JEE Main 2020 · January session

JEE Main 8 January 2020, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 8 were rated hard and 21 easy. Its hard-question count was the joint 7th highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 8; 11% of the shift
Chapters asked: 61; 14 questions with a figure

Key findings · 8 Jan 2020, Shift 2

1
8 hard questions (11%): the joint 7th highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
Physics was the hardest section, with 5 of 25 rated hard; Chemistry had the most easy questions (9 of 25).
3
59 questions tested a new idea, one no earlier year had asked: 92% of the 64 questions tagged to an idea.
4
5 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
5
20 shared an idea with another 2020 shift (31% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Electrostatic Potential and Capacitance in Physics (2), Coordination Compounds in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 7Medium 13Hard 5

Top chapters

Chemistry

25 Q · 5 numerical

Easy 9Medium 16Hard 0

Top chapters

Maths

25 Q · 5 numerical

Easy 5Medium 17Hard 3

Top chapters

Question format

Single correct45 Q
Numerical value15 Q
Diagram based13 Q
Assertion–reason2 Q

What each question asks you to do

Multi-step29 Q
Calculation21 Q
Conceptual10 Q
Application6 Q
Recall5 Q
Data or graph3 Q
Diagram reading1 Q

Most common: Multi-step.

Against the other 2020 shifts

This shift next to the 11 other 2020 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
8 Jan, Shift 1	74	22%	11%	20%	92%	34%
8 Jan, Shift 2	75	28%	11%	20%	92%	39%
9 Jan, Shift 1	75	23%	16%	20%	99%	40%
9 Jan, Shift 2	73	27%	7%	21%	95%	48%
2 Sep, Shift 1	75	28%	5%	20%	95%	40%
2 Sep, Shift 2	75	20%	7%	20%	97%	32%
3 Sep, Shift 1	74	32%	12%	20%	91%	37%
3 Sep, Shift 2	75	21%	16%	20%	98%	29%
4 Sep, Shift 1	75	20%	16%	20%	98%	37%
4 Sep, Shift 2	75	32%	13%	20%	97%	39%
5 Sep, Shift 1	75	36%	7%	20%	94%	31%
6 Sep, Shift 2	75	31%	13%	20%	97%	41%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open25 this shift3092 · 33%33%8/830299720720358540200225
Open25 this shift3084 · 33%33%8/830298716720359538199224
Open25 this shift3065 · 33%33%8/829299715710354533200225

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Every question

All 75 questions of this shift

The opening words of each question, with its chapter, topic, idea and how hard it was. Open one for the full text, options and the official answer. “New idea” means no earlier year had tested it.

Subject

Difficulty

Idea

Find

75 of 75 questions

Physics25 questions

7 easy13 medium5 hard

Chemistry25 questions

9 easy16 medium0 hard

Q26
For the following Assertion and Reason, the correct option is : Assertion : For hydrogenation reactions, the catalytic activity increases from Group 5 to Group 11 metals with maximum activity shown by Group 7 - 9 elements. Reason : The reactants are most…
Surface Chemistry
MediumAssertion–reason
Q27
Consider the following plots of rate constant versus $\frac{1}{T}$ for four different reactions. Which of the following orders is correct for the activation energies of these reactions ?
Chemical Kinetics Arrhenius Equation Log Base 10 Arrhenius Plot Slope
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q28
For the following Assertion and Reason, the correct option is : Assertion : The pH of water increases with increase in temperature. Reason : The dissociation of water into $\mathrm{H^+}$ and $\mathrm{OH^-}$ is an exothermic reaction.
Equilibrium pH and Buffers Temperature Dependence of Kw and Neutral pH
MediumAssertion–reasonNew idea
Q29
The radius of the second Bohr orbit, in terms of the Bohr radius, $\mathrm{a_0}$ , in $\mathrm{Li^{2+}}$ is :
Structure of Atom Bohr's Atomic Theory Bohr Radius Calculation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q30
Arrange the following bonds according to their average bond energies in descending order : C – Cl, C – Br, C – F, C – I
Chemical Bonding and Molecular Structure
EasySingle correct
Q31
Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form ?
The Solid State Solid State Defects AgBr Dual Defect Exception
EasySingle correctNew idea
Q32
The increasing order of the atomic radii of the following elements is : (a) C (b) O (c) F (d) Cl (e) Br
Classification of Elements and Periodicity in Properties Periodic Trends Atomic and Ionic Radii Trends
EasySingle correctNew ideaIdea asked in 3 years
Q33
Among the reactions (a) - (d), the reaction(s) that does/do not occur in the blast furnace during the extraction of iron is/are : (a) $\mathrm{CaO + SiO_2 \rightarrow CaSiO_3}$ (b) $\mathrm{3Fe_2O_3 + CO \rightarrow 2Fe_3O_4 + CO_2}$ (c)…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Iron Extraction Chemistry
EasySingle correctNew idea
Q34
Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are $(x)$ , $(y)$ and $(z)$ , the sum of $(x)$ , $(y)$ and $(z)$ is :
Hydrogen Hydrogen and Hydrides Isotopes of Hydrogen
EasySingle correctNew ideaIdea asked in 4 years
Q35
A metal (A) on heating in nitrogen gas gives compound B. B on treatment with $\mathrm{H_2O}$ gives a colourless gas which when passed through $\mathrm{CuSO_4}$ solution gives a dark blue-violet coloured solution. A and B respectively, are :
The s-Block Elements s-Block Elements Direct Formation of Nitrides
MediumSingle correctNew idea
Q36
White phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of $\mathrm{CO_2}$ gives phosphine and compound (X). (X) on acidification with HCl gives compound (Y). The basicity of compound (Y) is :
The p-Block Elements Group 15 & 16 Preparation of Phosphine
MediumSingle correctNew ideaIdea asked in 2 years
Q37
The correct order of the calculated spin-only magnetic moments of complexes (A) to (D) is : (A) $\mathrm{Ni(CO)_4}$ (B) $\mathrm{[Ni(H_2O)_6]Cl_2}$ (C) $\mathrm{Na_2[Ni(CN)_4]}$ (D) $\mathrm{PdCl_2(PPh_3)_2}$
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumSingle correctNew ideaIdea asked in 7 years
Q38
Among (a) – (d), the complexes that can display geometrical isomerism are : (a) $\mathrm{[Pt(NH_3)_3Cl]^+}$ (b) $\mathrm{[Pt(NH_3)Cl_5]^-}$ (c) $\mathrm{[Pt(NH_3)_2Cl(NO_2)]}$ (d) $\mathrm{[Pt(NH_3)_4ClBr]^{2+}}$
Coordination Compounds Coordination Isomerism Square Planar Geometry
MediumSingle correctNew ideaIdea asked in 3 years
Q39
Two monomers in maltose are :
Biomolecules Carbohydrates Maltose Structure and Linkage
EasySingle correctNew ideaIdea asked in 3 years
Q40
Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds ?
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
EasySingle correct · figureNew ideaIdea asked in 4 years
Q41
The major product in the following reaction is : [figure] $+\ \mathrm{H_3O^{\oplus}} \longrightarrow$
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q42
An unsaturated hydrocarbon X absorbs two hydrogen molecules on catalytic hydrogenation, and also gives following reaction : $\mathrm{X\ \xrightarrow[Zn/H_2O]{O_3}\ A\ \xrightarrow{[Ag(NH_3)_2]^+}}$ B(3-oxo-hexanedicarboxylic acid) X will be :
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
MediumDiagram based · figureNew ideaIdea asked in 7 years
Q43
Preparation of Bakelite proceeds via reactions :
Polymers Novolac to Bakelite Transition
MediumSingle correctNew idea
Q44
Among the compounds A and B with molecular formula $\mathrm{C_9H_{18}O_3}$ , A is having higher boiling point the B. The possible structures of A and B are :
Alcohols, Phenols and Ethers Alcohols and Phenols Hydrogen Bonding Trends in Alcohols
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q45
The major product [B] in the following sequence of reactions is :…
Hydrocarbons Alkenes and Alkynes Hydroboration-Oxidation
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q46
$\mathrm{NaClO_3}$ is used, even in spacecrafts, to produce $\mathrm{O_2}$ . The daily consumption of pure $\mathrm{O_2}$ by a person is 492 L at 1 atm, 300 K. How much amount of $\mathrm{NaClO_3}$ , in grams, is required to produce $\mathrm{O_2}$ for the…
Some Basic Concepts of Chemistry Stoichiometry Mass-Mass Stoichiometry
MediumNumerical valueNew ideaIdea asked in 3 years
Q47
At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J. The molar heat capacity at constant volume is _________.
Thermodynamics (Chemistry)
MediumNumerical value
Q48
For an electrochemical cell $\mathrm{Sn(s)|Sn^{2+}(aq,\ 1M)||Pb^{2+}(aq,\ 1M)|Pb(s)}$ the ratio $\frac{[\mathrm{Sn^{2+}}]}{[\mathrm{Pb^{2+}}]}$ when this cell attains equilibrium is __________.…
Electrochemistry Nernst Equation E°cell and Equilibrium
MediumNumerical valueNew ideaIdea asked in 3 years
Q49
Complexes ( $\mathrm{ML_5}$ ) of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal geometries, respectively. The sum of the $90^\circ$ , $120^\circ$ and $180^\circ$ L–M–L angles in the two complexes is _________.
Coordination Compounds VSEPR Theory Trigonal Bipyramidal Positions
MediumNumerical valueNew ideaIdea asked in 5 years
Q50
In the following sequence of reactions the maximum number of atoms present in molecule 'C' in one plane is __________. $\mathrm{A\ \xrightarrow[Cu\ tube]{Red\ hot}\ B\ \xrightarrow[Anhydrous\ AlCl_3]{CH_3Cl\ (1.\ eq.)}\ C}$ (A is a lowest molecular weight…
Hydrocarbons Aromatic Hydrocarbons Friedel-Crafts Alkylation
MediumNumerical valueNew ideaIdea asked in 5 years

Maths25 questions

5 easy17 medium3 hard

Q51
Let $f : (1, 3) \to \mathbf{R}$ be a function defined by $f(x) = \frac{x[x]}{1 + x^2}$ , where $[x]$ denotes the greatest integer $\leq x$ . Then the range of $f$ is :
Relations and Functions Functions and Domain Range Involving Mixed GIF and Fractional Part
MediumSingle correctNew idea
Q52
Let $\alpha = \frac{-1 + i\sqrt{3}}{2}$ . If $a = (1 + \alpha) \sum_{k=0}^{100} \alpha^{2k}$ and $b = \sum_{k=0}^{100} \alpha^{3k}$ , then a and b are the roots of the quadratic equation :
Complex Numbers and Quadratic Equations Roots of Unity Periodicity of Omega Powers
MediumSingle correctNew ideaIdea asked in 3 years
Q53
Let S be the set of all real roots of the equation, $3^x(3^x - 1) + 2 = |3^x - 1| + |3^x - 2|$ . Then S :
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumSingle correctNew ideaIdea asked in 6 years
Q54
If $A = \begin{pmatrix} 2 & 2 \\ 9 & 4 \end{pmatrix}$ and $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ , then $10A^{-1}$ is equal to :
Matrices Matrix Inverse Inverse via Characteristic Equation
EasySingle correctNew ideaIdea asked in 2 years
Q55
The system of linear equations $\lambda x + 2y + 2z = 5$ $2\lambda x + 3y + 5z = 8$ $4x + \lambda y + 6z = 10$ has :
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q56
If $\alpha$ and $\beta$ be the coefficients of $x^4$ and $x^2$ respectively in the expansion of $\left(x + \sqrt{x^2 - 1}\right)^6 + \left(x - \sqrt{x^2 - 1}\right)^6$ , then :
Binomial Theorem Binomial Coefficients Difference of Binomial Expansions
MediumSingle correctNew idea
Q57
If the $10^{\text{th}}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text{th}}$ term is $\frac{1}{10}$ , then the sum of its first 200 terms is :
Sequences and Series AP and GP AP pth term is 1/q Trick
MediumSingle correctNew idea
Q58
$\lim_{x \to 0} \frac{\int_0^x t \sin(10t)\,dt}{x}$ is equal to :
Integrals L'Hopital's Rule L'Hopital with Leibniz Rule
EasySingle correctNew ideaIdea asked in 2 years
Q59
Let S be the set of all functions $f : [0, 1] \to \mathbf{R}$ , which are continuous on $[0, 1]$ and differentiable on $(0, 1)$ . Then for every $f$ in S, there exists a $\mathrm{c} \in (0, 1)$ , depending on $f$ , such that :
Continuity and Differentiability Mean Value Theorem Proving Inequalities via LMVT
HardSingle correctNew idea
Q60
The length of the perpendicular from the origin, on the normal to the curve, $x^2 + 2xy - 3y^2 = 0$ at the point $(2, 2)$ is :
Application of Derivatives Tangents and Normals Equation of Normal
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q61
If $I = \int_1^2 \frac{dx}{\sqrt{2x^3 - 9x^2 + 12x + 4}}$ , then :
Integrals Definite Integral Properties Bounding and Estimation Property
HardSingle correctNew ideaIdea asked in 3 years
Q62
The area (in sq. units) of the region $\{(x, y) \in \mathbf{R}^2 : x^2 \leq y \leq 3 - 2x\}$ , is :
Application of Integrals Area Under Curves Area Between Parabola and Line
EasySingle correctNew ideaIdea asked in 4 years
Q63
The differential equation of the family of curves, $x^2 = 4\mathrm{b}(y + \mathrm{b})$ , $\mathrm{b} \in \mathbf{R}$ , is :
Differential Equations
MediumSingle correct
Q64
If a line, $y = mx + \mathrm{c}$ is a tangent to the circle, $(x - 3)^2 + y^2 = 1$ and it is perpendicular to a line $\mathrm{L}_1$ , where $\mathrm{L}_1$ is the tangent to the circle, $x^2 + y^2 = 1$ at the point…
Conic Sections Circle Tangents Condition of tangency
MediumSingle correctNew ideaIdea asked in 4 years
Q65
If a hyperbola passes through the point $\mathrm{P}(10, 16)$ and it has vertices at $(\pm 6, 0)$ , then the equation of the normal to it at P is :
Conic Sections Normals to Conics Hyperbola Normal Point Form
MediumSingle correctNew ideaIdea asked in 3 years
Q66
The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$ . Which of the following points lies on this plane ?
Three Dimensional Geometry Planes in 3D Image of a Point in a Plane
MediumSingle correctNew ideaIdea asked in 2 years
Q67
Let $\vec{a} = \hat{i} - 2\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b} \times \vec{c} = \vec{b} \times \vec{a}$ and $\vec{c} \cdot \vec{a} = 0$ , then $\vec{c} \cdot \vec{b}$ is…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctNew ideaIdea asked in 6 years
Q68
The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is :
Statistics Variance and SD Correcting Incorrect Variance
EasySingle correctNew ideaIdea asked in 6 years
Q69
Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that A or B occurs is $\frac{1}{2}$ , then the probability of both of them occur together is :
Probability Conditional Probability Conditional Prob via Venn Diagrams
EasySingle correctNew idea
Q70
Which of the following statements is a tautology ?
Mathematical Reasoning
MediumSingle correct
Q71
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word ‘EXAMINATION’ is __________.
Permutations and Combinations Permutations with Repetition
HardNumerical valueNew ideaIdea asked in 4 years
Q72
The sum, $\sum_{n=1}^{7} \frac{n(n+1)(2n+1)}{4}$ is equal to __________.
Sequences and Series
MediumNumerical value
Q73
Let $f(x)$ be a polynomial of degree 3 such that $f(-1) = 10$ , $f(1) = -6$ , $f(x)$ has a critical point at $x = -1$ and $f'(x)$ has a critical point at $x = 1$ . Then $f(x)$ has a local minima at $x =$ __________.
Application of Derivatives Maxima and Minima Determining Coefficients from Extrema
MediumNumerical valueNew ideaIdea asked in 3 years
Q74
Let a line $y = mx$ $(\mathrm{m} > 0)$ intersect the parabola, $y^2 = x$ at a point P, other than the origin. Let the tangent to it at P meet the $x$ -axis at the point Q. If area $(\Delta \mathrm{OPQ}) = 4$ sq. units, then m is equal to __________.
Conic Sections General Conic Section Tangent to General Conic (T=0)
MediumNumerical valueNew ideaIdea asked in 3 years
Q75
If $\frac{\sqrt{2}\sin\alpha}{\sqrt{1 + \cos 2\alpha}} = \frac{1}{7}$ and $\sqrt{\frac{1 - \cos 2\beta}{2}} = \frac{1}{\sqrt{10}}$ , $\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$ , then $\tan(\alpha + 2\beta)$ is equal to __________.
Trigonometric Functions Trigonometric Identities Compound Angle Formulas
MediumNumerical valueNew ideaIdea asked in 5 years

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2020 shifts.