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

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JEE Main 20245 Apr, Morning shift

Physics 19Chemistry 23Mathematics 30

Physics

Q56If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _ _ _ _ × 10⁻² ~MeV. (Given 1 u=931 ~MeV / c², atomic…Atoms and Nuclei
Q57Three capacitors of capacitances 25 μ F, 30 μ F and 45 μ F are connected in parallel to a supply of 100 ~V. Energy stored in the above combination is E. When…Electrostatics
Q58The electric field between the two parallel plates of a capacitor of 1.5 μ F capacitance drops to one third of its initial value in 6.6 μ s when the plates…Electrostatics
Q65A 2A current carrying straight metal wire of resistance 1 Ω, resistivity 2 × 10⁻⁶ Ω m, area of cross-section 10 ~mm² and mass 500 ~g is suspended horizontally…Magnetic Effects of Current and Magnetism
Q66A body moves on a frictionless plane starting from rest. If S n is distance moved between t=n-1 and t=n and S n-1 is distance moved between t=n-2 and t=n-1…Kinematics
Q67The density and breaking stress of a wire are 6 × 10⁴ ~kg / m³ and 1.2 × 10⁸ ~N / m² respectively. The wire is suspended from a rigid support on a planet…Properties of Solids and Liquids
Q73In Young's double slit experiment, carried out with light of wavelength 5000~ A^(o), the distance between the slits is 0.3 ~mm and the screen is at 200 ~cm…Optics
Q5932An alternating voltage of amplitude 40 ~V and frequency 4 ~kHz is applied directly across the capacitor of 12 μ F. The maximum displacement current between…Electromagnetic Induction and Alternating Currents
Q6030An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U)…Atoms and Nuclei
Q6936In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:Electrostatics
Q7241If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the √(uG):Gravitation
Q7242Match List I with List II: LIST I LIST II A. Kinetic energy of planet I. -GMm / a B. Gravitation Potential energy of sun-planet system II. GMm / 2 a C. Total…Gravitation
Q7437If the collision frequency of hydrogen molecules in a closed chamber at 27^(°) C is Z, then the collision frequency of the same system at 127^(°) C is:Thermodynamics
Q7603A wooden block of mass 5 ~kg rests on a soft horizontal floor. When an iron cylinder of mass 25 ~kg is placed on the top of the block, the floor yields and…Laws of Motion
Q7663In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:Magnetic Effects of Current and Magnetism
Q8036Given below are two statements: Statement I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact…Properties of Solids and Liquids
Q8177A simple pendulum doing small oscillations at a place R height above earth surface has time period of T₁=4 ~s. T₂ would be it's time period if it is brought…Oscillations and Waves
Q8322Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 ~s, 4.632 ~s, 4.6 ~s and 4.64 ~s…Units and Measurements
Q8385The angle between vector Q and the resultant of (2 Q+2 P) and (2 Q-2 P) is:Kinematics

Chemistry

Q5In the lewis dot structure for NO₂⁻, total number of valence electrons around nitrogen is _ _ _ _ _.Chemical Bonding and Molecular Structure
Q7During Kinetic study of reaction 2 A+B → C+D, the following results were obtained: | A [M] | B [M] | initial rate of formation of D I | 0.1 | 0.1 | 6.0×10⁻³…Chemical Kinetics
Q89.3 ~g of pure aniline is treated with bromine water at room temperature to give a white precipitate of the product ' P '. The mass of product ' P ' obtained…Organic Compounds Containing Nitrogen
Q11The spin-only magnetic moment value of the ion among Ti²⁺, V²⁺, Co³⁺ and Cr²⁺, that acts as strong oxidising agent in aqueous solution is _ _ _ _ B M (Near…Coordination Compounds
Q18An artificial cell is made by encapsulating 0.2 ~M glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell…Solutions
Q20The value of Rydberg constant (R H) is 2.18 × 10⁻¹⁸ ~J. The velocity of electron having mass 9.1 × 10⁻³¹ ~kg in Bohr's first orbit of hydrogen atom = _ _ _ _…Atomic Structure
Q22The heat of combustion of solid benzoic acid at constant volume is -321.30 ~kJ at 27^(°) C. The heat of combustion at constant pressure is (-321.30-x R) ~kJ…Chemical Thermodynamics
Q41Given below are two statement: Statements I: Bromination of phenol in solvent with low polarity such as CHCl₃ or CS₂ requires Lewis acid catalyst. Statements…Organic Compounds Containing Oxygen
Q107Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Cis form of alkene is found to be…Some Basic Principles of Organic Chemistry
Q220Which of the following gives a positive test with ninhydrin ?Biomolecules
Q265Number of σ and π bonds present in ethylene molecule is respectively:Chemical Bonding and Molecular Structure
Q438The following reaction occurs in the Blast furnance where iron ore is reduced to iron metal Fe₂ O 3(s) +3 CO (g) Fe (j) +3 CO 2(g) Using the Le-chatelier's…Equilibrium
Q661The correct order of ligands arranged in increasing field strength.Coordination Compounds
Q662Which one of the following complexes will exhibit the least paramagnetic behaviour ? [Atomic number, Cr=24, Mn=25, Fe=26, Co=27 ]Coordination Compounds
Q908The metal that shows highest and maximum number of oxidation state is:d- and f-Block Elements
Q922The reaction at cathode in the cells commonly used in clocks involves.Redox Reactions and Electrochemistry
Q956Molar ionic conductivities of divalent cation and anion are 57 ~S~cm² ~mol⁻¹ and 73 ~S~cm² ~mol⁻¹ respectively. The molar conductivity of solution of an…Redox Reactions and Electrochemistry
Q1463The number of neutrons present in the more abundant isotope of boron is ' x '. Amorphous boron upon heating with air forms a product, in which the oxidation…p-Block Elements
Q1565The statement(s) that are correct about the species O²⁻, F⁻, Na⁺ and Mg²⁺. (A) All are isoelectronic (B) All have the same nuclear charge (C) O²⁻ has the…Classification of Elements and Periodicity in Properties
Q1669Given below are two statements: Statement I: In group 13, the stability of +1 oxidation state increases down the group. Statement II: The atomic size of…Classification of Elements and Periodicity in Properties
Q2084An organic compound has 42.1% carbon, 6.4% hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is:Some Basic Concepts in Chemistry
Q2220The incorrect postulates of the Dalton's atomic theory are: (A) Atoms of different elements differ in mass. (B) Matter consists of divisible atoms. (C)…Atomic Structure
Q2362Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A): Enthalpy of neutralisation of strong…Chemical Thermodynamics

Mathematics

Q29The area of the region enclosed by the parabolas y=x²-5 x and y=7 x-x² is _ _ _ _.Integral Calculus
Q30If the constant term in the expansion of (1+2 x-3 x³)(3/2 x²-1/(3 x))⁹ is p, then 108 p is equal to _ _ _ _.Binomial Theorem and Its Simple Applications
Q38If S= R:|2 a-1|=3[a]+2, where [t] denotes the greatest integer less than or equal to t and represents the fractional part of t, then 72 Σ a S a is equal to _…Sets, Relations and Functions
Q40Let f be a differentiable function in the interval (0, ∞) such that f(1)=1 and lim t → x (t² f(x)-x² f(t))/(t-x)=1 for each x>0. Then 2 f(2)+3 f(3) is equal…Limit, Continuity and Differentiability
Q43Suppose AB is a focal chord of the parabola y²=12 x of length l and slope m<√(3). If the distance of the chord AB from the origin is d, then l ~d² is equal to…Coordinate Geometry
Q44The number of ways of getting a sum 16 on throwing a dice four times is _ _ _ _.Permutations and Combinations
Q46From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective…Statistics and Probability
Q47The number of distinct real roots of the equation |x||x+2|-5|x+1|-1=0 is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q48Let a₁, a₂, a₃, be in an arithmetic progression of positive terms. Let A k =a₁²-a₂²+a₃²-a₄²+ +a 2 k-1 ²-a 2 k ². If A₃=-153, ~A₅=-435 and a₁²+a₂²+a₃²=66, then…Sequence and Series
Q53Let a=i-3 j+7 k, b=2 i-j+k and c be a vector such that (a+2 b) × c=3(c × a). If a · c=130, then b · c is equal to _ _ _ _ _.Vector Algebra
Q2385If the line (2-x)/3=(3 y-2)/(4 λ+1)=4-z makes a right angle with the line (x+3)/(3 μ)=(1-2 y)/6=(5-z)/7, then 4 λ+9 μ is equal to:Three Dimensional Geometry
Q2539Let d be the distance of the point of intersection of the lines (x+6)/3=y/2=(z+1)/1 and (x-7)/4=(y-9)/3=(z-4)/2 from the point (7,8,9). Then d²+6 is equal to:Three Dimensional Geometry
Q2690Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle…Limit, Continuity and Differentiability
Q2736For the function f(x)= sin x+3 x-2/(π)(x²+x), where x [0, (π)/2], consider the following two statements: (I) f is increasing in (0, (π)/2). (II) f^() is…Limit, Continuity and Differentiability
Q2750Let f(x)=x⁵+2 x³+3 x+1, x R, and g(x) be a function such that g(f(x))=x for all x R. Then (g(7))/(g^()(7)) is equal to:Limit, Continuity and Differentiability
Q3143Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2) and parallel to the coordinate axes touch it. Then…Coordinate Geometry
Q3271Consider the following two statements: Statement I: For any two non-zero complex numbers z₁, z₂,(|z₁|+|z₂|)|z₁/(|z₁|)+z₂/(|z₂|)| ≤ 2(|z₁|+|z₂|), and Statement…Complex Numbers and Quadratic Equations
Q3485The integral ∫₀^(π / 4) (136 sin x)/(3 sin x+5 cos x) ~d x is equal to:Integral Calculus
Q3486The value of ∫ -π ^π (2 y(1+ sin y))/(1+ cos ² y) d y is:Integral Calculus
Q3569If y=y(x) is the solution of the differential equation (d y)/(~d x)+2 y= sin (2 x), y(0)=3/4, then y((π)/8) is equal to:Differential Equations
Q3739Let the line 2 x+3 y-k=0, k>0, intersect the x -axis and y -axis at the points A and B, respectively. If the equation of the circle having the line segment A…Coordinate Geometry
Q3811Let A=\1,3,7,9,11 and B=\2,4,5,7,8,10,12. Then the total number of one-one maps f: A → B, such that f(1)+f(3)=14, is:Sets, Relations and Functions
Q4166If the function f(x)=(sin 3 x+α sin x-β cos 3 x)/(x³), x R, is continuous at x=0, then f(0) is equal to:Limit, Continuity and Differentiability
Q4548Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2. Then |A^(T) A(adj(2 ~A))⁻¹(adj(4 ~B))(adj(AB))⁻¹ AA^(T)| is equal to:Matrices and Determinants
Q4640If the system of equations r 11 x+y+λ z=-5 2 x+3 y+5 z=3 8 x-19 y-39 z=μ has infinitely many solutions, then λ⁴-μ is equal to:Matrices and Determinants
Q4934The coefficients a, b, c in the quadratic equation a x²+b x+c=0 are chosen from the set \1,2,3,4,5,6,7,8. The probability of this equation having repeated…Statistics and Probability
Q5350If 1/(√(1)+√(2))+1/(√(2)+√(3))+ +1/(√(99)+√(100))=m and 1/(1 · 2)+1/(2 · 3)+ +1/(99 · 100)=n, then the point (m, n) lies on the lineSequence and Series
Q5507Let two straight lines drawn from the origin O intersect the line 3 x+4 y=12 at the points P and Q such that OPQ is an isosceles triangle and POQ=90^(°). If…Coordinate Geometry
Q5669Suppose θ [0, (π)/4] is a solution of 4 cos θ-3 sin θ=1. Then cos θ is equal to:Trigonometry
Q5857If A(1,-1,2), B(5,7,-6), C(3,4,-10) and D(-1,-4,-2) are the vertices of a quadrilateral ABCD, then its area is:Vector Algebra