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Friday, 9 October

JEE Main 2024 · April session

JEE Main 6 April 2024, Shift 2

89 questions (1 more dropped by NTA): 29 numerical-answer and 60 multiple choice. 13 were rated hard and 31 easy. By hard questions it ranks 2nd of the 8 2024 shifts Lumi analysed. The biggest chapter was Coordination Compounds, with 3 questions.

Questions
89
1 dropped by NTA
Numerical answer
29
33% of the shift
Hard
13
15% of the shift
Chapters asked
60
11 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

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

Top chapters

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

Top chapters

Maths
29 Q · 9 numerical
Easy 4Medium 17Hard 8

Top chapters

Question format
  • Single correct46 Q
  • Numerical value29 Q
  • Match the list4 Q
  • Other4 Q
  • Diagram based4 Q
  • Two statements2 Q
What each question asks you to do
  • Calculation35 Q
  • Multi-step29 Q
  • Application11 Q
  • Recall7 Q
  • Conceptual6 Q
  • Data or graph1 Q

Most common: Calculation.

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 car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30∘30^\circ. If coefficient of static friction is 0.2 then the…MediumLaws of Motion
  2. Q32Given below are two statements : Statement (I) : Dimensions of specific heat is [L2T−2K−1][\mathrm{L^2T^{-2}K^{-1}}]. Statement (II) : Dimensions of gas…MediumUnits and Measurements
  3. Q33A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1t_1. If it is projected vertically…MediumMotion in a Straight Line
  4. Q34A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if…EasyLaws of Motion
  5. Q35Match List-I with List-II : List-I (Y vs X) (A) Y = magnetic susceptibility, X = magnetising field (B) Y = magnetic field, X = distance from centre…MediumMagnetism and Matter
  6. Q36When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :EasyWork, Energy and Power
  7. Q37Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4R/4 depth…EasyGravitation
  8. Q38Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : RR = Radius of bubble, SS = Surface tension of bubble)EasyMechanical Properties of Fluids
  9. Q39A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2∘C2^\circ\mathrm{C}. The work done by…EasyThermodynamics
  10. Q40In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th4^{\text{th}} division coincides…MediumUnits and Measurements
  11. Q41Energy of 10 non rigid diatomic molecules at temperature TT is :MediumKinetic Theory
  12. Q42Two identical conducting spheres PP and SS with charge QQ on each, repel each other with a force 16 N. A third identical uncharged conducting…MediumElectric Charges and Fields
  13. Q43The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : (Given e=1.6×10−19 Ce=1.6\times10^{-19}\ \mathrm{C})EasyCurrent Electricity
  14. Q44In a coil, the current changes from −2-2 A to +2+2 A in 0.2 s and induces an emf of 0.1 V. The self inductance of the coil is :EasyElectromagnetic Induction
  15. Q45In the given electromagnetic wave Ey=600sin⁡(ωt−kx) Vm−1E_y=600\sin(\omega t-kx)\ \mathrm{Vm^{-1}}, intensity of the associated light beam is (in W/m2\mathrm{W/m^2}) :…MediumElectromagnetic Waves
  16. Q46For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of…EasyRay Optics and Optical Instruments
  17. Q47When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV, electron emission takes place. The stopping…EasyDual Nature of Radiation and Matter
  18. Q48The longest wavelength associated with Paschen series is : (Given RH=1.097×107R_H=1.097\times10^7 SI unit)EasyAtoms
  19. Q49The acceptor level of a p-type semiconductor is 6 eV. The maximum wavelength of light which can create a hole would be : Given…MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  20. Q50In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49 MSD;…HardRay Optics and Optical Instruments
  21. Q51Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th6^{\text{th}} and 5th5^{\text{th}} harmonics respectively. The difference of…EasyWavesNumerical
  22. Q52A capacitor of 10 μF10\ \mu\mathrm{F} capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm24\ \mathrm{cm}^2 is now…HardElectrostatic Potential and CapacitanceNumerical
  23. Q53In the given figure an ammeter AA consists of a 240 Ω240\ \Omega coil connected in parallel to a 10 Ω10\ \Omega shunt. The reading of the ammeter is…MediumCurrent ElectricityNumerical
  24. Q54Two coherent monochromatic light beams of intensities II and 4I4I are superimposed. The difference between maximum and minimum possible intensities…EasyWave OpticsNumerical
  25. Q55In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by…EasyAtomsNumerical
  26. Q56Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of…MediumSystem of Particles and Rotational MotionNumerical
  27. Q57A particle moves in a straight line so that its displacement xx at any time tt is given by x2=1+t2x^2=1+t^2. Its acceleration at any time tt is…MediumMotion in a Straight LineNumerical
  28. Q58A coil having 100 turns, area of 5×10−3 m25\times10^{-3}\ \mathrm{m^2}, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way…EasyMoving Charges and MagnetismNumerical
  29. Q59For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of…EasyAlternating CurrentNumerical
  30. Q60A wire of cross sectional area AA, modulus of elasticity 2×1011 Nm−22\times10^{11}\ \mathrm{Nm^{-2}} and length 2 m is stretched between two vertical rigid…HardMechanical Properties of SolidsNumerical

Chemistry Q61–90

  1. Q61Molality (mm) of 3 M aqueous solution of NaCl is : (Given : Density of solution =1.25 g mL−1=1.25\ \mathrm{g\,mL^{-1}}, Molar mass in g mol−1\mathrm{g\,mol^{-1}}…EasySolutions
  2. Q62Given below are two statements : Statement I : PF5\mathrm{PF_5} and BrF5\mathrm{BrF_5} both exhibit sp3dsp^3d hybridisation. Statement II : Both…MediumChemical Bonding and Molecular Structure
  3. Q63The ratio KPKC\frac{K_P}{K_C} for the reaction : CO(g)+12O2(g)⇌CO2(g)\mathrm{CO_{(g)}+\frac{1}{2}O_{2(g)}\rightleftharpoons CO_{2(g)}} is :EasyEquilibrium
  4. Q64Match List - I with List - II. List - I (Reaction) (A) N2(g)+O2(g)→2NO(g)\mathrm{N_{2(g)}+O_{2(g)}\rightarrow 2NO_{(g)}} (B)…EasyRedox Reactions
  5. Q65How can an electrochemical cell be converted into an electrolytic cell ?EasyElectrochemistry
  6. Q66Match List - I with List - II. List - I (Alkali Metal) (A) Li (B) Na (C) Rb (D) Cs List - II (Emission Wavelength in nm) (I) 589.2 (II) 455.5 (III)…HardThe s-Block Elements
  7. Q67The number of ions from the following that are expected to behave as oxidising agent is :…MediumThe p-Block Elements
  8. Q68Evaluate the following statements related to group 14 elements for their correctness. (A) Covalent radius decreases down the group from C to Pb in a…MediumThe p-Block Elements
  9. Q69Arrange the following elements in the increasing order of number of unpaired electrons in it. (A) Sc (B) Cr (C) V (D) Ti (E) Mn Choose the correct…EasyClassification of Elements and Periodicity in Properties
  10. Q70The correct IUPAC name of [PtBr2(PMe3)2][\mathrm{PtBr_2(PMe_3)_2}] is :EasyCoordination Compounds
  11. Q71Match List - I with List - II. List - I (Tetrahedral Complex) (A) TiCl4\mathrm{TiCl_4} (B) [FeO4]2−[\mathrm{FeO_4}]^{2-} (C) [FeCl4]−[\mathrm{FeCl_4}]^{-} (D)…MediumCoordination Compounds
  12. Q72During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in NH4OH\mathrm{NH_4OH}…EasyOrganic Chemistry: Some Basic Principles and Techniques
  13. Q73The correct statement among the following, for a "chromatography" purification method is :MediumOrganic Chemistry: Some Basic Principles and Techniques
  14. Q74Four aromatic compounds are shown: (I) toluene (benzene ring with CH3\mathrm{CH_3}), (II) benzene, (III) anisole (benzene ring with…EasyHydrocarbons
  15. Q75The incorrect statement regarding the geometrical isomers of 2-butene is :EasyHydrocarbons
  16. Q76Chemical reaction: (1-chloropropyl)cyclohexane [cyclohexyl ring attached to CHCl-CH2-CH3] ++ NaOH →H2O\xrightarrow{\mathrm{H_2O}} Major Product "A".…MediumHaloalkanes and Haloarenes
  17. Q77Identify the product (A) in the following reaction. Aniline (benzene ring with NH2\mathrm{NH_2})…MediumAmines
  18. Q78Consider the given reaction, identify the major product P. CH3−COOH\mathrm{CH_3-COOH}…MediumAldehydes, Ketones and Carboxylic Acids
  19. Q79The major products formed : Anisole (benzene ring with OCH3\mathrm{OCH_3}) →HNO3, H2SO4\xrightarrow{\mathrm{HNO_3,\ H_2SO_4}} 'A'…MediumHaloalkanes and Haloarenes
  20. Q80The incorrect statements regarding enzymes are : (A) Enzymes are biocatalysts. (B) Enzymes are non-specific and can catalyse different kinds of…EasyBiomolecules
  21. Q81For hydrogen atom, energy of an electron in first excited state is −3.4-3.4 eV, K.E. of the same electron of hydrogen atom is xx eV. Value of xx is…EasyStructure of AtomNumerical
  22. Q82Total number of species from the following with central atom utilising sp2\mathrm{sp^2} hybrid orbitals for bonding is ________.…MediumChemical Bonding and Molecular StructureNumerical
  23. Q83For the reaction at 298 K, 2A+B→C2A + B \rightarrow C, ΔH=400\Delta H = 400 kJ mol−1^{-1} and ΔS=0.2\Delta S = 0.2 kJ mol−1^{-1} K−1^{-1}. The reaction will…EasyThermodynamics (Chemistry)Numerical
  24. Q84When 'xx' ×10−2\times 10^{-2} mL methanol (molar mass =32= 32 g; density =0.792= 0.792 g/cm3^3) is added to 100 mL water (density =1= 1 g/cm3^3), the…MediumSolutionsNumerical
  25. Q85Consider the two different first order reactions given below A+B→CA + B \rightarrow C (Reaction 1) P→QP \rightarrow Q (Reaction 2) The ratio of the half…MediumChemical KineticsNumerical
  26. Q86Among VO2+\mathrm{VO_2^+}, MnO4−\mathrm{MnO_4^-} and Cr2O72−\mathrm{Cr_2O_7^{2-}}, the spin-only magnetic moment value of the species with least oxidising…MediumThe d- and f-Block ElementsNumerical
  27. Q87Consider the following reactions NiS+HNO3+HCl→A+NO+S+H2O\mathrm{NiS + HNO_3 + HCl \rightarrow A + NO + S + H_2O}…HardCoordination CompoundsNumerical
  28. Q88Number of carbocations from the following that are not stabilized by hyperconjugation is ________.MediumOrganic Chemistry: Some Basic Principles and TechniquesNumerical
  29. Q89Reaction: ethoxybenzene (benzene ring with OC2H5\mathrm{OC_2H_5}) →HNO3, H2SO4\xrightarrow{\mathrm{HNO_3,\ H_2SO_4}} P (major product)…MediumHaloalkanes and HaloarenesNumerical
  30. Q90An amine (X) is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to it the solution remains clear. Molar mass of…MediumAminesNumerical

Maths Q1–30

  1. Q1Let f(x)=17−sin⁡5xf(x)=\frac{1}{7-\sin 5x} be a function defined on R\mathbb{R}. Then the range of the function f(x)f(x) is equal to :EasyRelations and Functions
  2. Q2Let A={1,2,3,4,5}A=\{1,2,3,4,5\}. Let RR be a relation on AA defined by xRyxRy if and only if 4x≤5y4x\le 5y. Let mm be the number of elements in RR and nn be…MediumRelations and Functions
  3. Q3If z1,z2z_1, z_2 are two distinct complex number such that ∣z1−2z212−z1z2ˉ∣=2\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2, thenHardComplex Numbers and Quadratic Equations
  4. Q4If AA is a square matrix of order 3 such that det⁡(A)=3\det(A)=3 and…MediumDeterminants
  5. Q5If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at…MediumPermutations and Combinations
  6. Q6Let 0≤r≤n0\le r\le n. If n+1Cr+1:nCr:n−1Cr−1=55:35:21^{n+1}C_{r+1}:{}^{n}C_r:{}^{n-1}C_{r-1}=55:35:21, then 2n+5r2n+5r is equal to :MediumPermutations and Combinations
  7. Q7A software company sets up mm number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the…MediumSequences and Series
  8. Q8If the function f(x)=(1x)2xf(x)=\left(\frac{1}{x}\right)^{2x} ; x>0x>0 attains the maximum value at x=1ex=\frac{1}{e} then :HardApplication of Derivatives
  9. Q9lim⁡n→∞(12−1)(n−1)+(22−2)(n−2)+⋯+((n−1)2−(n−1))⋅1(13+23+⋯+n3)−(12+22+⋯+n2)\lim_{n\to\infty}\frac{(1^2-1)(n-1)+(2^2-2)(n-2)+\cdots+((n-1)^2-(n-1))\cdot 1}{(1^3+2^3+\cdots+n^3)-(1^2+2^2+\cdots+n^2)} is equal to :MediumLimits and Derivatives
  10. Q10Suppose for a differentiable function hh, h(0)=0h(0)=0, h(1)=1h(1)=1 and h′(0)=h′(1)=2h'(0)=h'(1)=2. If g(x)=h(ex)eh(x)g(x)=h(e^x)e^{h(x)}, then g′(0)g'(0) is equal to :MediumContinuity and Differentiability
  11. Q11If the area of the region {(x,y):ax2≤y≤1x, 1≤x≤2, 0<a<1}\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\} is (log⁡e2)−17(\log_e 2)-\frac{1}{7} then the value…MediumApplication of Integrals
  12. Q12If ∫1a2sin⁡2x+b2cos⁡2xdx=112tan⁡−1(3tan⁡x)+constant\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}, then the maximum value of asin⁡x+bcos⁡xa\sin x+b\cos x, is :MediumIntegrals
  13. Q13Suppose the solution of the differential equation dydx=(2+α)x−βy+2βx−2αy−(βγ−4α)\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)} represents a…HardDifferential Equations
  14. Q14If the locus of the point, whose distances from the point (2,1)(2,1) and (1,3)(1,3) are in the ratio 5:45:4, is ax2+by2+cxy+dx+ey+170=0ax^2+by^2+cxy+dx+ey+170=0, then the value…MediumStraight Lines
  15. Q15If P(6,1)P(6,1) be the orthocentre of the triangle whose vertices are A(5,−2)A(5,-2), B(8,3)B(8,3) and C(h,k)C(h,k), then the point CC lies on the circle :MediumStraight Lines
  16. Q16Let ABCABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABCABC and the same process…MediumSequences and Series
  17. Q17Let P(α,β,γ)P(\alpha,\beta,\gamma) be the image of the point Q(3,−3,1)Q(3,-3,1) in the line x−01=y−31=z−1−1\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1} and RR be the point…HardThree Dimensional Geometry
  18. Q18Let a⃗=2i^+j^−k^\vec{a}=2\hat{i}+\hat{j}-\hat{k}, b⃗=((a⃗×(i^+j^))×i^)×i^\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}. Then the…MediumVector Algebra
  19. Q19Let a⃗=6i^+j^−k^\vec{a}=6\hat{i}+\hat{j}-\hat{k} and b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}. If c⃗\vec{c} is a vector such that ∣c⃗∣≥6|\vec{c}|\ge 6,…HardVector Algebra
  20. Q20If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two…EasyProbability
  21. Q21Let α,β\alpha,\beta be roots of x2+2x−8=0x^2+\sqrt{2}x-8=0. If Un=αn+βnU_n=\alpha^n+\beta^n, then U10+2U92U8\frac{U_{10}+\sqrt{2}U_9}{2U_8} is equal to ________.EasyComplex Numbers and Quadratic EquationsNumerical
  22. Q22If the system of equations 2x+7y+λz=32x+7y+\lambda z=3 3x+2y+5z=43x+2y+5z=4 x+μy+32z=−1x+\mu y+32z=-1 has infinitely many solutions, then (λ−μ)(\lambda-\mu) is equal to…MediumDeterminantsNumerical
  23. Q23If S(x)=(1+x)+2(1+x)2+3(1+x)3+⋯+60(1+x)60S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\cdots+60(1+x)^{60}, x≠0x\ne 0, and (60)2S(60)=a(b)b+b(60)^2 S(60)=a(b)^b+b, where a,b∈Na,b\in\mathbb{N}, then (a+b)(a+b) equal to…HardBinomial TheoremNumerical
  24. Q24Let [t][t] denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:[0,\infty)\to\mathbb{R} be a function defined by…MediumContinuity and DifferentiabilityNumerical
  25. Q25Let [t][t] denote the largest integer less than or equal to tt. If…HardIntegralsNumerical
  26. Q26If the solution y(x)y(x) of the given differential equation (ey+1)cos⁡x dx+eysin⁡x dy=0(e^y+1)\cos x\,dx+e^y\sin x\,dy=0 passes through the point…EasyDifferential EquationsNumerical
  27. Q27The length of the latus rectum and directrices of a hyperbola with eccentricity ee are 9 and x=±43x=\pm\frac{4}{\sqrt{3}}, respectively. Let the line…HardConic SectionsNumericalDropped
  28. Q28If the shortest distance between the lines x−λ3=y−2−1=z−11\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1} and x+2−3=y+52=z−44\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4} is…MediumThree Dimensional GeometryNumerical
  29. Q29From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable XX denote the number of defective…HardProbabilityNumerical
  30. Q30In a triangle ABCABC, BC=7BC=7, AC=8AC=8, AB=α∈NAB=\alpha\in\mathbb{N} and cos⁡A=23\cos A=\frac{2}{3}. If 49cos⁡(3C)+42=mn49\cos(3C)+42=\frac{m}{n}, where gcd⁡(m,n)=1\gcd(m,n)=1, then…MediumTrigonometric FunctionsNumerical

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.