Learn

Friday, 9 October

JEE Main 2024 · January session

JEE Main 31 January 2024, Shift 2

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 12 were rated hard and 25 easy. By hard questions it ranks 3rd of the 8 2024 shifts Lumi analysed. The biggest chapter was Amines, with 3 questions.

Questions
89
1 dropped by NTA
Numerical answer
30
34% of the shift
Hard
12
13% of the shift
Chapters asked
61
14 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
29 Q · 10 numerical
Easy 13Medium 16Hard 0

Top chapters

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

Top chapters

Maths
30 Q · 10 numerical
Easy 3Medium 17Hard 10

Top chapters

Question format
  • Single correct44 Q
  • Numerical value30 Q
  • Diagram based7 Q
  • Two statements4 Q
  • Other3 Q
  • Match the list1 Q
What each question asks you to do
  • Multi-step27 Q
  • Calculation27 Q
  • Application15 Q
  • Conceptual11 Q
  • Recall7 Q
  • Diagram reading1 Q
  • Data or graph1 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. Q31Consider two physical quantities AA and BB related to each other as E=B−x2AtE=\frac{B-x^2}{At} where EE, xx and tt have dimensions of energy, length…MediumUnits and Measurements
  2. Q32If two vectors A⃗\vec{A} and B⃗\vec{B} having equal magnitude RR are inclined at an angle θ\theta, thenEasyMotion in a Plane
  3. Q33A light string passing over a smooth light fixed pulley connects two blocks of masses m1m_1 and m2m_2. If the acceleration of the system is g/8g/8,…EasyLaws of Motion
  4. Q34A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If F1⃗\vec{F_1} is the force required to just move the block up…MediumLaws of MotionDropped
  5. Q35A body of mass 2 kg begins to move under the action of a time dependent force given by F⃗=(6t i^+6t2 j^)\vec{F}=\left(6t\,\hat{i}+6t^2\,\hat{j}\right) N. The power…MediumWork, Energy and Power
  6. Q36The mass of the moon is 1144\frac{1}{144} times the mass of a planet and its diameter is 116\frac{1}{16} times the diameter of a planet. If the escape…EasyGravitation
  7. Q37A small spherical ball of radius rr, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same…MediumMechanical Properties of Fluids
  8. Q38The speed of sound in oxygen at S.T.P. will be approximately: (given, R=8.3 JK−1R=8.3\ \mathrm{JK^{-1}}, γ=1.4\gamma=1.4)MediumWaves
  9. Q39A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of…EasyThermodynamics
  10. Q40Force between two point charges q1q_1 and q2q_2 placed in vacuum at 'r' cm apart is FF. Force between them when placed in a medium having…EasyElectric Charges and Fields
  11. Q41By what percentage will the illumination of the lamp decrease if the current drops by 20%?EasyCurrent Electricity
  12. Q42A uniform magnetic field of 2×10−32\times10^{-3} T acts along positive YY-direction. A rectangular loop of sides 20 cm and 10 cm with current of 5 A is…MediumMoving Charges and Magnetism
  13. Q43An AC voltage V=20sin⁡200πtV=20\sin 200\pi t is applied to a series LCR circuit which drives a current I=10sin⁡(200πt+π3)I=10\sin\left(200\pi t+\frac{\pi}{3}\right). The…EasyAlternating Current
  14. Q44Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by…EasyElectromagnetic Waves
  15. Q45When unpolarized light is incident at an angle of 60∘60^\circ on a transparent medium from air, the reflected ray is completely polarized. The angle…EasyWave Optics
  16. Q46In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive…EasyDual Nature of Radiation and Matter
  17. Q47The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:EasyNuclei
  18. Q48The output of the given circuit diagram is -MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  19. Q49The resistance per centimeter of a meter bridge wire is rr, with X ΩX\ \Omega resistance in left gap. Balancing length from left end is at 40 cm…MediumCurrent Electricity
  20. Q50The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1…MediumUnits and Measurements
  21. Q51A body of mass 'mm' is projected with a speed 'uu' making an angle of 45∘45^\circ with the ground. The angular momentum of the body about the point…MediumMotion in a PlaneNumerical
  22. Q52Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm.…MediumSystem of Particles and Rotational MotionNumerical
  23. Q53Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is…MediumMechanical Properties of SolidsNumerical
  24. Q54The time period of simple harmonic motion of mass MM in the given figure is παM5k\pi\sqrt{\frac{\alpha M}{5k}}, where the value of α\alpha is…MediumOscillationsNumerical
  25. Q55The distance between charges +q+q and −q-q is 2l2l and between +2q+2q and −2q-2q is 4l4l. The electrostatic potential at point PP at a distance rr…MediumElectrostatic Potential and CapacitanceNumerical
  26. Q56In the following circuit, the battery has an emf of 2V and an internal resistance of 23Ω\frac{2}{3}\Omega. The power consumption in the entire…MediumCurrent ElectricityNumerical
  27. Q57Two circular coils PP and QQ of 100 turns each have same radius of π\pi cm. The currents in PP and RR are 1A1A and 2A2A respectively. PP and…MediumMoving Charges and MagnetismNumerical
  28. Q58The magnetic flux ϕ\phi (in weber) linked with a closed circuit of resistance 8 Ω8\ \Omega varies with time (in seconds) as ϕ=5t2−36t+1\phi=5t^2-36t+1. The…EasyElectromagnetic InductionNumerical
  29. Q59Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from…MediumRay Optics and Optical InstrumentsNumerical
  30. Q60A nucleus has mass number A1A_1 and volume V1V_1. Another nucleus has mass number A2A_2 and Volume V2V_2. If relation between mass number is…EasyNucleiNumerical

Chemistry Q61–90

  1. Q61A sample of CaCO3\mathrm{CaCO_3} and MgCO3\mathrm{MgCO_3} weighed 2.21 g is ignited to constant weight of 1.152 g. The composition of mixture is : (Given…MediumSome Basic Concepts of Chemistry
  2. Q62The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) areEasyStructure of Atom
  3. Q63Which of the following is least ionic?MediumChemical Bonding and Molecular Structure
  4. Q64A(g)⇌B(g)+C2(g)\mathrm{A_{(g)}\rightleftharpoons B_{(g)}+\frac{C}{2}{}_{(g)}} The correct relationship between Kp\mathrm{K_p}, α\alpha and equilibrium pressure…MediumEquilibrium
  5. Q65Given below are two statements : Statement I : S8\mathrm{S_8} solid undergoes disproportionation reaction under alkaline conditions to form…MediumRedox Reactions
  6. Q66Consider the following elements. Group ↓\downarrow A' B' →\rightarrow Period C' D' Which of the following is/are true about A', B', C' and D'? A.…MediumClassification of Elements and Periodicity in Properties
  7. Q67Given below are two statements : Statement I : Group 13 trivalent halides get easily hydrolyzed by water due to their covalent nature. Statement II…MediumThe p-Block Elements
  8. Q68Choose the correct statements from the following A. All group 16 elements form oxides of general formula EO2\mathrm{EO_2} and EO3\mathrm{EO_3}, where…MediumThe p-Block Elements
  9. Q69Choose the correct statements from the following A. Mn2O7\mathrm{Mn_2O_7} is an oil at room temperature B. V2O4\mathrm{V_2O_4} reacts with acid to give…MediumThe d- and f-Block Elements
  10. Q70Select the option with correct property -MediumCoordination Compounds
  11. Q71Match List I with List II LIST I (Complex ion) | LIST II (Electronic Configuration) A. [Cr(H2O)6]3+\mathrm{[Cr(H_2O)_6]^{3+}} | I. t2g2eg0t_{2g}^{2}e_g^{0} B.…MediumCoordination Compounds
  12. Q72The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in…EasyOrganic Chemistry: Some Basic Principles and Techniques
  13. Q73The correct order of reactivity in electrophilic substitution reaction of the following compounds is :EasyHydrocarbons
  14. Q74Identify structure of 2,3-dibromo-1-phenylpentane.EasyHaloalkanes and Haloarenes
  15. Q75Major product of the following reaction is -HardHydrocarbons
  16. Q76Identify A and B in the following reaction sequence. [reaction: bromobenzene --(Conc HNO3_3)--> A --((i) NaOH, (ii) HCl)--> B]HardHaloalkanes and Haloarenes
  17. Q77Identify major product 'P' formed in the following reaction. [reaction: benzene + benzoyl chloride (C6_6H5_5COCl) --(Anhydrous AlCl3_3)--> 'P'…EasyAldehydes, Ketones and Carboxylic Acids
  18. Q78Identify the name reaction. [reaction: benzene + CO, HCl --(anhydrous AlCl3_3/CuCl)--> benzaldehyde (C6_6H5_5CHO)]EasyAldehydes, Ketones and Carboxylic Acids
  19. Q79Given below are two statements : Statement I : Aniline reacts with con. H2SO4\mathrm{H_2SO_4}, followed by heating at 453 - 473 K gives p-aminobenzene…MediumAmines
  20. Q80The azo-dye (Y) formed in the following reactions is Sulphanilic acid + NaNO2\mathrm{NaNO_2} + CH3COOH\mathrm{CH_3COOH} →\rightarrow X. X + 1-naphthylamine…MediumAmines
  21. Q81A diatomic molecule has a dipole moment of 1.2 D. If the bond distance is 1A°, then fractional charge on each atom is ________ ×10−1\times 10^{-1} esu.…MediumChemical Bonding and Molecular StructureNumerical
  22. Q82If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is −x-x J. The…EasyThermodynamics (Chemistry)Numerical
  23. Q83The molarity of 1 L orthophosphoric acid (H3PO4\mathrm{H_3PO_4}) having 70% purity by weight (specific gravity 1.54 g cm−3^{-3}) is _________ M. (Molar…EasySome Basic Concepts of ChemistryNumerical
  24. Q84The values of conductivity of some materials at 298.15 K in Sm−1^{-1} are 2.1×1032.1 \times 10^{3}, 1.0×10−161.0 \times 10^{-16}, 1.2×101.2 \times 10, 3.913.91,…MediumThe Solid StateNumerical
  25. Q85r = k [A] for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is _________ minutes.MediumChemical KineticsNumerical
  26. Q86Number of moles of H+\mathrm{H^+} ions required by 1 mole of MnO4−\mathrm{MnO_4^-} to oxidise oxalate ion to CO2\mathrm{CO_2} is ________.MediumRedox ReactionsNumerical
  27. Q87Number of isomeric products formed by monochlorination of 2-methylbutane in presence of sunlight is __________.MediumHydrocarbonsNumerical
  28. Q88A compound (xx) with molar mass 108 g mol−1^{-1} undergoes acetylation to give product with molar mass 192 g mol−1^{-1}. The number of amino groups…MediumAminesNumerical
  29. Q89From the vitamins A, B1\mathrm{B_1}, B6\mathrm{B_6}, B12\mathrm{B_{12}}, C, D, E and K, the number of vitamins that can be stored in our body…MediumBiomoleculesNumerical
  30. Q90In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is…EasyThe d- and f-Block ElementsNumerical

Maths Q1–30

  1. Q1If the function f:(−∞,−1]→(a,b]f:(-\infty,-1]\to(a,b] defined by f(x)=ex3−3x+1f(x)=e^{x^3-3x+1} is one - one and onto, then the distance of the point P(2b+4, a+2)P(2b+4,\,a+2) from…MediumApplication of Derivatives
  2. Q2The number of solutions, of the equation esin⁡x−2e−sin⁡x=2e^{\sin x}-2e^{-\sin x}=2, is :MediumTrigonometric Functions
  3. Q3Let z1z_1 and z2z_2 be two complex numbers such that z1+z2=5z_1+z_2=5 and z13+z23=20+15iz_1^3+z_2^3=20+15i. Then, ∣z14+z24∣|z_1^4+z_2^4| equals -HardComplex Numbers and Quadratic Equations
  4. Q4Let AA be a 3×33\times3 real matrix such that A(101)=2(101)A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix},…MediumDeterminants
  5. Q5The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isEasyPermutations and Combinations
  6. Q6If for some m,nm,n; 6Cm+2(6Cm+1)+6Cm+2>8C3{}^6C_m+2\left({}^6C_{m+1}\right)+{}^6C_{m+2}>{}^8C_3 and n−1P3:nP4=1:8{}^{n-1}P_3:{}^nP_4=1:8, then nPm+1+n+1Cm{}^nP_{m+1}+{}^{n+1}C_m is equal toMediumPermutations and Combinations
  7. Q7Let 2nd2^{nd}, 8th8^{th} and 44th44^{th} terms of a non-constant A. P. be respectively the 1st1^{st}, 2nd2^{nd} and 3rd3^{rd} terms of a G. P. If the first…MediumSequences and Series
  8. Q8Consider the function f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} defined by f(x)=e−∣log⁡ex∣f(x)=e^{-|\log_e x|}. If mm and nn be respectively the number of points at which…MediumContinuity and Differentiability
  9. Q9Let f:R→(0,∞)f:\mathbb{R}\to(0,\infty) be strictly increasing function such that lim⁡x→∞f(7x)f(x)=1\lim_{x\to\infty}\frac{f(7x)}{f(x)}=1. Then, the value of…HardContinuity and Differentiability
  10. Q10Let a variable line passing through the centre of the circle x2+y2−16x−4y=0x^2+y^2-16x-4y=0, meet the positive co-ordinate axes at the points AA and BB. Then…MediumConic Sections
  11. Q11The area of the region enclosed by the parabolas y=4x−x2y=4x-x^2 and 3y=(x−4)23y=(x-4)^2 is equal toMediumApplication of Integrals
  12. Q12Let f,g:(0,∞)→Rf,g:(0,\infty)\to\mathbb{R} be two functions defined by f(x)=∫−xx(∣t∣−t2)e−t2dtf(x)=\int_{-x}^{x}\left(|t|-t^2\right)e^{-t^2}dt and…HardIntegrals
  13. Q13The temperature T(t)T(t) of a body at time t=0t=0 is 160∘160^\circ F and it decreases continuously as per the differential equation…EasyDifferential Equations
  14. Q14Let PP be a parabola with vertex (2,3)(2,3) and directrix 2x+y=62x+y=6. Let an ellipse E:x2a2+y2b2=1, a>bE:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b, of eccentricity…HardConic Sections
  15. Q15Let A(a,b)A(a,b), B(3,4)B(3,4) and C(−6,−8)C(-6,-8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point…MediumStraight Lines
  16. Q16Let (α,β,γ)(\alpha,\beta,\gamma) be the mirror image of the point (2,3,5)(2,3,5) in the line x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}. Then,…MediumThree Dimensional Geometry
  17. Q17The shortest distance, between lines L1L_1 and L2L_2, where L1:x−12=y+1−3=z+42L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2} and L2L_2 is the line, passing through…MediumThree Dimensional Geometry
  18. Q18Let the mean and the variance of 6 observations a,b,68,44,48,60a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a>ba>b, then a+3ba+3b isMediumStatistics
  19. Q19A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and…EasyProbability
  20. Q20If a=sin⁡−1(sin⁡(5))a=\sin^{-1}(\sin(5)) and b=cos⁡−1(cos⁡(5))b=\cos^{-1}(\cos(5)), then a2+b2a^2+b^2 is equal toMediumInverse Trigonometric Functions
  21. Q21Let A={1,2,3,…,100}A=\{1,2,3,\ldots,100\}. Let RR be a relation on AA defined by (x,y)∈R(x,y)\in R if and only if 2x=3y2x=3y. Let R1R_1 be a symmetric relation on AA…MediumRelations and FunctionsNumerical
  22. Q22Let A be a 3×33\times3 matrix and det⁡(A)=2\det(A)=2. If…MediumDeterminantsNumerical
  23. Q23Let the coefficient of xrx^r in the expansion of (x+3)n−1+(x+3)n−2(x+2)+(x+3)n−3(x+2)2+…+(x+2)n−1(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1} be αr\alpha_r. If…HardBinomial TheoremNumerical
  24. Q24Let a,b,ca, b, c be the lengths of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c)x+(b2+c2)=0(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0. If the set of all possible…HardComplex Numbers and Quadratic EquationsNumerical
  25. Q25If lim⁡x→0ax2ex−blog⁡e(1+x)+cxe−xx2sin⁡x=1\lim_{x\to0}\frac{ax^2e^x-b\log_e(1+x)+cxe^{-x}}{x^2\sin x}=1, then 16(a2+b2+c2)16(a^2+b^2+c^2) is equal to ________.HardLimits and DerivativesNumerical
  26. Q26∣120π3∫0πx2sin⁡xcos⁡xsin⁡4x+cos⁡4xdx∣\left|\frac{120}{\pi^3}\int_0^{\pi}\frac{x^2\sin x\cos x}{\sin^4x+\cos^4x}dx\right| is equal to ____________.HardIntegralsNumerical
  27. Q27Let y=y(x)y=y(x) be the solution of the differential equation sec⁡2x dx+(e2ytan⁡2x+tan⁡x)dy=0\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0, 0<x<π20<x<\frac{\pi}{2},…HardDifferential EquationsNumerical
  28. Q28Let A(−2,−1)A(-2,-1), B(1,0)B(1,0), C(α,β)C(\alpha,\beta) and D(γ,δ)D(\gamma,\delta) be the vertices of a parallelogram ABCDABCD. If the point CC lies on 2x−y=52x-y=5 and…MediumStraight LinesNumerical
  29. Q29A line passes through A(4,−6,−2)A(4,-6,-2) and B(16,−2,4)B(16,-2,4). The point P(a,b,c)P(a,b,c), where a,b,ca, b, c are non-negative integers, on the line ABAB lies at a…MediumThree Dimensional GeometryNumerical
  30. Q30Let a⃗=3i^+2j^+k^\vec{a}=3\hat{i}+2\hat{j}+\hat{k}, b⃗=2i^−j^+3k^\vec{b}=2\hat{i}-\hat{j}+3\hat{k} and c⃗\vec{c} be a vector such that…HardVector 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.