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JEE Main 2024 5 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20245 Apr, Evening shift

Physics 26Chemistry 21Mathematics 30

Physics

Q55The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915 A^(o). The longest wavelength of spectral lines in the Balmer…Atoms and Nuclei
Q57A wire of resistance 20 Ω is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs…Current Electricity
Q60The current in an inductor is given by I=(3 t+8) where t is in second. The magnitude of induced emf produced in the inductor is 12 ~mV. The self-inductance of…Electromagnetic Induction and Alternating Currents
Q68A solenoid of length 0.5 ~m has a radius of 1 ~cm and is made up of ' m ' number of turns. It carries a current of 5 ~A. If the magnitude of the magnetic…Magnetic Effects of Current and Magnetism
Q70The maximum height reached by a projectile is 64 ~m. If the initial velocity is halved, the new maximum height of the projectile is _ _ _ m.Kinematics
Q72A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x/5. The value…Rotational Motion
Q76In a single slit experiment, a parallel beam of green light of wavelength 550 ~nm passes through a slit of width 0.20 ~mm. The transmitted light is collected…Optics
Q77A sonometer wire of resonating length 90 ~cm has a fundamental frequency of 400 ~Hz when kept under some tension. The resonating length of the wire with…Oscillations and Waves
Q5933A series LCR circuit is subjected to an ac signal of 200 ~V, 50 ~Hz. If the voltage across the inductor (L=10 ~mH) is 31.4 ~V, then the current in this…Electromagnetic Induction and Alternating Currents
Q6031The angular momentum of an electron in a hydrogen atom is proportional to: (Where r is the radius of orbit of electron)Atoms and Nuclei
Q6298A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 ~m and completes 120 resolutions in 3 minutes. The magnitude of…Kinematics
Q6484A galvanometer of resistance 100 Ω when connected in series with 400 Ω measures a voltage of upto 10 ~V. The value of resistance required to convert the…Current Electricity
Q6670Which of the following statement is not true about stopping potential (V₀) ?Dual Nature of Matter and Radiation
Q6847Match List I with List II: LIST I EM-Wave LIST II Wavelength Range A. Infra-red I. <10⁻³ nm B. Ultraviolet II. 400 nm to 1 nm C. X-rays III. 1 mm to 700 nm D…Electromagnetic Waves
Q6937The vehicles carrying inflammable fluids usually have metallic chains touching the ground:Electrostatics
Q7224A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of…Gravitation
Q7438If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean…Kinetic Theory of Gases
Q7507During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of (C P)/(C V) for…Thermodynamics
Q7564A heavy box of mass 50 ~kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of…Laws of Motion
Q7604A particle moves in x - y plane under the influence of a force F such that its linear momentum is p(t)=i cos (kt)-j sin (kt). If k is constant, the angle…Laws of Motion
Q7768The electrostatic force (F₁) and magnetic force (F₂) acting on a charge q moving with velocity v can be written:Magnetic Effects of Current and Magnetism
Q7969Match List I with List II: LIST I LIST II A. A force that restores an elastic body of unit area to its original state I. Bulk modulus B. Two equal and…Properties of Solids and Liquids
Q8285What is the dimensional formula of a b⁻¹ in the equation (P+a/(V²))(V-b)=RT, where letters have their usual meaning.Units and Measurements
Q8367A vernier callipers has 20 divisions on the vernier scale, which coincides with 19^(th) division on the main scale. The least count of the instrument is 0.1…Experimental Skills
Q8407Given below are two statements: Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II: The…Optics
Q8612A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to:Work, Energy and Power

Chemistry

Q1In the Claisen-Schmidt reaction to prepare 351 ~g of dibenzalacetone using 87 ~g of acetone, the amount of benzaldehyde required is _ _ _ _ g. (Nearest integer)Organic Compounds Containing Oxygen
Q5Number of compounds from the following with zero dipole moment is _ _ _ _ _. HF, H₂, H₂ ~S, CO₂, NH₃, BF₃, CH₄, CHCl₃, SiF₄, H₂ O, BeF₂Chemical Bonding and Molecular Structure
Q8Consider the following single step reaction in gas phase at constant temperature. 2 ~A (g) +B (g) → C (g) The initial rate of the reaction is recorded as r₁…Chemical Kinetics
Q9X ~g of ethanamine was subjected to reaction with NaNO₂ / HCl followed by hydrolysis to liberate N₂ and HCl. The HCl generated was completely neutralised by…Organic Compounds Containing Nitrogen
Q13The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products A and B along with the evolution of CO₂. The sum of…d- and f-Block Elements
Q19Considering acetic acid dissociates in water, its dissociation constant is 6.25 × 10⁻⁵. If 5 ~mL of acetic acid is dissolved in 1 litre water, the solution…Solutions
Q21In an atom, total number of electrons having quantum numbers n=4,|~m l |=1 and m s =-1/2 is _ _ _ _ _.Atomic Structure
Q22Combustion of 1 mole of benzene is expressed at C₆ H₆(l)+15/2 O₂(~g) → 6 CO₂(~g)+3 H₂ O(l). The standard enthalpy of combustion of 2 ~mol of benzene is -^()…Chemical Thermodynamics
Q221Coagulation of egg, on heating is because of:Biomolecules
Q273Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): NH₃ and NF₃ molecule have pyramidal…Chemical Bonding and Molecular Structure
Q328Match List I with List II. LIST I LIST II A. ICl I. T - shape B. ICl₃ II. Square pyramidal C. ClF₅ III. Pentagonal bipyramidal D. IF₇ IV. Linear Choose the…Chemical Bonding and Molecular Structure
Q427Given below are two statements: Statement I: On passing HCl (g) through a saturated solution of BaCl₂, at room temperature white turbidity appears. Statement…Equilibrium
Q663The number of complexes from the following with no electrons in the t₂ orbital is _ _ _. TiCl₄,[MnO₄]⁻,[FeO₄]²⁻,[FeCl₄]⁻,[CoCl₄]²⁻Coordination Compounds
Q696The metal atom present in the complex MABXL (where A, B, X and L are unidentate ligands and M is metal) involves sp³ hybridization. The number of geometrical…Coordination Compounds
Q796While preparing crystals of Mohr's salt, dil H₂ SO₄ is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water…d- and f-Block Elements
Q909The number of ions from the following that have the ability to liberate hydrogen from a dilute acid is _ _ _ _ _. Ti²⁺, Cr²⁺ and V²⁺d- and f-Block Elements
Q957The quantity of silver deposited when one coulomb charge is passed through AgNO₃ solution:Redox Reactions and Electrochemistry
Q1011For the electro chemical cell M|M²⁺||X| X²⁻ If E (M²⁺ / M) ⁰=0.46 ~V and E (x / x²⁻) ⁰=0.34 ~V. Which of the following is correct?Redox Reactions and Electrochemistry
Q1464The correct statements from the following are: (A) The decreasing order of atomic radii of group 13 elements is Tl>In>Ga>Al>B. (B) Down the group 13…p-Block Elements
Q1566Given below are two statements: Statement I: The metallic radius of Na is 1.86 ~A^(°) and the ionic radius of Na⁺ is lesser than 1.86 ~A^(°) Statement II…Classification of Elements and Periodicity in Properties
Q2085The number of moles of methane required to produce 11 ~g ~CO₂(g) after complete combustion is: (Given molar mass of methane in g ~mol⁻¹: 16)Some Basic Concepts in Chemistry

Mathematics

Q24Let the point (-1, α, β) lie on the line of the shortest distance between the lines (x+2)/(-3)=(y-2)/4=(z-5)/2 and (x+2)/(-1)=(y+6)/2=(z-1)/0. Then (α-β)² is…Three Dimensional Geometry
Q25Let the maximum and minimum values of (√(8 x-x²-12)-4)²+(x-7)², x R be M and m, respectively. Then M²-m² is equal to _ _ _ _ _.Limit, Continuity and Differentiability
Q32If f(t)=∫₀^π (2 x ~d x)/(1- cos ² t sin ² x), 0<t<π, then the value of ∫₀^((π)/2) (π² dt)/(f(t)) equals _ _ _ _ _.Integral Calculus
Q34Let y=y(x) be the solution of the differential equation (d y)/(~d x)+(2 x)/((1+x²)²) y=x e^(1/((1+x²))); y(0)=0. Then the area enclosed by the curve f(x)=y(x)…Differential Equations
Q38Let a>0 be a root of the equation 2 x²+x-2=0. If lim x → 1/a (16(1- cos (2+x-2 x²)))/((1-a x)²)=α+β √(17), where α, β Z, then α+β is equal to _ _ _ _ _.Limit, Continuity and Differentiability
Q41Let a line perpendicular to the line 2 x-y=10 touch the parabola y²=4(x-9) at the point P. The distance of the point P from the centre of the circle x²+y²-14…Coordinate Geometry
Q45The number of real solutions of the equation x|x+5|+2|x+7|-2=0 is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q47If 1+(√(3)-√(2))/(2 √(3))+(5-2 √(6))/18+(9 √(3)-11 √(2))/(36 √(3))+(49-20 √(6))/180+ upto ∞=2+(√(b/a)+1) log e (a/b), where a and b are integers with gcd(a…Sequence and Series
Q48Let the mean and the standard deviation of the probability distribution X | α | 1 | 0 | - 3 P(X) | 1/3 | K | 1/6 | 1/4 be μ and σ, respectively. If σ-μ=2…Statistics and Probability
Q50The number of solutions of sin ² x+(2+2 x-x²) sin x-3(x-1)²=0, where -π ≤ x ≤ π, is _ _ _ _.Trigonometry
Q2540Let (α, β, γ) be the image of the point (8,5,7) in the line (x-1)/2=(y+1)/3=(z-2)/5. Then α+β+γ is equal to:Three Dimensional Geometry
Q2874The area enclosed between the curves y=x|x| and y=x-|x| is:Integral Calculus
Q2949If the constant term in the expansion of ((5√(3))/x+(2 x)/(3√(5)))¹², x ≠ 0, is α × 2⁸ × 5√(3), then 25 α is equal to:Binomial Theorem and Its Simple Applications
Q3031Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius…Coordinate Geometry
Q3117Let the circle C₁: x²+y²-2(x+y)+1=0 and C₂ be a circle having centre at (-1,0) and radius 2. If the line of the common chord of C₁ and C₂ intersects the y…Coordinate Geometry
Q3204Let S₁= C:|z| ≤ 5 S₂= C: Im((z+1-√(3) i)/(1-√(3) i)) ≥ 0 and S₃= C: Re(z) ≥ 0. Then the area of the region S₁ S₂ S₃ is:Complex Numbers and Quadratic Equations
Q3487Let β(m, n)=∫₀¹ x^(m-1)(1-x)ⁿ⁻¹ ~d x, ~m, n>0. If ∫₀¹(1-x¹⁰)²⁰ ~d x=a × β(b, c), then 100(a+b+c) equals _ _ _ _ _.Integral Calculus
Q3504The differential equation of the family of circles passing through the origin and having centre at the line y=x is:Differential Equations
Q3713If y(θ)=(2 cos θ+ cos 2 θ)/(cos 3 θ+4 cos 2 θ+5 cos θ+2), then at θ=(π)/2, y^()+y^()+y is equal to:Limit, Continuity and Differentiability
Q3836Let f, g: R → R be defined as: f(x)=|x-1| and g(x)= eˣ, x ≥ 0 x+1, x ≤ 0. Then the function f(g(x)) isSets, Relations and Functions
Q4167Let, f:[-1,2] → R be given by f(x)=2 x²+x+[x²]-[x], where [t] denotes the greatest integer less than or equal to t. The number of points, where f is not…Limit, Continuity and Differentiability
Q4430Let α β ≠ 0 and A=[ rrrβ α 3 α α β -β α 2 α ]. If B=[ rrr3 α -9 3 α -α 7 -2 α -2 α 5 -2 β ] is the matrix of cofactors of the elements of A, then det(A B) is…Matrices and Determinants
Q4641The values of m, n, for which the system of equations x+y+z=4, 2 x+5 y+5 z=17, x+2 y+m z=n has infinitely many solutions, satisfy the equation:Matrices and Determinants
Q4837Let the set S=\2,4,8,16,, 512 be partitioned into 3 sets A, B, C with equal number of elements such that A B C=S and A B=B C=A C=φ. The maximum number of such…Permutations and Combinations
Q485560 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50^(th) word is:Permutations and Combinations
Q4993The coefficients a, b, c in the quadratic equation a x²+bx+c=0 are from the set \1,2,3,4,5,6. If the probability of this equation having one real root bigger…Statistics and Probability
Q5238For x 0, the least value of K, for which 4¹⁺ˣ+4¹⁻ˣ, K/2, 16ˣ+16⁻ˣ are three consecutive terms of an A.P., is equal to:Sequence and Series
Q5572Let A(-1,1) and B(2,3) be two points and P be a variable point above the line AB such that the area of PAB is 10. If the locus of P is a x+by=15, then 5 a+2…Coordinate Geometry
Q5858Let a=2 i+5 j-k, b=2 i-2 j+2 k and c be three vectors such that (c+i) ×(a+b+i)=a ×(c+i). If a · c=-29, then c ·(-2 i+j+k) is equal to:Vector Algebra
Q5859Consider three vectors a, b, c. Let |a|=2,|b|=3 and a=b × c. If α [0, (π)/3] is the angle between the vectors b and c, then the minimum value of 27|c-a|² is…Vector Algebra