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JEE Main 2024 6 Apr Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 20246 Apr, Evening shift

Physics 26Chemistry 21Mathematics 30

Physics

Q52For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 ~nF. If resistance of 200 Ω and 100 ~mH…Electromagnetic Induction and Alternating Currents
Q56In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 ~V. The wavelength of light emitted by hydrogen atom…Dual Nature of Matter and Radiation
Q68A coil having 100 turns, area of 5 × 10⁻³ ~m², carrying current of 1 ~mA is placed in uniform magnetic field of 0.20 ~T such a way that plane of coil is…Magnetic Effects of Current and Magnetism
Q69A particle moves in a straight line so that its displacement x at any time t is given by x²=1+t². Its acceleration at any time t is x⁻ⁿ where n= _ _ _ _ _.Kinematics
Q72Three balls of masses 2 ~kg, 4 ~kg and 6 ~kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 ~m. The moment of inertia…Rotational Motion
Q75Two coherent monochromatic light beams of intensities I and 4 ~I are superimposed. The difference between maximum and minimum possible intensities in the…Optics
Q76Two open organ pipes of lengths 60 ~cm and 90 ~cm resonate at 6^(th) and 5^(th) harmonics respectively. The difference of frequencies for the given modes is _…Oscillations and Waves
Q6032The longest wavelength associated with Paschen series is: (Given R H =1.097 × 10⁷ SI unit)Atoms and Nuclei
Q6299A car of 800 ~kg is taking turn on a banked road of radius 300 ~m and angle of banking 30^(°). If coefficient of static friction is 0.2 then the maximum speed…Kinematics
Q6445The number of electrons flowing per second in the filament of a 110 ~W bulb operating at 220 ~V is: (Given e=1.6 × 10⁻¹⁹ C)Current Electricity
Q6671When UV light of wavelength 300 ~nm is incident on the metal surface having work function 2.13 ~eV, electron emission takes place. The stopping potential is…Dual Nature of Matter and Radiation
Q6691In a coil, the current changes from -2 ~A to +2 ~A in 0.2 ~s and induces an emf of 0.1 ~V. The self inductance of the coil is:Electromagnetic Induction and Alternating Currents
Q6829In the given electromagnetic wave E y =600 sin (ω t-kx) Vm⁻¹, intensity of the associated light beam is (in W / m²: (Given ε₀=9 × 10⁻¹² C² ~N⁻¹ ~m⁻²)Electromagnetic Waves
Q6889The acceptor level of a p-type semiconductor is 6 ~eV. The maximum wavelength of light which can create a hole would be: Given hc=1242 ~eV ~nm.Electronic Devices
Q6938Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 ~N. A third identical uncharged conducting sphere R is…Electrostatics
Q7058For the thin convex lens, the radii of curvature are at 15 ~cm and 30 ~cm respectively. The focal length the lens is 20 ~cm. The refractive index of the…Optics
Q7173Assuming the earth to be a sphere of uniform mass density, a body weighed 300 ~N on the surface of earth. How much it would weigh at R/4 depth under surface…Gravitation
Q7328Energy of 10 non rigid diatomic molecules at temperature T is:Thermodynamics
Q7439A total of 48 ~J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2^(°) C. The work done by the gas is: Given…Thermodynamics
Q7467Given below are two statements: Statement (I): Dimensions of specific heat is [L² ~T⁻² ~K⁻¹]. Statement (II): Dimensions of gas constant is [M L² ~T⁻¹ ~K⁻¹]…Thermodynamics
Q7545A body of weight 200 ~N is suspended from a tree branch through a chain of mass 10 ~kg. The branch pulls the chain by a force equal to (if g=10 ~m / s²):Laws of Motion
Q7871A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t₁. If it is projected vertically downwards from the…Kinematics
Q8037Pressure inside a soap bubble is greater than the pressure outside by an amount: (given: R= Radius of bubble, S= Surface tension of bubble)Properties of Solids and Liquids
Q8368In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4^(th) division coincides exactly with a certain…Experimental Skills
Q8369In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division =49 ~MSD; 20…Experimental Skills
Q8596When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:Work, Energy and Power

Chemistry

Q3Total number of species from the following with central atom utilising sp² hybrid orbitals for bonding is _ _ _ _. NH₃, SO₂, SiO₂, BeCl₂, C₂ H₂, C₂ H₄, BCl₃…Chemical Bonding and Molecular Structure
Q5Consider the two different first order reactions given below A+B → C (Reaction 1) P → Q (Reaction 2) The ratio of the half life of Reaction 1: Reaction 2 is…Chemical Kinetics
Q6An amine (X) is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to it the solution remains clear. Molar mass of the amine…Organic Compounds Containing Nitrogen
Q11Among VO₂⁺, MnO₄⁻ and Cr₂ O₇²⁻, the spin-only magnetic moment value of the species with least oxidising ability is _ _ _ _ _ BM (Nearest integer). (Given…d- and f-Block Elements
Q19For hydrogen atom, energy of an electron in first excited state is -3.4 ~eV, K. E. of the same electron of hydrogen atom is x ~eV. Value of x is _ _ _ _ _ ×…Atomic Structure
Q21For the reaction at 298 ~K, 2 ~A+B → C, Δ H=400 ~kJ ~mol⁻¹ and Δ S=0.2 ~kJ ~mol⁻¹ ~K⁻¹. The reaction will become spontaneous above _ _ _ _ _ K.Chemical Thermodynamics
Q108The incorrect statement regarding the geometrical isomers of 2-butene is:Some Basic Principles of Organic Chemistry
Q222The incorrect statements regarding enzymes are: (A) Enzymes are biocatalysts. (B) Enzymes are non-specific and can catalyse different kinds of reactions. (C)…Biomolecules
Q428The ratio K P /K C for the reaction: CO (g) +1/2 O 2(~g) CO 2(~g) is:Equilibrium
Q664Match List I with List II. LIST I Tetrahedral Complex LIST II Electronic configuration A. TiCl₄ I. e², t₂⁰ B. [FeO₄]²⁻ II. e⁴, t₂³ C. [FeCl₄]⁻ III. e⁰, t₂⁰ D…Coordination Compounds
Q703The correct IUPAC name of [PtBr₂(PMe₃)₂] is:Coordination Compounds
Q751Given below are two statements: Statement I: PF₅ and BrF₅ both exhibit sp³ ~d hybridisation. Statement II: Both SF₆ and [Co(NH₃)₆]³⁺ exhibit sp³ ~d²…Coordination Compounds
Q910Arrange the following elements in the increasing order of number of unpaired electrons in it. (A) Sc (B) Cr (C) V (D) Ti (E) Mn Choose the correct answer from…d- and f-Block Elements
Q1012How can an electrochemical cell be converted into an electrolytic cell ?Redox Reactions and Electrochemistry
Q1479Evaluate the following statements related to group 14 elements for their correctness. (A) Covalent radius decreases down the group from C to Pb in a regular…p-Block Elements
Q1765The correct statement among the following, for a "chromatography" purification method is:Purification and Characterisation of Organic Compounds
Q1784During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in NH₄ OH solution when sodium…Principles Related to Practical Chemistry
Q1803The number of ions from the following that are expected to behave as oxidising agent is: Sn⁴⁺, Sn²⁺, Pb²⁺, Tl³⁺, Pb⁴⁺, Tl⁺Redox Reactions and Electrochemistry
Q1820Match List I with List II. LIST I Reaction LIST II Type of redox reaction A. N 2(~g) +O 2(~g) → 2 NO (g) I. Decomposition B. 2 ~Pb(NO₃) 2(~s) → 2 PbO (s) +4…Redox Reactions and Electrochemistry
Q2053Molality (m) of 3 M aqueous solution of NaCl is: (Given: Density of solution =1.25 ~g ~mL⁻¹, Molar mass in g ~mol⁻¹: Na-23, Cl-35.5)Some Basic Concepts in Chemistry
Q2170Match List I with List II. LIST I Alkali Metal LIST II Emission Wavelength in nm A. Li I. 589.2 B. Na II. 455.5 C. Rb III. 670.8 D. Cs IV. 780.0 Choose the…Atomic Structure

Mathematics

Q23If the shortest distance between the lines (x-λ)/3=(y-2)/(-1)=(z-1)/1 and (x+2)/(-3)=(y+5)/2=(z-4)/4 is 44/(√(30)), then the largest possible value of |λ| is…Three Dimensional Geometry
Q27Let [t] denote the largest integer less than or equal to t. If ∫₀³([x²]+[(x²)/2]) d x=a+b √(2)-√(3)-√(5)+c √(6)-√(7), where a, b, c Z, then a+b+c is equal to…Integral Calculus
Q29If the solution y(x) of the given differential equation (e^(y)+1) cos x ~d x+e^(y) sin x ~d y=0 passes through the point ((π)/2, 0), then the value of…Differential Equations
Q33The length of the latus rectum and directrices of hyperbola with eccentricity e are 9 and x= ± 4/(√(3)), respectively. Let the line y-√(3) x+√(3)=0 touch this…Coordinate Geometry
Q35Let [t] denote the greatest integer less than or equal to t. Let f:[0, ∞) → R be a function defined by f(x)=[x/2+3]-[√(x)]. Let S be the set of all points in…Limit, Continuity and Differentiability
Q38If the system of equations 2 x+7 y+λ z=3 3 x+2 y+5 z=4 x+μ y+32 z=-1 has infinitely many solutions, then (λ-μ) is equal to _ _ _:Matrices and Determinants
Q42From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the…Statistics and Probability
Q43In a triangle ABC, BC=7, AC=8, AB=α N and cos A=2/3. If 49 cos (3 C)+42=m/n, where gcd(m, n)=1, then m+n is equal to _ _ _ _ _.Properties of Triangle
Q44Let α, β be roots of x²+√(2) x-8=0. If U n =αⁿ+βⁿ, then (U₁₀+√(2) U₉)/(2 U₈) is equal to _ _ _ _.Complex Numbers and Quadratic Equations
Q47If S(x)=(1+x)+2(1+x)²+3(1+x)³+ +60(1+x)⁶⁰, x ≠ 0, and (60)² ~S(60)=a(b)^(b)+b, where a, b N, then (a+b) equal to _ _ _ _ _.Sequence and Series
Q2541Let P(α, β, γ) be the image of the point Q(3,-3,1) in the line (x-0)/1=(y-3)/1=(z-1)/(-1) and R be the point (2,5,-1). If the area of the triangle PQR is λ…Three Dimensional Geometry
Q2875If the area of the region \(x, y): a/(x²) ≤ y ≤ 1/x, 1 ≤ x ≤ 2,0<a<1 is (log e 2)-1/7 then the value of 7 a-3 is equal to:Integral Calculus
Q3115If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2), B(8,3) and C(h, k), then the point C lies on the circle:Coordinate Geometry
Q3272If z₁, z₂ are two distinct complex number such that |(z₁-2 z₂)/(1/2-z₁ z₂)|=2, thenComplex Numbers and Quadratic Equations
Q3651Suppose the solution of the differential equation (d y)/(d x)=((2+α) x-β y+2)/(β x-2 α y-(β γ-4 α)) represents a circle passing through origin. Then the…Differential Equations
Q3661Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^()(0)=h^()(1)=2. If g(x)=h(eˣ) e^(h(x)), then g^()(0) is equal to:Limit, Continuity and Differentiability
Q3897If the function f(x)=(1/x)²ˣ; x>0 attains the maximum value at x=1/e then:Sets, Relations and Functions
Q3898Let f(x)=1/(7- sin 5 x) be a function defined on R. Then the range of the function f(x) is equal to:Sets, Relations and Functions
Q4057If ∫ 1/(a² sin ² x+b² cos ² x) ~d x=1/12 tan ⁻¹(3 tan x)+ constant, then the maximum value of a sin x+b cos x, is:Integral Calculus
Q4247lim n → ∞ ((1²-1)(n-1)+(2²-2)(n-2)+ +((n-1)²-(n-1)) · 1)/((1³+2³+ +n³)-(1²+2²+ +n²)) is equal to:Limit, Continuity and Differentiability
Q4431If A is a square matrix of order 3 such that det(A)=3 and det(adj(-4 adj(-3 adj(3 adj((2 ~A)⁻¹)))))=2^(m) 3ⁿ, then m+2 n is equal to:Matrices and Determinants
Q4838Let 0 ≤ r ≤ n. If ⁿ⁺¹ C r+1: ⁿ C r: ⁿ⁻¹ C r-1 =55: 35: 21, then 2 n+5 r is equal to:Permutations and Combinations
Q4856If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315^(th) position…Permutations and Combinations
Q4935If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:Statistics and Probability
Q5239A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4…Sequence and Series
Q5277Let A B C be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle A B C and the same process is…Sequence and Series
Q5397Let A=\1,2,3,4,5. Let R be a relation on A defined by x R y if and only if 4 x ≤ 5 y. Let m be the number of elements in R and n be the minimum number of…Sets, Relations and Functions
Q5573If the locus of the point, whose distances from the point (2,1) and (1,3) are in the ratio 5: 4, is a x²+b y²+c x y+d x+e y+170=0, then the value of a²+2 b+3…Coordinate Geometry
Q5860Let a=2 i+j-k, b=((a ×(i+j)) × i) × i. Then the square of the projection of a on b is:Vector Algebra
Q5861Let a=6 i+j-k and b=i+j. If c is a is vector such that |c| ≥ 6, a · c=6|c|,|c-a|=2 √(2) and the angle between a × b and c is 60^(°), then |(a × b) × c| is…Vector Algebra