Loading…

Questions and solutions are free, always.

Practise

Practice
Revision queue
Revision planner
Take a test
Build a test

Browse

All topics
Blog
Notes & printables
Physics
Chemistry
Mathematics

Account

Your numbers
Study plan
Saved
Plus
Privacy
Terms
Delete account

Skip to content

JEE Main 2024 31 Jan Morning shift Question Paper with Solutions | JEE Arc

Past papers

Ctrl K

Practice
Revise
Tests
Topics
More
Dashboard Settings My progress Notes & printables Revision planner Study plan Saved questions Explore Plus

81days to JEE Main

Study

PracticePractice

Study planPlanPlus

Library

Past papersPapers

ProgressProgress

SettingsSettings

JEE Arc Plus₹49 a month. Mocks, plans, notes.→?GuestSign in to save progress

JEE Main 202431 Jan, Morning shift

Physics 24Chemistry 26Mathematics 30

Physics

Q59The mass defect in a particular reaction is 0.4 ~g. The amount of energy liberated is n × 10⁷ ~kWh, where n= _ _ _ _ _. (speed of light.=3 × 10⁸ ~m / s)Atoms and Nuclei
Q60A parallel plate capacitor with plate separation 5 ~mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 ~mm…Electrostatics
Q61A body starts falling freely from height H hits an inclined plane in its path at height h. As a result of this perfectly elastic impact, the direction of the…Rotational Motion
Q63A solid circular disc of mass 50 ~kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 ~m / s. The absolute value of work done on…Rotational Motion
Q67A small square loop of wire of side l is placed inside a large square loop of wire of side L(L=l²). The loops are coplanar and their centers coincide. The…Electromagnetic Induction and Alternating Currents
Q74An electron moves through a uniform magnetic field B=B₀ i+2 B₀ j T. At a particular instant of time, the velocity of electron is u=3 i+5 j ~m / s. If the…Magnetic Effects of Current and Magnetism
Q76The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is _ _ _ m. (Take density of sea water =10³ kgm⁻³…Properties of Solids and Liquids
Q77A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is (2 A)/3. The new…Oscillations and Waves
Q80Two waves of intensity ratio 1: 9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is I₁ (b) Waves are…Optics
Q6025If the wavelength of the first member of Lyman series of hydrogen is λ. The wavelength of the second member will beAtoms and Nuclei
Q6255An artillery piece of mass M₁ fires a shell of mass M₂ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that…Rotational Motion
Q6294A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ. If the distance of the coin from the center of the disc is r, the…Kinematics
Q6525Two conductors have the same resistances at 0^(°) C but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients…Current Electricity
Q6666When a metal surface is illuminated by light of wavelength λ, the stopping potential is 8 ~V. When the same surface is illuminated by light of wavelength 3 λ…Dual Nature of Matter and Radiation
Q6715A coil is places perpendicular to a magnetic field of 5000 ~T. When the field is changed to 3000 ~T in 2 ~s, an induced emf of 22 ~V is produced in the coil…Electromagnetic Induction and Alternating Currents
Q6822In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 × 10¹⁰ ~Hz and an amplitude of 50 ~Vm⁻¹. The total average energy density…Electromagnetic Waves
Q6979Two charges q and 3 q are separated by a distance ' r ' in air. At a distance x from charge q, the resultant electric field is zero. The value of x is:Electrostatics
Q7127The refractive index of a prism with apex angle A is cot A / 2. The angle of minimum deviation is:Optics
Q7283Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is…Gravitation
Q7431The parameter that remains the same for molecules of all gases at a given temperature is:Thermodynamics
Q7888The relation between time ' t ' and distance ' x ' is t=α x²+β x, where α and β are constants. The relation between acceleration (a) and velocity (v) is:Kinematics
Q8277A force is represented by F=a x²+b t^(1/2) where x= distance and t= time. The dimensions of b² / a are:Units and Measurements
Q8319If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be:Units and Measurements
Q8512The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 ~cm, the…Oscillations and Waves

Chemistry

Q6The number of species from the following in which the central atom uses sp³ hybrid orbitals in its bonding is _ _ _ _ _. NH₃, SO₂, SiO₂, BeCl₂, CO₂, H₂ O…Chemical Bonding and Molecular Structure
Q10The 'Spin only' Magnetic moment for [Ni(NH₃)₆]²⁺ is _ _ _ _ _ × 10⁻¹ ~BM. (given = Atomic number of Ni: 28)Coordination Compounds
Q15Number of alkanes obtained on electrolysis of a mixture of CH₃ COONa and C₂ H₅ COONa is _ _ _ _.Redox Reactions and Electrochemistry
Q16One Faraday of electricity liberates x × 10⁻¹ gram atom of copper from copper sulphate. x is _ _ _ _.Redox Reactions and Electrochemistry
Q17Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Alcohols react both as nucleophiles and…Organic Compounds Containing Oxygen
Q23Molar mass of the salt from NaBr, NaNO₃, KI and CaF₂ which does not evolve coloured vapours on heating with concentrated H₂ SO₄ is _ _ _ _ g ~mol ⁻¹. (Molar…Some Basic Concepts in Chemistry
Q24Number of moles of methane required to produce 22 ~g ~CO 2(~g) after combustion is x × 10⁻² moles. The value of x is _ _ _ _ _.Some Basic Concepts in Chemistry
Q25The ionization energy of sodium in ~kJ ~mol⁻¹, if electromagnetic radiation of wavelength 242 ~nm is just sufficient to ionize sodium atom is _ _ _ _.Atomic Structure
Q27Consider the following reaction at 298 ~K · 3/2 O 2(g) O 3(g) · K P =2.47 × 10⁻²⁹. Δ r G^() for the reaction is _ _ _ _ k J. (Given R=8.314 ~JK⁻¹ ~mol⁻¹)Chemical Thermodynamics
Q36Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: pK a value of phenol is 10.0 while that of…Organic Compounds Containing Oxygen
Q111Given below are two statements: Statement I: IUPAC name of HO-CH₂-(CH₂)₃-CH₂-COCH₃ is 7-hydroxyheptan-2-one. Statement II: 2-oxoheptan-7-ol is the correct…Some Basic Principles of Organic Chemistry
Q145A species having carbon with sextet of electrons and can act as electrophile is calledSome Basic Principles of Organic Chemistry
Q183Match List I with List II List - I List - II (A) Glucose/ NaHCO₃/Δ (I) Gluconic acid (B) Glucose / HNO₃ (II) No reaction (C) Glucose / HI / Δ (III) n-hexane…Biomolecules
Q385The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining atomic orbitals A. have the same energy B. have the…Chemical Bonding and Molecular Structure
Q424For the given reaction, choose the correct expression of K C from the following:- Fe (aq) ³⁺+SCN (aq) ⁻ (FeSCN) (aq) ²⁺Equilibrium
Q478Integrated rate law equation for a first order gas phase reaction is given by (where P i is initial pressure and P t is total pressure at time t)Chemical Kinetics
Q748The correct statements from following are: A. The strength of anionic ligands can be explained by crystal field theory. B. Valence bond theory does not give a…Coordination Compounds
Q791Identify correct statements from below: A. The chromate ion is square planar. B. Dichromates are generally prepared from chromates. C. The green manganate ion…d- and f-Block Elements
Q792The metals that are employed in the battery industries are A. Fe B. Mn C. Ni D. Cr E. Cd Choose the correct answer from the options given below:d- and f-Block Elements
Q951Identify the factor from the following that does not affect electrolytic conductance of a solution.Redox Reactions and Electrochemistry
Q1477Consider the oxides of group 14 elements SiO₂, GeO₂, SnO₂, PbO₂, CO and GeO. The amphoteric oxides arep-Block Elements
Q1478The compound that is white in color isp-Block Elements
Q1542Give below are two statements: Statement - I: Noble gases have very high boiling points. Statement - II: Noble gases are monoatomic gases. They are held…p-Block Elements
Q1582The correct sequence of electron gain enthalpy of the elements listed below is A. Ar B. Br C. F D. S Choose the most appropriate from the options given below:Classification of Elements and Periodicity in Properties
Q2019Identify the mixture that shows positive deviations from Raoult's LawSolutions
Q2221'Adsorption' principle is used for which of the following purification method?Surface Chemistry

Mathematics

Q28Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x=y, z=1 and x=-y, z=-1 respectively. If QPR is a right angle, then 12 a² is…Three Dimensional Geometry
Q32In the expansion of (1+x)(1-x²)(1+3/x+3/(x²)+1/(x³))⁵, x ≠ 0, the sum of the coefficients of x³ and x⁻¹³ is equal to _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q34If α denotes the number of solutions of |1-i|ˣ=2ˣ and β=((|z|)/(arg (z))), where z=(π)/4(1+i)⁴[(1-√(π) i)/(√(π)+i)+(√(π)-i)/(1+√(π) i)], i=√(-1), then the…Complex Numbers and Quadratic Equations
Q35Let S=(-1, ∞) and f: S → R be defined as f(x)=∫₋₁ˣ(e^(t)-1)¹¹(2 t-1)⁵(t-2)⁷(t-3)¹²(2 t-10)⁶¹ d t, Let p= Sum of squares of the values of x, where f(x) attains…Integral Calculus
Q36If the integral 525 ∫₀^((π)/2) sin 2 x cos ^(11/2) x(1+Cos^(5/2) x)^(1/2) d x is equal to (n √(2)-64), then n is equal to _ _ _ _ _.Integral Calculus
Q37Let f: R → R be a function defined by f(x)=(4ˣ)/(4ˣ+2) and M=∫ f(a) ^(f(1-a)) x sin ⁴(x(1-x)) d x, N=∫ f(a) ^(f(1-a)) sin ⁴(x(1-x)) d x; a ≠ 1/2. If α M=β N…Integral Calculus
Q42Let the foci and length of the latus rectum of an ellipse (x²)/(a²)+(y²)/(b²)=1, a>b b e(± 5,0) and √(50), respectively. Then, the square of the eccentricity…Coordinate Geometry
Q47The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to _ _ _ _…Permutations and Combinations
Q53Let A=\1,2,3,4 and R=\(1,2),(2,3),(1,4) be a relation on A. Let S be the equivalence relation on A such that R S and the number of elements in S is n. Then…Sets, Relations and Functions
Q57Let a and b be two vectors such that |a|=1,|b|=4, and a · b=2. If c=(2 a × b)-3 b and the angle between b and c is α, then 192 sin ² α is equal to _ _ _ _.Vector Algebra
Q2749If f(x)=| ccc x³ 2 x²+1 1+3 x 3 x²+2 2 x x³+6 x³-x 4 x²-2 | for all x R, then 2 f(0)+f^()(0) is equal toLimit, Continuity and Differentiability
Q2867The area of the region \(x, y): y² ≤ 4 x, x<4, (x y(x-1)(x-2))/((x-3)(x-4))>0, x ≠ 3 isIntegral Calculus
Q2959Let a be the sum of all coefficients in the expansion of (1-2 x+2 x²)²⁰²³(3-4 x²+2 x³)²⁰²⁴ and b= lim x → 0 ((∫₀ˣ (log (1+t))/(t²⁰²⁴+1) d t)/(x²)). If the…Binomial Theorem and Its Simple Applications
Q3035If one of the diameters of the circle x²+y²-10 x+4 y+13=0 is a chord of another circle C, whose center is the point of intersection of the lines 2 x+3 y=12…Coordinate Geometry
Q3643Let y=y(x) be the solution of the differential equation (d y)/(d x)=((tan x)+y)/(sin x(sec x- sin x tan x)), x (0, (π)/2) satisfying the condition y((π)/4)=2…Differential Equations
Q3644The solution curve of the differential equation y (d x)/(d y)=x(log e x- log e y+1), x>0, y>0 passing through the point (e, 1) isDifferential Equations
Q3834If f(x)=(4 x+3)/(6 x-4), x ≠ 2/3 and (f° f)(x)=g(x), where g: R-\2/3 → R-\2/3, then (g ogog)(4) is equal toSets, Relations and Functions
Q3979If the foci of a hyperbola are same as that of the ellipse (x²)/9+(y²)/25=1 and the eccentricity of the hyperbola is 15/8 times the eccentricity of the…Coordinate Geometry
Q4118For α, β, γ ≠ 0, if sin ⁻¹ α+ sin ⁻¹ β+ sin ⁻¹ γ=π and (α+β+γ)(α-γ+β)=3 α β, then γ equalsTrigonometry
Q4162Let g(x) be a linear function and f(x)=\ clg(x), x ≤ 0 ((1+x)/(2+x))^(1/x), x>0., is continuous at x=0. If f^()(1)=f(-1), then the value g(3) isLimit, Continuity and Differentiability
Q4258lim x → 0 (e^(2| sin x|)-2| sin x|-1)/(x²)Limit, Continuity and Differentiability
Q4634If the system of linear equations x-2 y+z=-4 2 x+α y+3 z=5 3 x-y+β z=3 has infinitely many solutions, then 12 α+13 β is equal toMatrices and Determinants
Q4968Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing…Statistics and Probability
Q5007Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples…Statistics and Probability
Q5071Let S be the set of positive integral values of a for which (a x²+2(a+1) x+9 a+4)/(x²-8 x+32) < 0, x R. Then, the number of elements in S is:Complex Numbers and Quadratic Equations
Q5187For 0 < c < b < a, let (a+b-2 c) x²+(b+c-2 a) x+(c+a-2 b)=0 and α ≠ 1 be one of its root. Then, among the two statements (I) If α (-1,0), then b cannot be the…Sequence and Series
Q5347The sum of the series 1/(1-3 · 1²+1⁴)+2/(1-3 · 2²+2⁴)+3/(1-3 · 3²+3⁴)+ up to 10 -terms isSequence and Series
Q5622Let α, β, γ, δ Z and let A(α, β), B(1,0), C(γ, δ) and D(1,2) be the vertices of a parallelogram ABCD. If A B=√(10) and the points A and C lie on the line 3…Coordinate Geometry
Q5846Let a=3 i+j-2 k, b=4 i+j+7 k and c=i-3 j+4 k be three vectors. If a vectors p satisfies p × b=c × b and p · a=0, then p ·(i-j-k) is equal toVector Algebra
Q5847The distance of the point Q(0,2,-2) form the line passing through the point P(5,-4, 3) and perpendicular to the lines r=(-3 i+2 k)+λ(2 i+3 j+5 k), λ R and…Vector Algebra