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Friday, 9 October

JEE Main 2020 · January session

JEE Main 8 January 2020, Shift 1

74 questions (1 more dropped by NTA): 15 numerical-answer and 59 multiple choice. 8 were rated hard and 16 easy. By hard questions it ranks 2nd of the 4 2020 shifts Lumi analysed. The biggest chapter was Ray Optics and Optical Instruments, with 3 questions.

Questions
74
1 dropped by NTA
Numerical answer
15
20% of the shift
Hard
8
11% of the shift
Chapters asked
61
15 questions with a figure

The shift at a glance

Subjects, difficulty and chapters

Physics
24 Q · 5 numerical
Easy 4Medium 19Hard 1

Top chapters

Chemistry
25 Q · 5 numerical
Easy 6Medium 16Hard 3

Top chapters

Maths
25 Q · 5 numerical
Easy 6Medium 15Hard 4

Top chapters

Question format
  • Single correct50 Q
  • Numerical value15 Q
  • Diagram based5 Q
  • Other4 Q
What each question asks you to do
  • Multi-step25 Q
  • Calculation18 Q
  • Application12 Q
  • Conceptual7 Q
  • Data or graph6 Q
  • Recall6 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. Q1The dimension of stopping potential V0V_0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant…MediumDual Nature of Radiation and MatterDropped
  2. Q2A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length ll. The other end is fixed. The system is…MediumLaws of Motion
  3. Q3The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown in figure)…EasySystem of Particles and Rotational Motion
  4. Q4Consider a uniform rod of mass M = 4m and length ll pivoted about its centre. A mass m moving with velocity vv making angle…MediumSystem of Particles and Rotational Motion
  5. Q5Consider two solid spheres of radii R1=1R_1 = 1 m, R2=2R_2 = 2 m and masses M1M_1 and M2M_2, respectively. The gravitational field due to sphere (1) and…MediumGravitation
  6. Q6Consider a solid sphere of radius R and mass density ρ(r)=ρ0(1−r2R2)\rho(r) = \rho_0\left(1-\frac{r^2}{R^2}\right), 0<r≤R0 < r \le R. The minimum density of a…HardMechanical Properties of Fluids
  7. Q7A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0∘0^\circC such…MediumMechanical Properties of Fluids
  8. Q8A thermodynamic cycle xyzxxyzx is shown on a V-T diagram. The P-V diagram that best describes this cycle is : (Diagrams are schematic and not to scale)MediumThermodynamics
  9. Q9The plot that depicts the behavior of the mean free time τ\tau (time between two successive collisions) for the molecules of an ideal gas, as a…MediumKinetic Theory
  10. Q10Three charged particles A, B and C with charges −4q-4q, 2q2q and −2q-2q are present on the circumference of a circle of radius d. The charged…MediumElectric Charges and Fields
  11. Q11Effective capacitance of parallel combination of two capacitors C1C_1 and C2C_2 is 10 μ\muF. When these capacitors are individually connected to a…MediumElectrostatic Potential and Capacitance
  12. Q12Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 101210^{12} m/s2^2 by an applied magnetic field (west to…MediumMoving Charges and Magnetism
  13. Q13In finding the electric field using Gauss law the formula ∣E⃗∣=qencϵ0∣A∣\left|\vec{E}\right| = \frac{q_{enc}}{\epsilon_0 |A|} is applicable. In the formula…MediumElectric Charges and Fields
  14. Q14At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the…MediumElectromagnetic Induction
  15. Q15The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 43\frac{4}{3} for this…MediumRay Optics and Optical Instruments
  16. Q16The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye piece ?EasyRay Optics and Optical Instruments
  17. Q17When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TAT_A eV and de-Broglie…MediumDual Nature of Radiation and Matter
  18. Q18The graph which depicts the results of Rutherford gold foil experiment with α\alpha-particles is : θ\theta : Scattering angle Y : Number of…MediumAtoms
  19. Q19Boolean relation at the output stage-Y for the following circuit is :MediumSemiconductor Electronics: Materials, Devices and Simple Circuits
  20. Q20The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a cell of emf 5 V and internal resistance of 20 Ω\Omega, the…MediumCurrent Electricity
  21. Q21A particle is moving along the xx-axis with its coordinate with time 't' given by x(t)=10+8t−3t2x(t) = 10+8t-3t^2. Another particle is moving along the…MediumMotion in a PlaneNumerical
  22. Q22A body A, of mass m = 0.1 kg has an initial velocity of 3i^3\hat{i} ms−1^{-1}. It collides elastically with another body, B of the same mass which…MediumWork, Energy and PowerNumerical
  23. Q23A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP…MediumWavesNumerical
  24. Q24Four resistances of 15 Ω\Omega, 12 Ω\Omega, 4 Ω\Omega and 10 Ω\Omega respectively in cyclic order to form Wheatstone's network. The resistance…EasyCurrent ElectricityNumerical
  25. Q25A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the…EasyRay Optics and Optical InstrumentsNumerical

Chemistry Q26–50

  1. Q26The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :HardEquilibrium
  2. Q27The rate of a certain biochemical reaction at physiological temperature (T) occurs 10610^6 times faster with enzyme than without. The change in the…MediumChemical Kinetics
  3. Q28As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :MediumSurface Chemistry
  4. Q29The predominant intermolecular forces present in ethyl acetate, a liquid, are :MediumChemical Bonding and Molecular Structure
  5. Q30For the Balmer series in the spectrum of H atom, νˉ=RH{1n12−1n22}\bar{\nu} = R_H\left\{\frac{1}{n_1^2}-\frac{1}{n_2^2}\right\}, the correct statements among (I)…MediumStructure of Atom
  6. Q31A graph of vapour pressure and temperature for three different liquids X, Y, and Z is shown below : The following inferences are made : (A) X has…MediumStates of Matter
  7. Q32The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :EasyClassification of Elements and Periodicity in Properties
  8. Q33The strength of an aqueous NaOH solution is most accurately determined by titrating : (Note : consider that an appropriate indicator is used)MediumSome Basic Concepts of Chemistry
  9. Q34When gypsum is heated to 393 K, it forms :EasyThe s-Block Elements
  10. Q35The number of bonds between sulphur and oxygen atoms in S2O82−\mathrm{S_2O_8^{2-}} and the number of bonds between sulphur and sulphur atoms in rhombic…MediumThe p-Block Elements
  11. Q36The third ionization enthalpy is minimum for :MediumThe d- and f-Block Elements
  12. Q37The complex that can show facfac- and mermer- isomers is :EasyCoordination Compounds
  13. Q38Among the gases (a) - (e), the gases that cause greenhouse effect are : (a) CO2\mathrm{CO_2} (b) H2O\mathrm{H_2O} (c) CFCs (d) O2\mathrm{O_2} (e)…EasyEnvironmental Chemistry
  14. Q39The most suitable reagent for the given conversion is :MediumAldehydes, Ketones and Carboxylic Acids
  15. Q40A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at 63 ∘^\circC while the other boils at 60 ∘^\circC. What is…EasyOrganic Chemistry: Some Basic Principles and Techniques
  16. Q41Arrange the following compounds in increasing order of C−-OH bond length : methanol, phenol, p-ethoxyphenolMediumAlcohols, Phenols and Ethers
  17. Q42Which of the following statement is not true for glucose ?MediumBiomolecules
  18. Q43The major products A and B in the following reactions are : (CH3)2CH−CH(CH3)−CN(\mathrm{CH_3})_2\mathrm{CH{-}CH(CH_3){-}CN}…HardHydrocarbons
  19. Q44The decreasing order of reactivity towards dehydrohalogenation (E1\mathrm{E_1}) reaction of the following compounds is : (A)…MediumHaloalkanes and Haloarenes
  20. Q45The major product of the following reaction is : (CH3)2C=CH−CH2−CH2−C(CH3)=CH−CH2OH(\mathrm{CH_3})_2\mathrm{C{=}CH{-}CH_2{-}CH_2{-}C(CH_3){=}CH{-}CH_2OH}…HardAlcohols, Phenols and Ethers
  21. Q46Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of…MediumSome Basic Concepts of ChemistryNumerical
  22. Q47The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is ______.EasyThermodynamics (Chemistry)Numerical
  23. Q48What would be the electrode potential for the given half cell reaction at pH=5 ? ______.…MediumElectrochemistryNumerical
  24. Q49The volume (in mL) of 0.125 M AgNO3\mathrm{AgNO_3} required to quantitatively precipitate chloride ions in 0.3 g of…MediumCoordination CompoundsNumerical
  25. Q50The number of chiral centres in penicillin is ______.MediumChemistry in Everyday LifeNumerical

Maths Q51–75

  1. Q51The inverse function of f(x)=82x−8−2x82x+8−2xf(x)=\dfrac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}}, x∈(−1,1)x\in(-1,1), is ______.MediumRelations and Functions
  2. Q52If the equation, x2+bx+45=0x^2+bx+45=0 (b∈Rb\in R) has conjugate complex roots and they satisfy ∣z+1∣=210|z+1|=2\sqrt{10}, then :MediumComplex Numbers and Quadratic Equations
  3. Q53For which of the following ordered pairs (μ,δ)(\mu, \delta), the system of linear equations x+2y+3z=1x+2y+3z=1 3x+4y+5z=μ3x+4y+5z=\mu 4x+4y+4z=δ4x+4y+4z=\delta is…MediumDeterminants
  4. Q54Let two points be A(1,−1)A(1,-1) and B(0,2)B(0,2). If a point P(x′,y′)P(x',y') be such that the area of ΔPAB=5\Delta PAB=5 sq. units and it lies on the line,…MediumStraight Lines
  5. Q55If a, b and c are the greatest values of 19Cp^{19}C_p, 20Cq^{20}C_q and 21Cr^{21}C_r respectively, then :EasyBinomial Theorem
  6. Q56Let f:R→Rf:\mathbf{R}\to\mathbf{R} be such that for all x∈Rx\in\mathbf{R}, (21+x+21−x)(2^{1+x}+2^{1-x}), f(x)f(x) and (3x+3−x)(3^x+3^{-x}) are in A.P., then the minimum…MediumSequences and Series
  7. Q57lim⁡x→0(3x2+27x2+2)1/x2\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2} is equal to :EasyLimits and Derivatives
  8. Q58Let f(x)=xcos⁡−1(−sin⁡∣x∣)f(x)=x\cos^{-1}(-\sin|x|), x∈[−π2,π2]x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right], then which of the following is true ?HardContinuity and Differentiability
  9. Q59If c is a point at which Rolle's theorem holds for the function, f(x)=log⁡e(x2+α7x)f(x)=\log_e\left(\dfrac{x^2+\alpha}{7x}\right) in the interval [3,4][3,4], where…MediumContinuity and Differentiability
  10. Q60If ∫cos⁡x dxsin⁡3x (1+sin⁡6x)2/3=f(x) (1+sin⁡6x)1/λ+c\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c where c is a constant of integration, then…HardIntegrals
  11. Q61For a>0a>0, let the curves C1:y2=axC_1: y^2=ax and C2:x2=ayC_2: x^2=ay intersect at origin O and a point P. Let the line x=bx=b (0<b<a0<b<a) intersect the chord OP…HardApplication of Integrals
  12. Q62Let y=y(x)y=y(x) be a solution of the differential equation, 1−x2 dydx+1−y2=0\sqrt{1-x^2}\,\dfrac{dy}{dx}+\sqrt{1-y^2}=0, ∣x∣<1|x|<1. If…MediumDifferential Equations
  13. Q63The locus of a point which divides the line segment joining the point (0,−1)(0,-1) and a point on the parabola, x2=4yx^2=4y, internally in the ratio 1:21:2,…MediumConic Sections
  14. Q64Let the line y=mxy=mx and the ellipse 2x2+y2=12x^2+y^2=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the…MediumConic Sections
  15. Q65The shortest distance between the lines x−33=y−8−1=z−31\dfrac{x-3}{3}=\dfrac{y-8}{-1}=\dfrac{z-3}{1} and x+3−3=y+72=z−64\dfrac{x+3}{-3}=\dfrac{y+7}{2}=\dfrac{z-6}{4} is :MediumThree Dimensional Geometry
  16. Q66Let the volume of a parallelopiped whose coterminous edges are given by u⃗=i^+j^+λk^\vec{u}=\hat{i}+\hat{j}+\lambda\hat{k}, v⃗=i^+j^+3k^\vec{v}=\hat{i}+\hat{j}+3\hat{k}…MediumVector Algebra
  17. Q67The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then…MediumStatistics
  18. Q68Let A and B be two independent events such that P(A)=13P(A)=\frac{1}{3} and P(B)=16P(B)=\frac{1}{6}. Then, which of the following is TRUE ?MediumProbability
  19. Q69Let f(x)=(sin⁡(tan⁡−1x)+sin⁡(cot⁡−1x))2−1f(x)=\left(\sin(\tan^{-1}x)+\sin(\cot^{-1}x)\right)^2-1, ∣x∣>1|x|>1. If dydx=12ddx(sin⁡−1(f(x)))\dfrac{dy}{dx}=\dfrac{1}{2}\dfrac{d}{dx}\left(\sin^{-1}(f(x))\right)…HardInverse Trigonometric Functions
  20. Q70Which one of the following is a tautology ?EasyMathematical Reasoning
  21. Q71The least positive value of 'a' for which the equation, 2x2+(a−10)x+332=2a2x^2+(a-10)x+\frac{33}{2}=2a has real roots is ______.EasyComplex Numbers and Quadratic EquationsNumerical
  22. Q72The number of all 3×33\times3 matrices A, with enteries from the set {−1,0,1}\{-1,0,1\} such that the sum of the diagonal elements of AATAA^T is 3, is ______.MediumMatricesNumerical
  23. Q73The sum ∑k=120(1+2+3+…+k)\displaystyle\sum_{k=1}^{20}(1+2+3+\ldots+k) is ______.EasySequences and SeriesNumerical
  24. Q74Let the normal at a point P on the curve y2−3x2+y+10=0y^2-3x^2+y+10=0 intersect the yy-axis at (0,32)\left(0,\frac{3}{2}\right). If m is the slope of the tangent…MediumApplication of DerivativesNumerical
  25. Q75An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most…EasyPermutations and CombinationsNumerical

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.