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Saturday, 10 October

JEE Main 2021 · July session

JEE Main 3 August 2021, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 6 were rated hard and 29 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
60
12 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 14Medium 13Hard 3

Top chapters

Chemistry
30 Q · 10 numerical
Easy 9Medium 20Hard 1

Top chapters

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

Top chapters

Question format
  • Single correct52 Q
  • Numerical value30 Q
  • Assertion–reason3 Q
  • Diagram based2 Q
  • Two statements1 Q
  • Other1 Q
  • Match the list1 Q
What each question asks you to do
  • Calculation34 Q
  • Multi-step22 Q
  • Application14 Q
  • Conceptual9 Q
  • Recall7 Q
  • Diagram reading3 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. Q1A particle is executing simple harmonic motion with time period TT. What is the time taken by the particle to go directly to 12\frac{1}{\sqrt{2}}…EasyOscillations
  2. Q2A block of mass m rigidly attached with a spring of spring constant KK, is compressed through a small distance A. If the block is now released, the…MediumOscillations
  3. Q3One mole Argon gas is sealed inside a thermally isolated chamber of 1 litre. A 100 W heater kept inside the chamber is switched on for 30 seconds.…MediumThermodynamics
  4. Q4A solid sphere of radius RR has mass MM. A rod of mass mm is attached tangentially to the sphere. What would be the moment of inertia of the…MediumSystem of Particles and Rotational Motion
  5. Q5One end of a metal wire is fixed at the centre of a uniform disc of radius 4.0 cm and mass 100 g. The other end of the wire is fixed with a clamp.…MediumOscillations
  6. Q6A particle is projected from the mid-point of the line joining two fixed particles each of mass mm in free space. If the separation between the…HardGravitation
  7. Q7A solid sphere of mass MM and radius RR lies on a horizontal rough surface. A horizontal force FF is applied at the centre of the sphere. The…MediumSystem of Particles and Rotational Motion
  8. Q8A projectile is thrown with initial velocity of (3i^+4j^) m/s(3\hat{i}+4\hat{j})\ \mathrm{m/s}. Here 'i^\hat{i}' is along the horizontal direction and…MediumMotion in a Plane
  9. Q9The velocity of a particle starting from origin which is set into motion at t=0t = 0 varies as V=V0(2−t)V = V_0(2-t), where V0V_0 is a positive constant.…MediumMotion in a Straight Line
  10. Q10The following diagram shows the relation between stress and strain of two materials A and B. The ratio of Young's modulus of A and B is -EasyMechanical Properties of Solids
  11. Q11An electric charge 10−2 μC10^{-2}\,\mu\mathrm{C} is placed at the origin (0, 0) of X–Y coordinate system. The coordinates of two points A and B are…EasyElectrostatic Potential and Capacitance
  12. Q12If AA, ZZ and MM represents the number of nucleons, protons and mass of the nucleus respectively, then mass defect ΔM\Delta M is represented by…EasyNuclei
  13. Q13A magnetic needle of length 12 cm, suspended at its middle point by a thread, stays at an angle of 45∘45^\circ with the horizontal. If the pole…HardMagnetism and Matter
  14. Q14Two concentric and coplanar circular coils have radius aa and b (≫a)b\ (\gg a) as shown in figure. Resistance of the inner coil is RR. Current in the…MediumElectromagnetic Induction
  15. Q15To view a small object with angular magnification 5, the power of the microscope needed is [The final image is formed at infinity] (Distance of…EasyRay Optics and Optical Instruments
  16. Q16If a man having the least distance of distinct vision of 50 cm, what should be the focal length of the spectacles for the man ?EasyRay Optics and Optical Instruments
  17. Q17Identify the resulting gate for the following circuit.MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  18. Q18A radioactive isotope has a half life of T years. After how much time is its activity reduced to 6.25% of its original activity ?EasyNuclei
  19. Q19Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R. Assertion A : Communication techniques which…EasyElectromagnetic Waves
  20. Q20A block of mass 4.0 kg is pulled up on a smooth incline of angle 30∘30^\circ with the horizontal. If the block moves with an acceleration of 1.0…MediumWork, Energy and Power
  21. Q21‾×10−10\underline{\hspace{2em}}\times10^{-10} J (joule) energy is contained in a 120 m length of a laser beam operating at 4mW.MediumElectromagnetic WavesNumerical
  22. Q22The magnetic flux linked with a coil at any instant 't' is given by ϕ=5t3−100t+300\phi = 5t^3 - 100t + 300 (SI unit). The emf induced in the coil at t = 2 s is…EasyElectromagnetic InductionNumerical
  23. Q23The ratio of shortest wavelength to the largest wavelength in Brackett series of atomic spectra for hydrogen atom is x:25x : 25, where the value of…MediumAtomsNumerical
  24. Q24A train left the station at uniform acceleration of 2 m/s2^2. A man behind the train at a distance of 5 m is running with a constant speed of 6 m/s…EasyMotion in a Straight LineNumerical
  25. Q25A sample undergoing beta decay, reduced to 116th\frac{1}{16}^{\mathrm{th}} of its initial mass in 48 years. Its half life period is…EasyNucleiNumerical
  26. Q26Two particles of equal mass 'm' go round a circle of radius RR under the action of their mutual gravitational attraction. The speed of each…MediumGravitationNumerical
  27. Q27In Young's double slit experiment, 58 fringes are observed in the field of view when a light of wavelength 6000 A˚\mathrm{\AA} was used. Number of…EasyWave OpticsNumerical
  28. Q28As the switch S is closed in the circuit shown in figure, current passed through it is ‾\underline{\hspace{2em}} A.EasyCurrent ElectricityNumerical
  29. Q29The electric potential at point (x,0,0)(x, 0, 0) is V=(1000x+1500x2+500x3)V = \left(\frac{1000}{x}+\frac{1500}{x^2}+\frac{500}{x^3}\right) volt. The electric field strength…EasyElectrostatic Potential and CapacitanceNumerical
  30. Q30A body of mass 20 kg is placed at a latitude of 45∘45^\circ on earth of radius RR and angular speed ω\omega. The change in weight of the body (if…HardGravitationNumerical

Chemistry Q31–60

  1. Q31Given below are two statements : Statement I : In dichromate ion, all the Cr—O bonds are of equal length. Statement II : In dichromate ion, the…MediumThe d- and f-Block Elements
  2. Q32The lowest freezing point among the following solutions will be observed in [Atomic weight : C = 12, Mg = 24, Na = 23, Cl = 35.5, O = 16, N = 14]EasySolutions
  3. Q33The correct order of the basic character for the following metal hydroxides isMediumThe s-Block Elements
  4. Q34Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Fluoride based compound is added…EasyGeneral Principles and Processes of Isolation of Elements
  5. Q35Which one of the following statements is incorrect? A. The correct order of increasing first ionization enthalpy is Li < H < F. B. Out of the three…MediumHydrogen
  6. Q36A white solid (X) on heating forms a solid (Y) and a gas (Z). Another solid (B) forms (X) by reacting with (Z). (Y) can be converted into (X) and…MediumThe s-Block Elements
  7. Q37Silicones are group of organosilicon polymers. Which one among the following acts as a chain terminating unit in silicone polymerization?EasyThe p-Block Elements
  8. Q38Which one of the following set will give coloured aqueous solution?EasyThe d- and f-Block Elements
  9. Q39Which one of the following statements is correct?MediumThe d- and f-Block Elements
  10. Q40The oxidation states of Fe in [Fe(NCS)(NH3)5]SO4\mathrm{[Fe(NCS)(NH_3)_5]SO_4}, Na3[Fe(S2O3)3]\mathrm{Na_3[Fe(S_2O_3)_3]} and [Fe(CO)5]\mathrm{[Fe(CO)_5]} respectively areEasyCoordination Compounds
  11. Q41Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Fluoride ion concentration above…EasyEnvironmental Chemistry
  12. Q42In the detection of nitrogen in an organic compound by Lassaigne's test, the iron compounds formed areMediumOrganic Chemistry: Some Basic Principles and Techniques
  13. Q43Order of reactivity for hydrolysis of substituted chlorobenzenes in the presence of aqueous NaOH isMediumHaloalkanes and Haloarenes
  14. Q44The correct structure of ciscis–2,4-dimethylhept-3-ene is,MediumOrganic Chemistry: Some Basic Principles and Techniques
  15. Q45Arrange the following halides in the increasing order of their reactivity towards SN1\mathrm{S_N1} reaction mechanism.MediumHaloalkanes and Haloarenes
  16. Q46Which one of the following reagents are not suitable for the preparation of benzaldehyde from benzene?MediumAldehydes, Ketones and Carboxylic Acids
  17. Q47A. →2) Heat1) NaNO2(aq.), HCl\xrightarrow[\text{2) Heat}]{\text{1) }\mathrm{NaNO_{2(aq.)}},\ \mathrm{HCl}} B. →conc. H2SO4NO2+\xrightarrow[\text{conc. }\mathrm{H_2SO_4}]{\mathrm{NO_2^+}}…EasyAmines
  18. Q48Match List I with II List I | List II (Ion detected) A. Borax Bead test | I. As3+\mathrm{As^{3+}} B. Charcoal cavity test | II. Al3+\mathrm{Al^{3+}} C.…MediumPractical Chemistry (Qualitative Analysis)
  19. Q49Select the odd groupMediumPolymers
  20. Q50Which one of the following represents the correct structure of a dinucleotide?MediumBiomolecules
  21. Q51Chlorine is prepared according to the following equation : 4HCl+MnO2(s)⟶2H2O(l)+MnCl2(aq)+Cl2(g)\mathrm{4HCl + MnO_{2(s)} \longrightarrow 2H_2O_{(l)} + MnCl_{2(aq)} + Cl_{2(g)}}. 10g…MediumSome Basic Concepts of ChemistryNumerical
  22. Q52The total kinetic energy of 10 moles of a monoatomic ideal gas at 25°C in kJ is ‾\underline{\hspace{2em}}. (Nearest integer) [R = 8.314 J K−1^{-1}…EasyStates of MatterNumerical
  23. Q53The ratio of radii for the first and third orbits of hydrogen atom is 1:x1 : x. The value of xx is ‾\underline{\hspace{2em}}. (Integer answer)EasyStructure of AtomNumerical
  24. Q54The work done by an ideal monoatomic gas when it is taken along the path ABCD as shown in the figure is xP0V0xP_0V_0. The value of (−x)(-x) is…HardThermodynamics (Chemistry)Numerical
  25. Q55The pH of the solution resulted when 150 mL of 0.1 M ammonia solution is titrated with 50 mL of 0.1M HCl [pKb(NH3)\mathrm{pK_b(NH_3)} = 4.7] is…MediumEquilibriumNumerical
  26. Q56The potential of a cell containing two hydrogen electrodes, one in contact with 10−810^{-8} M H+\mathrm{H^+} concentration and the other in contact…MediumElectrochemistryNumerical
  27. Q57The inactivation process of virus is first order with respect to virus concentration and 2% of the virus was inactivated in the first one minute.…MediumChemical KineticsNumerical
  28. Q58In an adsorption isotherm, it is seen that the graph of log⁡(xm)\log\left(\frac{x}{m}\right) vs log⁡P\log P, where PP is in atm, is a straight line inclined…MediumSurface ChemistryNumerical
  29. Q59The number of electrophiles in the list below is ‾\underline{\hspace{2em}}. (Integer answer)…MediumOrganic Chemistry: Some Basic Principles and TechniquesNumerical
  30. Q60The number of isomers with molecular formula C3H9N\mathrm{C_3H_9N}, which will react with CHCl3+KOH\mathrm{CHCl_3 + KOH} is ‾\underline{\hspace{2em}}.…MediumAminesNumerical

Maths Q61–90

  1. Q61Let R\mathbb{R} be the set of real numbers and '*' be a binary operation on R−{0}\mathbb{R} - \{0\} defined by a∗b=a+2b+aba * b = a + 2b + \frac{a}{b}. Then…MediumRelations and Functions
  2. Q62If the equations 2x2+kx−5=02x^2 + kx - 5 = 0 and x2−3x−4=0x^2 - 3x - 4 = 0 have one root in common, then a value of 'kk' isEasyComplex Numbers and Quadratic Equations
  3. Q63Let A=(aij)A = (a_{ij}) be a 3×33\times3 matrix, where aij=7max⁡{i,j}a_{ij} = 7^{\max\{i,j\}}. Then det⁡A\det A is equal toMediumDeterminants
  4. Q64Let AA be a 3×33\times3 matrix and ∣A∣=−1|A| = -1. A matrix BB is obtained from the matrix AA by applying the following elementary row operations :…EasyDeterminants
  5. Q65For the system of linear equations (k−3)x+y+z=0(k-3)x + y + z = 0 x+(k−3)y+z=0x + (k-3)y + z = 0 x+y+(k−3)z=0x + y + (k-3)z = 0 the number of distinct values of kk, for which it…MediumDeterminants
  6. Q66In the Binomial expansion of (2xx+3y116)33\left(2x\sqrt{x} + 3y^{\frac{1}{16}}\right)^{33}, the number of terms, having positive integral powers of xx and yy…MediumBinomial Theorem
  7. Q67If 'mm' is the arithmetic mean of two distinct real numbers ll and nn (l,n>1)(l, n > 1) and G1G_1, G2G_2 and G3G_3 are three geometric means between…MediumSequences and Series
  8. Q68lim⁡x→0(1+x)1ex−1\lim_{x\to0}(1+x)^{\frac{1}{e^x-1}} is equal toEasyLimits and Derivatives
  9. Q69If for non-zero distinct real numbers aa, bb and cc,…MediumContinuity and Differentiability
  10. Q70Let f:R→Rf : \mathbb{R} \to \mathbb{R} be a differentiable function such that f(0)=2f(0) = 2. If ∣dfdx∣≤3\left|\frac{df}{dx}\right| \le 3, for all…MediumApplication of Derivatives
  11. Q71If the function f:R→Rf : \mathbb{R} \to \mathbb{R} defined by f(x)=x33−(2a+3b)x2+24abx+5f(x) = \frac{x^3}{3} - (2a+3b)x^2 + 24abx + 5 has a local maxima at −4-4 and a local…MediumApplication of Derivatives
  12. Q72The integral ∫dx2x+5−2x+3\int \frac{dx}{\sqrt{2x+5}-\sqrt{2x+3}} is equal to (where C is a constant of integration)MediumIntegrals
  13. Q73A curve passes through the point (−1,4)(-1, 4). If the normal to it at any point (x,y)(x, y) on it passes through (2,0)(2, 0), then its equation isMediumDifferential Equations
  14. Q74If an ellipse passes through the point (4,1)(4, 1) and has foci at (±3,0)(\pm3, 0), then its eccentricity isMediumConic Sections
  15. Q75The tangents, to the parabola y2=2−xy^2 = 2 - x at the points of its intersection with the line y=x−2y = x - 2, intersect at the pointMediumConic Sections
  16. Q76Let L1L_1 and L2L_2 be two lines passing through the points P(b−c,c−a,a−b)P(b-c, c-a, a-b) and Q(1l,1m,1n)Q\left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)…HardThree Dimensional Geometry
  17. Q77A plane intersects the yzyz-plane at x=0, 2y−3z=5x = 0,\ 2y - 3z = 5 and it intersects the xyxy-plane at z=0, 7x+4y=10z = 0,\ 7x + 4y = 10. Then the distance of the…MediumThree Dimensional Geometry
  18. Q78A dice is thrown twice. If AA is the event that the sum of numbers appearing on them is 7 and BB is the event that number 5 appears at least once,…EasyProbability
  19. Q79The maximum value of (cos⁡θ1)⋅(cos⁡θ2)⋅(cos⁡θ3)⋅…⋅(cos⁡θ10)(\cos\theta_1)\cdot(\cos\theta_2)\cdot(\cos\theta_3)\cdot\ldots\cdot(\cos\theta_{10}) under the restrictions…HardTrigonometric Functions
  20. Q80The statement ∼(p↔∼q)\sim(p \leftrightarrow \sim q) is equivalent toEasyMathematical Reasoning
  21. Q81The number of elements in the set {x∈R:(∣x∣−2)⋅∣2x+3∣=1}\{x \in \mathbb{R} : (|x| - 2)\cdot|2x+3| = 1\} is ‾\underline{\hspace{2em}}.MediumRelations and FunctionsNumerical
  22. Q82If six letter words (with or without meaning) are formed using A, B, C, D, E and F, then the number of words, in which exactly one of these…MediumPermutations and CombinationsNumerical
  23. Q83If the sum of all 3-digit numbers which are multiples of 9 is 41k41k, then 'kk' is equal to ‾\underline{\hspace{2em}}.EasySequences and SeriesNumerical
  24. Q84If [x][x] denotes the greatest integer ≤x\le x, then the value of ∫−24∣[x]−x∣dx\int_{-2}^{4}\left|[x] - x\right|dx is ‾\underline{\hspace{2em}}.MediumIntegralsNumerical
  25. Q85If the area (in sq. units) bounded by the parabolas 5x2−y=05x^2 - y = 0 and 2x2−y+b=02x^2 - y + b = 0 (b>0)(b > 0) is 12312\sqrt{3}, then 'bb' is equal to…MediumApplication of IntegralsNumerical
  26. Q86The circles, x2+y2+2x+4y−4=0x^2 + y^2 + 2x + 4y - 4 = 0 and x2+y2−4x+4y+k=0x^2 + y^2 - 4x + 4y + k = 0 touch each other internally. If the point of contact of these circles…MediumConic SectionsNumerical
  27. Q87If the solution y=y(x)y = y(x) of the differential equation (y+3x4)dxdy=x, x>0\left(y + 3x^4\right)\frac{dx}{dy} = x,\ x > 0, satisfies y(1)=−1y(1) = -1, then the value of…MediumDifferential EquationsNumerical
  28. Q88The mean and variance of 7 observations are 7 and 18 respectively. If 5 of the observations are 2, 4, 10, 11, 13 and the remaining observations are…MediumStatisticsNumerical
  29. Q89A vertical pole of height 10310\sqrt{3} meters is observed from three points, A, B and C in the same horizontal line passing through the foot 'O' of…MediumTrigonometric FunctionsNumerical
  30. Q90Let a⃗=2i^+αj^+k^\vec{a} = 2\hat{i} + \alpha\hat{j} + \hat{k} and b⃗=βi^−5j^+γk^\vec{b} = \beta\hat{i} - 5\hat{j} + \gamma\hat{k}, where α\alpha, β\beta and γ\gamma are…MediumVector AlgebraNumerical

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.