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

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JEE Main 202430 Jan, Morning shift

Physics 20Chemistry 19Mathematics 30

Physics

Q54A electron of hydrogen atom on an excited state is having energy E n =-0.85 ~eV. The maximum number of allowed transitions to lower energy level is _ _ _ _ _.Atoms and Nuclei
Q55A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2 C and potential 2 ~V. Then the loss of energy…Electrostatics
Q59A ceiling fan having 3 blades of length 80 ~cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and…Electromagnetic Induction and Alternating Currents
Q62The distance between object and its two times magnified real image as produced by a convex lens is 45 ~cm. The focal length of the lens used is _ _ _ c m.Optics
Q65The horizontal component of earth's magnetic field at a place is 3.5 × 10⁻⁵ ~T. A very long straight conductor carrying current of √(2) ~A in the direction…Magnetic Effects of Current and Magnetism
Q66The displacement and the increase in the velocity of a moving particle in the time interval of t to (t+1) s are 125 ~m and 50 ~m / s, respectively. The…Kinematics
Q71In a closed organ pipe, the frequency of fundamental note is 30 ~Hz. A certain amount of water is now poured in the organ pipe so that the fundamental…Oscillations and Waves
Q5927A series L.R circuit connected with an ac source E=(25 sin 1000 t) V has a power factor of 1/(√(2)). If the source of emf is changed to E=(20 sin 2000 t) V…Electromagnetic Induction and Alternating Currents
Q6027The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5^(t)h excited state of a hydrogen atom is:Atoms and Nuclei
Q6256A spherical body of mass 100 ~g is dropped from a height of 10 ~m from the ground. After hitting the ground, the body rebounds to a height of 5 ~m. The…Rotational Motion
Q6442An electric toaster has resistance of 60 Ω at room temperature (27^(°) C). The toaster is connected to a 220 ~V supply. If the current flowing through it…Current Electricity
Q6667The work function of a substance is 3.0 ~eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;Dual Nature of Matter and Radiation
Q6824The electric field of an electromagnetic wave in free space is represented as E=E₀ cos (ω t-kz) i. The corresponding magnetic induction vector will be:Electromagnetic Waves
Q6951The electrostatic potential due to an electric dipole at a distance ' r ' varies as:Electrostatics
Q7240The gravitational potential at a point above the surface of earth is -5.12 × 10⁷ ~J / kg and the acceleration due to gravity at that point is 6.4 ~m / s²…Gravitation
Q7434At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47^(°) C ?Kinetic Theory of Gases
Q7967Young's modules of material of a wire of length ' L ' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved…Properties of Solids and Liquids
Q8061A particle of mass m is projected with a velocity ' u ' making an angle of 30^(°) with the horizontal. The magnitude of angular momentum of the projectile…Rotational Motion
Q8279Match List I with List II. List I List II (A) Coefficient of viscosity (I) [M L² ~T⁻²] (B) Surface tension (II) [M L² ~T⁻¹] (C) Angular momentum (III) [M L⁻¹…Units and Measurements
Q8406The diffraction pattern of a light of wavelength 400 ~nm diffracting from a slit of width 0.2 ~mm is focused on the focal plane of a convex lens of focal…Optics

Chemistry

Q5The total number of molecular orbitals formed from 2 s and 2 p atomic orbitals of a diatomic molecule is _ _ _ _ _.Chemical Bonding and Molecular Structure
Q6The rate of First order reaction is 0.04 ~mol ~L⁻¹ ~s⁻¹ at 10 minutes and 0.03 ~mol ~L⁻¹ ~s⁻¹ at 20 minutes after initiation. Half life of the reaction is _ _…Chemical Kinetics
Q7The compound formed by the reaction of ethanal with semicarbazide contains _ _ _ _ n umber of nitrogen atoms.Organic Compounds Containing Nitrogen
Q11The pH at which Mg(OH)₂[~K sp =1 × 10⁻¹¹] begins to precipitate from a solution containing 0.10 ~M ~Mg²⁺ ions is _ _ _ _ _.Equilibrium
Q15If IUPAC name of an element is "Unununnium" then the element belongs to n^(t)h group of Periodic table. The value of n is _ _ _ _.Classification of Elements and Periodicity in Properties
Q16On a thin layer chromatographic plate, an organic compound moved by 3.5 ~cm, while the solvent moved by 5 ~cm. The retardation factor of the organic compound…Principles Related to Practical Chemistry
Q172 MnO₄⁻+bI⁻+cH₂ O → x I₂+y MnO₂+z O H If the above equation is balanced with integer coefficients, the value of z is _ _ _ _.Redox Reactions and Electrochemistry
Q19The mass of sodium acetate (CH₃ COONa) required to prepare 250 ~mL of 0.35 ~M aqueous solution is _ _ _ _ g. (Molar mass of CH₃ COONa is 82.02 ~g ~mol⁻¹)Some Basic Concepts in Chemistry
Q200.05 ~cm thick coating of silver is deposited on a plate of 0.05 ~m² area. The number of silver atoms deposited on plate are _ _ _ _ × 10²³. (At mass Ag=108…Some Basic Concepts in Chemistry
Q185Sugar which does not give reddish brown precipitate with Fehling's reagent, is:Biomolecules
Q258Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): There is a considerable increase in…Chemical Bonding and Molecular Structure
Q321Aluminium chloride in acidified aqueous solution forms an ion having geometryChemical Bonding and Molecular Structure
Q576Choose the correct statements from the following: (A) Ethane-1, 2-diamine is a chelating ligand. (B) Metallic aluminium is produced by electrolysis of…Coordination Compounds
Q838Diamagnetic Lanthanoid ions are:d- and f-Block Elements
Q1521Given below are two statements: Statement (I): The gas liberated on warming a salt with dil H₂ SO₄, turns a piece of paper dipped in lead acetate into black…p-Block Elements
Q1536The Lassiagne's extract is boiled with dil HNO₃ before testing for halogens because,p-Block Elements
Q1665Match List I with List II. List I Species List II Electronic distribution (A) Cr⁺² (I) 3d⁸ (B) Mn⁺ (II) 3d³4s¹ (C) Ni⁺² (III) 3d⁴ (D) V⁺ (IV) 3d⁵4s¹ Choose…Classification of Elements and Periodicity in Properties
Q1984What happens to freezing point of benzene when small quantity of napthalene is added to benzene?Solutions
Q2215Given below are two statements: Statement (I): The orbitals having same energy are called as degenerate orbitals. Statement (II): In hydrogen atom, 3p and 3d…Atomic Structure

Mathematics

Q24If d₁ is the shortest distance between the lines x+1=2 y=-12 z, x=y+2=6 z-6 and d₂ is the shortest distance between the lines (x-1)/2=(y+8)/(-7)=(z-4)/5…Three Dimensional Geometry
Q27Number of integral terms in the expansion of \7^((1/2))+11^((1/6))\⁸²⁴ is equal to _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q32The value of 9 ∫₀⁹[√((10 x)/(x+1))] d x, where [t] denotes the greatest integer less than or equal to t, isIntegral Calculus
Q33Let y=y(x) be the solution of the differential equation (1-x²) d y=[x y+(x³+2) √(3(1-x²))] d x, -1< x<1, y(0)=0. If y(1/2)=m/n, m and n are co-prime numbers…Differential Equations
Q38Let A=\1,2,3,, 7 and let P(A) denote the power set of A. If the number of functions f: A → P(A) such that a f(a), a A is mⁿ, m and n N and m is least, then…Sets, Relations and Functions
Q40Let the latus rectum of the hyperbola (x²)/9-(y²)/(b²)=1 subtend an angle of (π)/3 at the centre of the hyperbola. If b² is equal to l/(~m)(1+√(n)), where l…Coordinate Geometry
Q41If the function f(x)= 1/(|x|), |x| 2 a x²+2 ~b, |x|<2 is differentiable on R, then 48(a+b) is equal to _ _ _ _ _.Limit, Continuity and Differentiability
Q44A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of…Statistics and Probability
Q45Let α, β N be roots of the equation x²-70 x+λ=0, where (λ)/2, (λ)/3 N. If λ assumes the minimum possible value, then ((√(α-1)+√(β-1))(λ+35))/(|α-β|) is equal…Complex Numbers and Quadratic Equations
Q47Let α=1²+4²+8²+13²+19²+26²+ upto 10 terms and β=Σ n=1 ¹⁰ n⁴. If 4 α-β=55 k+40, then k is equal to _ _ _ _ _.Sequence and Series
Q2474Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram A B C D. If the diagonal BD=i+2 j+3 k, then the area of the parallelogram is equal to:Three Dimensional Geometry
Q2531Let (α, β, γ) be the foot of perpendicular from the point (1,2,3) on the line (x+3)/5=(y-1)/2=(z+4)/3. Then 19(α+β+γ) is equal to:Three Dimensional Geometry
Q2684The maximum area of a triangle whose one vertex is at (0,0) and the other two vertices lie on the curve y=-2 x²+54 at points (x, y) and (-x, y), where y>0, is:Limit, Continuity and Differentiability
Q2868The area (in square units) of the region bounded by the parabola y²=4(x-2) and the line y=2 x-8, is:Integral Calculus
Q3101If the circles (x+1)²+(y+2)²=r² and x²+y²-4 x-4 y+4=0 intersect at exactly two distinct points, thenCoordinate Geometry
Q3168If z=x+i y, x y ≠ 0, satisfies the equation z²+i z=0, then |z²| is equal to:Complex Numbers and Quadratic Equations
Q3298The value of lim n → ∞ Σ k=1 ⁿ (n³)/((n²+k²)(n²+3 k²)) is:Integral Calculus
Q3478Let f:[-(π)/2, (π)/2] → R be a differentiable function such that f(0)=1/2. If the lim x → 0 (x ∫₀ˣ f(t) dt)/(e^(x²)-1)=α, then 8 α² is equal to:Integral Calculus
Q3646Let y=y(x) be the solution of the differential equation sec x ~d y+\2(1-x) tan x+x(2-x) d x=0 such that y(0)=2. Then y(2) is equal to:Differential Equations
Q3702Let g: R → R be a non constant twice differentiable function such that g^()(1/2)=g^()(3/2). If a real valued function f is defined as f(x)=1/2[g(x)+g(2-x)]…Limit, Continuity and Differentiability
Q3712If f(x)=| ccc 2 cos ⁴ x 2 sin ⁴ x 3+ sin ² 2 x 3+2 cos ⁴ x 2 sin ⁴ x sin ² 2 x 2 cos ⁴ x 3+2 sin ⁴ x sin ² 2 x |, then 1/5 f^()(0)= is equal to:Limit, Continuity and Differentiability
Q3770If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is:Coordinate Geometry
Q3850If the domain of the function f(x)= cos ⁻¹((2-|x|)/4)+ log e (3-x)\⁻¹ is [-α, β)-\γ, then α+β+γ is equal to:Sets, Relations and Functions
Q4636Consider the system of linear equations x+y+z=4 μ, x+2 y+2 λ z=10 μ, x+3 y+4 λ² z=μ²+15 where λ, μ R. Which one of the following statements is NOT correct ?Matrices and Determinants
Q4931Two integers x and y are chosen with replacement from the set \0,1,2,3,, 10. Then the probability that |x-y|>5, is:Statistics and Probability
Q5237Let S n denote the sum of first n terms of an arithmetic progression. If S₂₀=790 and S₁₀=145, then S₁₅-S₅ is:Sequence and Series
Q5418Let M denote the median of the following frequency distribution Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 3 9 10 8 6 Then 20M is equal to:Statistics and Probability
Q5623A line passing through the point A(9,0) makes an angle of 30^(°) with the positive direction of x -axis. If this line is rotated about A through an angle of…Coordinate Geometry
Q5631If 2 sin ³ x+ sin 2 x cos x+4 sin x-4=0 has exactly 3 solutions in the interval [0, (n π)/2], n N, then the roots of the equation x²+n x+(n-3)=0 belong to:Trigonometry
Q5851Let a=a₁ i+a₂ j+a₃ k and b=b₁ i+b₂ j+b₃ k be two vectors such that |a|=1, a · b=2 and |b|=4. If c=2(a × b)-3 b, then the angle between b and c is equal to:Vector Algebra