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JEE Main 2022 30 Jun Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202230 Jun, Morning shift

Physics 24Chemistry 18Mathematics 29

Physics

Q49A series LCR circuit with R = 250/11 Ω and X L = 70/11 Ω is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average…Electromagnetic Induction and Alternating Currents
Q51A hydrogen atom in its first excited state absorbs a photon of energy x × 10⁻² eV and excited to a higher energy state where the potential energy of electron…Atoms and Nuclei
Q57Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will…Electrostatics
Q58The refractive index of an equilateral prism is 2. The angle of emergence under minimum deviation position of prism, in degree, is _ _ _ _ _ _.Optics
Q67The excess pressure inside a liquid drop is 500 Nm⁻². If the radius of the drop is 2 mm, the surface tension of liquid is x × 10⁻³ Nm⁻¹. The value of x is _ _…Properties of Solids and Liquids
Q71An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh⁻¹ in the…Oscillations and Waves
Q5905In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f₂) and new quality factor (Q₂) will be: (f₁ =…Electromagnetic Induction and Alternating Currents
Q6010A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by:Atoms and Nuclei
Q6242Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be:Rotational Motion
Q6361A speech signal given by 11 sin(2200 π t) V is used for amplitude modulation with a carrier signal given by 44 sin(6600 π t) V. The minimum amplitude of…Communication Systems
Q6386An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 Ω. If this single copper wire of the cable is replaced by seven identical…Current Electricity
Q6603A source of monochromatic light liberates 9 × 10²⁰ photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second…Dual Nature of Matter and Radiation
Q6793An expression for oscillating electric field in a plane electromagnetic wave is given as E z = 300 sin(5 π × 10³x - 3 π × 10¹¹t) Vm⁻¹ Then, the value of…Electromagnetic Waves
Q7149The radii of two planets A and B are in the ratio 2: 3. Their densities are 3 ρ and 5 ρ respectively. The ratio of their acceleration due to gravity is:Gravitation
Q7402The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid…Properties of Solids and Liquids
Q7490A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm³ to 150 cm³ adiabatically. In this…Thermodynamics
Q7688A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r₁ and r₂ respectively. When a current of strength I is passed…Magnetic Effects of Current and Magnetism
Q7763A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be: (Take: e = 1.6…Magnetic Effects of Current and Magnetism
Q7792At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms⁻². At t = 20 s, a ball is released from the top of the…Kinematics
Q7793Two projectiles P₁ and P₂ thrown with speed in the ratio 3: 2, attain the same height during their motion. If P₂ is thrown at an angle of 60° with the…Kinematics
Q7914An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed v. The coefficient of viscosity of the solution is…Properties of Solids and Liquids
Q8357If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is…Experimental Skills
Q8446Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio…Optics
Q8506Which of the following equations correctly represents a travelling wave having wavelength λ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis…Oscillations and Waves

Chemistry

Q1A hydrocarbon 'X' is found to have molar mass of 80. A 10.0 mg of compound 'X' on hydrogenation consumed 8.40 mL of H₂ gas (measured at STP). Ozonolysis of…Organic Compounds Containing Oxygen
Q3Amongst the following, the number of molecule/(s) having net resultant dipole moment is _ _ _ _ _ _. NF₃, BF₃, BeF₂, CHCl₃, H₂S, SiF₄, CCl₄, PF₅Chemical Bonding and Molecular Structure
Q5For the reaction P → B, the values of frequency factor A and activation energy E A are 4 × 10¹³ s⁻¹ and 8.3 kJ mol⁻¹ respectively. If the reaction is of first…Chemical Kinetics
Q7In the following brown complex, the oxidation state of iron is + _ _ _ _ _ _ _. [Fe (H₂O)₆ ]²⁺ + NO → [Fe (H₂O)₅ (NO)] ²⁺ Brown complex + H₂OCoordination Compounds
Q8Spin only magnetic moment (μ s) of K₃[Fe (CN)₆ ] is _ _ _ _ _ _ B.M. (Nearest integer)Coordination Compounds
Q12An organic compound with 51.6% sulfur is heated in a Carius tube. The amount of this compound which will form 0.752 g of barium sulphate is _ _ _ _ _ _ × 10⁻¹…Principles Related to Practical Chemistry
Q16Blister copper is produced by reaction of copper oxide with copper sulphide. 2Cu₂O + Cu₂S → 6Cu + SO₂ When 2.86 × 10³ g of Cu₂O and 4.77 × 10³ g of Cu₂S are…Some Basic Concepts in Chemistry
Q241The sugar produced after complete hydrolysis of DNA isBiomolecules
Q421The equilibrium constant for the reversible reaction 2A(g) 2B(g) + C(g) is K₁ 3/2 A(g) 3/2 B(g) + 3/4 C(g) is K₂. K₁ and K₂ are related as:Equilibrium
Q564Correct formula of the compound which gives a white precipitate with BaCl₂ solution, but not with AgNO₃ solution, is:Coordination Compounds
Q1002In which of the following half cells, electrochemical reaction is pH dependent?Redox Reactions and Electrochemistry
Q1493A 0pt ^(573 K) Red phosphorus 0pt under pressure ^(heat; 803 K) B Red phosphorus is obtained by heating "A" at 573 K, and can be converted to "B" by heating…p-Block Elements
Q1578The correct order of electron gain enthalpy (- ve value) is:Classification of Elements and Periodicity in Properties
Q1754The reagent neutral ferric chloride is used to detect the presence of _ _ _ _ _ _ _Principles Related to Practical Chemistry
Q1831Correct statement about alkali metal oxides is:S Block Elements
Q1930An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm⁻³. The number of atoms present in 300 g…Solid State
Q2205The number of radial nodes and total number of nodes in 4p orbital respectively are:Atomic Structure
Q2272TLC analysis of a mixture having 3 components (A, B, C) using silica gel as the stationary phase gave following R f values; for A = 0.72, B = 0.48, C = 0.20…Surface Chemistry

Mathematics

Q20Consider a triangle ABC whose vertices are A(0, α, α), B(α, 0, α) and C(α, α, 0), α > 0. Let D be a point moving on the line x + z - 3 = 0 = y and G be the…Three Dimensional Geometry
Q23A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate at which…Limit, Continuity and Differentiability
Q24If for some α > 0, the area of the region (x,y):|x + α | ≤ y ≤ 2 - |x| is equal to 3/2, then the area of the region (x,y):0 ≤ y ≤ x + 2α, |x| ≤ 1 is equal to…Integral Calculus
Q29Let f(t) = ∫₀^(t) e^(x³)((x⁸)/((x⁶ + 2x³ + 2)²))dx. If f(1) + f'(1) = α e - 1/6, then the value of 150 α is equal to _ _ _ _ _ _.Integral Calculus
Q34Suppose lim x → 0 (F(x))/(x³) exists and is equal to L, where F(x) = | a + sin x/2 - b cos x 0 - b cos x 0 a + sin x/2 0 a + sin x/2 - b cos x |. Then, - 112…Limit, Continuity and Differentiability
Q38Let PQ be a focal chord of length 6.25 units of the parabola y² = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of Δ POQ is…Coordinate Geometry
Q39The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is _ _ _ _ _ _.Permutations and Combinations
Q41The probability distribution of X is: X | 0 | 1 | 2 | 3 P(X) | (1 - d)/4 | (1 + 2d)/4 | (1 - 4d)/4 | (1 + 3d)/4 For the minimum possible value of d, sixty…Statistics and Probability
Q44Let for f(x) = a₀x² + a₁x + a₂, f'(0) = 1 and f'(1) = 0. If a₀, a₁, a₂ are in an arithmatico-geometric progression, whose corresponding A.P. has common…Sequence and Series
Q2448The distance of the point (3, 2, - 1) from the plane 3x - y + 4z + 1 = 0 along the line (2 - x)/2 = (y - 3)/2 = (z + 1)/1 is equal to:Three Dimensional Geometry
Q2666If xy⁴ attains maximum value at the point (x, y) on the line passing through the points (50 + α, 0) and (0, 50 + α), α > 0, then (x, y) also lies on the line:Limit, Continuity and Differentiability
Q2667Let f(x) = 4x³ - 11x² + 8x - 5, x R. Then f:Limit, Continuity and Differentiability
Q2938For two positive real numbers a and b such that 1/(a²) + 1/(b³) = 4, then minimum value of the constant term in the expansion of (a x^(1/8) + b x^(- 1/12))¹⁰…Binomial Theorem and Its Simple Applications
Q3106Consider three circles: C₁:x² + y² = r² C₂:(x - 1)² + (y - 1)² = r² C₃:(x - 2)² + (y - 1)² = r² If a line L: y = mx + c be a common tangent to C₁, C₂ and C₃…Coordinate Geometry
Q3225The real part of the complex number ((1 + 2i)⁸. (1 - 2i)²)/((3 + 2i). (4 - 6i)) is equal to:Complex Numbers and Quadratic Equations
Q3292lim n → ∞ Σ r = 1 ⁿ r/(2r² - 7rn + 6n²) is equal to:Integral Calculus
Q3499Let dy/dx = (ax - by + a)/(bx + cy + a), a,b,c R, represents a circle with center (α, β). Then, α + 2 β is equal to:Differential Equations
Q3762Let the eccentricity of the ellipse x² + a²y² = 25a² be b times the eccentricity of the hyperbola x² - a²y² = 5, where a is the minimum distance between the…Coordinate Geometry
Q4076Let α = tan ((5π)/16 sin (2 cos ⁻¹(1/(5)))) and β = cos (sin ⁻¹(4/5) + sec ⁻¹(5/3)) where the inverse trigonometric functions take principal values. Then, the…Trigonometry
Q4110Let m and M respectively be the minimum and the maximum values of f(x) = sin ⁻¹2x + sin 2x + cos ⁻¹2x + cos 2x, x [ 0,(π)/8 ]. Then m + M is equal to:Trigonometry
Q4369The conditional statement ((p q) → ((p) r)) (((p) r) → (p q)) is:Mathematical Reasoning
Q4469Let A = [ 1 - 2 α α 2 - 1 ] and B = [ 2 α - 1 2 4 - 5 ], α C. Then the absolute value of the sum of all values of α for which det(AB) = 0 is:Matrices and Determinants
Q4533Let A and B be two square matrices of order 2. If det (A) = 2, det (B) = 3 and det ((det 5(det A)B)A²) = 2^(a) 3^(b) 5^(c) for some a, b, c, N, then a + b + c…Matrices and Determinants
Q4890If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then (P(X = 2))/(P(X = 3)) is equal to:Statistics and Probability
Q5070Let S₁ = x R - 1,2:((x + 2)(x² + 3x + 5))/(- 2 + 3x - x²) ≥ 0 and S₂ = x R:3²ˣ - 3ˣ⁺¹ - 3ˣ⁺² + 27 ≤ 0. Then, S₁ S₂ is equal to:Complex Numbers and Quadratic Equations
Q5102Let S be the set of all integral values of α for which the sum of squares of two real roots of the quadratic equation 3x² + (α - 6)x + (α + 3) = 0 is minimum…Complex Numbers and Quadratic Equations
Q5335The value of 1 + 1/(1 + 2) + 1/(1 + 2 + 3) +.... + 1/(1 + 2 + 3 +..... + 11) is equal to:Sequence and Series
Q5523Let α ₁, α ₂ (α ₁ < α ₂) be the values of α fo the points (α, - 3), (2, 0) and (1, α) to be collinear. Then the equation of the line, passing through (α ₁, α…Coordinate Geometry
Q5738Let a vector c be coplanar with the vectors a = - i + j + k and b = 2 i + j - k. If the vector c also satisfies the conditions c. [ (a + b) × (a × b) ] = - 42…Vector Algebra