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JEE Main 2024 9 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20249 Apr, Evening shift

Physics 20Chemistry 24Mathematics 30

Physics

Q55A capacitor of reactance 4 √(3) Ω and a resistor of resistance 4 Ω are connected in series with an ac source of peak value 8 √(2) ~V. The power dissipation in…Electromagnetic Induction and Alternating Currents
Q59At room temperature (27^(°) C), the resistance of a heating element is 50 Ω. The temperature coefficient of the material is 2.4 × 10⁻⁴ ^(°) C⁻¹. The…Current Electricity
Q64A straight magnetic strip has a magnetic moment of 44 ~Am². If the strip is bent in a semicircular shape, its magnetic moment will be _ _ _ _ Am². (given…Magnetic Effects of Current and Magnetism
Q69A circular disc reaches from top to bottom of an inclined plane of length l. When it slips down the plane, if takes t ~s. When it rolls down the plane then it…Rotational Motion
Q70A particle of mass 0.50 ~kg executes simple harmonic motion under force F=-50(Nm⁻¹) x. The time period of oscillation is x/35 s. The value of x is _ _ _ _ _…Oscillations and Waves
Q72The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B is _ _ _ _ _°.Kinematics
Q73Monochromatic light of wavelength 500 ~nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is…Optics
Q74A force (3 x²+2 x-5) N displaces a body from x=2 ~m to x=4 ~m. Work done by this force is _ _ _ _ J.Work, Energy and Power
Q6028A hydrogen atom in ground state is given an energy of 10.2 ~eV. How many spectral lines will be emitted due to transition of electrons?Atoms and Nuclei
Q6061A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2: 1. After disintegration they will move:Atoms and Nuclei
Q6062The energy released in the fusion of 2 ~kg of hydrogen deep in the sun is E H and the energy released in the fission of 2 ~kg of ²³⁵ U is E U. The ratio E H…Atoms and Nuclei
Q6668UV light of 4.13 ~eV is incident on a photosensitive metal surface having work function 3.13 ~eV. The maximum kinetic energy of ejected photoelectrons will be:Dual Nature of Matter and Radiation
Q6825The magnetic field in a plane electromagnetic wave is B y =(3.5 × 10⁻⁷) sin (1.5 × 10³ x+0.5 × 10¹¹ t) T. The corresponding electric field will be:Electromagnetic Waves
Q7221A satellite of 10³ ~kg mass is revolving in circular orbit of radius 2 R. If (10⁴ R)/6 ~J energy is supplied to the satellite, it would revolve in a new…Gravitation
Q7435The temperature of a gas is -78^(°) C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational…Thermodynamics
Q7766A proton and a deutron (q=+e, m=2.0 u) having same kinetic energies enter a region of uniform magnetic field B, moving perpendicular to B. The ratio of the…Magnetic Effects of Current and Magnetism
Q7852Two cars are travelling towards each other at speed of 20 ~m ~s⁻¹ each. When the cars are 300 ~m apart, both the drivers apply brakes and the cars retard at…Kinematics
Q7921A spherical ball of radius 1 × 10⁻⁴ ~m and density 10⁵ ~kg / m³ falls freely under gravity through a distance h before entering a tank of water, If after…Properties of Solids and Liquids
Q8034The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second…Properties of Solids and Liquids
Q8280The de-Broglie wavelength associated with a particle of mass m and energy E is h / √(2 m E). The dimensional formula for Planck's constant is:Units and Measurements

Chemistry

Q4Total number of electrons present in (π^) molecular orbitals of O₂, O₂⁺ and O₂⁻ is _ _ _ _.Chemical Bonding and Molecular Structure
Q5Consider the following first order gas phase reaction at constant temperature A(g) → 2 B(~g)+C(g) If the total pressure of the gases is found to be 200 torr…Chemical Kinetics
Q6Number of compounds from the following which cannot undergo Friedel-Crafts reactions is: _ _ _ _ t oluene, nitrobenzene, xylene, cumene, aniline…Organic Compounds Containing Nitrogen
Q9Consider the following test for a group-IV cation. M²⁺+H₂ S → A (Black precipitate)+ byproduct A+ aqua regia → B+NOCl+S+H₂ O B+KNO₂+CH₃ COOH → C+ byproduct…Coordination Compounds
Q12A transition metal ' M ' among Sc, Ti, V, Cr, Mn and Fe has the highest second ionisation enthalpy. The spin-only magnetic moment value of M⁺ ion is _ _ _ B M…d- and f-Block Elements
Q17Number of oxygen atoms present in chemical formula of fuming sulphuric acid is _ _ _ _ _ _.p-Block Elements
Q21The vapor pressure of pure benzene and methyl benzene at 27^(°) C is given as 80 Torr and 24 Torr, respectively. The mole fraction of methyl benzene in vapor…Solutions
Q22Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter 10⁻¹⁵ ~m is _ _…Atomic Structure
Q24When Δ H vap =30 ~kJ / mol and Δ S vap =75 ~J ~mol⁻¹ ~K⁻¹, then the temperature of vapour, at one atmosphere is _ _ _ _ K.Chemical Thermodynamics
Q65Which of the following compounds will give silver mirror with ammoniacal silver nitrate? A. Formic acid B. Formaldehyde C. Benzaldehyde D. Acetone Choose the…Organic Compounds Containing Oxygen
Q186The incorrect statement about Glucose is:Biomolecules
Q322The correct increasing order for bond angles among BF₃, PF₃ and ClF₃ is:Chemical Bonding and Molecular Structure
Q749Match List I with List II LIST I LIST II A. K₂[Ni(CN)₄] I. sp³ B. [Ni(CO)₄] II. sp³d² C. [Co(NH₃)₆] Cl₃ III. dsp² D. Na₃[CoF₆] IV. d²sp³ Choose the correct…Coordination Compounds
Q750The coordination environment of Ca²⁺ ion in its complex with EDTA⁴⁻ is:Coordination Compounds
Q839The electronic configuration of Einsteinium is: (Given atomic number of Einsteinium =99)d- and f-Block Elements
Q904Give below are two statements: Statement I: The higher oxidation states are more stable down the group among transition elements unlike p-block elements…d- and f-Block Elements
Q920Match List I with List II LIST I (Cell) LIST II (Use/Property/Reaction) A. Leclanche cell I. Converts energy of combustion into electrical energy B. Ni - Cd…Redox Reactions and Electrochemistry
Q953Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols…Redox Reactions and Electrochemistry
Q1174The incorrect statement regarding ethyne isHydrocarbons
Q1348For a sparingly soluble salt AB₂, the equilibrium concentrations of A²⁺ ions and B⁻ ions are 1.2 × 10⁻⁴ M and 0.24 × 10⁻³ M, respectively. The solubility…Equilibrium
Q1623Match List I with List II LIST I LIST II A. Melting Point [K] I. T 1>In>Ga>A 1>B B. Ionic Radius [M⁺³ / pm] II. B>T 1>Al ≈ Ga>In C. Δ i H₁[~kJ ~mol⁻¹] III. T…Classification of Elements and Periodicity in Properties
Q1666Match List I with List II LIST I (Element) LIST II (Electronic Configuration) A. N I. [Ar] 3 ~d¹⁰ 4 ~s² 4 p⁵ B. S II. [Ne] 3 ~s² 3 p⁴ C. Br III. [He] 2 ~s² 2…Classification of Elements and Periodicity in Properties
Q1736Match List I with List II LIST I (Test) LIST II (Observation) A. Br₂ water test I. Yellow orange or orange red precipitate formed B. Ceric ammonium nitrate…Principles Related to Practical Chemistry
Q2179The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency ' A ' × 10¹² hertz and that has a…Atomic Structure

Mathematics

Q26The square of the distance of the image of the point (6,1,5) in the line (x-1)/3=y/2=(z-2)/4, from the origin is _ _ _ _ _.Three Dimensional Geometry
Q27Let the set of all values of p, for which f(x)=(p²-6 p+8)(sin ² 2 x- cos ² 2 x)+2(2-p) x+7 does not have any critical point, be the interval (a, b). Then 16 a…Limit, Continuity and Differentiability
Q35For a differentiable function f: R → R, suppose f^()(x)=3 f(x)+α, where α R, f(0)=1 and lim x →-∞ f(x)=7. Then 9 f(- log e 3) is equal to _ _ _ _ _.Differential Equations
Q37Let A=\(x, y): 2 x+3 y=23, x, y N and B=:(x, y) A. Then the number of one-one functions from A to B is equal to _ _ _ _ _.Sets, Relations and Functions
Q40Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin ⁻¹ x+3 cos ⁻¹ x=(2 π)/5, is _ _ _ _ _.Trigonometry
Q43Consider the matrices: A=[ cc2 -5 3 m ], B=[ l20 m ] and X=[ lx y ]. Let the set of all m, for which the system of equations A X=B has a negative solution…Matrices and Determinants
Q44Consider the circle C: x²+y²=4 and the parabola P: y²=8 x. If the set of all values of α, for which three chords of the circle C on three distinct lines…Coordinate Geometry
Q45Let A, B and C be three points on the parabola y²=6 x and let the line segment A B meet the line L through C parallel to the x -axis at the point D. Let M and…Coordinate Geometry
Q46The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is _ _ _ _ _.Permutations and Combinations
Q51If (1/(α+1)+1/(α+2)+..+1/(α+1012))-(1/(2 · 1)+1/(4 · 3)+1/(6 · 5)+ +1/(2024 · 2023))=1/2024, then α is equal to _ _ _ _ _ _.Sequence and Series
Q2532Consider the line L passing through the points (1,2,3) and (2,3,5). The distance of the point (11/3, 11/3, 19/3) from the line L along the line (3 x-11)/2=(3…Three Dimensional Geometry
Q2869The area (in square units) of the region enclosed by the ellipse x²+3 y²=18 in the first quadrant below the line y=x isIntegral Calculus
Q3014The sum of the coefficient of x^(2 / 3) and x^(-2 / 5) in the binomial expansion of (x^(2 / 3)+1/2 x^(-2 / 5))⁹ isBinomial Theorem and Its Simple Applications
Q3202Let z be a complex number such that the real part of (z-2 i)/(z+2 i) is zero. Then, the maximum value of |z-(6+8 i)| is equal toComplex Numbers and Quadratic Equations
Q3322lim x → (π)/2 ((∫ x³ ^((π / 2)³)(sin (2 t^(1 / 3))+ cos (t^(1 / 3))) d t)/((x-(π)/2)²)) is equal toIntegral Calculus
Q3479The integral ∫ 1 / 4 ^(3 / 4) cos (2 cot ⁻¹ √((1-x)/(1+x))) d x is equal toIntegral Calculus
Q3480The value of the integral ∫₋₁² log e (x+√(x²+1)) d x isIntegral Calculus
Q3566Let ∫₀ˣ √(1-(y^()(t))²) d t=∫₀ˣ y(t) d t, 0 ≤ x ≤ 3, y ≥ 0, y(0)=0. Then at x=2, y^()+y+1 is equal toDifferential Equations
Q3683If log e y=3 sin ⁻¹ x, then (1-x²) y^()-x y^() at x=1/2 is equal toLimit, Continuity and Differentiability
Q3896Let the range of the function f(x)=1/(2+ sin 3 x+ cos 3 x), x R be [a, b]. If α and β ar respectively the A.M. and the G.M. of a and b, then (α)/(β) is equal toSets, Relations and Functions
Q3981Let the foci of a hyperbola H coincide with the foci of the ellipse E: ((x-1)²)/100+((y-1)²)/75=1 and the eccentricity of the hyperbola H be the reciprocal of…Coordinate Geometry
Q4259lim x → 0 (e-(1+2 x)^(1/(2 x)))/x is equal toLimit, Continuity and Differentiability
Q4487Let B=[ ll1 3 1 5 ] and A be a 2 × 2 matrix such that A B⁻¹=A⁻¹. If B C B⁻¹=A and C⁴+α C²+β I=O, then 2 β-α is equal toMatrices and Determinants
Q4932If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i^(th) roll than the number obtained in the (i-1)^(th) roll…Statistics and Probability
Q5032Two vertices of a triangle ABC are A(3,-1) and B(-2,3), and its orthocentre is P(1,1). If the coordinates of the point C are (α, β) and the centre of the of…Properties of Triangle
Q5168Let α, β; α>β, be the roots of the equation x²-√(2) x-√(3)=0. Let P n =αⁿ-βⁿ, n N. Then (11 √(3)-10 √(2)) P₁₀+(11 √(2)+10) P₁₁-11 P₁₂ is equal toComplex Numbers and Quadratic Equations
Q5274Let a, a r, a r²,............ be an infinite G.P. If Σ n=0 ^(∞) a rⁿ=57 and Σ n=0 ^(∞) a³ r³ⁿ=9747, then a+18 r is equal toSequence and Series
Q5494If the variance of the frequency distribution x c 2c 3c 4c 5c 6c f 2 1 1 1 1 1 is 160, then the value of c N isStatistics and Probability
Q5852Between the following two statements: Statement I: Let a=i+2 j-3 k and b=2 i+j-k. Then the vector r satisfying a × r=a × b and a · r=0 is of magnitude √(10)…Vector Algebra
Q5853Let a=2 i+α j+k, b=-i+k, c=β j-k, where α and β are integers and α β=-6. Let the values of the ordered pair (α, β), for which the area of the parallelogram of…Vector Algebra