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. Its hard-question count was the joint 7th highest of the 12 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

Key findings · 8 Jan 2020, Shift 1

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
Maths was the hardest section, with 4 of 25 rated hard; Chemistry had the most easy questions (6 of 25).
3
58 questions tested a new idea, one no earlier year had asked: 92% of the 63 questions tagged to an idea.
4
5 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
5
28 shared an idea with another 2020 shift (44% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Ray Optics and Optical Instruments in Physics (3), Alcohols, Phenols and Ethers in Chemistry (2) and Complex Numbers and Quadratic Equations in Maths (2).

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.

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 shift3065 · 33%33%8/829299715710354533200225
Open24 this shift3084 · 33%33%8/830298716720359538199224

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 74 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

74 of 74 questions

Physics24 questions

4 easy19 medium1 hard

Chemistry25 questions

6 easy16 medium3 hard

Q26
The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :
Equilibrium Solubility Product Ksp Expression Writing
HardSingle correct · figureNew ideaIdea asked in 2 years
Q27
The rate of a certain biochemical reaction at physiological temperature (T) occurs $10^6$ times faster with enzyme than without. The change in the activation energy upon adding enzyme is :
Chemical Kinetics Arrhenius Equation Catalyst Effect on Arrhenius Parameters
MediumSingle correctNew ideaIdea asked in 3 years
Q28
As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :
Surface Chemistry Colloids Hardy-Schulze Rule
MediumSingle correctNew ideaIdea asked in 3 years
Q29
The predominant intermolecular forces present in ethyl acetate, a liquid, are :
Chemical Bonding and Molecular Structure
MediumSingle correct
Q30
For the Balmer series in the spectrum of H atom, $\bar{\nu} = R_H\left\{\frac{1}{n_1^2}-\frac{1}{n_2^2}\right\}$ , the correct statements among (I) to (IV) are : (I) As wavelength decreases, the lines in the series converge (II) The integer $n_1$ is equal to…
Structure of Atom Bohr's Atomic Theory Longest and Shortest Wavelengths in a Series
MediumOtherNew ideaIdea asked in 2 years
Q31
A 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 higher intermolecular interactions compared to Y. (B) X has lower intermolecular interactions compared to Y. (C)…
States of Matter Colligative Properties Vapor Pressure-Temperature Graph Interpretation
MediumOther · figureNew idea
Q32
The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :
Classification of Elements and Periodicity in Properties Periodic Trends Penetration Effect on Ionization Enthalpy
EasySingle correctNew ideaIdea asked in 2 years
Q33
The strength of an aqueous NaOH solution is most accurately determined by titrating : (Note : consider that an appropriate indicator is used)
Some Basic Concepts of Chemistry
MediumSingle correct
Q34
When gypsum is heated to 393 K, it forms :
The s-Block Elements s-Block Elements Thermal Dehydration of Gypsum
EasySingle correctNew idea
Q35
The number of bonds between sulphur and oxygen atoms in $\mathrm{S_2O_8^{2-}}$ and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are :
The p-Block Elements Group 15 & 16 Sulfur Oxoacids
MediumSingle correctNew ideaIdea asked in 4 years
Q36
The third ionization enthalpy is minimum for :
The d- and f-Block Elements d-Block Elements Ionization Enthalpy Irregularities
MediumSingle correctNew ideaIdea asked in 4 years
Q37
The complex that can show $fac$ - and $mer$ - isomers is :
Coordination Compounds Coordination Isomerism Facial and Meridional Isomerism in MA3B3
EasySingle correctNew ideaIdea asked in 3 years
Q38
Among the gases (a) - (e), the gases that cause greenhouse effect are : (a) $\mathrm{CO_2}$ (b) $\mathrm{H_2O}$ (c) CFCs (d) $\mathrm{O_2}$ (e) $\mathrm{O_3}$
Environmental Chemistry Greenhouse Effect
EasyOtherNew ideaIdea asked in 4 years
Q39
The most suitable reagent for the given conversion is :
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Reduction of Acids
MediumSingle correct · figureNew ideaIdea asked in 5 years
Q40
A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at 63 $^\circ$ C while the other boils at 60 $^\circ$ C. What is the best way to separate the two liquids and which one will be distilled out first ?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q41
Arrange the following compounds in increasing order of C $-$ OH bond length : methanol, phenol, p-ethoxyphenol
Alcohols, Phenols and Ethers Resonance and Hyperconjugation Mesomeric Effect
MediumSingle correctNew ideaIdea asked in 3 years
Q42
Which of the following statement is not true for glucose ?
Biomolecules Carbohydrates Reactions Confirming the Carbonyl Group
MediumSingle correctNew idea
Q43
The major products A and B in the following reactions are : $(\mathrm{CH_3})_2\mathrm{CH{-}CH(CH_3){-}CN}$ $\xrightarrow[\text{Heat}]{\text{Peroxide}}$ [A] [A] + (an unbranched zigzag terminal alkene) $\longrightarrow$ B
Hydrocarbons
HardDiagram based · figure
Q44
The decreasing order of reactivity towards dehydrohalogenation ( $\mathrm{E_1}$ ) reaction of the following compounds is : (A) $\mathrm{CH_3CH_2CH_2CH_2CH_2Cl}$ (1-chloropentane, skeletal) (B) $\mathrm{ClCH_2CH_2CH_2CH{=}CH_2}$ (5-chloropent-1-ene, skeletal)…
Haloalkanes and Haloarenes
MediumOther · figure
Q45
The major product of the following reaction is : $(\mathrm{CH_3})_2\mathrm{C{=}CH{-}CH_2{-}CH_2{-}C(CH_3){=}CH{-}CH_2OH}$ $\xrightarrow{\text{dil. }\mathrm{H_2SO_4}}$
Alcohols, Phenols and Ethers
HardDiagram based · figure
Q46
Ferrous 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 wheat is ______. Atomic weight : Fe = 55.85; S = 32.00; O = 16.00
Some Basic Concepts of Chemistry Mole Concept PPM and Mass Percentage
MediumNumerical valueNew ideaIdea asked in 5 years
Q47
The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is ______.
Thermodynamics (Chemistry)First Law of Thermodynamics Work Done from P-V Graph Area
EasyNumerical value · figureNew ideaIdea asked in 2 years
Q48
What would be the electrode potential for the given half cell reaction at pH=5 ? ______. $2\mathrm{H_2O} \rightarrow \mathrm{O_2} + 4\mathrm{H}^{\oplus} + 4e^{-}$ ; $E^0_{red} = 1.23\ \mathrm{V}$ ( $R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$ ; Temp…
Electrochemistry Nernst Equation pH Dependence of Electrode Potential
MediumNumerical valueNew ideaIdea asked in 4 years
Q49
The volume (in mL) of 0.125 M $\mathrm{AgNO_3}$ required to quantitatively precipitate chloride ions in 0.3 g of $[\mathrm{Co(NH_3)_6}]\mathrm{Cl_3}$ is ______. $^{M}[\mathrm{Co(NH_3)_6}]\mathrm{Cl_3} = 267.46\ \mathrm{g/mol}$ …
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q50
The number of chiral centres in penicillin is ______.
Chemistry in Everyday Life Stereoisomerism Chiral Centers
MediumNumerical valueNew ideaIdea asked in 5 years

Maths25 questions

6 easy15 medium4 hard

Q51
The inverse function of $f(x)=\dfrac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}}$ , $x\in(-1,1)$ , is ______.
Relations and Functions
MediumSingle correct
Q52
If the equation, $x^2+bx+45=0$ ( $b\in R$ ) has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$ , then :
Complex Numbers and Quadratic Equations Quadratic Roots Complex Conjugate Roots
MediumSingle correctNew ideaIdea asked in 4 years
Q53
For which of the following ordered pairs $(\mu, \delta)$ , the system of linear equations $x+2y+3z=1$ $3x+4y+5z=\mu$ $4x+4y+4z=\delta$ is inconsistent ?
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q54
Let two points be $A(1,-1)$ and $B(0,2)$ . If a point $P(x',y')$ be such that the area of $\Delta PAB=5$ sq. units and it lies on the line, $3x+y-4\lambda=0$ , then a value of $\lambda$ is :
Straight Lines Straight Line Distance Distance via Determinant Area
MediumSingle correctNew idea
Q55
If a, b and c are the greatest values of $^{19}C_p$ , $^{20}C_q$ and $^{21}C_r$ respectively, then :
Binomial Theorem Binomial Coefficients Maximum Binomial Coefficient
EasySingle correctNew ideaIdea asked in 3 years
Q56
Let $f:\mathbf{R}\to\mathbf{R}$ be such that for all $x\in\mathbf{R}$ , $(2^{1+x}+2^{1-x})$ , $f(x)$ and $(3^x+3^{-x})$ are in A.P., then the minimum value of $f(x)$ is :
Sequences and Series AP and GP AM-GM Inequality Application
MediumSingle correctNew ideaIdea asked in 2 years
Q57
$\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2}$ is equal to :
Limits and Derivatives L'Hopital's Rule e-Power Shortcut for 1^infinity Forms
EasySingle correctNew ideaIdea asked in 3 years
Q58
Let $f(x)=x\cos^{-1}(-\sin|x|)$ , $x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ , then which of the following is true ?
Continuity and Differentiability Modulus Traps in Trigonometric Functions
HardSingle correctNew ideaIdea asked in 2 years
Q59
If c is a point at which Rolle's theorem holds for the function, $f(x)=\log_e\left(\dfrac{x^2+\alpha}{7x}\right)$ in the interval $[3,4]$ , where $\alpha\in\mathbf{R}$ , then $f''(c)$ is equal to :
Continuity and Differentiability Rolle's Theorem Logarithmic Function Application
MediumSingle correctNew idea
Q60
If $\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c$ where c is a constant of integration, then $\lambda f\left(\frac{\pi}{3}\right)$ is equal to :
Integrals Integration by Substitution Factoring Highest Power for Substitution
HardSingle correctNew ideaIdea asked in 3 years
Q61
For $a>0$ , let the curves $C_1: y^2=ax$ and $C_2: x^2=ay$ intersect at origin O and a point P. Let the line $x=b$ ( $0<b<a$ ) intersect the chord OP and the $x$ -axis at points Q and R, respectively. If the line $x=b$ bisects the area bounded by the curves,…
Application of Integrals Area Under Curves Bisection of Bounded Areas
HardSingle correctNew ideaIdea asked in 2 years
Q62
Let $y=y(x)$ be a solution of the differential equation, $\sqrt{1-x^2}\,\dfrac{dy}{dx}+\sqrt{1-y^2}=0$ , $|x|<1$ . If $y\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2}$ , then $y\left(\frac{-1}{\sqrt{2}}\right)$ is equal to :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q63
The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola, $x^2=4y$ , internally in the ratio $1:2$ , is :
Conic Sections
MediumSingle correct
Q64
Let the line $y=mx$ and the ellipse $2x^2+y^2=1$ intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at $\left(-\frac{1}{3\sqrt{2}},0\right)$ and $(0,\beta)$ , then $\beta$ is equal to :
Conic Sections Normals to Conics Ellipse Normal Point Form
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q65
The shortest distance between the lines $\dfrac{x-3}{3}=\dfrac{y-8}{-1}=\dfrac{z-3}{1}$ and $\dfrac{x+3}{-3}=\dfrac{y+7}{2}=\dfrac{z-6}{4}$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctNew ideaIdea asked in 6 years
Q66
Let the volume of a parallelopiped whose coterminous edges are given by $\vec{u}=\hat{i}+\hat{j}+\lambda\hat{k}$ , $\vec{v}=\hat{i}+\hat{j}+3\hat{k}$ and $\vec{w}=2\hat{i}+\hat{j}+\hat{k}$ be 1 cu. unit. If $\theta$ be the angle between the edges $\vec{u}$ …
Vector Algebra Triple Products STP Geometric Interpretation
MediumSingle correctNew ideaIdea asked in 2 years
Q67
The 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 reduced by q, where $p\neq 0$ and $q\neq 0$ . If the new mean and new s.d. become half of their original values,…
Statistics Variance and SD Effect of Linear Transformations
MediumSingle correctNew ideaIdea asked in 2 years
Q68
Let A and B be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$ . Then, which of the following is TRUE ?
Probability Conditional Probability Conditioning on a Complementary Event
MediumSingle correctNew idea
Q69
Let $f(x)=\left(\sin(\tan^{-1}x)+\sin(\cot^{-1}x)\right)^2-1$ , $|x|>1$ . If $\dfrac{dy}{dx}=\dfrac{1}{2}\dfrac{d}{dx}\left(\sin^{-1}(f(x))\right)$ and $y(\sqrt{3})=\frac{\pi}{6}$ , then $y(-\sqrt{3})$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities sin^-1(2x/(1+x^2)) Piecewise Conversion
HardSingle correctNew idea
Q70
Which one of the following is a tautology ?
Mathematical Reasoning
EasySingle correct
Q71
The least positive value of 'a' for which the equation, $2x^2+(a-10)x+\frac{33}{2}=2a$ has real roots is ______.
Complex Numbers and Quadratic Equations Quadratic Roots Nature of Roots
EasyNumerical valueNew ideaIdea asked in 3 years
Q72
The number of all $3\times3$ matrices A, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $AA^T$ is 3, is ______.
Matrices Matrix Multiplication Trace of A times A Transpose
MediumNumerical valueNew ideaIdea asked in 2 years
Q73
The sum $\displaystyle\sum_{k=1}^{20}(1+2+3+\ldots+k)$ is ______.
Sequences and Series AP and GP AP Sum of n terms
EasyNumerical valueNew ideaIdea asked in 7 years
Q74
Let the normal at a point P on the curve $y^2-3x^2+y+10=0$ intersect the $y$ -axis at $\left(0,\frac{3}{2}\right)$ . If m is the slope of the tangent at P to the curve, then $|m|$ is equal to ______.
Application of Derivatives Tangents and Normals Tangents to Implicit Curves
MediumNumerical valueNew ideaIdea asked in 2 years
Q75
An 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 three of them are red is ______.
Permutations and Combinations Combinations of Distinct Objects
EasyNumerical valueIdea asked in 8 yearsAsked the year before

Dropped from the final key and left out of every count: Q1.

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.