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JEE Main 2024 30 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202430 Jan, Evening shift

Physics 22Chemistry 22Mathematics 29

Physics

Q54A power transmission line feeds input power at 2.3 ~kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at…Electromagnetic Induction and Alternating Currents
Q58Two resistance of 100 Ω and 200 Ω are connected in series with a battery of 4 ~V and negligible internal resistance. A voltmeter is used to measure voltage…Current Electricity
Q61Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37^(°) with each other. When suspended in a liquid of…Electrostatics
Q63A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m…Gravitation
Q67The current of 5 ~A flows in a square loop of sides 1 ~m is placed in air. The magnetic field at the centre of the loop is X √(2) × 10⁻⁷ T. The value of X is…Magnetic Effects of Current and Magnetism
Q68A big drop is formed by coalescing 1000 small identical drops of water. If E₁ be the total surface energy of 1000 small drops of water and E₂ be the surface…Properties of Solids and Liquids
Q69Two discs of moment of inertia I₁=4 ~kg ~m² and I₂=2 ~kg ~m², about their central axes normal to their planes, rotating with angular speeds 10 ~rad / s 4 ~rad…Rotational Motion
Q72A vector has magnitude same as that of A=3 i+4 j and is parallel to B=4 i+3 j. The x and y components of this vector in first quadrant are x and 3…Kinematics
Q74A point source is emitting sound waves of intensity 16 × 10⁻⁸ ~Wm⁻² at the origin. The difference in intensity (magnitude only) at two points located at a…Oscillations and Waves
Q5926An alternating voltage V(t)=220 sin 100 π t volt is applied to a purely resistive load of 50 Ω. The time taken for the current to rise from half of the peak…Electromagnetic Induction and Alternating Currents
Q6026An electron revolving in n^(th) Bohr orbit has magnetic moment μ n. If μ n ∝ nˣ, the value of x isAtoms and Nuclei
Q6060In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass…Atoms and Nuclei
Q6441When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves…Current Electricity
Q6610If the total energy transferred to a surface in time t is 6.48 × 10⁵ ~J, then the magnitude of the total momentum delivered to this surface for complete…Dual Nature of Matter and Radiation
Q6717Match List I with List II List I List II (A) Gauss's law of magnetostatics (I) E · d a=1/(ε₀) ∫ ρ d V (B) Faraday's law of electro magnetic induction (II) B ·…Electromagnetic Induction and Alternating Currents
Q6987A particle of charge ' -q ' and mass ' m ' moves in a circle of radius ' r ' around an infinitely long line charge of linear charge density ' +λ '. Then time…Electrostatics
Q7220Escape velocity of a body from earth is 11.2 ~km / s. If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the…Gravitation
Q7325If three moles of monoatomic gas (γ=5/3) is mixed with two moles of a diatomic gas (γ=7/5), the value of adiabatic exponent γ for the mixture isThermodynamics
Q7562A block of mass m is placed on a surface having vertical crossection given by y=x² / 4. If coefficient of friction is 0.5, the maximum height above the ground…Laws of Motion
Q8278If mass is written as m=k c^(P) G^(-1 / 2) h^(1 / 2) then the value of P will be: (Constants have their usual meaning with k a dimensionless constant)Units and Measurements
Q8363If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 ~mm, the Vernier constant…Experimental Skills
Q8471A beam of unpolarised light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane…Optics

Chemistry

Q2The total number of correct statements, regarding the nucleic acids is _ _ _ _ _. A. RNA is regarded as the reserve of genetic information B. DNA molecule…Biomolecules
Q5NO₂ required for a reaction is produced by decomposition of N₂ O₅ in CCl₄ as by equation 2 ~N₂ O 5(~g) → 4 NO 2(~g) +O 2(~g) The initial concentration of N₂…Chemical Kinetics
Q7Number of complexes which show optical isomerism among the following is _ _ _ _. cis- [Cr(ox)₂ Cl₂]³⁻,[Co(en)₃]³⁺, cis- [Pt(en)₂ Cl₂]²⁺, cis- [Co(en)₂ Cl₂]⁺…Coordination Compounds
Q9Number of metal ions characterized by flame test among the following is _ _ _ _. Sr²⁺, Ba²⁺, Ca²⁺, Cu²⁺, Zn²⁺, Co²⁺, Fe²⁺d- and f-Block Elements
Q132-chlorobutane +Cl₂ → C₄ H₈ Cl₂ (isomers) Total number of optically active isomers shown by C₄ H₈ Cl₂, obtained in the above reaction is _ _ _ _ _.Organic Compounds Containing Halogens
Q14The pH of an aqueous solution containing 1 M benzoic acid (pK a =4.20) and 1 M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 ~mL of this…Equilibrium
Q19Total number of species from the following which can undergo disproportionation reaction is _ _ _ _. H₂ O₂, ClO₃⁻, P₄, Cl₂, Ag, Cu⁺¹, ~F₂, NO₂, K⁺Redox Reactions and Electrochemistry
Q22Number of spectral lines obtained in He⁺ spectra, when an electron makes transition from fifth excited state to first excited state will beAtomic Structure
Q23Two reactions are given below: 2 Fe (s) +3/2 O 2(~g) → Fe₂ O 3(~s), Δ H^(°)=-822 ~kJ / mol C (s) +1/2 O 2(~g) → CO (g), Δ H^(°)=-110 ~kJ / mol Then enthalpy…Chemical Thermodynamics
Q141Which among the following purification methods is based on the principle of "Solubility" in two different solvents?Some Basic Principles of Organic Chemistry
Q320The molecule / ion with square pyramidal shape isChemical Bonding and Molecular Structure
Q601The coordination geometry around the manganese in decacarbonyldimanganese (0) isCoordination Compounds
Q795The orange colour of K₂ Cr₂ O₇ and purple colour of KMnO₄ is due tod- and f-Block Elements
Q952Alkaline oxidative fusion of MnO₂ gives "A" which on electrolytic oxidation in alkaline solution produces B. A and B respectively areRedox Reactions and Electrochemistry
Q1006Reduction potential of ions are given below: ccc ClO₄⁻ IO₄⁻ BrO₄⁻ E^(°)=1.19 ~V E^(°)=1.65 ~V E^(°)=1.74 ~V The correct order of their oxidising power is:Redox Reactions and Electrochemistry
Q1154Given below are two statements: Statement - I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky…Organic Compounds Containing Halogens
Q1499Choose the correct statements about the hydrides of group 15 elements. A. The stability of the hydrides decreases in the order NH₃>PH₃>AsH₃> SbH₃>BiH₃. B. The…p-Block Elements
Q1520A and B formed in the following reactions are: CrO₂ Cl₂+4 NaOH → A+2 NaCl+2 H₂ O, A+2 HCl+2 H₂ O₂ → B+3 H₂ Op-Block Elements
Q1642Given below are two statements: Statement - I: Along the period, the chemical reactivity of the elements gradually increases from group 1 to group 18…Classification of Elements and Periodicity in Properties
Q1664Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: H₂ Te is more acidic than H₂ ~S. Reason R…Classification of Elements and Periodicity in Properties
Q1983The solution from the following with highest depression in freezing point/lowest freezing point isSolutions
Q2051If a substance ' A ' dissolves in solution of a mixture of ' B ' and ' C ' with their respective number of moles as n A, n B and n C₃. Mole fraction of C in…Some Basic Concepts in Chemistry

Mathematics

Q25Let a line passing through the point (-1,2,3) intersect the lines L₁: (x-1)/3=(y-2)/2=(z+1)/(-2) at M(α, β, γ) and L₂: (x+2)/(-3)=(y-2)/(-2)=(z-1)/4 at N(a…Three Dimensional Geometry
Q27The area of the region enclosed by the parabola (y-2)²=x-1, the line x-2 y+4=0 and the positive coordinate axes is _ _ _ _ _.Integral Calculus
Q28Let α=Σ k=0 ⁿ(((ⁿ C k)²)/(k+1)) and β=Σ k=0 ⁿ⁻¹(ⁿ C k ⁿ C k+1 k+2) If 5 α=6 β, then n equals _ _ _ _.Binomial Theorem and Its Simple Applications
Q29Consider two circles C₁: x²+y²=25 and C₂:(x-α)²+y²=16, where α (5,9). Let the angle between the two radii (one to each circle) drawn from one of the…Coordinate Geometry
Q35Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y-y=Y^()(x)(X-x) and the co-ordinate axes, where (x, y) is any point…Differential Equations
Q42In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A student is…Permutations and Combinations
Q44The number of real solutions of the equation x(x²+3|x|+5|x-1|+6|x-2|)=0 is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q46Let S n be the sum to n -terms of an arithmetic progression 3,7,11, If 40<(6/(n(n+1)) Σ k=1 ⁿ S k)<42, then n equals _ _ _ _.Sequence and Series
Q47The number of symmetric relations defined on the set \1,2,3,4 which are not reflexive is _ _ _ _ _.Sets, Relations and Functions
Q48The variance σ² of the data x i | 0 | 1 | 5 | 6 | 10 | 12 | 17 f i | 3 | 2 | 3 | 2 | 6 | 3 | 3 is _ _ _ _ _.Statistics and Probability
Q2530Let L₁: r=(i-j+2 k)+λ(i-j+2 k), λ R, L₂: r=(j-k)+μ(3 i+j+p k), μ R, and L₃: r=δ(i+m j+n k), δ R be three lines such that L₁ is perpendicular to L₂ and L₃ is…Three Dimensional Geometry
Q2683Let f(x)=(x+3)²(x-2)³, x [-4,4]. If M and m are the maximum and minimum values of f, respectively in [-4,4], then the value of M-m isLimit, Continuity and Differentiability
Q3276If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵+z¹⁰⁰+1=0 and z³+2 z²+2 z+1=0, is equal toComplex Numbers and Quadratic Equations
Q3321Let f: R → R be defined as f(x)=a e²ˣ+b eˣ+c x. If f(0)=-1, f^()(log e 2)=21 and ∫₀^(log e 4)(f(x)-c x) d x=39/2, then the value of |a+b+c| equalsIntegral Calculus
Q3475Let f: R → R be a function defined by f(x)=x/((1+x⁴)^(1 / 4)), and g(x)=f(f(f(f(x)))). Then, 18 ∫₀^(√(2 √(5))) x² g(x) d x is equal toIntegral Calculus
Q3476Let y=f(x) be a thrice differentiable function in (-5,5). Let the tangents to the curve y=f(x) at (1, f(1)) and (3, f(3)) make angles π / 6 and π / 4…Integral Calculus
Q3477Let a and b be real constants such that the function f defined by f(x)=\ llx²+3 x+a, x ≤ 1 b x+2, x>1. be differentiable on R. Then, the value of ∫₋₂² f(x) d…Integral Calculus
Q3701Let f: R-\0 → R be a function satisfying f(x/y)=(f(x))/(f(y)) for all x, y, f(y) ≠ 0. If f^()(1)=2024, thenLimit, Continuity and Differentiability
Q3769Let A(α, 0) and B(0, β) be the points on the line 5 x+7 y=50. Let the point P divide the line segment A B internally in the ratio 7:3. Let 3 x-25=0 be a…Coordinate Geometry
Q3849If the domain of the function f(x)= log e ((2 x+3)/(4 x²+x-3))+ cos ⁻¹((2 x-1)/(x+2)) is (α, β], then the value of 5 β-4 α is equal toSets, Relations and Functions
Q3980Let P be a point on the hyperbola H: (x²)/9-(y²)/4=1, in the first quadrant such that the area of triangle formed by P and the two foci of H is 2 √(13). Then…Coordinate Geometry
Q4635Consider the system of linear equations x+y+z=5, x+2 y+λ² z=9, x+3 y+λ z=μ, where λ, μ R. Then, which of the following statement is NOT correct?Matrices and Determinants
Q4656Let R=(cccx 0 0 0 y 0 0 0 z) be a non-zero 3 × 3 matrix, where x sin θ=y sin (θ+(2 π)/3)=z sin (θ+(4 π)/3) ≠ 0, θ (0,2 π). For a square matrix M, let trace…Matrices and Determinants
Q4863Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of…Statistics and Probability
Q5273Let a and b be be two distinct positive real numbers. Let 11^(th) term of a GP, whose first term is a and third term is b, is equal to p^(th) term of another…Sequence and Series
Q5558If x²-y²+2 h x y+2 g x+2 f y+c=0 is the locus of a point, which moves such that it is always equidistant from the lines x+2 y+7=0 and 2 x-y+8=0, then the…Coordinate Geometry
Q5640For α, β (0, π / 2), let 3 sin (α+β)=2 sin (α-β) and a real number k be such that tan α=k tan β. Then, the value of k is equal toTrigonometry
Q5849Let a=i+α j+β k, α, β R. Let a vector b be such that the angle between a and b is (π)/4 and |b|²=6. If a · b=3 √(2), then the value of (α²+β²)|a × b|² is…Vector Algebra
Q5850Let a and b be two vectors such that |b|=1 and |b × a|=2. Then |(b × a)-b|² is equal toVector Algebra