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JEE Main 2024 4 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20244 Apr, Evening shift

Physics 23Chemistry 24Mathematics 30

Physics

Q56The disintegration energy Q for the nuclear fission of ²³⁵ U → ¹⁴⁰ Ce+ ⁹⁴ Zr+n is _ _ _ M eV. Given atomic masses of ²³⁵ U: 235.0439 u; ¹⁴⁰ Ce: 139.9054 u, ⁹⁴…Atoms and Nuclei
Q57A parallel plate capacitor of capacitance 12.5 ~pF is charged by a battery connected between its plates to potential difference of 12.0 ~V. The battery is now…Electrostatics
Q58In a system two particles of masses m₁=3 ~kg and m₂=2 ~kg are placed at certain distance from each other. The particle of mass m₁ is moved towards the center…Rotational Motion
Q60Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 ~mm and wire B has radius of 4.0 ~mm. The resistance of…Current Electricity
Q64A light ray is incident on a glass slab of thickness 4 √(3) ~cm and refractive index √(2) The angle of incidence is equal to the critical angle for the glass…Optics
Q71A rod of length 60 ~cm rotates with a uniform angular velocity 20 ~rad s⁻¹ about its perpendicular bisector, in a uniform magnetic filed 0.5 T. The direction…Magnetic Effects of Current and Magnetism
Q72A bus moving along a straight highway with speed of 72 ~km / h is brought to halt within 4 s after applying the brakes. The distance travelled by the bus…Kinematics
Q73Mercury is filled in a tube of radius 2 ~cm up to a height of 30 ~cm. The force exerted by mercury on the bottom of the tube is _ _ _ _ N. (Given, atmospheric…Properties of Solids and Liquids
Q75The displacement of a particle executing SHM is given by x=10 sin (w t+(π)/3) m. The time period of motion is 3.14 ~s. The velocity of the particle at t=0 is…Oscillations and Waves
Q6029According to Bohr's theory, the moment of momentum of an electron revolving in 4^(th) orbit of hydrogen atom is:Atoms and Nuclei
Q6443An electric bulb rated 50 ~W-200 ~V is connected across a 100 ~V supply. The power dissipation of the bulb is:Current Electricity
Q6669Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Number of photons increases with increase…Dual Nature of Matter and Radiation
Q6846Arrange the following in the ascending order of wavelength: A. Gamma rays (λ₁) B. x - rays (λ₂) C. Infrared waves (λ₃) D. Microwaves (λ₄) Choose the most…Electromagnetic Waves
Q6988A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is:Electrostatics
Q7172A 90 ~kg body placed at 2 R distance from surface of earth experiences gravitational pull of: (R= Radius of earth, g=10 ~m ~s⁻²)Gravitation
Q7223Correct formula for height of a satellite from earths surface is:Gravitation
Q7326The translational degrees of freedom (f t) and rotational degrees of freedom (f r) of CH₄ molecule are:Kinetic Theory of Gases
Q7505A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ=3 / 2. The work done by the gas in the…Thermodynamics
Q7571A 2 ~kg brick begins to slide over a surface which is inclined at an angle of 45^(°) with respect to horizontal axis. The co-efficient of static friction…Laws of Motion
Q7617The magnetic moment of a bar magnet is 0.5 ~Am². It is suspended in a uniform magnetic field of 8 × 10⁻² ~T. The work done in rotating it from its most stable…Magnetic Effects of Current and Magnetism
Q8035Given below are two statements: Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well…Properties of Solids and Liquids
Q8283Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is…Units and Measurements
Q8454The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in…Optics

Chemistry

Q2Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and π electrons is _ _ _ _ _.Organic Compounds Containing Oxygen
Q3The total number of 'sigma' and 'pi' bonds in 2-oxohex-4-ynoic acid is _ _ _.Some Basic Principles of Organic Chemistry
Q5Number of compounds / species from the following with non-zero dipole moment is _ _ _ _ _. BeCl₂, BCl₃, NF₃, XeF₄, CCl₄, H₂ O, H₂ ~S, HBr, CO₂, H₂, HClChemical Bonding and Molecular Structure
Q9Consider the following reaction, the rate expression of which is given below A+B → C rate =k[A]^(1 / 2)[~B]^(1 / 2) The reaction is initiated by taking 1 ~M…Chemical Kinetics
Q13A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of formula M₂ O n (where…d- and f-Block Elements
Q192.7 ~kg of each of water and acetic acid are mixed. The freezing point of the solution will be -x^(°) C. Consider the acetic acid does not dimerise in water…Solutions
Q20From 6.55 ~g of aniline, the maximum amount of acetanilide that can be prepared will be _ _ _ _ × 10⁻¹ ~g.Some Basic Concepts in Chemistry
Q21The maximum number of orbitals which can be identified with n=4 and m l =0 is _ _ _ _ _.Atomic Structure
Q24Three moles of an ideal gas are compressed isothermally from 60 ~L to 20 ~L using constant pressure of 5 ~atm. Heat exchange Q for the compression is - _ _ _…Chemical Thermodynamics
Q39Common name of Benzene - 1,2 - diol is -Organic Compounds Containing Oxygen
Q187Match List I with List II LIST I LIST II A. α - Glucose and α - Galactose I. Functional isomers B. α - Glucose and β - Glucose II. Homologous C. α - Glucose…Biomolecules
Q325The number of species from the following that have pyramidal geometry around the central atom is _ _ _ _ S ₂ O₃²⁻, SO₄²⁻, SO₃²⁻, S₂ O₇²⁻Chemical Bonding and Molecular Structure
Q338The correct statement/s about Hydrogen bonding is/are A. Hydrogen bonding exists when H is covalently bonded to the highly electro negative atom. B…Chemical Bonding and Molecular Structure
Q425The equilibrium constant for the reaction SO₃(~g) SO₂(~g)+1/2 O₂(~g) is K c =4.9 × 10⁻². The value of K c for the reaction given below is 2 SO₂(~g)+O₂(~g) 2…Equilibrium
Q657If an iron (III) complex with the formula [Fe(NH₃) x (CN) y ]^(- h)as no electron in its e g orbital, then the value of x+y isCoordination Compounds
Q658The number of unpaired d-electrons in [Co(H₂ O)₆]³⁺ is _ _ _ _.Coordination Compounds
Q659A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 ~BM. The atomic number of the metal isCoordination Compounds
Q921Fuel cell, using hydrogen and oxygen as fuels, A. has been used in spaceship B. has as efficiency of 40% to produce electricity C. uses aluminum as catalysts…Redox Reactions and Electrochemistry
Q954For a strong electrolyte, a plot of molar conductivity against (concentration) ^(1 / 2) is a straight line, with a negative slope, the correct unit for the…Redox Reactions and Electrochemistry
Q1625The correct order of the first ionization enthalpy isClassification of Elements and Periodicity in Properties
Q1626Given below are two statements: Statement I: The correct order of first ionization enthalpy values of Li, Na, F and Cl is Na<Li<Cl<F. Statement II: The…Classification of Elements and Periodicity in Properties
Q1801When MnO₂ and H₂ SO₄ is added to a salt (A), the greenish yellow gas liberated as salt (A) is:Redox Reactions and Electrochemistry
Q2219Choose the Incorrect Statement about Dalton's Atomic TheoryAtomic Structure
Q2222The adsorbent used in adsorption chromatography is/are - A. silica gel B. alumina C. quick lime D. magnesia Choose the most appropriate answer from the…Surface Chemistry

Mathematics

Q26Consider a line L passing through the points P(1,2,1) and Q(2,1,-1). If the mirror image of the point A(2,2,2) in the line L is (α, β, γ), then α+β+6 γ is…Three Dimensional Geometry
Q35Let y=y(x) be the solution of the differential equation (x+y+2)² d x=d y, y(0)=-2. Let the maximum and minimum values of the function y=y(x) in [0, (π)/3] be…Differential Equations
Q36Let f: R → R be a thrice differentiable function such that f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=-2. Then, the minimum number of zeros of (3 f^() f^()+f…Limit, Continuity and Differentiability
Q37Consider the function f: R → R defined by f(x)=(2 x)/(√(1+9 x²)). If the composition of f, (f° f° f°° f) 10 times (x)=(2¹⁰ x)/(√(1+9 α x²)), then the value of…Sets, Relations and Functions
Q39If ∫ cosec⁵ x d x=α cot x cosec x(cosec² x+3/2)+β log x | tan x/2|+C where α, β R and C is the constant of integration, then the value of 8(α+β) equals _ _ _…Integral Calculus
Q43Let A be a 2 × 2 symmetric matrix such that A[ l1 1 ]=[ l3 7 ] and the determinant of A be 1. If A⁻¹=α A+β I, where I is an identity matrix of order 2 × 2…Matrices and Determinants
Q45There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4…Permutations and Combinations
Q46In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 1/3 and 2/3 respectively. Let x be the number of matches that…Statistics and Probability
Q48Consider a triangle ABC having the vertices A(1,2), B(α, β) and C(γ, δ) and angles A B C=(π)/6 and B A C=(2 π)/3. If the points B and C lie on the line y=x+4…Properties of Triangle
Q52Let S= sin ² 2 θ:(sin ⁴ θ+ cos ⁴ θ) x²+(sin 2 θ) x+(sin ⁶ θ+ cos ⁶ θ)=0. has real roots. If α and β be the smallest and largest elements of the set S…Trigonometry
Q2536Let P be the point of intersection of the lines (x-2)/1=(y-4)/5=(z-2)/1 and (x-3)/2=(y-2)/3=(z-3)/2. Then, the shortest distance of P from the line 4 x=2 y=z isThree Dimensional Geometry
Q2686Let f(x)=3 √(x-2)+√(4-x) be a real valued function. If α and β are respectively the minimum and the maximum values of f, then α²+2 β² is equal toLimit, Continuity and Differentiability
Q2872The area (in sq. units) of the region described by \(x, y): y² ≤ 2 x, and y ≥ 4 x-1\ isIntegral Calculus
Q3016If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1+x)ⁿ are in the arithmetic progression, then the maximum value of n is:Binomial Theorem and Its Simple Applications
Q3058Let C be a circle with radius √(10) units and centre at the origin. Let the line x+y=2 intersects the circle C at the points P and Q. Let MN be a chord of C…Coordinate Geometry
Q3203The area (in sq. units) of the region S= C:|z-1| ≤ 2;(z+z)+i(z-z) ≤ 2, lm(z) ≥ 0 isComplex Numbers and Quadratic Equations
Q3323Let f(x)=∫₀ˣ(t+ sin (1-e^(t))) d t, x R. Then, lim x → 0 (f(x))/(x³) is equal toIntegral Calculus
Q3482If the value of the integral ∫₋₁¹ (cos α x)/(1+3ˣ) d x is 2/(π).Then, a value of α isIntegral Calculus
Q3648Let y=y(x) be the solution of the differential equation (x²+4)² d y+(2 x³ y+8 x y-2) d x=0. If y(0)=0, then y(2) is equal toDifferential Equations
Q3993Consider a hyperbola H having centre at the origin and foci on the x -axis. Let C₁ be the circle touching the hyperbola H and having the centre at the origin…Coordinate Geometry
Q4082Given that the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [-1,1] such that cos ⁻¹ x- sin ⁻¹ y=α, (-π)/2…Trigonometry
Q4164If the function f(x)= (72ˣ-9ˣ-8ˣ+1)/(√(2)-√(1+ cos x)), x ≠ 0 a log e 2 log e 3, x=0 is continuous at x=0, then the value of a² is equal toLimit, Continuity and Differentiability
Q4429Let A=[ ll1 2 0 1 ] and B=I+adj(A)+(adj A)²+ +(adj A)¹⁰. Then, the sum of all the elements of the matrix B is:Matrices and Determinants
Q4676Let P Q be a chord of the parabola y²=12 x and the midpoint of P Q be at (4,1). Then, which of the following point lies on the line passing through the points…Coordinate Geometry
Q5008If the mean of the following probability distribution of a radam variable X: X 0 2 4 6 8 P(X) a 2a a+b 2b 3b is 46/9, then the variance of the distribution isStatistics and Probability
Q5188Let three real numbers a, b, c be in arithmetic progression and a+1, b, c+3 be in geometric progression. If a>10 and the arithmetic mean of a, b and c is 8…Sequence and Series
Q5349The value of (1 × 2²+2 × 3²+ +100 ×(101)²)/(1² × 2+2² × 3+.+100² × 101) isSequence and Series
Q5395Let a relation R on N × N be defined as: (x₁, y₁) R(x₂, y₂) if and only if x₁ ≤ x₂ or y₁ ≤ y₂. Consider the two statements: (I) R is reflexive but not…Sets, Relations and Functions
Q5756Let a=i+j+k, b=2 i+4 j-5 k and c=x i+2 j+3 k, x R. If d is the unit vector in the direction of b+c such that a · d=1, then (a × b) · c is equal toVector Algebra
Q5787For λ>0, let θ be the angle between the vectors a=i+λ j-3 k and b=3 i-j+2 k. If the vectors a+b and a-b are mutually perpendicular, then the value of (14 cos…Vector Algebra