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Friday, 9 October

JEE Main 2021 · July session

JEE Main 25 July 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 28 easy. By hard questions it ranks 1st of the 4 2021 shifts Lumi analysed. The biggest chapter was Amines, with 3 questions.

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

The shift at a glance

Subjects, difficulty and chapters

Physics
30 Q · 10 numerical
Easy 11Medium 17Hard 2

Top chapters

Chemistry
30 Q · 10 numerical
Easy 11Medium 16Hard 3

Top chapters

Maths
30 Q · 10 numerical
Easy 6Medium 17Hard 7

Top chapters

Question format
  • Single correct52 Q
  • Numerical value30 Q
  • Diagram based3 Q
  • Assertion–reason2 Q
  • Match the list1 Q
  • Two statements1 Q
  • Other1 Q
What each question asks you to do
  • Multi-step31 Q
  • Calculation24 Q
  • Application14 Q
  • Conceptual10 Q
  • Recall6 Q
  • Diagram reading3 Q
  • Data or graph2 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 Q1–30

  1. Q1The half-life of 198Au^{198}\mathrm{Au} is 3 days. If atomic weight of 198Au^{198}\mathrm{Au} is 198 g/mol then the activity of 2 mg of…MediumNuclei
  2. Q2A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor…HardElectrostatic Potential and Capacitance
  3. Q3Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th4^{\mathrm{th}} second after its fall…MediumMotion in a Straight Line
  4. Q4In Amplitude Modulation, the message signal Vm(t)=10sin⁡(2π×105t)V_m(t)=10\sin(2\pi\times10^5t) volts and Carrier signal Vc(t)=20sin⁡(2π×107t)V_c(t)=20\sin(2\pi\times10^7t) volts The…EasyCommunication Systems
  5. Q5Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed…MediumNuclei
  6. Q6What should be the order of arrangement of de-Broglie wavelength of electron (λe\lambda_e), an α\alpha-particle (λα\lambda_\alpha) and proton…EasyDual Nature of Radiation and Matter
  7. Q7A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie…EasyDual Nature of Radiation and Matter
  8. Q8In the Young's double slit experiment, the distance between the slits varies in time as d(t)=d0+a0sin⁡ωtd(t)=d_0+a_0\sin\omega t ; where d0d_0, ω\omega and a0a_0…MediumWave Optics
  9. Q9A ray of laser of a wavelength 630 nm is incident at an angle of 30∘30^\circ at the diamond-air interface. It is going from diamond to air. The…EasyRay Optics and Optical Instruments
  10. Q10A linearly polarized electromagnetic wave in vacuum is E=3.1cos⁡[(1.8)z−(5.4×106)t]i^E=3.1\cos\left[(1.8)z-\left(5.4\times10^6\right)t\right]\hat{i} N/C is incident normally on…MediumElectromagnetic Waves
  11. Q11In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 Ω0.1\ \Omega per cm. Across AB, a…MediumCurrent Electricity
  12. Q12Identify the logic operation carried out.EasySemiconductor Electronics: Materials, Devices and Simple Circuits
  13. Q13For a gas CP−CV=RC_P-C_V=R in a state P and CP−CV=1.10 RC_P-C_V=1.10\,R in a state Q, TPT_P and TQT_Q are the temperatures in two different states P and Q…HardThermodynamics
  14. Q14Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies…MediumThermal Properties of Matter
  15. Q15Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of a circular…EasySystem of Particles and Rotational Motion
  16. Q16Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected…MediumLaws of Motion
  17. Q17Match List I with List II. List I: (a) C⃗−A⃗−B⃗=0\vec{C}-\vec{A}-\vec{B}=0 (b) A⃗−C⃗−B⃗=0\vec{A}-\vec{C}-\vec{B}=0 (c) B⃗−A⃗−C⃗=0\vec{B}-\vec{A}-\vec{C}=0 (d)…MediumMotion in a Plane
  18. Q18Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1Y_1 and Y2Y_2. The…MediumMechanical Properties of Solids
  19. Q19The minimum and maximum distances of a planet revolving around the Sun are x1x_1 and x2x_2. If the minimum speed of the planet on its trajectory is…EasyGravitation
  20. Q20A monoatomic ideal gas, initially at temperature T1T_1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand…EasyThermodynamics
  21. Q21A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original…MediumSystem of Particles and Rotational MotionNumerical
  22. Q22In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched…MediumOscillationsNumerical
  23. Q23A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of…EasyWork, Energy and PowerNumerical
  24. Q24An inductor of 10 mH is connected to a 20 V battery through a resistor of 10 kΩ\Omega and a switch. After a long time, when maximum current is set…MediumElectromagnetic InductionNumerical
  25. Q25A particle of mass 'mm' is moving in time 'tt' on a trajectory given by r⃗=10αt2i^+5β(t−5)j^\vec{r}=10\alpha t^2\hat{i}+5\beta(t-5)\hat{j} Where α\alpha and…MediumSystem of Particles and Rotational MotionNumerical
  26. Q26A circular conducting coil of radius 1 m is being heated by the change of magnetic field B⃗\vec{B} passing perpendicular to the plane in which the…MediumElectromagnetic InductionNumerical
  27. Q27An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so…EasyCurrent ElectricityNumerical
  28. Q28A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same…MediumElectric Charges and FieldsNumerical
  29. Q29Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual…MediumUnits and MeasurementsNumerical
  30. Q30The value of aluminium susceptibility is 2.2×10−52.2\times10^{-5}. The percentage increase in the magnetic field if space within a current carrying toroid…EasyMagnetism and MatterNumerical

Chemistry Q31–60

  1. Q31For the following graphs, (a) Rate vs Time: horizontal line (b) t1/2t_{1/2} vs Initial concentration: straight line through origin with positive slope…MediumChemical Kinetics
  2. Q32Sodium stearate CH3(CH2)16COO−Na+\mathrm{CH_3(CH_2)_{16}COO^-Na^+} is an anionic surfactant which forms micelles in oil. Choose the correct statement for it from…MediumSurface Chemistry
  3. Q33The ionic radii of K+\mathrm{K^+}, Na+\mathrm{Na^+}, Al3+\mathrm{Al^{3+}} and Mg2+\mathrm{Mg^{2+}} are in the order :EasyClassification of Elements and Periodicity in Properties
  4. Q34In the leaching of alumina from bauxite, the ore expected to leach out in the process by reacting with NaOH is :EasyGeneral Principles and Processes of Isolation of Elements
  5. Q35At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol−1^{-1}) for hydrogen (EH\mathrm{E_H}) and its isotope, deuterium…MediumHydrogen
  6. Q36Given below are two statements : Statement I : None of the alkaline earth metal hydroxides dissolve in alkali. Statement II : Solubility of alkaline…MediumThe s-Block Elements
  7. Q37Which one of the following compounds of Group-14 elements is not known ?MediumThe p-Block Elements
  8. Q38The correct order of following 3d metal oxides, according to their oxidation numbers is : (a) CrO3\mathrm{CrO_3} (b) Fe2O3\mathrm{Fe_2O_3} (c)…EasyThe d- and f-Block Elements
  9. Q39Which one of the following species responds to an external magnetic field ?EasyCoordination Compounds
  10. Q40Which one of the following chemical agent is not being used for dry-cleaning of clothes ?MediumChemistry in Everyday Life
  11. Q41Which one among the following resonating structures is not correct ?MediumOrganic Chemistry: Some Basic Principles and Techniques
  12. Q42An Organic compound 'A' C4H8\mathrm{C_4H_8} on treatment with KMnO4/H+\mathrm{KMnO_4/H^+} yields compound 'B' C3H6O\mathrm{C_3H_6O}. Compound 'A' also yields…MediumHydrocarbons
  13. Q43[figure: but-3-en-2-one, CH2=CH-C(=O)-CH3, treated with (i) C2H5MgBr\mathrm{C_2H_5MgBr}, dry ether (ii) H2O\mathrm{H_2O}, HCl giving P (Major Product)]…HardAldehydes, Ketones and Carboxylic Acids
  14. Q44[figure: 3,3-dimethylcyclopentanone (ketone C=O, gem-dimethyl on adjacent ring carbon) reacts with CH3CHO\mathrm{CH_3CHO}, NaOH to give 'P' (Major…HardAldehydes, Ketones and Carboxylic Acids
  15. Q45[figure: phenol converted to 4-bromophenol (Major Product)] The given reaction can occur in the presence of : (a) Bromine water (b) Br2\mathrm{Br_2}…MediumHaloalkanes and Haloarenes
  16. Q46Which one of the products of the following reactions does not react with Hinsberg reagent to form sulphonamide ?MediumAmines
  17. Q47Given below are two statements, one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Gabriel phthalimide synthesis…EasyAmines
  18. Q48[figure: polymer repeating unit −(CH2-(\mathrm{CH_2}-C6H3(OH)-CH2\mathrm{CH_2}-C6H3(OH)-CH2)−\mathrm{CH_2})-, phenol rings joined through CH2 groups at…EasyPolymers
  19. Q49The water soluble protein is :EasyBiomolecules
  20. Q50Which one of the following compounds will liberate CO2\mathrm{CO_2}, when treated with NaHCO3\mathrm{NaHCO_3} ?MediumAmines
  21. Q51When 10 mL of an aqueous solution of Fe2+\mathrm{Fe^{2+}} ions was titrated in the presence of dil H2SO4\mathrm{H_2SO_4} using diphenylamine indicator,…MediumSome Basic Concepts of ChemistryNumerical
  22. Q52A home owner uses 4.00×103 m34.00\times10^3\ \mathrm{m^3} of methane (CH4\mathrm{CH_4}) gas, (assume CH4\mathrm{CH_4} is an ideal gas) in a year to heat his…EasyStates of MatterNumerical
  23. Q53A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of…MediumStructure of AtomNumerical
  24. Q54The number of sigma bonds in H3C−C(H)=CH−C≡C−H\mathrm{H_3C-C(H)=CH-C\equiv C-H} (the H on the second carbon drawn below it) is ____________.EasyChemical Bonding and Molecular StructureNumerical
  25. Q55At 298 K, the enthalpy of fusion of a solid (X) is 2.8 kJ mol−1^{-1} and the enthalpy of vaporisation of the liquid (X) is 98.2 kJ mol−1^{-1}. The…EasyThermodynamics (Chemistry)Numerical
  26. Q56CO2\mathrm{CO_2} gas is bubbled through water during a soft drink manufacturing process at 298 K. If CO2\mathrm{CO_2} exerts a partial pressure of…MediumSolutionsNumerical
  27. Q57For the reaction A+B⇌2C\mathrm{A+B\rightleftharpoons 2C} the value of equilibrium constant is 100 at 298 K. If the initial concentration of all the…MediumEquilibriumNumerical
  28. Q58Consider the cell at 25∘^\circC Zn∣Zn2+(aq),(1 M) ∣∣ Fe3+(aq),Fe2+(aq)∣Pt(s)\mathrm{Zn|Zn^{2+}(aq),(1\ M)\,||\,Fe^{3+}(aq),Fe^{2+}(aq)|Pt(s)} The fraction of total iron present as…HardElectrochemistryNumerical
  29. Q59Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is ________×10−1\times10^{-1} g. (in nearest…EasySome Basic Concepts of ChemistryNumerical
  30. Q60Three moles of AgCl get precipitated when one mole of an octahedral co-ordination compound with empirical formula CrCl3.3NH3.3H2O\mathrm{CrCl_3.3NH_3.3H_2O}…MediumCoordination CompoundsNumerical

Maths Q61–90

  1. Q61Let an ellipse E:x2a2+y2b2=1E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a2>b2a^2>b^2, passes through (32,1)\left(\sqrt{\frac{3}{2}},1\right) and has eccentricity…HardConic Sections
  2. Q62Let y=y(x)y=y(x) be the solution of the differential equation dydx=1+xey−x\frac{dy}{dx}=1+xe^{y-x}, −2<x<2-\sqrt2<x<\sqrt2, y(0)=0y(0)=0 then, the minimum value of…HardDifferential Equations
  3. Q63The area (in sq. units) of the region, given by the set {(x,y)∈R×R∣x≥0, 2x2≤y≤4−2x}\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^2\le y\le4-2x\} is :EasyApplication of Integrals
  4. Q64Let f:[0,∞)→[0,∞)f:[0,\infty)\to[0,\infty) be defined as f(x)=∫0x[y] dyf(x)=\int_0^x[y]\,dy where [x][x] is the greatest integer less than or equal to xx. Which of the…MediumContinuity and Differentiability
  5. Q65Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as…MediumContinuity and Differentiability
  6. Q66Let g:N→Ng:\mathbf{N}\to\mathbf{N} be defined as g(3n+1)=3n+2g(3n+1)=3n+2, g(3n+2)=3n+3g(3n+2)=3n+3, g(3n+3)=3n+1g(3n+3)=3n+1, for all n≥0n\ge0. Then which of the following…HardRelations and Functions
  7. Q67Let f(x)=3sin⁡4x+10sin⁡3x+6sin⁡2x−3f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3, x∈[−π6,π2]x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]. Then, ff is :MediumApplication of Derivatives
  8. Q68Let a parabola P be such that its vertex and focus lie on the positive xx-axis at a distance 2 and 4 units from the origin, respectively. If…MediumConic Sections
  9. Q69Let the foot of perpendicular from a point P(1, 2, −1-1) to the straight line L:x1=y0=z−1L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1} be N. Let a line be drawn…MediumThree Dimensional Geometry
  10. Q70If b is very small as compared to the value of a, so that the cube and other higher powers of ba\frac{b}{a} can be neglected in the identity…HardBinomial Theorem
  11. Q71Let the vectors (2+a+b)i^+(a+2b+c)j^−(b+c)k^(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}, (1+b)i^+2bj^−bk^(1+b)\hat{i}+2b\hat{j}-b\hat{k} and (2+b)i^+2bj^+(1−b)k^(2+b)\hat{i}+2b\hat{j}+(1-b)\hat{k},…MediumVector Algebra
  12. Q72The number of real roots of the equation e6x−e4x−2e3x−12e2x+ex+1=0e^{6x}-e^{4x}-2e^{3x}-12e^{2x}+e^x+1=0 is :HardComplex Numbers and Quadratic Equations
  13. Q73A spherical gas balloon of radius 16 meter subtends an angle 60∘60^\circ at the eye of the observer A while the angle of elevation of its center from…MediumTrigonometric Functions
  14. Q74Let 9 distinct balls be distributed among 4 boxes, B1B_1, B2B_2, B3B_3 and B4B_4. If the probability that B3B_3 contains exactly 3 balls is…MediumProbability
  15. Q75The locus of the centroid of the triangle formed by any point P on the hyperbola 16x2−9y2+32x+36y−164=016x^2-9y^2+32x+36y-164=0, and its foci is :HardConic Sections
  16. Q76Let SnS_n be the sum of the first n terms of an arithmetic progression. If S3n=3S2nS_{3n}=3S_{2n}, then the value of S4nS2n\frac{S_{4n}}{S_{2n}} is :EasySequences and Series
  17. Q77The Boolean expression (p⇒q)∧(q⇒∼p)(p\Rightarrow q)\wedge(q\Rightarrow\sim p) is equivalent to :EasyMathematical Reasoning
  18. Q78The value of the definite integral ∫π/245π/24dx1+tan⁡2x3\int_{\pi/24}^{5\pi/24}\frac{dx}{1+\sqrt[3]{\tan2x}} is :MediumIntegrals
  19. Q79The values of a and b, for which the system of equations 2x+3y+6z=82x+3y+6z=8 x+2y+az=5x+2y+az=5 3x+5y+9z=b3x+5y+9z=b has no solution, are :EasyDeterminants
  20. Q80The sum of all values of xx in [0,2π][0,2\pi], for which sin⁡x+sin⁡2x+sin⁡3x+sin⁡4x=0\sin x+\sin2x+\sin3x+\sin4x=0, is equal to :MediumTrigonometric Functions
  21. Q81The term independent of 'xx' in the expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)10\left(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\right)^{10}, where x≠0,1x\ne0,1 is equal…MediumBinomial TheoremNumerical
  22. Q82Let p⃗=2i^+3j^+k^\vec{p}=2\hat{i}+3\hat{j}+\hat{k} and q⃗=i^+2j^+k^\vec{q}=\hat{i}+2\hat{j}+\hat{k} be two vectors. If a vector…EasyVector AlgebraNumerical
  23. Q83The ratio of the coefficient of the middle term in the expansion of (1+x)20(1+x)^{20} and the sum of the coefficients of two middle terms in expansion of…EasyBinomial TheoremNumerical
  24. Q84If the value of…MediumSequences and SeriesNumerical
  25. Q85Let y=y(x)y=y(x) be solution of the following differential equation eydydx−2eysin⁡x+sin⁡xcos⁡2x=0e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0, y(π2)=0y\left(\frac{\pi}{2}\right)=0. If…MediumDifferential EquationsNumerical
  26. Q86Consider the following frequency distribution : Class : 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 Frequency : α\alpha | 110 | 54 | 30 |…MediumStatisticsNumerical
  27. Q87Let…MediumMatricesNumerical
  28. Q88Let M={A=(abcd):a,b,c,d∈{±3,±2,±1,0}}M=\left\{A=\begin{pmatrix}a&b\\c&d\end{pmatrix}:a,b,c,d\in\{\pm3,\pm2,\pm1,0\}\right\}. Define f:M→Zf:M\to\mathbf{Z}, as f(A)=det⁡(A)f(A)=\det(A), for all…MediumDeterminantsNumerical
  29. Q89There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected…HardPermutations and CombinationsNumerical
  30. Q90If α,β\alpha,\beta are roots of the equation x2+5(2)x+10=0x^2+5(\sqrt2)x+10=0, α>β\alpha>\beta and Pn=αn−βnP_n=\alpha^n-\beta^n for each positive integer n, then the…MediumComplex Numbers and Quadratic EquationsNumerical

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.