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Friday, 9 October

JEE Main 2023 · April session

JEE Main 13 April 2023, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 30 easy. By hard questions it ranks 3rd of the 4 2023 shifts Lumi analysed. The biggest chapter was Three Dimensional Geometry, with 3 questions.

Questions
90
none dropped
Numerical answer
30
33% of the shift
Hard
12
13% of the shift
Chapters asked
67
9 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 18Medium 12Hard 0

Top chapters

Chemistry
30 Q · 10 numerical
Easy 8Medium 19Hard 3

Top chapters

Maths
30 Q · 10 numerical
Easy 4Medium 17Hard 9

Top chapters

Question format
  • Single correct44 Q
  • Numerical value30 Q
  • Two statements6 Q
  • Assertion–reason5 Q
  • Other2 Q
  • Match the list2 Q
  • Diagram based1 Q
What each question asks you to do
  • Multi-step29 Q
  • Calculation28 Q
  • Application13 Q
  • Conceptual10 Q
  • Recall9 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. Q31In the equation [X+aY2][Y−b]=RT\left[X+\frac{a}{Y^2}\right][Y-b]=RT, XX is pressure, YY is volume, R is universal gas constant and TT is temperature. The…MediumUnits and Measurements
  2. Q32The distance travelled by an object in time t is given by s=(2.5)t2s=(2.5)t^2. The instantaneous speed of the object at t=5t=5 s will be:EasyMotion in a Straight Line
  3. Q33A passenger sitting in a train A moving at 9090 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train…EasyMotion in a Straight Line
  4. Q34A vehicle of mass 200200 kg is moving along a levelled curved road of radius 7070 m with angular velocity of 0.20.2 rad/s. The centripetal force…EasyLaws of Motion
  5. Q35Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the…EasyGravitation
  6. Q36Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius…MediumMechanical Properties of Fluids
  7. Q37Two planets A and B of radii R and 1.5 R have densities ρ\rho and ρ/2\rho/2 respectively. The ratio of acceleration due to gravity at the surface of…EasyGravitation
  8. Q38The initial pressure and volume of an ideal gas are P0P_0 and V0V_0. The final pressure of the gas when the gas is suddenly compressed to volume…EasyThermodynamics
  9. Q39The mean free path of molecules of a certain gas at STP is 1500d1500d, where dd is the diameter of the gas molecules. While maintaining the standard…MediumKinetic Theory
  10. Q40A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is:EasyOscillations
  11. Q41A 10 μ10\ \muC charge is divided into two parts and placed at 11 cm distance so that the repulsive force between them is maximum. The charges of the…EasyElectric Charges and Fields
  12. Q42In the network shown below, the charge accumulated in the capacitor in steady state will be:MediumCurrent Electricity
  13. Q43An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will…EasyMoving Charges and Magnetism
  14. Q44Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.…MediumAlternating Current
  15. Q45In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along…EasyElectromagnetic Waves
  16. Q46In a Young's double slits experiment, the ratio of amplitude of light coming from slits is 2:1. The ratio of the maximum to minimum intensity in the…EasyWave Optics
  17. Q47Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the…EasyDual Nature of Radiation and Matter
  18. Q48Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The binding energy per nucleon is…MediumNuclei
  19. Q49The output from a NAND gate having inputs A and B given below will be,MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  20. Q50To radiate EM signal of wavelength λ\lambda with high efficiency, the antennas should have a minimum size equal to :EasyCommunication Systems
  21. Q51A car accelerates from rest to u m/s. The energy spent in this process is E J. The energy required to accelerate the car from u m/s to 2u m/s is nE…EasyWork, Energy and PowerNumerical
  22. Q52A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of…MediumSystem of Particles and Rotational MotionNumerical
  23. Q53Two plates A and B have thermal conductivities 84 Wm−1K−184\ \mathrm{Wm^{-1}K^{-1}} and 126 Wm−1K−1126\ \mathrm{Wm^{-1}K^{-1}} respectively. They have same surface…EasyThermal Properties of MatterNumerical
  24. Q54In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is…EasyWavesNumerical
  25. Q55Three point charges q, −2q-2q and 2q2q are placed on x-axis at a distance x=0x=0, x=34Rx=\frac{3}{4}R and x=Rx=R respectively from origin as shown. If…MediumElectric Charges and FieldsNumerical
  26. Q56In the circuit shown, the energy stored in the capacitor is n μn\ \muJ. The value of n is ______.MediumCurrent ElectricityNumerical
  27. Q57A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.400.40 T as shown…MediumMoving Charges and MagnetismNumerical
  28. Q58An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24 cm224\ \mathrm{cm^2}. The two ends of…EasyElectromagnetic InductionNumerical
  29. Q59A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after…EasyRay Optics and Optical InstrumentsNumerical
  30. Q60An atom absorbs a photon of wavelength 500500 nm and emits another photon of wavelength 600600 nm. The net energy absorbed by the atom in this process…MediumAtomsNumerical

Chemistry Q61–90

  1. Q61Given below are two statements : Statement I : SO2\mathrm{SO_2} and H2O\mathrm{H_2O} both possess V-shaped structure. Statement II : The bond angle of…MediumChemical Bonding and Molecular Structure
  2. Q62What happens when methane undergoes combustion in systems A and B respectively? System A: Adiabatic system System B: Diathermic containerMediumThermodynamics (Chemistry)
  3. Q63Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The diameter of colloidal…MediumSolutions
  4. Q64The covalency and oxidation state respectively of boron in [BF4]−[\mathrm{BF_4}]^{-}, areMediumChemical Bonding and Molecular Structure
  5. Q65Given below are two statements related to Ellingham diagram: Statement I : Ellingham diagrams can be constructed for formation of oxides, sulfides…MediumGeneral Principles and Processes of Isolation of Elements
  6. Q66Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Isotopes of hydrogen have almost…MediumHydrogen
  7. Q67Better method for preparation of BeF2\mathrm{BeF_2}, among the following isHardThe s-Block Elements
  8. Q68Identify the correct order of standard enthalpy of formation of sodium halides.MediumThermodynamics (Chemistry)
  9. Q69The correct group of halide ions which can be oxidised by oxygen in acidic medium isMediumElectrochemistry
  10. Q70Which of the following complexes will exhibit maximum attraction to an applied magnetic field?EasyCoordination Compounds
  11. Q71Which of the following are the Green house gases? A. Water vapour B. Ozone C. I2\mathrm{I_2} D. Molecular hydrogen Choose the most appropriate…EasyEnvironmental Chemistry
  12. Q72The total number of stereoisomers for the complex [Cr(ox)2ClBr]3−[\mathrm{Cr}(ox)_2\mathrm{ClBr}]^{3-} (where oxox = oxalate) is:MediumCoordination Compounds
  13. Q73In the wet tests for detection of various cations by precipitation, Ba2+\mathrm{Ba^{2+}} cations are detected by obtaining precipitate ofEasyPractical Chemistry (Qualitative Analysis)
  14. Q74Given below are two statements : Statement I : Tropolone is an aromatic compound and has 8 π\pi electrons. Statement II : π\pi electrons of >>C =…HardOrganic Chemistry: Some Basic Principles and Techniques
  15. Q75Match List I with List II 1 - Bromopropane is reacted with reagents in List I to give product in List II LIST I - Reagent | LIST II - Product A. KOH…MediumHaloalkanes and Haloarenes
  16. Q76Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Order of acidic nature of the…MediumAlcohols, Phenols and Ethers
  17. Q77The major product for the following reaction is: CH2=CH−CN\mathrm{CH_2{=}CH{-}CN} + HO−CH2CH2−SH\mathrm{HO{-}CH_2CH_2{-}SH} (arrow)MediumAldehydes, Ketones and Carboxylic Acids
  18. Q78Compound A from the following reaction sequence is: A →0−5∘CBr2, CS2\xrightarrow[0-5^\circ\mathrm{C}]{\mathrm{Br_2,\ CS_2}} B…MediumAmines
  19. Q79The naturally occurring amino acid that contains only one basic functional group in its chemical structure isMediumBiomolecules
  20. Q80Match List I with List II LIST I | LIST II A. Weak intermolecular forces of attraction | I. Hexamethylenediamine + adipic acid B. Hydrogen bonding |…MediumPolymers
  21. Q811g of a carbonate (M2CO3\mathrm{M_2CO_3}) on treatment with excess HCl produces 0.01 mol of CO2\mathrm{CO_2}. The molar mass of M2CO3\mathrm{M_2CO_3} is…EasySome Basic Concepts of ChemistryNumerical
  22. Q82Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is ______ ×10−1\times10^{-1} Å…EasyThe Solid StateNumerical
  23. Q83The orbital angular momentum of an electron in 3s orbital is xh2π\frac{xh}{2\pi}. The value of xx is ______ (nearest integer)EasyStructure of AtomNumerical
  24. Q84Sea water contains 29.25% NaCl and 19% MgCl2\mathrm{MgCl_2} by weight of solution. The normal boiling point of the sea water is ______ ∘^\circC…MediumSolutionsNumerical
  25. Q8520 mL of 0.1 M NaOH is added to 50 mL of 0.1 M acetic acid solution. The pH of the resulting solution is ______ ×10−2\times10^{-2} (Nearest integer)…MediumEquilibriumNumerical
  26. Q86At 298 K, the standard reduction potential for Cu2+/Cu\mathrm{Cu^{2+}/Cu} electrode is 0.34 V. Given : Ksp Cu(OH)2=1×10−20K_{sp}\ \mathrm{Cu(OH)_2}=1\times10^{-20} Take…HardElectrochemistryNumerical
  27. Q87A(g)→2B(g)+C(g)\mathrm{A(g)\rightarrow 2B(g)+C(g)} is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to…MediumChemical KineticsNumerical
  28. Q88See the following chemical reaction:…EasyRedox ReactionsNumerical
  29. Q89If the formula of Borax is Na2B4Ox(OH)y⋅zH2O\mathrm{Na_2B_4O_x(OH)_y\cdot zH_2O}, then x+y+z=x+y+z= ______MediumThe p-Block ElementsNumerical
  30. Q900.400 g of an organic compound (X) gave 0.376 g of AgBr in Carius method for estimation of bromine. % of bromine in the compound (X) is ______ .…EasyOrganic Chemistry: Some Basic Principles and TechniquesNumerical

Maths Q1–30

  1. Q1The range of f(x)=4sin⁡−1(x2x2+1)f(x)=4\sin^{-1}\left(\frac{x^2}{x^2+1}\right) isMediumInverse Trigonometric Functions
  2. Q2Let S={z∈C:zˉ=i(z2+Re(zˉ))}S=\{z\in\mathbb{C}: \bar{z}=i(z^2+Re(\bar{z}))\}. Then ∑z∈S∣z∣2\sum_{z\in S}|z|^2 is equal toHardComplex Numbers and Quadratic Equations
  3. Q3Let α,β\alpha, \beta be the roots of the equation x2−2x+2=0x^2-\sqrt{2}x+2=0. Then α14+β14\alpha^{14}+\beta^{14} is equal toMediumComplex Numbers and Quadratic Equations
  4. Q4If the system of equations 2x+y−z=52x+y-z=5 2x−5y+λz=μ2x-5y+\lambda z=\mu x+2y−5z=7x+2y-5z=7 has infinitely many solutions, then (λ+μ)2+(λ−μ)2(\lambda+\mu)^2+(\lambda-\mu)^2 is…MediumDeterminants
  5. Q5Let for A=[123α31112]A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}, ∣A∣=2|A|=2. If ∣2 adj(2 adj(2A))∣=32n|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n, then 3n+α3n+\alpha is…MediumDeterminants
  6. Q6All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial…EasyPermutations and Combinations
  7. Q7The coefficient of x5x^5 in the expansion of (2x3−13x2)5\left(2x^3-\frac{1}{3x^2}\right)^5 isEasyBinomial Theorem
  8. Q8Let a1,a2,a3,…a_1, a_2, a_3, \ldots be a G.P. of increasing positive numbers. Let the sum of its 6th6^{th} and 8th8^{th} terms be 22 and the product of its…MediumSequences and Series
  9. Q9If lim⁡x→0eax−cos⁡(bx)−cxe−cx21−cos⁡(2x)=17\lim_{x\to0}\dfrac{e^{ax}-\cos(bx)-\dfrac{cxe^{-cx}}{2}}{1-\cos(2x)}=17, then 5a2+b25a^2+b^2 is equal toHardLimits and Derivatives
  10. Q10The value of…HardIntegrals
  11. Q11The area of the region {(x,y):x2≤y≤∣x2−4∣, y≥1}\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\} isHardApplication of Integrals
  12. Q12Let (α,β)(\alpha,\beta) be the centroid of the triangle formed by the lines 15x−y=8215x-y=82, 6x−5y=−46x-5y=-4 and 9x+4y=179x+4y=17. Then α+2β\alpha+2\beta and…MediumStraight Lines
  13. Q13Let the centre of a circle C be (α,β)(\alpha,\beta) and its radius r<8r<8. Let 3x+4y=243x+4y=24 and 3x−4y=323x-4y=32 be two tangents and 4x+3y=14x+3y=1 be a normal to C.…MediumConic Sections
  14. Q14The plane, passing through the points (0,−1,2)(0,-1,2) and (−1,2,1)(-1,2,1) and parallel to the line passing through (5,1,−7)(5,1,-7) and (1,−1,−1)(1,-1,-1), also passes…MediumThree Dimensional Geometry
  15. Q15The line, that is coplanar to the line x+3−3=y−11=z−55\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}, isMediumThree Dimensional Geometry
  16. Q16Let N be the foot of perpendicular from the point P (1,−2,3)(1,-2,3) on the line passing through the points (4,5,8)(4,5,8) and (1,−7,5)(1,-7,5). Then the distance of…MediumThree Dimensional Geometry
  17. Q17Let ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=3|\vec{b}|=3 and the angle between the vectors a⃗\vec{a} and b⃗\vec{b} be π4\frac{\pi}{4}. Then…MediumVector Algebra
  18. Q18Let for a triangle ABC, AB→=−2i^+j^+3k^\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k} CB→=αi^+βj^+γk^\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}…MediumVector Algebra
  19. Q19The random variable X follows binomial distribution B(n,p)(n, p), for which the difference of the mean and the variance is 11. If 2P(X=2)=3P(X=1)2P(X=2)=3P(X=1),…MediumProbability
  20. Q20The statement (p∧(∼q))∨((∼p)∧q)∨((∼p)∧(∼q))(p\wedge(\sim q))\vee((\sim p)\wedge q)\vee((\sim p)\wedge(\sim q)) is equivalent to ______EasyMathematical Reasoning
  21. Q21Let A={−4,−3,−2,0,1,3,4}A=\{-4,-3,-2,0,1,3,4\} and R={(a,b)∈A×A:b=∣a∣ or b2=a+1}R=\{(a,b)\in A\times A: b=|a| \text{ or } b^2=a+1\} be a relation on A. Then the minimum number of elements, that…MediumRelations and FunctionsNumerical
  22. Q22Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______MediumPermutations and CombinationsNumerical
  23. Q23The remainder, when 71037^{103} is divided by 17, is ______MediumBinomial TheoremNumerical
  24. Q24Let [α][\alpha] denote the greatest integer ≤α\le\alpha. Then [1]+[2]+[3]+…+[120][\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}] is equal to ______MediumRelations and FunctionsNumerical
  25. Q25Let f(x)=∑k=110k xkf(x)=\sum_{k=1}^{10}k\,x^k, x∈Rx\in\mathbb{R}. If 2f(2)+f′(2)=119(2)n+12f(2)+f'(2)=119(2)^n+1 then nn is equal to ______HardLimits and DerivativesNumerical
  26. Q26Let fn=∫0π2(∑k=1nsin⁡k−1x)(∑k=1n(2k−1)sin⁡k−1x)cos⁡x dxf_n=\int_0^{\frac{\pi}{2}}\left(\sum_{k=1}^{n}\sin^{k-1}x\right)\left(\sum_{k=1}^{n}(2k-1)\sin^{k-1}x\right)\cos x\,dx, n∈Nn\in\mathbb{N}. Then…HardIntegralsNumerical
  27. Q27If y=y(x)y=y(x) is the solution of the differential equation dydx+4x(x2−1)y=x+2(x2−1)52\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}, x>1x>1 such that…HardDifferential EquationsNumerical
  28. Q28The foci of a hyperbola are (±2,0)(\pm2,0) and its eccentricity is 32\frac{3}{2}. A tangent, perpendicular to the line 2x+3y=62x+3y=6, is drawn at a point in…HardConic SectionsNumerical
  29. Q29The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25…EasyStatisticsNumerical
  30. Q30For x∈(−1,1]x\in(-1,1], the number of solutions of the equation sin⁡−1x=2tan⁡−1x\sin^{-1}x=2\tan^{-1}x is equal to ______.HardInverse Trigonometric 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 2023 shifts.