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Friday, 9 October

JEE Main 2024 · April session

JEE Main 8 April 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 8 were rated hard and 28 easy. By hard questions it ranks 8th of the 8 2024 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 3 questions.

Questions
90
none dropped
Numerical answer
30
33% of the shift
Hard
8
9% of the shift
Chapters asked
59
19 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 16Medium 13Hard 1

Top chapters

Chemistry
30 Q · 10 numerical
Easy 10Medium 19Hard 1

Top chapters

Maths
30 Q · 10 numerical
Easy 2Medium 22Hard 6

Top chapters

Question format
  • Single correct44 Q
  • Numerical value30 Q
  • Diagram based5 Q
  • Match the list4 Q
  • Two statements3 Q
  • Other3 Q
  • Assertion–reason1 Q
What each question asks you to do
  • Multi-step33 Q
  • Calculation24 Q
  • Application13 Q
  • Conceptual9 Q
  • Recall8 Q
  • Data or graph2 Q
  • Diagram reading1 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. Q31In an expression a×10ba\times10^b:EasyUnits and Measurements
  2. Q32A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel xx distance more…EasyMotion in a Plane
  3. Q33A stationary particle breaks into two parts of masses mAm_A and mBm_B which move with velocities vAv_A and vBv_B respectively. The ratio of their…EasySystem of Particles and Rotational Motion
  4. Q34A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force…EasyLaws of Motion
  5. Q35Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :EasyWork, Energy and Power
  6. Q36Correct Bernoulli's equation is (symbols have their usual meaning) :EasyMechanical Properties of Fluids
  7. Q37Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio…MediumThermodynamics
  8. Q38Two planets A and B having masses m1m_1 and m2m_2 move around the sun in circular orbits of r1r_1 and r2r_2 radii respectively. If angular momentum…HardGravitation
  9. Q39A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27∘27^\circC). The ratio of specific…EasyKinetic Theory
  10. Q40In the given circuit, the terminal potential difference of the cell is :EasyCurrent Electricity
  11. Q41Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field.…MediumMagnetism and Matter
  12. Q42Average force exerted on a non-reflecting surface at normal incidence is 2.4×10−42.4\times10^{-4} N. If 360 W/cm2^2 is the light energy flux during span…MediumElectromagnetic Waves
  13. Q43Critical angle of incidence for a pair of optical media is 45∘45^\circ. The refractive indices of first and second media are in the ratio:EasyRay Optics and Optical Instruments
  14. Q44A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h=6.63×10−34h=6.63\times10^{-34} J s,…EasyDual Nature of Radiation and Matter
  15. Q45Two charged conducting spheres of radii aa and bb are connected to each other by a conducting wire. The ratio of charges of the two spheres…EasyElectrostatic Potential and Capacitance
  16. Q46Binding energy of a certain nucleus is 18×10818\times10^8 J. How much is the difference between total mass of all the nucleons and nuclear mass of the…EasyNuclei
  17. Q47The output Y of following circuit for given inputs is :MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  18. Q48Young's modulus is determined by the equation given by Y=49000mldynecm2Y=49000\frac{m}{l}\frac{\mathrm{dyne}}{\mathrm{cm}^2} where MM is the mass and ll is the…MediumUnits and Measurements
  19. Q49The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The…MediumUnits and Measurements
  20. Q50A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters…EasyAlternating Current
  21. Q51Three vectors OP→\overrightarrow{OP}, OQ→\overrightarrow{OQ} and OR→\overrightarrow{OR} each of magnitude AA are acting as shown in figure. The…EasyMotion in a PlaneNumerical
  22. Q52A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of xx and yy coordinates of center of mass of plate in n9\frac{n}{9}.…MediumSystem of Particles and Rotational MotionNumerical
  23. Q53A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is…MediumMechanical Properties of FluidsNumerical
  24. Q54A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is (a−1a)\left(\frac{a-1}{a}\right) then the…MediumWavesNumerical
  25. Q55An electric field, E⃗=2i^+6j^+8k^6\vec{E}=\frac{2\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{6}} passes through the surface of 4 m2^2 area having unit vector…EasyElectric Charges and FieldsNumerical
  26. Q56Resistance of a wire at 0 ∘0\,^\circC, 100 ∘100\,^\circC and t ∘t\,^\circC is found to be 10 Ω10\ \Omega, 10.2 Ω10.2\ \Omega and 10.95 Ω10.95\ \Omega respectively.…MediumCurrent ElectricityNumerical
  27. Q57An electron with kinetic energy 5 eV enters a region of uniform magnetic field of 3 μ\muT perpendicular to its direction. An electric field E is…MediumMoving Charges and MagnetismNumerical
  28. Q58In an alpha particle scattering experiment distance of closest approach for the α\alpha particle is 4.5×10−144.5\times10^{-14} m. If target nucleus has…MediumAtomsNumerical
  29. Q59A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second…EasyWave OpticsNumerical
  30. Q60A square loop PQRS having 10 turns, area 3.6×10−3 m23.6\times10^{-3}\ \mathrm{m^2} and resistance 100 Ω100\ \Omega is slowly and uniformly being pulled out of a…MediumElectromagnetic InductionNumerical

Chemistry Q61–90

  1. Q61Combustion of glucose (C6H12O6\mathrm{C_6H_{12}O_6}) produces CO2\mathrm{CO_2} and water. The amount of oxygen (in g) required for the complete combustion…EasySome Basic Concepts of Chemistry
  2. Q62Match List I with List II LIST I (Molecule): A. NH3\mathrm{NH_3}; B. BrF5\mathrm{BrF_5}; C. PCl5\mathrm{PCl_5}; D. CH4\mathrm{CH_4} LIST II (Shape): I.…EasyChemical Bonding and Molecular Structure
  3. Q63For the given hypothetical reactions, the equilibrium constants are as follows : X⇌Y\mathrm{X\rightleftharpoons Y}; K1=1.0K_1=1.0…EasyEquilibrium
  4. Q64Thiosulphate reacts differently with iodine and bromine in the reactions given below:…MediumRedox Reactions
  5. Q65Among the following halogens F2\mathrm{F_2}, Cl2\mathrm{Cl_2}, Br2\mathrm{Br_2} and I2\mathrm{I_2} Which can undergo disproportionation reactions?EasyThe p-Block Elements
  6. Q66Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The stability order of +1…EasyThe p-Block Elements
  7. Q67Given below are two statements: Statement I: N(CH3)3\mathrm{N(CH_3)_3} and P(CH3)3\mathrm{P(CH_3)_3} can act as ligands to form transition metal complexes.…MediumCoordination Compounds
  8. Q68Match List I with List II LIST I (Elements): A. Cl, S; B. Ge, As; C. Fr, Ra; D. F, O LIST II (Properties in their respective groups): I. Elements…MediumClassification of Elements and Periodicity in Properties
  9. Q69Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. Fe3+\mathrm{Fe^{3+}} oxidises the iodide ion B. Fe3+\mathrm{Fe^{3+}}…MediumChemical Kinetics
  10. Q70An octahedral complex with the formula CoCl3⋅nNH3\mathrm{CoCl_3\cdot nNH_3} upon reaction with excess of AgNO3\mathrm{AgNO_3} solution gives 2 moles of AgCl.…MediumCoordination Compounds
  11. Q71Number of Complexes with even number of electrons in t2g\mathrm{t_{2g}} orbitals is - [Fe(H2O)6]2+[\mathrm{Fe(H_2O)_6}]^{2+}, [Co(H2O)6]2+[\mathrm{Co(H_2O)_6}]^{2+},…MediumCoordination Compounds
  12. Q72Match List I with List II LIST I (Name of the test): A. Borax bead test; B. Charcoal cavity test; C. Cobalt nitrate test; D. Flame test LIST II…MediumThe d- and f-Block Elements
  13. Q73Match List I with List II LIST I (Compound): A. Fe4[Fe(CN)6]3⋅xH2O\mathrm{Fe_4[Fe(CN)_6]_3\cdot xH_2O}; B. [Fe(CN)5NOS]4−[\mathrm{Fe(CN)_5NOS}]^{4-}; C.…MediumThe d- and f-Block Elements
  14. Q74Given below are two statements: Statement I: [figure: Compound A, a benzene ring bearing Cl, and two NO2\mathrm{NO_2} groups] IUPAC name of Compound…EasyOrganic Chemistry: Some Basic Principles and Techniques
  15. Q75In the given compound, the number of 2∘2^\circ carbon atom/s is ____________.…EasyOrganic Chemistry: Some Basic Principles and Techniques
  16. Q76Which of the following are aromatic? A. [figure: fused bicyclic ring system, two six-membered rings] B. [figure: benzene ring with a vinyl group] C.…MediumHaloalkanes and Haloarenes
  17. Q77Which among the following compounds will undergo fastest SN2\mathrm{S_N2} reaction.EasyHaloalkanes and Haloarenes
  18. Q78Identify the major products A and B respectively in the following set of reactions. [figure: 1-methylcyclohexan-1-ol (ring carbon bearing CH3 and…MediumAlcohols, Phenols and Ethers
  19. Q79Identify the product (P) in the following reaction: [figure: cyclopentanecarboxylic acid]…EasyAldehydes, Ketones and Carboxylic Acids
  20. Q80The incorrect statement regarding the given structure is [figure: Fischer projection: CHO at top; then H-C-OH, HO-C-H, H-C-OH, H-C-OH; CH2_2OH at…MediumBiomolecules
  21. Q81A hypothetical electromagnetic wave is show below. [figure: sinusoidal wave along an axis with a distance marked 1.5 pm between two dashed vertical…EasyStructure of AtomNumerical
  22. Q82Number of molecules from the following which are exceptions to octet rule is ___________.…MediumChemical Bonding and Molecular StructureNumerical
  23. Q83Consider the figure provided. 1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18∘18^\circ C. If the piston…MediumThermodynamics (Chemistry)Numerical
  24. Q84A solution containing 10 g of an electrolyte AB2\mathrm{AB_2} in 100 g of water boils at 100.52∘100.52^\circC. The degree of ionization of the electrolyte…MediumSolutionsNumerical
  25. Q85Consider the following reaction A+B→C\mathrm{A + B \rightarrow C} The time taken for A to become 1/4th1/4^{\mathrm{th}} of its initial concentration is…MediumChemical KineticsNumerical
  26. Q86The 'spin only' magnetic moment value of MO42−\mathrm{MO_4^{2-}} is ____________ BM. (Where M is a metal having least metallic radii. among Sc, Ti, V,…MediumThe d- and f-Block ElementsNumerical
  27. Q87If 279 g of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be ________ g.…MediumAminesNumerical
  28. Q88The number of optical isomers in following compound is:__________ [figure: three fused cyclohexane rings in a linear (anthracene-type) perhydro…HardHaloalkanes and HaloarenesNumerical
  29. Q89Major product B of the following reaction has _________ π\pi-bond. [figure: ethylbenzene (C6H5CH2CH3\mathrm{C_6H_5CH_2CH_3})]…MediumAldehydes, Ketones and Carboxylic AcidsNumerical
  30. Q90Number of amine compounds from the following giving solids which are soluble in NaOH upon reaction with Hinsberg's reagent is __________. [figure:…MediumAminesNumerical

Maths Q1–30

  1. Q1Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \to \mathbb{Z} be the…MediumRelations and Functions
  2. Q2Let zz be a complex number such that ∣z+2∣=1|z+2|=1 and Im(z+1z+2)=15\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}. Then the value of…MediumComplex Numbers and Quadratic Equations
  3. Q3The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}-16\cdot(8)^x+48=0 is :EasyComplex Numbers and Quadratic Equations
  4. Q4Let A=[2a013105b]A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}. If A3=4A2−A−21IA^3=4A^2-A-21I, where II is the identity matrix of order 3×33\times3, then 2a+3b2a+3b is…MediumMatrices
  5. Q5The equations of two sides AB and AC of a triangle ABC are 4x+y=144x+y=14 and 3x−2y=53x-2y=5, respectively. The point (2,−43)\left(2,-\frac{4}{3}\right) divides…MediumStraight Lines
  6. Q6If the set R={(a,b):a+5b=42,a,b∈N}R=\{(a,b): a+5b=42, a,b\in\mathbb{N}\} has mm elements and ∑n=1m(1−in!)=x+iy\sum_{n=1}^{m}\left(1-i^{n!}\right)=x+iy, where i=−1i=\sqrt{-1}, then the…MediumComplex Numbers and Quadratic Equations
  7. Q7For the function f(x)=(cos⁡x)−x+1f(x)=(\cos x)-x+1, x∈Rx\in\mathbb{R}, between the following two statements (S1) f(x)=0f(x)=0 for only one value of xx in [0,π][0,\pi].…MediumApplication of Derivatives
  8. Q8The number of critical points of the function f(x)=(x−2)2/3(2x+1)f(x)=(x-2)^{2/3}(2x+1) isMediumApplication of Derivatives
  9. Q9Let f(x)=4cos⁡3x+33cos⁡2x−10f(x)=4\cos^3x+3\sqrt{3}\cos^2x-10. The number of points of local maxima of ff in interval (0,2π)(0,2\pi) isHardApplication of Derivatives
  10. Q10Let I(x)=∫6sin⁡2x(1−cot⁡x)2dxI(x)=\int\frac{6}{\sin^2x(1-\cot x)^2}dx. If I(0)=3I(0)=3, then I(π12)I\left(\frac{\pi}{12}\right) is equal toMediumIntegrals
  11. Q11The value of k∈Nk\in\mathbb{N} for which the integral In=∫01(1−xk)ndxI_n=\int_0^1(1-x^k)^n dx, n∈Nn\in\mathbb{N}, satisfies 147I20=148I21147I_{20}=148I_{21} isHardIntegrals
  12. Q12Let f(x)f(x) be a positive function such that the area bounded by y=f(x)y=f(x), y=0y=0 from x=0x=0 to x=a>0x=a>0 is e−a+4a2+a−1e^{-a}+4a^2+a-1. Then the differential…HardDifferential Equations
  13. Q13Let y=y(x)y=y(x) be the solution of the differential equation (1+y2)etan⁡xdx+cos⁡2x (1+e2tan⁡x)dy=0(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0, y(0)=1y(0)=1. Then…MediumDifferential Equations
  14. Q14If the shortest distance between the lines L1:r⃗=(2+λ)i^+(1−3λ)j^+(3+4λ)k^L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k}, λ∈R\lambda\in\mathbb{R}…MediumThree Dimensional Geometry
  15. Q15Let the circles C1:(x−α)2+(y−β)2=r12C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2 and C2:(x−8)2+(y−152)2=r22C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2 touch each other externally at the point…MediumConic Sections
  16. Q16Let H:−x2a2+y2b2=1H:\frac{-x^2}{a^2}+\frac{y^2}{b^2}=1 be the hyperbola, whose eccentricity is 3\sqrt{3} and the length of the latus rectum is 434\sqrt{3}.…MediumConic Sections
  17. Q17Let P(x,y,z)P(x,y,z) be a point in the first octant, whose projection in the xyxy-plane is the point QQ. Let OP=γOP=\gamma; the angle between OQOQ and the…MediumThree Dimensional Geometry
  18. Q18The set of all α\alpha, for which the vectors a⃗=αti^+6j^−3k^\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k} and b⃗=ti^−2j^−2αtk^\vec{b}=t\hat{i}-2\hat{j}-2\alpha t\hat{k} are…MediumVector Algebra
  19. Q19Let the sum of two positive integers be 24. If the probability, that their product is not less than 34\frac{3}{4} times their greatest possible…MediumProbability
  20. Q20If sin⁡x=−35\sin x=-\frac{3}{5}, where π<x<3π2\pi<x<\frac{3\pi}{2}, then 80(tan⁡2x−cos⁡x)80(\tan^2x-\cos x) is equal toEasyTrigonometric Functions
  21. Q21If the range of f(θ)=sin⁡4θ+3cos⁡2θsin⁡4θ+cos⁡2θf(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}, θ∈R\theta\in\mathbb{R} is [α,β][\alpha,\beta], then the sum of…MediumTrigonometric FunctionsNumerical
  22. Q22Let A=[2−111]A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}. If the sum of the diagonal elements of A13A^{13} is 3n3^n, then nn is equal to ____________.MediumMatricesNumerical
  23. Q23The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible…MediumPermutations and CombinationsNumerical
  24. Q24Let α=∑r=0n(4r2+2r+1) nCr\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r and β=(∑r=0nnCrr+1)+1n+1\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}. If…HardBinomial TheoremNumerical
  25. Q25Let the positive integers be written in the form : 1 2 3 4 5 6 7 8 9 10 ... If the kthk^{\mathrm{th}} row contains exactly kk numbers for every…MediumSequences and SeriesNumerical
  26. Q26The value of lim⁡x→02(1−cos⁡xcos⁡2xcos⁡3x3⋯cos⁡10x10x2)\lim_{x\to0}2\left(\frac{1-\cos x\sqrt{\cos2x}\sqrt[3]{\cos3x}\cdots\sqrt[10]{\cos10x}}{x^2}\right) is ____________.MediumLimits and DerivativesNumerical
  27. Q27Let the area of the region enclosed by the curve y=min⁡{sin⁡x,cos⁡x}y=\min\{\sin x,\cos x\} and the xx-axis between x=−πx=-\pi to x=πx=\pi be AA. Then A2A^2 is equal…MediumApplication of IntegralsNumerical
  28. Q28Let a⃗=9i^−13j^+25k^\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}, b⃗=3i^+7j^−13k^\vec{b}=3\hat{i}+7\hat{j}-13\hat{k} and c⃗=17i^−2j^+k^\vec{c}=17\hat{i}-2\hat{j}+\hat{k} be three given vectors.…HardVector AlgebraNumerical
  29. Q29If the orthocentre of the triangle formed by the lines 2x+3y−1=02x+3y-1=0, x+2y−1=0x+2y-1=0 and ax+by−1=0ax+by-1=0, is the centroid of another triangle, whose…HardStraight LinesNumerical
  30. Q30Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables XX and YY respectively denote the number…MediumProbabilityNumerical

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.