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Friday, 9 October

JEE Main 2024 · January session

JEE Main 31 January 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 35 easy. By hard questions it ranks 4th of the 8 2024 shifts Lumi analysed. The biggest chapter was Complex Numbers and Quadratic Equations, with 4 questions.

Questions
90
none dropped
Numerical answer
30
33% of the shift
Hard
11
12% of the shift
Chapters asked
61
8 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 16Medium 12Hard 2

Top chapters

Chemistry
30 Q · 10 numerical
Easy 17Medium 13Hard 0

Top chapters

Maths
30 Q · 10 numerical
Easy 2Medium 19Hard 9

Top chapters

Question format
  • Single correct48 Q
  • Numerical value30 Q
  • Other5 Q
  • Two statements3 Q
  • Match the list2 Q
  • Assertion–reason2 Q
What each question asks you to do
  • Multi-step31 Q
  • Calculation23 Q
  • Application17 Q
  • Recall12 Q
  • Conceptual5 Q
  • Data or graph2 Q

Most common: Multi-step.

Every question

All 90 questions, with answers

Open a question for the full text, options, the official answer and the same idea in other shifts.

Physics Q31–60

  1. Q31A force is represented by F=ax2+bt12F=ax^2+bt^{\frac{1}{2}} where xx = distance and tt = time. The dimensions of b2/ab^2/a are:EasyUnits and Measurements
  2. Q32The relation between time 't' and distance 'x' is t=αx2+βxt=\alpha x^2+\beta x, where α\alpha and β\beta are constants. The relation between…MediumMotion in a Straight Line
  3. Q33A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ\mu. If the distance of the coin from the center of the…EasyLaws of Motion
  4. Q34In the given arrangement of a doubly inclined plane two blocks of masses MM and mm are placed. The blocks are connected by a light string passing…MediumLaws of Motion
  5. Q35An artillery piece of mass M1M_1 fires a shell of mass M2M_2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the…EasySystem of Particles and Rotational Motion
  6. Q36Four identical particles of mass mm are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other…EasyGravitation
  7. Q37A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity…EasyMechanical Properties of Fluids
  8. Q38The given figure represents two isobaric processes for the same mass of an ideal gas, thenEasyThermal Properties of Matter
  9. Q39The parameter that remains the same for molecules of all gases at a given temperature is :EasyKinetic Theory
  10. Q40Two charges qq and 3q3q are separated by a distance 'r ' in air. At a distance xx from charge qq, the resultant electric field is zero. The value…EasyElectric Charges and Fields
  11. Q41Two conductors have the same resistances at 0∘0^\circC but their temperature coefficients of resistance are α1\alpha_1 and α2\alpha_2. The…MediumCurrent Electricity
  12. Q42A rigid wire consists of a semicircular portion of radius RR and two straight sections. The wire is partially immerged in a perpendicular magnetic…MediumMoving Charges and Magnetism
  13. Q43A 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…EasyElectromagnetic Induction
  14. Q44In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5×10105\times10^{10} Hz and an amplitude of 50 Vm−1^{-1}. The total…EasyElectromagnetic Waves
  15. Q45The refractive index of a prism with apex angle AA is cot⁡A/2\cot A/2. The angle of minimum deviation is :MediumRay Optics and Optical Instruments
  16. Q46When a metal surface is illuminated by light of wavelength λ\lambda, the stopping potential is 8V. When the same surface is illuminated by light of…MediumDual Nature of Radiation and Matter
  17. Q47If the wavelength of the first member of Lyman series of hydrogen is λ\lambda. The wavelength of the second member will beEasyAtoms
  18. Q48Identify the logic operation performed by the given circuit.EasySemiconductor Electronics: Materials, Devices and Simple Circuits
  19. Q49The 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…EasyWaves
  20. Q50If 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:EasyUnits and Measurements
  21. Q51A body starts falling freely from height HH hits an inclined plane in its path at height hh. As a result of this perfectly elastic impact, the…HardMotion in a PlaneNumerical
  22. Q52A 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…MediumSystem of Particles and Rotational MotionNumerical
  23. Q53The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ________ mm. (Take density of sea water…EasyMechanical Properties of SolidsNumerical
  24. Q54A particle performs simple harmonic motion with amplitude AA. Its speed is increased to three times at an instant when its displacement is…MediumOscillationsNumerical
  25. Q55A 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…MediumElectrostatic Potential and CapacitanceNumerical
  26. Q56Equivalent resistance of the following network is ________ Ω\Omega.MediumCurrent ElectricityNumerical
  27. Q57An electron moves through a uniform magnetic field B⃗=B0i^+2B0j^ T\vec{B}=B_0\hat{i}+2B_0\hat{j}\ T. At a particular instant of time, the velocity of electron is…MediumMoving Charges and MagnetismNumerical
  28. Q58A small square loop of wire of side ll is placed inside a large square loop of wire of side LL (L=l2L=l^2). The loops are coplanar and their centers…HardElectromagnetic InductionNumerical
  29. Q59Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is I1I_1 (b)…MediumWave OpticsNumerical
  30. Q60The mass defect in a particular reaction is 0.4g. The amount of energy liberated is n×107n\times10^7 kWh, where n=n= _______. (speed of light =…EasyNucleiNumerical

Chemistry Q61–90

  1. Q61The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining atomic orbitals A. have the same energy B.…EasyChemical Bonding and Molecular Structure
  2. Q62Identify the mixture that shows positive deviations from Raoult's LawMediumSolutions
  3. Q63For the given reaction, choose the correct expression of KC\mathrm{K_C} from the following :-…EasyEquilibrium
  4. Q64Identify the factor from the following that does not affect electrolytic conductance of a solution.EasyElectrochemistry
  5. Q65Integrated rate law equation for a first order gas phase reaction is given by (where Pi\mathrm{P_i} is initial pressure and Pt\mathrm{P_t} is total…MediumChemical Kinetics
  6. Q66The 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…MediumClassification of Elements and Periodicity in Properties
  7. Q67Consider the oxides of group 14 elements SiO2\mathrm{SiO_2}, GeO2\mathrm{GeO_2}, SnO2\mathrm{SnO_2}, PbO2\mathrm{PbO_2}, CO and GeO. The amphoteric oxides areMediumThe p-Block Elements
  8. Q68Identify correct statements from below: A. The chromate ion is square planar. B. Dichromates are generally prepared from chromates. C. The green…MediumThe d- and f-Block Elements
  9. Q69The 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:EasyThe d- and f-Block Elements
  10. Q70The correct statements from following are: A. The strength of anionic ligands can be explained by crystal field theory. B. Valence bond theory does…MediumCoordination Compounds
  11. Q71'Adsorption' principle is used for which of the following purification method?EasyOrganic Chemistry: Some Basic Principles and Techniques
  12. Q72Match List I with List II LIST I (Technique) A. Distillation B. Fractional distillation C. Steam distillation D. Distillation under reduced pressure…MediumOrganic Chemistry: Some Basic Principles and Techniques
  13. Q73Give below are two statements: Statement - I: Noble gases have very high boiling points. Statement - II: Noble gases are monoatomic gases. They are…EasyThe p-Block Elements
  14. Q74A species having carbon with sextet of electrons and can act as electrophile is calledEasyOrganic Chemistry: Some Basic Principles and Techniques
  15. Q75Given below are two statements: Statement I: IUPAC name of HO−CH2−(CH2)3−CH2−COCH3\mathrm{HO-CH_2-(CH_2)_3-CH_2-COCH_3} is 7-hydroxyheptan-2-one. Statement II:…EasyOrganic Chemistry: Some Basic Principles and Techniques
  16. Q76The product (C) in the below mentioned reaction is :…EasyHaloalkanes and Haloarenes
  17. Q77Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: pKa\mathrm{pK_a} value of phenol…EasyAlcohols, Phenols and Ethers
  18. Q78Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Alcohols react both as…MediumAlcohols, Phenols and Ethers
  19. Q79Match List I with List II LIST I A. Glucose/NaHCO3\mathrm{NaHCO_3}/Δ\Delta B. Glucose/HNO3\mathrm{HNO_3} C. Glucose/HI/Δ\Delta D. Glucose/Bromine water…MediumBiomolecules
  20. Q80The compound that is white in color isEasyPractical Chemistry (Qualitative Analysis)
  21. Q81Number of moles of methane required to produce 22g CO2(g)\mathrm{CO_{2(g)}} after combustion is x×10−2\mathrm{x}\times10^{-2} moles. The value of x is…EasySome Basic Concepts of ChemistryNumerical
  22. Q82The ionization energy of sodium in kJ mol−1^{-1}, if electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom is…MediumStructure of AtomNumerical
  23. Q83The number of species from the following in which the central atom uses sp3\mathrm{sp^3} hybrid orbitals in its bonding is _________.…MediumChemical Bonding and Molecular StructureNumerical
  24. Q84Consider the following reaction at 298 K. 32O2(g)⇌O3(g)\frac{3}{2}\mathrm{O_{2(g)}} \rightleftharpoons \mathrm{O_{3(g)}}. Kp=2.47×10−29\mathrm{K_p} = 2.47\times10^{-29}.…EasyThermodynamics (Chemistry)Numerical
  25. Q85One Faraday of electricity liberates x×10−1x\times10^{-1} gram atom of copper from copper sulphate. xx is _________.EasyElectrochemistryNumerical
  26. Q86The 'Spin only' Magnetic moment for [Ni(NH3)6]2+[\mathrm{Ni(NH_3)_6}]^{2+} is _________ ×10−1\times10^{-1} BM. (given = Atomic number of Ni : 28)EasyCoordination CompoundsNumerical
  27. Q87Number of alkanes obtained on electrolysis of a mixture of CH3COONa\mathrm{CH_3COONa} and C2H5COONa\mathrm{C_2H_5COONa} is _________.MediumHydrocarbonsNumerical
  28. Q88CH3CH2Br+NaOH\mathrm{CH_3CH_2Br + NaOH} with C2H5OH\mathrm{C_2H_5OH} gives Product A, and with H2O\mathrm{H_2O} gives Product B. The total number of hydrogen atoms…EasyHaloalkanes and HaloarenesNumerical
  29. Q89The product of the following reaction is P. 4-Hydroxybenzaldehyde, (i) PhMgBr (1 equiv.), (ii) aq. NH4Cl\mathrm{NH_4Cl}, gives P The number of hydroxyl…MediumAldehydes, Ketones and Carboxylic AcidsNumerical
  30. Q90Molar mass of the salt from NaBr\mathrm{NaBr}, NaNO3\mathrm{NaNO_3}, KI\mathrm{KI} and CaF2\mathrm{CaF_2} which does not evolve coloured vapours on heating…EasyPractical Chemistry (Qualitative Analysis)Numerical

Maths Q1–30

  1. Q1If f(x)=4x+36x−4, x≠23f(x)=\frac{4x+3}{6x-4},\ x\neq\frac{2}{3} and (f∘f)(x)=g(x)(f\circ f)(x)=g(x), where…MediumRelations and Functions
  2. Q2Let S be the set of postive integral values of aa for which ax2+2(a+1)x+9a+4x2−8x+32<0, ∀x∈R\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}<0,\ \forall x\in\mathbb{R}. Then, the number of…EasyComplex Numbers and Quadratic Equations
  3. Q3If f(x)=∣x32x2+11+3x3x2+22xx3+6x3−x4x2−2∣f(x)=\begin{vmatrix}x^3 & 2x^2+1 & 1+3x\\ 3x^2+2 & 2x & x^3+6\\ x^3-x & 4 & x^2-2\end{vmatrix} for all x∈Rx\in\mathbb{R}, then 2f(0)+f′(0)2f(0)+f'(0) is…MediumDeterminants
  4. Q4If the system of linear equations x−2y+z=−4x-2y+z=-4 2x+αy+3z=52x+\alpha y+3z=5 3x−y+βz=33x-y+\beta z=3 has infinitely many solutions, then 12α+13β12\alpha+13\beta is equal toMediumDeterminants
  5. Q5The sum of the series 11−3⋅12+14+21−3⋅22+24+31−3⋅32+34+…\frac{1}{1-3\cdot1^2+1^4}+\frac{2}{1-3\cdot2^2+2^4}+\frac{3}{1-3\cdot3^2+3^4}+\ldots up to 10-terms isMediumSequences and Series
  6. Q6lim⁡x→0e2∣sin⁡x∣−2∣sin⁡x∣−1x2\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}MediumLimits and Derivatives
  7. Q7Let aa be the sum of all coefficients in the expansion of (1−2x+2x2)2023(3−4x2+2x3)2024(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024} and…HardComplex Numbers and Quadratic Equations
  8. Q8For 0<c<b<a0<c<b<a, let (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 and α≠1\alpha\neq1 be one of its root. Then, among the two statements (I) If α∈(−1,0)\alpha\in(-1,0),…MediumComplex Numbers and Quadratic Equations
  9. Q9Let g(x)g(x) be a linear funchion and f(x)={g(x),x≤0(1+x2+x)1x,x>0f(x)=\begin{cases}g(x), & x\leq0\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}, & x>0\end{cases} is continuous…HardContinuity and Differentiability
  10. Q10The area of the region {(x,y):y2≤4x, x<4, xy(x−1)(x−2)(x−3)(x−4)>0, x≠3}\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\} isHardApplication of Integrals
  11. Q11Let y=y(x)y=y(x) be the solution of the differential equation…HardDifferential Equations
  12. Q12The solution curve of the differential equation ydxdy=x(log⁡ex−log⁡ey+1), x>0, y>0y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0 passing through the point (e,1)(e,1) isMediumDifferential Equations
  13. Q13If one of the diameters of the circle x2+y2−10x+4y+13=0x^2+y^2-10x+4y+13=0 is a chord of another circle C, whose center is the point of intersection of the lines…MediumConic Sections
  14. Q14Let α,β,γ,δ∈Z\alpha,\beta,\gamma,\delta\in\mathbb{Z} and let A(α,β)A(\alpha,\beta), B(1,0)B(1,0), C(γ,δ)C(\gamma,\delta) and D(1,2)D(1,2) be the vertices of a…MediumStraight Lines
  15. Q15The distance of the point Q(0,2,−2)Q(0,2,-2) form the line passing through the point P(5,−4,3)P(5,-4,3) and perpendicular to the lines…MediumThree Dimensional Geometry
  16. Q16If the foci of a hyperbola are same as that of the ellipse x29+y225=1\frac{x^2}{9}+\frac{y^2}{25}=1 and the eccentricity of the hyperbola is 158\frac{15}{8}…HardConic Sections
  17. Q17Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable xx to be the number of rotten apples in a draw of…MediumProbability
  18. Q18Let a⃗=3i^+j^−2k^\vec{a}=3\hat{i}+\hat{j}-2\hat{k}, b⃗=4i^+j^+7k^\vec{b}=4\hat{i}+\hat{j}+7\hat{k} and c⃗=i^−3j^+4k^\vec{c}=\hat{i}-3\hat{j}+4\hat{k} be three vectors. If a vectors…MediumVector Algebra
  19. Q19Two 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…EasyProbability
  20. Q20For α,β,γ≠0\alpha,\beta,\gamma\neq0, if sin⁡−1α+sin⁡−1β+sin⁡−1γ=π\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi and…HardInverse Trigonometric Functions
  21. Q21Let A={1,2,3,4}A=\{1,2,3,4\} and R={(1,2),(2,3),(1,4)}R=\{(1,2),(2,3),(1,4)\} be a relation on A. Let S be the equivalence relation on A such that R⊂SR\subset S and the number…MediumRelations and FunctionsNumerical
  22. Q22If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1-i|^x=2^x and β=(∣z∣arg⁡(z))\beta=\left(\frac{|z|}{\arg(z)}\right), where…MediumComplex Numbers and Quadratic EquationsNumerical
  23. Q23The 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…MediumPermutations and CombinationsNumerical
  24. Q24In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5, x≠0(1+x)(1-x^2)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5,\ x\neq0, the sum of the coefficients of x3x^3 and…MediumBinomial TheoremNumerical
  25. Q25Let S=(−1,∞)S=(-1,\infty) and f:S→Rf:S\to\mathbb{R} be defined as f(x)=∫−1x(et−1)11(2t−1)5(t−2)7(t−3)12(2t−10)61 dtf(x)=\int_{-1}^{x}(e^t-1)^{11}(2t-1)^5(t-2)^7(t-3)^{12}(2t-10)^{61}\,dt, Let p = Sum of…HardApplication of DerivativesNumerical
  26. Q26Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a function defined by f(x)=4x4x+2f(x)=\frac{4^x}{4^x+2} and…HardIntegralsNumerical
  27. Q27If the integral 525∫0π2sin⁡2xcos⁡112x(1+cos⁡52x)12dx525\int_0^{\frac{\pi}{2}}\sin2x\cos^{\frac{11}{2}}x\left(1+\cos^{\frac{5}{2}}x\right)^{\frac{1}{2}}dx is equal to…HardIntegralsNumerical
  28. Q28Let the foci and length of the latus rectum of an ellipse x2a2+y2b2=1, a>b\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b be (±5,0)(\pm5,0) and 50\sqrt{50}, respectively.…MediumConic SectionsNumerical
  29. Q29Let Q and R be the feet of perpendiculars from the point P(a,a,a)P(a,a,a) on the lines x=y, z=1x=y,\ z=1 and x=−y, z=−1x=-y,\ z=-1 respectively. If ∠QPR\angle QPR is a…MediumThree Dimensional GeometryNumerical
  30. Q30Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣a⃗∣=1, ∣b⃗∣=4|\vec{a}|=1,\ |\vec{b}|=4, and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2. If…MediumVector AlgebraNumerical

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2024 shifts.