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Friday, 9 October

JEE Main 2024 · April session

JEE Main 9 April 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 28 easy. By hard questions it ranks 5th of the 8 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions
90
none dropped
Numerical answer
30
33% of the shift
Hard
10
11% of the shift
Chapters asked
56
14 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 12Medium 15Hard 3

Top chapters

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

Top chapters

Maths
30 Q · 10 numerical
Easy 3Medium 21Hard 6

Top chapters

Question format
  • Single correct53 Q
  • Numerical value30 Q
  • Two statements3 Q
  • Assertion–reason3 Q
  • Other1 Q
What each question asks you to do
  • Multi-step45 Q
  • Calculation16 Q
  • Conceptual10 Q
  • Recall9 Q
  • Application9 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. Q31The dimensional formula of latent heat is :EasyUnits and Measurements
  2. Q32A particle moving in a straight line covers half the distance with speed 66 m/s. The other half is covered in two equal time intervals with speeds…MediumMotion in a Straight Line
  3. Q33A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ\theta with…EasySystem of Particles and Rotational Motion
  4. Q34A light unstretchable string passing over a smooth light pulley connects two blocks of masses m1m_1 and m2m_2. If the acceleration of the system is…EasyLaws of Motion
  5. Q35A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v=αxv=\alpha\sqrt{x}, where…EasyWork, Energy and Power
  6. Q36An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5318.5 km. From…MediumGravitation
  7. Q37A sphere of relative density σ\sigma and diameter D has concentric cavity of diameter d. The ratio of Dd\frac{D}{d}, if it just floats on water in…MediumMechanical Properties of Fluids
  8. Q38A sample of 11 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ=32\gamma=\frac{3}{2},…MediumThermodynamics
  9. Q39The volume of an ideal gas (γ=1.5\gamma=1.5) is changed adiabatically from 55 litres to 44 litres. The ratio of initial pressure to final pressure is :EasyThermodynamics
  10. Q40A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is…MediumElectrostatic Potential and Capacitance
  11. Q41The equivalent resistance between A and B is :MediumCurrent Electricity
  12. Q42Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the…HardElectromagnetic Waves
  13. Q43A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the…MediumAlternating Current
  14. Q44A plane EM wave is propagating along xx direction. It has a wavelength of 44 mm. If electric field is in yy direction with the maximum magnitude…MediumElectromagnetic Waves
  15. Q45Given below are two statements : Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the…MediumRay Optics and Optical Instruments
  16. Q46A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :EasyDual Nature of Radiation and Matter
  17. Q47The energy equivalent of 11 g of substance is :EasyNuclei
  18. Q48A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.421.42 eV. The wavelength of light emitted from the…EasySemiconductor Electronics: Materials, Devices and Simple Circuits
  19. Q49One main scale division of a vernier caliper is equal to m units. If nthn^{th} division of main scale coincides with (n+1)th(n+1)^{th} division of vernier…MediumUnits and Measurements
  20. Q50A galvanometer has a coil of resistance 200 Ω200\ \Omega with a full scale deflection at 20 μ20\ \muA. The value of resistance to be added to use it as…EasyMoving Charges and Magnetism
  21. Q51If a⃗\vec{a} and b⃗\vec{b} makes an angle cos⁡−1(59)\cos^{-1}\left(\frac{5}{9}\right) with each other, then ∣a⃗+b⃗∣=2 ∣a⃗−b⃗∣|\vec{a}+\vec{b}|=\sqrt{2}\,|\vec{a}-\vec{b}|…MediumMotion in a PlaneNumerical
  22. Q52A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm20.40\ \mathrm{kgm^2} and radius 1010 cm. The wheel is free to rotate about its…EasySystem of Particles and Rotational MotionNumerical
  23. Q53Two persons pull a wire towards themselves. Each person exerts a force of 200200 N on the wire. Young's modulus of the material of wire is…EasyMechanical Properties of SolidsNumerical
  24. Q54The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 44 m, 2 ms−12\ \mathrm{ms^{-1}}…MediumOscillationsNumerical
  25. Q55At the centre of a half ring of radius R=10R=10 cm and linear charge density 4 nC m−14\ \mathrm{nC\,m^{-1}}, the potential is xπx\pi V. The value of xx is…EasyElectrostatic Potential and CapacitanceNumerical
  26. Q56The current flowing through the 1 Ω1\ \Omega resistor is n10\frac{n}{10} A. The value of n is ________.MediumCurrent ElectricityNumerical
  27. Q57A square loop of edge length 22 m carrying current of 22 A is placed with its edges parallel to the xx-yy axis. A magnetic field is passing…HardMoving Charges and MagnetismNumerical
  28. Q58When a coil is connected across a 2020 V dc supply, it draws a current of 55 A. When it is connected across 2020 V, 5050 Hz ac supply, it draws a…MediumAlternating CurrentNumerical
  29. Q59In a Young's double slit experiment, the intensity at a point is (14)th\left(\frac{1}{4}\right)^{th} of the maximum intensity, the minimum distance of…MediumWave OpticsNumerical
  30. Q60A star has 100%100\% helium composition. It starts to convert three 4He{}^4\mathrm{He} into one 12C{}^{12}\mathrm{C} via triple alpha process as…HardNucleiNumerical

Chemistry Q61–90

  1. Q61Compare the energies of following sets of quantum numbers for multielectron system. (A) n=4,l=1n=4, l=1 (B) n=4,l=2n=4, l=2 (C) n=3,l=1n=3, l=1 (D) n=3,l=2n=3, l=2 (E)…EasyStructure of Atom
  2. Q62In which one of the following pairs the central atoms exhibit sp2sp^2 hybridization ?EasyChemical Bonding and Molecular Structure
  3. Q630.05M CuSO40.05\mathrm{M}\ \mathrm{CuSO_4} when treated with 0.01M K2Cr2O70.01\mathrm{M}\ \mathrm{K_2Cr_2O_7} gives green colour solution of Cu2Cr2O7\mathrm{Cu_2Cr_2O_7}. The…MediumSolutions
  4. Q64The molar conductivity for electrolytes A and B are plotted against C1/2C^{1/2} as shown below. Electrolytes A and B respectively are :EasyElectrochemistry
  5. Q65Given below are two statements : Statement (I) : The oxidation state of an element in a particular compound is the charge acquired by its atom on…MediumRedox Reactions
  6. Q66Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Both rhombic and…MediumThe p-Block Elements
  7. Q67The F−\mathrm{F^-} ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder…MediumEnvironmental Chemistry
  8. Q68The electronic configuration of Cu(II) is 3d93d^9 whereas that of Cu(I) is 3d103d^{10}. Which of the following is correct ?EasyThe d- and f-Block Elements
  9. Q69Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The total number of…MediumCoordination Compounds
  10. Q70Methods used for purification of organic compounds are based on :EasyOrganic Chemistry: Some Basic Principles and Techniques
  11. Q71Relative stability of the contributing structures is : (I) CH2=CH−C∥O¨:−H\mathrm{CH_2=CH-\overset{\ddot{O}:}{\overset{\|}{C}}-H} ⟷\longleftrightarrow (II)…MediumOrganic Chemistry: Some Basic Principles and Techniques
  12. Q72[figure: benzene + succinic anhydride (cyclic five-membered anhydride) →AlCl3\xrightarrow{\mathrm{AlCl_3}} A…MediumAldehydes, Ketones and Carboxylic Acids
  13. Q73Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : SN2\mathrm{S_N2} reaction…EasyHaloalkanes and Haloarenes
  14. Q74In the following sequence of reaction, the major products B and C respectively are : [figure: Cl-cyclobutane-Br (1,3-disubstituted cyclobutane)…HardOrganic Chemistry: Some Basic Principles and Techniques
  15. Q75Identify major product "X" formed in the following reaction : [figure: benzene →Anhydrous AlCl3/CuClCO, HCl\xrightarrow[\mathrm{Anhydrous\ AlCl_3/CuCl}]{\mathrm{CO,\ HCl}} X…EasyAldehydes, Ketones and Carboxylic Acids
  16. Q76Identify the product A and product B in the following set of reactions. [figure: CH3−CH=CH2\mathrm{CH_3-CH=CH_2} →H2O, H+\xrightarrow{\mathrm{H_2O,\ H^+}} major…EasyAlcohols, Phenols and Ethers
  17. Q77For the given compounds, the correct order of increasing pKa\mathrm{pK_a} value : (A) phenol (B) 4-nitrophenol (O2N\mathrm{O_2N} and OH para on…MediumAlcohols, Phenols and Ethers
  18. Q78Correct order of basic strength of Pyrrole (five-membered ring with NH), Pyridine (six-membered aromatic ring with N) and Piperidine (saturated…MediumAmines
  19. Q79On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed ?MediumThe p-Block Elements
  20. Q80Identify the incorrect statements regarding primary standard of titrimetric analysis. (A) It should be purely available in dry form. (B) It should…MediumSome Basic Concepts of Chemistry
  21. Q81Molarity (M) of an aqueous solution containing xx g of anhyd. CuSO4\mathrm{CuSO_4} in 500 mL solution at 32 ∘^\circC is 2×10−12\times10^{-1} M. Its…MediumSolutionsNumerical
  22. Q82The total number of species from the following in which one unpaired electron is present, is ________.…MediumChemical Bonding and Molecular StructureNumerical
  23. Q83The heat of solution of anhydrous CuSO4\mathrm{CuSO_4} and CuSO4⋅5H2O\mathrm{CuSO_4\cdot5H_2O} are −70-70 kJ mol−1^{-1} and +12+12 kJ mol−1^{-1} respectively.…EasyThermodynamics (Chemistry)Numerical
  24. Q84When equal volume of 1M HCl and 1M H2SO4\mathrm{H_2SO_4} are separately neutralised by excess volume of 1M NaOH solution, xx and yy kJ of heat is…EasyThermodynamics (Chemistry)Numerical
  25. Q85The standard reduction potentials at 298 K for the following half cells are given below :…MediumElectrochemistryNumerical
  26. Q86Given below are two statements : Statement I : The rate law for the reaction A+B→C\mathrm{A + B \rightarrow C} is rate…EasyChemical KineticsNumerical
  27. Q87Number of colourless lanthanoid ions among the following is ________. Eu3+,Lu3+,Nd3+,La3+,Sm3+\mathrm{Eu^{3+}, Lu^{3+}, Nd^{3+}, La^{3+}, Sm^{3+}}MediumThe d- and f-Block ElementsNumerical
  28. Q88Number of ambidentate ligands among the following is ________. NO2−,SCN−,C2O42−,NH3,CN−,SO42−,H2O\mathrm{NO_2^-, SCN^-, C_2O_4^{2-}, NH_3, CN^-, SO_4^{2-}, H_2O}.EasyCoordination CompoundsNumerical
  29. Q89How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects ? [figure: eight structures: anisole…MediumOrganic Chemistry: Some Basic Principles and TechniquesNumerical
  30. Q90Total number of essential amino acid among the given list of amino acids is ________. Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine,…EasyBiomoleculesNumerical

Maths Q1–30

  1. Q1If the domain of the function f(x)=sin⁡−1(x−12x+3)f(x)=\sin^{-1}\left(\frac{x-1}{2x+3}\right) is R−(α,β)\mathbf{R}-(\alpha,\beta), then 12αβ12\alpha\beta is equal to :MediumRelations and Functions
  2. Q2Let α,β\alpha,\beta be the roots of the equation x2+22 x−1=0x^2+2\sqrt{2}\,x-1=0. The quadratic equation, whose roots are α4+β4\alpha^4+\beta^4 and…MediumComplex Numbers and Quadratic Equations
  3. Q3Let λ,μ∈R\lambda,\mu\in\mathbf{R}. If the system of equations 3x+5y+λz=33x+5y+\lambda z=3 7x+11y−9z=27x+11y-9z=2 97x+155y−189z=μ97x+155y-189z=\mu has infinitely many solutions, then…MediumDeterminants
  4. Q4The coefficient of x70x^{70} in x2(1+x)98+x3(1+x)97+x4(1+x)96+…+x54(1+x)46x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46} is 99Cp−46Cq{}^{99}C_p-{}^{46}C_q. Then a possible value…HardBinomial Theorem
  5. Q5If the sum of the series 11⋅(1+d)+1(1+d)(1+2d)+…+1(1+9d)(1+10d)\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)} is equal to 55, then 50d50d is equal to :MediumSequences and Series
  6. Q6Let f(x)=ax3+bx2+cx+41f(x)=ax^3+bx^2+cx+41 be such that f(1)=40f(1)=40, f′(1)=2f'(1)=2 and f′′(1)=4f''(1)=4. Then a2+b2+c2a^2+b^2+c^2 is equal to :EasyApplication of Derivatives
  7. Q7A variable line L passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points A and B. The minimum area of the…MediumStraight Lines
  8. Q8Let ∫2−tan⁡x3+tan⁡x dx=12(αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int\frac{2-\tan x}{3+\tan x}\,dx=\frac{1}{2}\left(\alpha x+\log_e|\beta\sin x+\gamma\cos x|\right)+C, where C is the constant of integration.…MediumIntegrals
  9. Q9The parabola y2=4xy^2=4x divides the area of the circle x2+y2=5x^2+y^2=5 in two parts. The area of the smaller part is equal to :MediumApplication of Integrals
  10. Q10The solution of the differential equation (x2+y2)dx−5xy dy=0(x^2+y^2)dx-5xy\,dy=0, y(1)=0y(1)=0, is :MediumDifferential Equations
  11. Q11The solution curve, of the differential equation 2ydydx+3=5dydx2y\frac{dy}{dx}+3=5\frac{dy}{dx}, passing through the point (0,1)(0,1) is a conic, whose vertex lies…MediumDifferential Equations
  12. Q12Let f(x)=x2+9f(x)=x^2+9, g(x)=xx−9g(x)=\frac{x}{x-9} and a=f∘g(10)a=f\circ g(10), b=g∘f(3)b=g\circ f(3). If ee and ll denote the eccentricity and the length of the latus…EasyConic Sections
  13. Q13Let a circle passing through (2,0)(2,0) have its centre at the point (h,k)(h,k). Let (xc,yc)(x_c,y_c) be the point of intersection of the lines 3x+5y=13x+5y=1 and…MediumConic Sections
  14. Q14A ray of light coming from the point P(1,2)P(1,2) gets reflected from the point Q on the xx-axis and then passes through the point R(4,3)R(4,3). If the…MediumStraight Lines
  15. Q15Let the line L intersect the lines x−2=−y=z−1x-2=-y=z-1, 2(x+1)=2(y−1)=z+12(x+1)=2(y-1)=z+1 and be parallel to the line x−23=y−11=z−22\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}. Then…MediumThree Dimensional Geometry
  16. Q16The shortest distance between the lines x−34=y+7−11=z−15\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5} and x−53=y−9−6=z+21\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1} is :EasyThree Dimensional Geometry
  17. Q17Let OA→=2a⃗\overrightarrow{OA}=2\vec{a}, OB→=6a⃗+5b⃗\overrightarrow{OB}=6\vec{a}+5\vec{b} and OC→=3b⃗\overrightarrow{OC}=3\vec{b}, where O is the origin. If the area…MediumVector Algebra
  18. Q18Let three vectors a⃗=αi^+4j^+2k^\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}, b⃗=5i^+3j^+4k^\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}, c⃗=xi^+yj^+zk^\vec{c}=x\hat{i}+y\hat{j}+z\hat{k} form a…MediumVector Algebra
  19. Q19The frequency distribution of the age of students in a class of 40 students is given below. | Age | 15 | 16 | 17 | 18 | 19 | 20 |…HardStatistics
  20. Q20Let ∣cos⁡θcos⁡(60∘−θ)cos⁡(60∘+θ)∣≤18\left|\cos\theta\cos(60^\circ-\theta)\cos(60^\circ+\theta)\right|\le\frac{1}{8}, θ∈[0,2π]\theta\in[0,2\pi]. Then, the sum of all…MediumTrigonometric Functions
  21. Q21Let A={2,3,6,7}A=\{2,3,6,7\} and B={4,5,6,8}B=\{4,5,6,8\}. Let R be a relation defined on A×BA\times B by (a1,b1) R (a2,b2)(a_1,b_1)\,R\,(a_2,b_2) if and only if a1+a2=b1+b2a_1+a_2=b_1+b_2.…MediumRelations and FunctionsNumerical
  22. Q22The sum of the square of the modulus of the elements in the set {z=a+ib: a,b∈Z, z∈C, ∣z−1∣≤1, ∣z−5∣≤∣z−5i∣}\{z=a+ib:\ a,b\in\mathbf{Z},\ z\in\mathbf{C},\ |z-1|\le1,\ |z-5|\le|z-5i|\} is…MediumComplex Numbers and Quadratic EquationsNumerical
  23. Q23Let A be a non-singular matrix of order 3. If det⁡(3 adj(2 adj((det⁡A)A)))=3−13⋅2−10\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10} and…HardDeterminantsNumerical
  24. Q24Let f:(0,π)→Rf:(0,\pi)\to\mathbf{R} be a function given by…HardContinuity and DifferentiabilityNumerical
  25. Q25The remainder when 4282024428^{2024} is divided by 2121 is ________.MediumBinomial TheoremNumerical
  26. Q26If a function ff satisfies f(m+n)=f(m)+f(n)f(m+n)=f(m)+f(n) for all m,n∈Nm,n\in\mathbf{N} and f(1)=1f(1)=1, then the largest natural number λ\lambda such that…MediumSequences and SeriesNumerical
  27. Q27Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))(1+x(\lambda^2-x^2)) satisfies…MediumApplication of DerivativesNumerical
  28. Q28Let…HardIntegralsNumerical
  29. Q29Let the centre of a circle, passing through the points (0,0)(0,0), (1,0)(1,0) and touching the circle x2+y2=9x^2+y^2=9, be (h,k)(h,k). Then for all possible…HardConic SectionsNumerical
  30. Q30Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,41,2,3,4. If the probability…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.