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JEE Main 2023 6 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20236 Apr, Morning shift

Physics 23Chemistry 21Mathematics 30

Physics

Q54An ideal transformer with purely resistive load operates at 12 ~kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 ~V…Electromagnetic Induction and Alternating Currents
Q55The radius of fifth orbit of the Li⁺⁺ is _ _ _ _ _ × 10⁻¹² ~m. Take: radius of hydrogen atom = 0.51 A^(o)Atoms and Nuclei
Q59The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%. The percentage change in resistance of the metallic wire is…Current Electricity
Q64A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 ~m within water when sunlight is incident at angle of 30^(°) with…Optics
Q72A steel rod has a radius of 20 ~mm and a length of 2.0 ~m. A force of 62.8 ~kN stretches it along its length. Young's modulus of steel is 2.0 × 10¹¹ ~N / m²…Properties of Solids and Liquids
Q73Two identical solid spheres each of mass 2 ~kg and radii 10 ~cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40…Rotational Motion
Q75A person driving car at a constant speed of 15 ~m / s is approaching a vertical wall. The person notices a change of 40 ~Hz in the frequency of his car's horn…Oscillations and Waves
Q76A particle of mass 10 ~g moves in a straight line with retardation 2 x, where x is the displacement in SI units. Its loss of kinetic energy for above…Work, Energy and Power
Q6288A particle is moving with constant speed in a circular path. When the particle turns by an angle 90^(°), the ratio of instantaneous velocity to its average…Kinematics
Q6289A small block of mass 100 ~g is tied to a spring of spring constant 7.5 ~N / m and length 20 ~cm. The other end of spring is fixed at a particular point A. If…Kinematics
Q6334By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21% ?Communication Systems
Q6588The kinetic energy of an electron, α -particle and a proton are given as 4 ~K, 2 ~K and K respectively. The de-Broglie wavelength associated with electron (λ…Dual Nature of Matter and Radiation
Q6713The induced emf can be produced in a coil by A. moving the coil with uniform speed inside uniform magnetic field B. moving the coil with non uniform speed…Electromagnetic Induction and Alternating Currents
Q6816For the plane electromagnetic wave given by E=E₀ sin (ω t-k x) and B=B₀ sin (ω t-k x), the ratio of average electric energy density to average magnetic energy…Electromagnetic Waves
Q7124A monochromatic light wave with wavelength λ₁ and frequency v₁ in air enters another medium. If the angle of incidence and angle of refraction at the…Optics
Q7216Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Earth has atmosphere whereas moon doesn't…Gravitation
Q7281A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:Gravitation
Q7423The number of air molecules per cm ³ increased from 3×10¹⁹ to 12×10¹⁹. The ratio of collision frequency of air molecules before and after the increase in…Thermodynamics
Q7538A source supplies heat to a system at the rate of 1000 ~W. If the system performs work at a rate of 200 ~W. The rate at which internal energy of the system…Thermodynamics
Q7695A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The…Magnetic Effects of Current and Magnetism
Q7806Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: When a body is projected at an angle 45^(°)…Kinematics
Q7919A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ₀. After some time, the ball falls with a constant velocity. What is the…Properties of Solids and Liquids
Q8315Two resistances are given as R₁=(10 ± 0.5) Ω and R₂=(15 ± 0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in…Units and Measurements

Chemistry

Q3The number of species from the following which have square pyramidal structure is _ _ _ _ P F₅, BrF₄⁻, IF₅, BrF₅, XeOF₄, ICl₄⁻Chemical Bonding and Molecular Structure
Q6Number of ambidentate ligands in a representative metal complex [M(en)(SCN)₄] is _ _ _ _ _ _. [en = ethylenediamine]Coordination Compounds
Q11Number of bromo derivatives obtained on treating ethane with excess of Br₂ in diffused sunlight is _ _ _ _ _ _Hydrocarbons
Q17In ammonium - phosphomolybdate, the oxidation state of Mo is + _ _ _ _ _ _Redox Reactions and Electrochemistry
Q20Mass of Urea (NH₂ CONH₂) required to be dissolved in 1000 ~g of water in order to reduce the vapour pressure of water by 25% is _ _ _ _ g. (Nearest integer)…Solutions
Q21If 5 moles of BaCl₂ is mixed with 2 moles of Na₃ PO₄, the maximum number of moles of Ba₃(PO₄)₂ formed is _ _ _ _ _ _ (Nearest integer)Some Basic Concepts in Chemistry
Q22The wavelength of an electron of kinetic energy 4.50×10⁻²⁹ J is _ _ _ _ _ × 10⁻⁵ m. (Nearest integer) Given: mass of electron is 9×10⁻³¹ kg, h =6.6×10⁻³⁴ J sAtomic Structure
Q23The value of log K for the reaction A B at 298 ~K is _ _ _ _ _ _. (Nearest integer) Given: Δ H^(°)=-54.07 ~kJ ~mol⁻¹ Δ S^(°)=10 ~J ~K⁻¹ ~mol⁻¹ (Take 2.303 ×…Chemical Thermodynamics
Q217Match List I with List II LIST I Enzymatic reaction LIST II Enzyme A. Sucrose → Glocuse and Fructose I. Zymase B. Glucose → ethyl alcohol and CO ₂ II. Pepsin…Biomolecules
Q422For a concentrated solution of a weak electrolyte (K eq = equilibrium constant) A₂ B₃ of concentration ' c ', the degree of dissociation ' α ' is:Equilibrium
Q518Match List I with List II LIST I Vitamin LIST II Deficiency disease A. Vitamin A I. Beri-Beri B. Thiamine II. Cheilosis C. Ascorbic acid III. Xeropthalmia D…Chemistry in Everyday Life
Q648Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The spin only magnetic moment value for…Coordination Compounds
Q834Strong reducing and oxidizing agents among the following, respectively, are:d- and f-Block Elements
Q1005The standard electrode potential of M⁺ / M in aqueous solution does not depend onRedox Reactions and Electrochemistry
Q1052The possibility of photochemical smog formation is more at:Environmental Chemistry
Q1265Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Loss of electron from hydrogen atom results…Hydrogen
Q1429The setting time of Cement is increased by adding:Isolation of Elements
Q1581The difference between electron gain enthalpies will be maximum between:Classification of Elements and Periodicity in Properties
Q1761Match List I with List II LIST I Element detected LIST II Reagent used / Product formed A. Nitrogen I. Na₂[Fe(CN)₅NO] B. Sulphur II. AgNO₃ C. Phosphorous III…Principles Related to Practical Chemistry
Q1818Which of the following options are correct for the reaction 2[Au(CN)₂]⁻(aq)+Zn(s) → 2 Au(s)+[Zn(CN)₄]²⁻(aq) A. Redox reaction B. Displacement reaction C…Redox Reactions and Electrochemistry
Q1911A compound is formed by two elements X and Y. The element Y forms cubic close packed arrangement and those of element X occupy one third of the tetrahedral…Solid State

Mathematics

Q26Let the image of the point P(1,2,3) in the plane 2 x-y+z=9 be Q. If the coordinates of the point R are (6,10,7), then the square of the area of the triangle…Three Dimensional Geometry
Q27If the area of the region S=\(x, y): 2 y-y² ≤ x² ≤ 2 y, x ≥ y is equal to (n+2)/(n+1)-(π)/(n-1), then the natural number n is equal to _ _ _ _ _ _.Integral Calculus
Q30The coefficient of x¹⁸ in the expansion of (x⁴-1/(x³))¹⁵ is _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q31Let the point (p, p+1) lie inside the region E=\(x, y): 3-x ≤ y ≤ √(9-x²), 0 ≤ x ≤ 3. If the set of all values of p is the interval (a, b), then b²+b-a² is…Coordinate Geometry
Q32A circle passing through the point P(α, β) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line A B. The…Coordinate Geometry
Q34Let y=y(x) be a solution of the differential equation (x cos x) d y+(x y sin x+y cos x-1) d x=0,0 < x < (π)/2. If (π)/3 y((π)/3)=√(3), then |(π)/6…Differential Equations
Q38Let a Z and [t] be the greatest integer ≤ t. Then the number of points, where the function f(x)=[a+13 sin x], x (0, π) is not differentiable, is _ _ _ _ _.Limit, Continuity and Differentiability
Q43Let the tangent to the curve x²+2 x-4 y+9=0 at the point P(1,3) on it meet the y -axis at A. Let the line passing through P and parallel to the line x-3 y=6…Coordinate Geometry
Q44The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _ _ _ _ _ _.Permutations and Combinations
Q49Let A=\1,2,3,4,., 10 and B=\0,1,2,3,4. The number of elements in the relation R=\(a, b) A × A: 2(a-b)²+3(a-b) B is _ _ _ _ _ _.Sets, Relations and Functions
Q2472If the equation of the plane passing through the line of intersection of the planes 2 x-y+z=3,4 x-3 y+5 z+9=0 and parallel to the line…Three Dimensional Geometry
Q2520One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x, y and z axes are 3,4 and 5 units respectively. Let P be…Three Dimensional Geometry
Q2946If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (4√(2)+1/(4√(3)))ⁿ is √(6): 1, then the third term from…Binomial Theorem and Its Simple Applications
Q3011If ²ⁿ C₃: ⁿ C₃=10: 1, then the ratio (n²+3 n):(n²-3 n+4) is:Binomial Theorem and Its Simple Applications
Q3465Let 5 f(x)+4 f(1/x)=1/x+3, x > 0. Then 18 ∫₁² f(x) d x is equal to:Integral Calculus
Q3692If 2 x^(y)+3 yˣ=20, then (d y)/(d x) at (2,2) is equal to:Limit, Continuity and Differentiability
Q3936From the top A of a vertical wall AB of height 30 ~m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15^(°) and 60^(°)…Height and Distance
Q3997Let I(x)=∫ (x²(x sec ² x+ tan x))/((x tan x+1)²) d x. If I(0)=0, then I((π)/4) is equal to:Integral Calculus
Q4245Let a₁, a₂, a₃,, a n be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then lim n → ∞…Limit, Continuity and Differentiability
Q4397Statement (P ⇒ Q) (R ⇒ Q) is logically equivalent to:Mathematical Reasoning
Q4510Let A=[a ij ] 2 × 2, where a ij ≠ 0 for all i, j and A²=I. Let a be the sum of all diagonal elements of A and b=|A|. Then 3 a²+4 b² is equal to:Matrices and Determinants
Q4629If the system of equations x+y+a z=b 2 x+5 y+2 z=6 x+2 y+3 z=3 has infinitely many solutions, then 2 a+3 b is equal to:Matrices and Determinants
Q4898A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is k/(3¹¹), then k is equal…Statistics and Probability
Q5064Let A = x R:[x + 3] + [x + 4] ≤ 3, B = \ x R:3ˣ (Σ r = 1 ^∞ 3/(10^(r)))ˣ⁻³ < 3⁻³ˣ \, where [t] denotes greatest integer function. Then,Complex Numbers and Quadratic Equations
Q5165The sum of all the roots of the equation |x²-8 x+15|-2 x+7=0 is:Complex Numbers and Quadratic Equations
Q5345The sum of the first 20 terms of the series 5+11+19+29+41+ is:Sequence and Series
Q5488The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and σ² respectively. If the…Statistics and Probability
Q5621The straight lines l₁ and l₂ pass through the origin and trisect the line segment of the line L: 9 x+5 y=45 between the axes. If m₁ and m₂ are the slopes of…Coordinate Geometry
Q5752Let the position vectors of the points A, B, C and D be 5 i+5 j+2 λ k, i+2 j+3 k,-2 i+λ j+4 k and -i+5 j+6 k. Let the set S=\λ R: the points A, B, C and D are…Vector Algebra
Q5843Let a=2 i+3 j+4 k, b=i-2 j-2 k and c=-i+4 j+3 k. If d is a vector perpendicular to both b and c, and a · d=18, then |a × d|² is equal to:Vector Algebra