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Saturday, 10 October

JEE Main 2021 · March session

JEE Main 16 March 2021, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 6 were rated hard and 28 easy. By hard questions it ranks 3rd of the 4 2021 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions
90
none dropped
Numerical answer
30
33% of the shift
Hard
6
7% of the shift
Chapters asked
67
11 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 14Medium 16Hard 0

Top chapters

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

Top chapters

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

Top chapters

Question format
  • Single correct47 Q
  • Numerical value30 Q
  • Diagram based8 Q
  • Two statements2 Q
  • Other2 Q
  • Match the list1 Q
What each question asks you to do
  • Calculation30 Q
  • Multi-step30 Q
  • Application13 Q
  • Recall10 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 Q1–30

  1. Q1Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of…MediumCommunication Systems
  2. Q2The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should…MediumDual Nature of Radiation and Matter
  3. Q3The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index ?…EasyRay Optics and Optical Instruments
  4. Q4Red light differs from blue light as they have :EasyWave Optics
  5. Q5The magnetic field in a region is given by B⃗=Bo(xa)k^\vec{B}=B_o\left(\frac{x}{a}\right)\hat{k}. A square loop of side d is placed with its edges along the…MediumElectromagnetic Induction
  6. Q6Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g, Decay constant = 20 g/s then how…MediumOscillations
  7. Q7Calculate the value of mean free path (λ\lambda) for oxygen molecules at temperature 27∘C27^\circ\mathrm{C} and pressure 1.01×1051.01\times10^5 Pa. Assume…EasyKinetic Theory
  8. Q8What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min ? The radius of the tap and…MediumMechanical Properties of Fluids
  9. Q9A charge Q is moving dl⃗\vec{dl} distance in the magnetic field B⃗\vec{B}. Find the value of work done by B⃗\vec{B}.EasyMoving Charges and Magnetism
  10. Q10Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.EasyNuclei
  11. Q11For the given circuit, comment on the type of transformer used.EasyAlternating Current
  12. Q12The half-life of Au198\mathrm{Au^{198}} is 2.7 days. The activity of 1.50 mg of Au198\mathrm{Au^{198}} if its atomic weight is 198 g mol−1\mathrm{mol^{-1}}…MediumNuclei
  13. Q13A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of…EasyThermal Properties of Matter
  14. Q14A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets…MediumWork, Energy and Power
  15. Q15Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh−1\mathrm{kmh^{-1}} and takes a sharp circular turn along a path of radius…MediumLaws of Motion
  16. Q16A mosquito is moving with a velocity v⃗=0.5 t2i^+3tj^+9k^\vec{v}=0.5\,t^2\hat{i}+3t\hat{j}+9\hat{k} m/s and accelerating in uniform conditions. What will be the…MediumMotion in a Plane
  17. Q17In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured…MediumUnits and Measurements
  18. Q18A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5 A to 3 A, what…EasyCurrent Electricity
  19. Q19Find out the surface charge density at the intersection of point x=3x=3 m plane and xx-axis, in the region of uniform line charge of 8 nC/m lying…MediumElectric Charges and Fields
  20. Q20The following logic gate is equivalent to :MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  21. Q21If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will…MediumGravitationNumerical
  22. Q22A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the…EasyMotion in a PlaneNumerical
  23. Q23A body of mass 2 kg moves under a force of (2i^+3j^+5k^)(2\hat{i}+3\hat{j}+5\hat{k}) N. It starts from rest and was at the origin initially. After 4 s, its new…EasyMotion in a Straight LineNumerical
  24. Q24A force F⃗=4i^+3j^+4k^\vec{F}=4\hat{i}+3\hat{j}+4\hat{k} is applied on an intersection point of x=2x=2 plane and xx-axis. The magnitude of torque of this force…EasySystem of Particles and Rotational MotionNumerical
  25. Q25A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle θ\theta with the horizontal. The…MediumSystem of Particles and Rotational MotionNumerical
  26. Q26For an ideal heat engine, the temperature of the source is 127∘127^\circC. In order to have 60% efficiency the temperature of the sink should be…EasyThermodynamicsNumerical
  27. Q27In a parallel plate capacitor set up, the plate area of capacitor is 2 m22\ \mathrm{m^2} and the plates are separated by 1 m. If the space between the…EasyElectrostatic Potential and CapacitanceNumerical
  28. Q28The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is ________Ω\Omega. (Round…EasyCurrent ElectricityNumerical
  29. Q29A deviation of 2∘2^\circ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of…MediumRay Optics and Optical InstrumentsNumerical
  30. Q30A closed organ pipe of length L and an open organ pipe contain gases of densities ρ1\rho_1 and ρ2\rho_2 respectively. The compressibility of gases…MediumWavesNumerical

Chemistry Q31–60

  1. Q31The INCORRECT statement regarding the structure of C60\mathrm{C_{60}} is :MediumThe p-Block Elements
  2. Q32The INCORRECT statements below regarding colloidal solutions is :EasySurface Chemistry
  3. Q33The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are :MediumClassification of Elements and Periodicity in Properties
  4. Q34Which of the following reduction reaction CANNOT be carried out with coke ?EasyGeneral Principles and Processes of Isolation of Elements
  5. Q35The correct statements about H2O2\mathrm{H_2O_2} are : (A) used in the treatment of effluents. (B) used as both oxidising and reducing agents. (C) the…MediumHydrogen
  6. Q36Identify the elements X and Y using the ionisation energy values given below : Ionization energy (kJ/mol) 1st 2nd X 495 4563 Y 731 1450EasyClassification of Elements and Periodicity in Properties
  7. Q37The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H3PO3\mathrm{H_3PO_3} solution and 100 mL of 2 M H3PO2\mathrm{H_3PO_2}…MediumThe p-Block Elements
  8. Q38Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system. (Atomic…MediumThe d- and f-Block Elements
  9. Q39FeX2\mathrm{FeX_2} and FeY3\mathrm{FeY_3} are known when xx and yy are :MediumThe d- and f-Block Elements
  10. Q40The green house gas/es is (are ) : (A) Carbon dioxide (B) Oxygen (C) Water vapour (D) Methane Choose the most appropriate answer from the options…EasyEnvironmental Chemistry
  11. Q41Match List-I with List-II : List-I (Test/Reagents/Observation(s)) (a) Lassaigne's Test (b) Cu(II) oxide (c) Silver nitrate (d) The sodium fusion…MediumOrganic Chemistry: Some Basic Principles and Techniques
  12. Q42Statement I : Sodium hydride can be used as an oxidising agent. Statement II : The lone pair of electrons on nitrogen in pyridine makes it basic.…EasyHydrogen
  13. Q43An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammonical silver nitrate forms a bright silver mirror along the…MediumHydrocarbons
  14. Q44[figure: cyclohexene reacts with reagent A to give 1,4-dichlorocyclohex-2-ene (a cyclohexene ring with Cl on the two ring carbons para to each…MediumHydrocarbons
  15. Q45[figure: 3-methylanisole (benzene ring with CH3 and OCH3 meta to each other) --"A"--> 3-methoxybenzoic acid (benzene ring with COOH and OCH3 meta to…EasyAldehydes, Ketones and Carboxylic Acids
  16. Q46[figure: 2-substituted benzonitrile (benzene ring bearing CN and a CH(CH3)(OCH3) group ortho to each other)] reacts with (i) C6H5MgBr\mathrm{C_6H_5MgBr}…MediumAldehydes, Ketones and Carboxylic Acids
  17. Q47Which of the following is least basic ?EasyAmines
  18. Q48Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and tertiary amines. The purpose…MediumAmines
  19. Q49Which of the following polymer is used in the manufacture of wood laminates ?EasyPolymers
  20. Q50The secondary structure of protein is stabilised by :EasyBiomolecules
  21. Q51When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, ________ ×10−5\times10^{-5} moles of lead sulphate…MediumSome Basic Concepts of ChemistryNumerical
  22. Q52Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ________ ×1021\times10^{21}.…MediumThe Solid StateNumerical
  23. Q53The number of orbitals with n=5n=5, ml=+2m_l=+2 is ________. (Round off to the Nearest Integer).EasyStructure of AtomNumerical
  24. Q54At 25∘25^\circC, 50 g of iron reacts with HCl to form FeCl2\mathrm{FeCl_2}. The evolved hydrogen gas expands against a constant pressure of 1 bar. The…MediumThermodynamics (Chemistry)Numerical
  25. Q55At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is…EasySolutionsNumerical
  26. Q56Sulphurous acid (H2SO3\mathrm{H_2SO_3}) has Ka1=1.7×10−2K_{a_1}=1.7\times10^{-2} and Ka2=6.4×10−8K_{a_2}=6.4\times10^{-8}. The pH of 0.588 M H2SO3\mathrm{H_2SO_3} is…MediumEquilibriumNumerical
  27. Q57A 5.0 m mol dm−3\mathrm{dm^{-3}} aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 cm−1\mathrm{cm^{-1}}.…MediumElectrochemistryNumerical
  28. Q58A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A…MediumChemical KineticsNumerical
  29. Q59[Ti(H2O)6]3+\mathrm{[Ti(H_2O)_6]^{3+}} absorbs light of wavelength 498 nm during a d-d transition. The octahedral splitting energy for the above complex is…EasyCoordination CompoundsNumerical
  30. Q60In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The…MediumOrganic Chemistry: Some Basic Principles and TechniquesNumerical

Maths Q61–90

  1. Q61If the foot of the perpendicular from point (4, 3, 8) on the line L1:x−al=y−23=z−b4L_1:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}, l≠0l\neq0 is (3, 5, 7), then the…MediumThree Dimensional Geometry
  2. Q62Let the lengths of intercepts on xx-axis and yy-axis made by the circle x2+y2+ax+2ay+c=0x^2+y^2+ax+2ay+c=0, (a<0a<0) be 222\sqrt2 and 252\sqrt5, respectively.…MediumConic Sections
  3. Q63Let a⃗=i^+2j^−3k^\vec a=\hat i+2\hat j-3\hat k and b⃗=2i^−3j^+5k^\vec b=2\hat i-3\hat j+5\hat k. If r⃗×a⃗=b⃗×r⃗\vec r\times\vec a=\vec b\times\vec r,…HardVector Algebra
  4. Q64Let ff be a real valued function, defined on R−{−1,1}\mathbf R-\{-1,1\} and given by f(x)=3log⁡e∣x−1x+1∣−2x−1f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}. Then in…MediumApplication of Derivatives
  5. Q65If the points of intersections of the ellipse x216+y2b2=1\frac{x^2}{16}+\frac{y^2}{b^2}=1 and the circle x2+y2=4bx^2+y^2=4b, b>4b>4 lie on the curve y2=3x2y^2=3x^2,…MediumConic Sections
  6. Q66Let C be the locus of the mirror image of a point on the parabola y2=4xy^2=4x with respect to the line y=xy=x. Then the equation of tangent to C at P(2,…MediumConic Sections
  7. Q67Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is…MediumProbability
  8. Q68If y=y(x)y=y(x) is the solution of the differential equation dydx+(tan⁡x) y=sin⁡x\frac{dy}{dx}+(\tan x)\,y=\sin x, 0≤x≤π30\le x\le\frac{\pi}{3}, with y(0)=0y(0)=0, then…MediumDifferential Equations
  9. Q69Let α∈R\alpha\in\mathbf R be such that the function…HardContinuity and Differentiability
  10. Q70If (x,y,z)(x,y,z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of the…MediumThree Dimensional Geometry
  11. Q71Let A={2,3,4,5,…,30}A=\{2,3,4,5,\ldots,30\} and '≃\simeq' be an equivalence relation on A×AA\times A, defined by (a,b)≃(c,d)(a,b)\simeq(c,d), if and only if ad=bcad=bc. Then…MediumRelations and Functions
  12. Q72Let P(x)=x2+bx+cP(x)=x^2+bx+c be a quadratic polynomial with real coefficients such that ∫01P(x) dx=1\int_0^1P(x)\,dx=1 and P(x)P(x) leaves remainder 5 when it is divided…EasyIntegrals
  13. Q73Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let α\alpha be the number of…MediumPermutations and Combinations
  14. Q74Consider the integral I=∫010[x] e[x]ex−1 dxI=\int_0^{10}\frac{[x]\,e^{[x]}}{e^{x-1}}\,dx, where [x][x] denotes the greatest integer less than or equal to xx. Then the…MediumIntegrals
  15. Q75Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y=mxy=mx, m>0m>0, intersects lines AC and BC at point P and Q respectively. Let A1A_1…MediumStraight Lines
  16. Q76The least value of ∣z∣|z| where zz is complex number which satisfies the inequality…MediumComplex Numbers and Quadratic Equations
  17. Q77The maximum value of f(x)=∣sin⁡2x1+cos⁡2xcos⁡2x1+sin⁡2xcos⁡2xcos⁡2xsin⁡2xcos⁡2xsin⁡2x∣f(x)=\begin{vmatrix}\sin^2x & 1+\cos^2x & \cos2x\\ 1+\sin^2x & \cos^2x & \cos2x\\ \sin^2x & \cos^2x & \sin2x\end{vmatrix},…MediumDeterminants
  18. Q78Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xx which satisfy…MediumInverse Trigonometric Functions
  19. Q79Let f:S→Sf:S\to S where S=(0,∞)S=(0,\infty) be a twice differentiable function such that f(x+1)=xf(x)f(x+1)=xf(x). If g:S→Rg:S\to\mathbf R be defined as…HardApplication of Derivatives
  20. Q80Let C1C_1 be the curve obtained by the solution of differential equation 2xydydx=y2−x22xy\frac{dy}{dx}=y^2-x^2, x>0x>0. Let the curve C2C_2 be the solution of…HardApplication of Integrals
  21. Q81For real numbers α,β,γ\alpha,\beta,\gamma and δ\delta, if…HardIntegralsNumerical
  22. Q82In △\triangleABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of △\triangleABC is 30 cm2\mathrm{cm^2} and R and r…MediumTrigonometric FunctionsNumerical
  23. Q83If the distance of the point (1, −2-2, 3) from the plane x+2y−3z+10=0x+2y-3z+10=0 measured parallel to the line, x−13=2−ym=z+31\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}…MediumThree Dimensional GeometryNumerical
  24. Q84Let c⃗\vec c be a vector perpendicular to the vectors a⃗=i^+j^−k^\vec a=\hat i+\hat j-\hat k and b⃗=i^+2j^+k^\vec b=\hat i+2\hat j+\hat k. If…MediumVector AlgebraNumerical
  25. Q85Let f:R→Rf:\mathbf R\to\mathbf R and g:R→Rg:\mathbf R\to\mathbf R be defined as f(x)={x+a,x<0∣x−1∣,x≥0f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases} and…MediumContinuity and DifferentiabilityNumerical
  26. Q86Consider the statistics of two sets of observations as follows : Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the variance of the…EasyStatisticsNumerical
  27. Q87Let n be a positive integer. Let…MediumBinomial TheoremNumerical
  28. Q88Let A=[a1a2]A=\begin{bmatrix}a_1\\a_2\end{bmatrix} and B=[b1b2]B=\begin{bmatrix}b_1\\b_2\end{bmatrix} be two 2×12\times1 matrices with real entries such that…MediumMatricesNumerical
  29. Q89Let 116\frac{1}{16}, a and b be in G.P. and 1a,1b\frac1a,\frac1b, 6 be in A.P., where a,b>0a,b>0. Then 72(a+b)72(a+b) is equal to ________.MediumSequences and SeriesNumerical
  30. Q90Let Sn(x)=log⁡a1/2x+log⁡a1/3x+log⁡a1/6x+log⁡a1/11x+log⁡a1/18x+log⁡a1/27x+…S_n(x)=\log_{a^{1/2}}x+\log_{a^{1/3}}x+\log_{a^{1/6}}x+\log_{a^{1/11}}x+\log_{a^{1/18}}x+\log_{a^{1/27}}x+\ldots up to n-terms, where a>1a>1.…HardSequences and SeriesNumerical

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 2021 shifts.