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JEE Main 2023 13 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202313 Apr, Morning shift

Physics 23Chemistry 21Mathematics 30

Physics

Q52The radius of 2^(nd) orbit of He⁺ of Bohr's model is r₁ and that of fourth orbit of Be³⁺ is represented as r₂. Now the ratio (r₂)/(r₁) is x: 1. The value of x…Atoms and Nuclei
Q56A potential V₀ is applied across a uniform wire of resistance R. The power dissipation is P₁. The wire is then cut into two equal halves and a potential of V₀…Current Electricity
Q57When a resistance of 5 ~Ω is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of 250 ~mA, however when 1050 ~Ω…Current Electricity
Q61A thin infinite sheet charge and an infinite line charge of respective charge densities +σ and +λ are placed parallel at 5 ~m distance from each other. Points…Electrostatics
Q63A fish rising vertically upward with a uniform velocity of 8 ~ms⁻¹, observes that a bird is diving vertically downward towards the fish with the velocity of…Optics
Q69The elastic potential energy stored in a steel wire of length 20 ~m stretched through 2 ~cm is 80 ~J. The cross sectional area of the wire is _ _ _ _ _ mm²…Properties of Solids and Liquids
Q70A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of…Rotational Motion
Q71At a given point of time the value of displacement of a simple harmonic oscillator is given as y=A cos (30^(°)). If amplitude is 40 ~cm and kinetic energy at…Oscillations and Waves
Q6056₉₂²³⁸A → ₉₀²³⁴B + ₂⁴D + Q In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of ₉₂²³⁸ ~A=238.05079 × 931.5 ~MeV /…Atoms and Nuclei
Q6251A bullet of 10 ~g leaves the barrel of gun with a velocity of 600 ~m / s. If the barrel of gun is 50 ~cm long and mass of gun is 3 ~kg, then value of impulse…Rotational Motion
Q6329Match List - I with List - II List - I (Layer of atmosphere) List - II (Approximate height over earth's surface) (A) F₁ - Layer (I) 10 km (B) D - Layer (II)…Communication Systems
Q6660The difference between threshold wavelengths for two metal surfaces A and B having work function φ A =9 ~eV and φ B =4 · 5 ~eV in nm is: Given, hc =1242 ~eV nmDual Nature of Matter and Radiation
Q6811Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:Electromagnetic Waves
Q6948Two charges each of magnitude 0.01 ~C and separated by a distance of 0.4 ~mm constitute an electric dipole. If the dipole is placed in an uniform electric…Electrostatics
Q7121A vessel of depth ' d ' is half filled with oil of refractive index n₁ and the other half is filled with water of refractive index n₂. The apparent depth of…Optics
Q7208A planet having mass 9 Me and radius 4 R e, where Me and Re are mass and radius of earth respectively, has escape velocity in km / s given by: (Given escape…Gravitation
Q7318The rms speed of oxygen molecule in a vessel at particular temperature is (1+5/x)^(1/2) v, where v is the average speed of the molecule. The value of x will…Kinetic Theory of Gases
Q7718The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a…Magnetic Effects of Current and Magnetism
Q7878Two trains 'A' and 'B' of length ' l ' and ' 4 l ' are travelling into a tunnel of length ' L ' in parallel tracks from opposite directions with velocities…Kinematics
Q7961Under isothermal condition, the pressure of a gas is given by P=a ~V⁻³, where a is a constant and V is the volume of the gas. The bulk modulus at constant…Properties of Solids and Liquids
Q8312A body of mass (5 ± 0.5) ~kg is moving with a velocity of (20 ± 0.4) ~m / s. Its kinetic energy will beUnits and Measurements
Q8591Two bodies are having kinetic energies in the ratio 16: 9. If they have same linear momentum, the ratio of their masses respectively is:Work, Energy and Power
Q8610The ratio of powers of two motors is (3 √(x))/(√(x)+1), that are capable of raising 300 ~kg water in 5 minutes and 50 ~kg water in 2 minutes respectively from…Work, Energy and Power

Chemistry

Q4t 87.5 is the time required for the reaction to undergo 87.5% completion and t₅₀ is the time required for the reaction to undergo 50% completion. The relation…Chemical Kinetics
Q7A metal surface of 100 ~cm² area has to be coated with nickel layer of thickness 0.001 ~mm. A current of 2 ~A was passed through a solution of Ni(NO₃)₂ for '…Redox Reactions and Electrochemistry
Q9A certain quantity of real gas occupies a volume of 0.15~ dm³ at 100 ~atm and 500 ~K when its compressibility factor is 1.07. Its volume at 300 atm and 300 ~K…Gaseous State
Q1125.0 ~mL of 0.050 ~M ~Ba(NO₃)₂ is mixed with 25.0 ~mL of 0.020 ~M ~NaF. K Sp of BaF₂ is 0.5 × 10⁻⁶ at 298 ~K. The ratio of [Ba²⁺][F⁻]² and K sp is _ _ _ _ _…Equilibrium
Q15KMnO₄ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute H₂ SO₄. Number of water molecules produced for 2 molecules of KMnO₄ is _ _…Principles Related to Practical Chemistry
Q16Solution of 12 ~g of non-electrolyte (A) prepared by dissolving it in 1000 ~mL of water exerts the same osmotic pressure as that of 0.05 ~M glucose solution…Solutions
Q1720 ~mL of calcium hydroxide was consumed when it was reacted with 10 ~mL of unknown solution of H₂ SO₄. Also 20 ~mL standard solution of 0.5 ~M ~HCl…Some Basic Concepts in Chemistry
Q18An organic compound gives 0.220 ~g of CO₂ and 0.126 ~g of H₂ O on complete combustion. If the% of carbon is 24 then the% of hydrogen is _ _ _ _ _ × 10⁻¹…Some Basic Concepts in Chemistry
Q202-Methyl propyl bromide reacts with C₂ H₅ O⁻ and gives 'A' whereas on reaction with C₂ H₅ OH it gives 'B'. The mechanism followed in these reactions and the…Organic Compounds Containing Oxygen
Q21A₂+B₂ → 2 AB. Δ H f ⁰=-200 ~kJ ~mol⁻¹ AB, A₂ and B₂ are diatomic molecules. If the bond enthalpies of A₂, ~B₂ and AB are in the ratio 1: 0.5: 1, then the bond…Chemical Thermodynamics
Q317ClF₅ at room temperature is a:Chemical Bonding and Molecular Structure
Q382In which of the following processes, the bond order increases and paramagnetic character changes to diamagnetic one ?Chemical Bonding and Molecular Structure
Q568The mismatched combinations are A. Chlorophyll - Co B. Water hardness - EDTA C. Photography -[Ag(CN)₂]⁻ D. Wilkinson catalyst -[(Ph₃ P)₃ RhCl] E. Chelating…Coordination Compounds
Q832The pair of lanthanides in which both elements have high third - ionization energy is:d- and f-Block Elements
Q1048The radical which mainly causes ozone depletion in the presence of UV radiations is:Environmental Chemistry
Q1204Given below are two statements: Statement I: Permutit process is more efficient compared to the synthetic resin method for the softening of water. Statement…Hydrogen
Q1447Which one of the following is most likely a mismatch ?Isolation of Elements
Q1640Which of the following statements are not correct? A. The electron gain enthalpy of F is more negative than that of Cl. B. Ionization enthalpy decreases in a…Classification of Elements and Periodicity in Properties
Q1708Match the following Column A Column B (a) Nylon 6 (I) Natural Rubber (b) Vulcanized Rubber (II) Cross Linked (c) cis-1, 4-polyisoprene (III) Caprolactam (d)…Polymers
Q2127The energy of an electron in the first Bohr orbit of hydrogen atom is -2.18 × 10⁻¹⁸ ~J. Its energy in the third Bohr orbit is _ _ _ _ _ _.Atomic Structure
Q2282What happens when a lyophilic sol is added to a lyophobic sol?Surface Chemistry

Mathematics

Q24Let the image of the point (5/3, 5/3, 8/3) in the plane x-2 y+z-2=0 be P. If the distance of the point Q(6,-2, α), α > 0, from P is 13, then α is equal to _ _…Three Dimensional Geometry
Q28Let α be the constant term in the binomial expansion of (√(x)-6/(x^(3/2)))ⁿ, n ≤ 15. If the sum of the coefficients of the remaining terms in the expansion is…Binomial Theorem and Its Simple Applications
Q29Let w=z z+k₁ z+k₂ i z+λ(1+i), k₁, k₂ R. Let Re(w)=0 be the circle C of radius 1 in the first quadrant touching the line y=1 and the y -axis. If the curve…Complex Numbers and Quadratic Equations
Q32Let for x R, S₀(x)=x, S k (x)=C k x+k ∫₀ˣ S k-1 (t) d t, where C₀=1, C k =1-∫₀¹ S k-1 (x) d x, k=1,2,3, Then S₂(3)+6 C₃ is equal to _ _ _ _ _ _.Integral Calculus
Q37Let m₁ and m₂ be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H: (y²)/25-(x²)/16=1. If Q is the point from which the tangents drawn…Coordinate Geometry
Q38If S= R: sin ⁻¹((x+1)/(√(x²+2 x+2)))- sin ⁻¹(x/(√(x²+1)))=(π)/4, then Σ x s (sin ((x²+x+5) (π)/2)- cos ((x²+x+5) π)) is equal to _ _ _ _ _ _.Trigonometry
Q44The number of seven digit positive integers formed using the digits 1,2,3 and 4 only and sum of the digits equal to 12 is _ _ _ _ _ _.Permutations and Combinations
Q48The sum to 20 terms of the series 2 · 2²-3²+2 · 4²-5²+2 · 6²- is equal to _ _ _ _ _.Sequence and Series
Q49Let the mean of the data x | 1 | 3 | 5 | 7 | 9 Frequency (f) | 4 | 24 | 28 | α | 8 be 5. If m and σ² are respectively the mean deviation about the mean and…Statistics and Probability
Q51Let a=3 i+j-k and c=2 i-3 j+3 k. If b is a vector such that a=b × c and |b|²=50, then |72-| b+.c|² is equal to _ _ _ _ _.Vector Algebra
Q2466The distance of the point (-1,2,3) from the plane r ·(i-2 j+3 k)=10 parallel to the line of the shortest distance between the lines r=(i-j)+λ(2 i+k) and r=(2…Three Dimensional Geometry
Q2608Let the equation of plane passing through the line of intersection of the planes x+2 y+a z=2 and x-y+z=3 be 5 x-11 y+b z=6 a-1. For c Z, if the distance of…Three Dimensional Geometry
Q2678max 0 ≤ x ≤ π -2 sin x cos x+1/3 sin 3 x\=Limit, Continuity and Differentiability
Q2860The area of the region enclosed by the curve f(x)= max sin x, cos x -π ≤ x ≤ π and the x -axis isIntegral Calculus
Q2899Fractional part of the number (4²⁰²²)/15 is equal toBinomial Theorem and Its Simple Applications
Q3297Among (S1): lim n → ∞ 1/(n²)(2+4+6+ +2 n)=1 (S2): lim n → ∞ 1/(n¹⁶)(1¹⁵+2¹⁵+3¹⁵+ +n¹⁵)=1/16Integral Calculus
Q3461∫₀^(∞) 6/(e³ˣ+6 e²ˣ+11 eˣ+6) d x=Integral Calculus
Q3637Let y=y₁(x) and y=y₂(x) be the solution curves of the differential equation (d y)/(d x)=y+7 with initial conditions y₁(0)=0 and y₂(0)=1 respectively. Then the…Differential Equations
Q3699For the differentiable function f: R-\0 → R, let 3 f(x)+2 f(1/x)=1/x-10, then |f(3)+f^()(1/4)| is equal toLimit, Continuity and Differentiability
Q3734Let the tangent and normal at the point (3 √(3), 1) on the ellipse (x²)/36+(y²)/4=1 meet the y -axis at the points A and B respectively. Let the circle C be…Coordinate Geometry
Q3831For x R, two real valued functions f(x) and g(x) are such that, g(x)=√(x)+1 and f° g(x)=x+3-√(x). Then f(0) is equal toSets, Relations and Functions
Q4390The negation of the statement ((A (B C)) ⇒(A B)) ⇒ A isMathematical Reasoning
Q4426Let B=[ lll1 3 α 1 2 3 α α 4 ], α > 2 be the adjoint of a matrix A and |A|=2. Then [ cccα -2 α α ] B[ cα -2 α α ] is equal to:Matrices and Determinants
Q4625For the system of linear equations 2 x+4 y+2 a z=b x+2 y+3 z=4 2 x-5 y+2 z=8 which of the following is NOT correct?Matrices and Determinants
Q4650The number of symmetric matrices of order 3, with all the entries from the set \0,1,2,3,4,5,6,7,8,9 is:Matrices and Determinants
Q4674Let PQ be a focal chord of the parabola y²=36 x of length 100, making an acute angle with the positive x -axis. Let the ordinate of P be positive and M be the…Coordinate Geometry
Q5004A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of…Statistics and Probability
Q5088The set of all a R for which the equation x|x-1|+|x+2|+a=0 has exactly one real root, is:Complex Numbers and Quadratic Equations
Q5229Let s₁, s₂, s₃,, s₁₀ respectively be the sum to 12 terms of 10 A.P. s whose first terms are 1,2,3,.10 and the common differences are 1,3,5,, 19 respectively…Sequence and Series
Q5838Let a=i+4 j+2 k, b=3 i-2 j+7 k and c=2 i-j+4 k. If a vector d satisfies d × b=c × b and d · a=24, then |d|² is equal to:Vector Algebra