chemistry
Q2265A 42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol in 2 hours is: [Given: Molar…Surface Chemistry

Mathematics

Q26For real numbers a, b (a > b > 0), let Area (x,y):x² + y² ≤ a² and (x²)/(a²) + (y²)/(b²) ≥ 1 = 30π and Area (x,y):x² + y² ≤ b² and (x²)/(a²) + (y²)/(b²) ≤ 1 =…Integral Calculus
Q27Let the coefficients of x⁻¹ and x⁻³ in the expansion of (2x^(1/5) - 1/(x^(1/5)))¹⁵,x > 0, be m and n respectively. If r is a positive integer such that m n² =…Binomial Theorem and Its Simple Applications
Q33Let y = y(x), x > 1, be the solution of the differential equation (x - 1)dy/dx + 2xy = 1/(x - 1), with y(2) = (1 + e⁴)/(2e⁴). If y(3) = (e^α + 1)/(β e^α)…Differential Equations
Q35Let f and g be twice differentiable even functions on (- 2, 2) such that f(1/4) = 0, f(1/2) = 0, f(1) = 1 and g(3/4) = 0, g(1) = 2. Then, the minimum number…Limit, Continuity and Differentiability
Q36Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x² - 2x and g(f(x)) = 4x² + 6x + 1, then the value of f(2) + g(2) is _…Sets, Relations and Functions
Q40Let M = [ 0 - α α 0 ], where α is a non-zero real number an N = Σ k = 1 ⁴⁹ M^(2k). If (I - M²)N = - 2I, then the positive integral value of α is _ _ _ _ _ _.Matrices and Determinants
Q43The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _ _ _ _ _ _.Permutations and Combinations
Q46Let 3, 6, 9, 12,....... upto 78 terms and 5, 9, 13, 17,...... upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to _…Sequence and Series
Q2440Let (x - 2)/3 = (y + 1)/(- 2) = (z + 3)/(- 1) lie on the plane px - qy + z = 5, for some p, q R. The shortest distance of the plane from the origin is:Three Dimensional Geometry
Q2441Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the…Three Dimensional Geometry
Q2784Let f: R → R be a function defined by f(x) = (x - 3)ⁿ₁ (x - 5)ⁿ₂, n₁, n₂ N. Then, which of the following is NOT true?Limit, Continuity and Differentiability
Q3000Let n ≥ 5 be an integer. If 9ⁿ - 8n - 1 = 64 α and 6ⁿ - 5n - 1 = 25 β, then α - β is equal toBinomial Theorem and Its Simple Applications
Q3026Let a triangle ABC be inscribed in the circle x² - 2 (x + y) + y² = 0 such that BAC = (π)/2. If the length of side AB is 2, then the area of the Δ ABC is…Coordinate Geometry
Q3192Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z - 1) - arg(z + 1) = (π)/4 intersect:Complex Numbers and Quadratic Equations
Q3426Let f be a real valued continuous function on [0, 1] and f(x) = x + ∫₀¹ (x - t)f(t)dt. Then, which of the following points (x, y) lies on the curve y = f(x) ?Integral Calculus
Q3427If ∫₀² (√(2x) - √(2x - x²))dx = ∫₀¹ (1 - √(1 - y²) - (y²)/2)dy + ∫₁² (2 - (y²)/2)dy + I, then I equalsIntegral Calculus
Q3620If y = y(x) is the solution of the differential equation (1 + e²ˣ)dy/dx + 2(1 + y²)eˣ = 0 and y (0) = 0, then 6(y'(0) + (y(log e 3))²) is equal toDifferential Equations
Q3928From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then…Height and Distance
Q4289The value of lim x → 1 ((x² - 1) sin ²(π x))/(x⁴ - 2x³ + 2x - 1) is equal to:Limit, Continuity and Differentiability
Q4360Negation of the Boolean statement (p q) ⇒ ((r) p) is equivalent to:Mathematical Reasoning
Q4527Let A = (2 - 1 0 2). If B = I - ⁵C₁(adj A) + ⁵C₂(adj A)² -..... - ⁵C₅(adj A)⁵, then the sum of all elements of the matrix B isMatrices and Determinants
Q4748Let P: y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of (π)/4 with the line y = 3x + 5 touch the parabola P at…Coordinate Geometry
Q5021The probability that a relation R from x, y to x, y is both symmetric and transitive, is equal to:Statistics and Probability
Q5048Let α be a root of the equation 1 + x² + x⁴ = 0. Then, the value of α ¹⁰¹¹ + α ²⁰²² - α ³⁰³³ is equal to:Complex Numbers and Quadratic Equations
Q5331The sum of the infinite series 1 + 5/6 + 12/(6²) + 22/(6³) + 35/(6⁴) + 51/(6⁵) + 70/(6⁶) +..... is equal to:Sequence and Series
Q5471The number of values of a N such that the variance of 3, 7, 12, a, 43 - a is a natural number is:Statistics and Probability
Q5538The distance of the origin from the centroid of the triangle whose two sides have the equations x - 2y + 1 = 0 and 2x - y - 1 = 0 and whose orthocenter is…Coordinate Geometry
Q5695Let A, B, C be three points whose position vectors respectively are a = i + 4 j + 3 k b = 2 i + α j + 4 k, α R c = 3 i - 2 j + 5 k If α is the smallest…Vector Algebra