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Friday, 9 October

JEE Main 2020 · January session

JEE Main 9 January 2020, Shift 2

73 questions (2 more dropped by NTA): 15 numerical-answer and 58 multiple choice. 5 were rated hard and 20 easy. By hard questions it ranks 3rd of the 4 2020 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions
73
2 dropped by NTA
Numerical answer
15
21% of the shift
Hard
5
7% of the shift
Chapters asked
54
14 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
24 Q · 5 numerical
Easy 5Medium 18Hard 1

Top chapters

Chemistry
25 Q · 5 numerical
Easy 9Medium 14Hard 2

Top chapters

Maths
24 Q · 5 numerical
Easy 6Medium 16Hard 2

Top chapters

Question format
  • Single correct56 Q
  • Numerical value15 Q
  • Other2 Q
What each question asks you to do
  • Multi-step35 Q
  • Calculation15 Q
  • Application12 Q
  • Recall5 Q
  • Conceptual4 Q
  • Data or graph2 Q

Most common: Multi-step.

Every question

All 75 questions, with answers

Open a question for the full text, options, the official answer and the same idea in other shifts.

Physics Q1–25

  1. Q1For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i)…MediumCurrent ElectricityDropped
  2. Q2A particle starts from the origin at t=0t=0 with an initial velocity of 3.0 i^3.0\,\hat{i} m/s and moves in the xx-yy plane with a constant…EasyMotion in a Plane
  3. Q3A uniformly thick wheel with moment of inertia II and radius RR is free to rotate about its centre of mass (see fig). A massless string is wrapped…MediumSystem of Particles and Rotational Motion
  4. Q4A particle of mass mm is projected with a speed uu from the ground at an angle θ=π3\theta = \frac{\pi}{3} w.r.t. horizontal (xx-axis). When it has…MediumMotion in a Plane
  5. Q5A rod of length LL has non-uniform linear mass density given by ρ(x)=a+b(xL)2\rho(x) = a + b\left(\frac{x}{L}\right)^2, where aa and bb are constants and…EasySystem of Particles and Rotational Motion
  6. Q6A spring mass system (mass mm, spring constant kk and natural length ll) rests in equilibrium on a horizontal disc. The free end of the spring is…MediumLaws of Motion
  7. Q7Planet A has mass MM and radius RR. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B…EasyGravitation
  8. Q8Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1:41:4,…MediumMechanical Properties of Solids
  9. Q9A small spherical droplet of density dd is floating exactly half immersed in a liquid of density ρ\rho and surface tension TT. The radius of the…MediumMechanical Properties of Fluids
  10. Q10Two gases - argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are…MediumKinetic Theory
  11. Q11A wire of length LL and mass per unit length 6.0×10−3 kg m−16.0\times10^{-3}\ \mathrm{kg\,m^{-1}} is put under tension of 540 N. Two consecutive frequencies…MediumWaves
  12. Q12Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuits as shown below at time t=0t=0. If the…MediumElectrostatic Potential and Capacitance
  13. Q13A small circular loop of conducting wire has radius aa and carries current II. It is placed in a uniform magnetic field BB perpendicular to its…MediumMoving Charges and Magnetism
  14. Q14An electron gun is placed inside a long solenoid of radius RR on its axis. The solenoid has nn turns/length and carries a current II. The…MediumMoving Charges and Magnetism
  15. Q15In LC circuit the inductance L=40L = 40 mH and capacitance C=100 μC = 100\ \muF. If a voltage V(t)=10sin⁡(314 t)V(t) = 10\sin(314\,t) is applied to the circuit, the…MediumAlternating Current
  16. Q16A plane electromagnetic wave is propagating along the direction i^+j^2\frac{\hat{i}+\hat{j}}{\sqrt{2}}, with its polarization along the direction…MediumElectromagnetic Waves
  17. Q17There is a small source of light at some depth below the surface of water (refractive index =43= \frac{4}{3}) in a tank of large cross sectional…HardRay Optics and Optical Instruments
  18. Q18An electron of mass mm and magnitude of charge ∣e∣|e| initially at rest gets accelerated by a constant electric field EE. The rate of change of…MediumDual Nature of Radiation and Matter
  19. Q19The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the…MediumAtoms
  20. Q20The current ii in the network is :MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  21. Q21Starting at temperature 300 K, one mole of an ideal diatomic gas (γ=1.4\gamma = 1.4) is first compressed adiabatically from volume V1V_1 to…MediumThermodynamicsNumerical
  22. Q22An electric field E⃗=4x i^−(y2+1) j^\vec{E} = 4x\,\hat{i} - (y^2+1)\,\hat{j} N/C passes through the box shown in figure. The flux of the electric field through…MediumElectric Charges and FieldsNumerical
  23. Q23In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is l=25l = 25 cm. If R is replaced…EasyCurrent ElectricityNumerical
  24. Q24In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes…EasyWave OpticsNumerical
  25. Q25The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as input, the power dissipated (in mW) in each diode is;…MediumSemiconductor Electronics: Materials, Devices and Simple CircuitsNumerical

Chemistry Q26–50

  1. Q26The true statement amongst the following is :EasyThermodynamics (Chemistry)
  2. Q27The solubility product of Cr(OH)3\mathrm{Cr(OH)_3} at 298 K is 6.0×10−316.0\times10^{-31}. The concentration of hydroxide ions in a saturated solution of…MediumEquilibrium
  3. Q28Amongst the following, the form of water with the lowest ionic conductance at 298 K is :EasyElectrochemistry
  4. Q29A mixture of gases O2\mathrm{O_2}, H2\mathrm{H_2} and CO\mathrm{CO} are taken in a closed vessel containing charcoal. The graph that represents the…EasySurface Chemistry
  5. Q30In the figure shown below reactant A (represented by square) is in equilibrium with product B (represented by circle). The equilibrium constant is :EasyEquilibrium
  6. Q31The number of sp2sp^2 hybrid orbitals in a molecule of benzene is :EasyChemical Bonding and Molecular Structure
  7. Q32The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol−1^{-1}, respectively. How many moles of HCl and H2SO4\mathrm{H_2SO_4},…EasyClassification of Elements and Periodicity in Properties
  8. Q335 g of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b) aqueous sodium hydroxide. The ratio of the volumes of…MediumThe d- and f-Block Elements
  9. Q34Among the statements (a)-(d), the correct ones are : (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is…MediumThe s-Block Elements
  10. Q35The reaction of H3N3B3Cl3\mathrm{H_3N_3B_3Cl_3} (A) with LiBH4\mathrm{LiBH_4} in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A)…MediumThe p-Block Elements
  11. Q36The isomer(s) of [Co(NH3)4Cl2]\mathrm{[Co(NH_3)_4Cl_2]} that has/have a Cl-Co-Cl angle of 90∘90^\circ, is/are :EasyCoordination Compounds
  12. Q37The correct order of the spin-only magnetic moments of the following complexes is : (I) [Cr(H2O)6]Br2\mathrm{[Cr(H_2O)_6]Br_2} (II) Na4[Fe(CN)6]\mathrm{Na_4[Fe(CN)_6]}…MediumCoordination Compounds
  13. Q38Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm) :EasyEnvironmental Chemistry
  14. Q39The decreasing order of basicity of the following amines is :MediumAmines
  15. Q40Which of the following has the shortest C-Cl bond ?MediumHaloalkanes and Haloarenes
  16. Q41A, B and C are three biomolecules. The results of the tests performed on them are given below : | | Molisch's Test | Barfoed Test | Biuret Test |…MediumBiomolecules
  17. Q42Which polymer has 'chiral' monomer(s) ?MediumPolymers
  18. Q43Which of the following reactions will not produce a racemic product ?HardHaloalkanes and Haloarenes
  19. Q44In the following reaction A is : A…MediumAldehydes, Ketones and Carboxylic Acids
  20. Q45Consider the following reactions, [P] →(i) NaNO2/HCl, 0-5 °C; (ii) β-naphthol/NaOH\xrightarrow{\text{(i) NaNO}_2\text{/HCl, 0-5 °C; (ii) }\beta\text{-naphthol/NaOH}} Colored Solid [P]…MediumAmines
  21. Q46A cylinder containing an ideal gas (0.1 mol of 1.0 dm3^3) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene…HardSolutionsNumerical
  22. Q4710.30 mg of O2\mathrm{O_2} is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of O2\mathrm{O_2} in ppm is ______.EasySolutionsNumerical
  23. Q48A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The…MediumChemical KineticsNumerical
  24. Q49The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is ______.MediumThe d- and f-Block ElementsNumerical
  25. Q50Consider the following reactions A →(ii) H3O+(i) CH3MgBr\xrightarrow[\text{(ii) } H_3O^+]{\text{(i) } CH_3MgBr} B →573 KCu\xrightarrow[573\text{ K}]{Cu} 2-methyl-2-butene…MediumAlcohols, Phenols and EthersNumerical

Maths Q51–75

  1. Q51If A={x∈R:∣x∣<2}A=\{x\in\mathbf{R}:|x|<2\} and B={x∈R:∣x−2∣≥3}B=\{x\in\mathbf{R}:|x-2|\ge 3\}; then :EasyRelations and Functions
  2. Q52Let a,b∈Ra,b\in\mathbf{R}, a≠0a\ne0 be such that the equation, ax2−2bx+5=0ax^2-2bx+5=0 has a repeated root α\alpha, which is also a root of the equation,…MediumComplex Numbers and Quadratic Equations
  3. Q53If zz be a complex number satisfying ∣Re(z)∣+∣Im(z)∣=4|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4, then ∣z∣|z| cannot be :MediumComplex Numbers and Quadratic Equations
  4. Q54Let a−2b+c=1a-2b+c=1. If f(x)=∣x+ax+2x+1x+bx+3x+2x+cx+4x+3∣f(x)=\begin{vmatrix}x+a&x+2&x+1\\x+b&x+3&x+2\\x+c&x+4&x+3\end{vmatrix}, then :MediumDeterminants
  5. Q55The following system of linear equations 7x+6y−2z=07x+6y-2z=0 3x+4y+2z=03x+4y+2z=0 x−2y−6z=0x-2y-6z=0, hasEasyDeterminants
  6. Q56In the expansion of (xcos⁡θ+1xsin⁡θ)16\left(\frac{x}{\cos\theta}+\frac{1}{x\sin\theta}\right)^{16}, if l1l_1 is the least value of the term independent of xx when…HardBinomial Theorem
  7. Q57Let ana_n be the nthn^{\mathrm{th}} term of a G.P. of positive terms. If ∑n=1100a2n+1=200\sum_{n=1}^{100}a_{2n+1}=200 and ∑n=1100a2n=100\sum_{n=1}^{100}a_{2n}=100, then…MediumSequences and Series
  8. Q58Let [t][t] denote the greatest integer ≤t\le t and lim⁡x→0x[4x]=A\lim_{x\to0}x\left[\frac{4}{x}\right]=A. Then the function, f(x)=[x2]sin⁡(πx)f(x)=[x^2]\sin(\pi x) is…MediumContinuity and Differentiability
  9. Q59If x=2sin⁡θ−sin⁡2θx=2\sin\theta-\sin2\theta and y=2cos⁡θ−cos⁡2θy=2\cos\theta-\cos2\theta, θ∈[0,2π]\theta\in[0,2\pi], then d2ydx2\frac{d^2y}{dx^2} at θ=π\theta=\pi is :MediumContinuity and DifferentiabilityDropped
  10. Q60Let ff and gg be differentiable functions on R\mathbf{R} such that f∘gf\circ g is the identity function. If for some a,b∈Ra,b\in\mathbf{R}, g′(a)=5g'(a)=5…EasyContinuity and Differentiability
  11. Q61Let a function f:[0,5]→Rf:[0,5]\to\mathbf{R} be continuous, f(1)=3f(1)=3 and FF be defined as : F(x)=∫1xt2g(t) dtF(x)=\int_1^x t^2g(t)\,dt, where g(t)=∫1tf(u) dug(t)=\int_1^t f(u)\,du.…MediumApplication of Derivatives
  12. Q62If ∫dθcos⁡2θ(tan⁡2θ+sec⁡2θ)=λtan⁡θ+2log⁡e∣f(θ)∣+C\int\frac{d\theta}{\cos^2\theta(\tan2\theta+\sec2\theta)}=\lambda\tan\theta+2\log_e|f(\theta)|+C where CC is a constant of integration, then…MediumIntegrals
  13. Q63Given : f(x)={x,0≤x<1212,x=121−x,12<x≤1f(x)=\begin{cases}x, & 0\le x<\frac{1}{2}\\ \frac{1}{2}, & x=\frac{1}{2}\\ 1-x, & \frac{1}{2}<x\le1\end{cases} and…MediumApplication of Integrals
  14. Q64If dydx=xyx2+y2\frac{dy}{dx}=\frac{xy}{x^2+y^2}; y(1)=1y(1)=1; then a value of xx satisfying y(x)=ey(x)=e is :MediumDifferential Equations
  15. Q65The length of the minor axis (along yy-axis) of an ellipse in the standard form is 43\frac{4}{\sqrt3}. If this ellipse touches the line, x+6y=8x+6y=8;…MediumConic Sections
  16. Q66If one end of a focal chord AB of the parabola y2=8xy^2=8x is at A(12,−2)A\left(\frac{1}{2},-2\right), then the equation of the tangent to it at B is :MediumConic Sections
  17. Q67A random variable X has the following probability distribution : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | K2K^2 | 2K2K | KK |…EasyProbability
  18. Q68If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :MediumProbability
  19. Q69If x=∑n=0∞(−1)ntan⁡2nθx=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta and y=∑n=0∞cos⁡2nθy=\sum_{n=0}^{\infty}\cos^{2n}\theta, for 0<θ<π40<\theta<\frac{\pi}{4}, then :EasySequences and Series
  20. Q70If p→(p∧∼q)p\to(p\wedge\sim q) is false, then the truth values of pp and qq are respectively :EasyMathematical Reasoning
  21. Q71If Cr≡25CrC_r\equiv{}^{25}C_r and C0+5⋅C1+9⋅C2+…+(101)⋅C25=225⋅kC_0+5\cdot C_1+9\cdot C_2+\ldots+(101)\cdot C_{25}=2^{25}\cdot k, then kk is equal to ______.MediumBinomial TheoremNumerical
  22. Q72The number of terms common to the two A.P.'s 3,7,11,…,4073,7,11,\ldots,407 and 2,9,16,…,7092,9,16,\ldots,709 is ______.MediumSequences and SeriesNumerical
  23. Q73If the curves, x2−6x+y2+8=0x^2-6x+y^2+8=0 and x2−8y+y2+16−k=0x^2-8y+y^2+16-k=0, (k>0)(k>0) touch each other at a point, then the largest value of kk is ______.MediumConic SectionsNumerical
  24. Q74If the distance between the plane, 23x−10y−2z+48=023x-10y-2z+48=0 and the plane containing the lines x+12=y−34=z+13\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3} and…HardThree Dimensional GeometryNumerical
  25. Q75Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be three vectors such that ∣a⃗∣=3|\vec{a}|=\sqrt3, ∣b⃗∣=5|\vec{b}|=5, b⃗⋅c⃗=10\vec{b}\cdot\vec{c}=10 and the angle between…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 2020 shifts.