JEE Main 2020 · September session

JEE Main 3 September 2020, Shift 1

74 questions (1 more dropped by NTA): 15 numerical-answer and 59 multiple choice. 9 were rated hard and 24 easy. Its hard-question count was the 6th highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Complex Numbers and Quadratic Equations, with 3 questions.

Questions: 74; 1 dropped by NTA
Numerical answer: 15; 20% of the shift
Hard: 9; 12% of the shift
Chapters asked: 56; 12 questions with a figure

Key findings · 3 Sep 2020, Shift 1

1
9 hard questions (12%): the 6th highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
58 questions tested a new idea, one no earlier year had asked: 91% of the 64 questions tagged to an idea.
3
6 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
4
22 shared an idea with another 2020 shift (34% of tagged questions). Shifts in the same year can test the same idea in a new setting.
5
Biggest chapters: System of Particles and Rotational Motion in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Complex Numbers and Quadratic Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 10Medium 10Hard 5

Top chapters

Chemistry

24 Q · 5 numerical

Easy 8Medium 13Hard 3

Top chapters

Maths

25 Q · 5 numerical

Easy 6Medium 18Hard 1

Top chapters

Question format

Single correct57 Q
Numerical value15 Q
Other2 Q

What each question asks you to do

Multi-step27 Q
Calculation24 Q
Application10 Q
Conceptual8 Q
Recall5 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 shift3084 · 33%33%8/830298716720359538199224
Open25 this shift3065 · 33%33%8/829299715710354533200225
Open24 this shift3092 · 33%33%8/830299720720358540200225

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

Physics25 questions

10 easy10 medium5 hard

Chemistry24 questions

8 easy13 medium3 hard

Q26
It is true that :
Chemical Kinetics Rate Laws Order vs Molecularity
EasySingle correctNew ideaIdea asked in 2 years
Q27
Of the species, NO, $\mathrm{NO^+}$ , $\mathrm{NO^{2+}}$ and $\mathrm{NO^-}$ , the one with minimum bond strength is :
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Stability Comparison
MediumSingle correctNew idea
Q28
Henry’s constant (in kbar) for four gases $\alpha$ , $\beta$ , $\gamma$ and $\delta$ in water at 298 K is given below : | | $\alpha$ | $\beta$ | $\gamma$ | $\delta$ | | $\mathrm{K_H}$ | 50 | 2 | $2\times10^{-5}$ | 0.5 | (density of water $=10^3$ …
Solutions
MediumSingle correct · figure
Q30
An acidic buffer is obtained on mixing :
Equilibrium pH and Buffers Buffer Formation via Partial Neutralization
MediumSingle correctNew ideaIdea asked in 2 years
Q31
Tyndall effect is observed when :
Surface Chemistry Colloids Optical and Kinetic Properties
EasySingle correctIdea asked in 5 yearsAsked the year before
Q32
The atomic number of the element unnilennium is :
Classification of Elements and Periodicity in Properties Periodic Trends IUPAC Nomenclature for Z > 100
EasySingle correctNew ideaIdea asked in 3 years
Q33
If the boiling point of $\mathrm{H_2O}$ is 373 K, the boiling point of $\mathrm{H_2S}$ will be :
Chemical Bonding and Molecular Structure Periodic Trends Boiling Point Anomalies of p-Block Hydrides
EasySingle correctNew ideaIdea asked in 2 years
Q34
In a molecule of pyrophosphoric acid, the number of $\mathrm{P-OH}$ , $\mathrm{P=O}$ and $\mathrm{P-O-P}$ bonds/moiety(ies) respectively are :
The p-Block Elements Group 15 & 16 Phosphorus Oxoacids
MediumSingle correctNew ideaIdea asked in 4 years
Q35
Aqua regia is used for dissolving noble metals (Au, Pt, etc.). The gas evolved in this process is :
The d- and f-Block Elements
EasySingle correct
Q36
The complex that can show optical activity is :
Coordination Compounds Coordination Isomerism Optical Activity of Cis-M(AA)2B2
MediumSingle correctNew idea
Q37
The electronic spectrum of $\mathrm{[Ti(H_2O)_6]^{3+}}$ shows a single broad peak with a maximum at 20,300 $\mathrm{cm^{-1}}$ . The crystal field stabilization energy (CFSE) of the complex ion, in $\mathrm{kJ\ mol^{-1}}$ , is : (…
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumSingle correctNew ideaIdea asked in 6 years
Q38
Thermal power plants can lead to :
Environmental Chemistry Acid Rain Mechanism
EasySingle correctNew ideaIdea asked in 4 years
Q39
Which one of the following compounds possesses the most acidic hydrogen ?
Aldehydes, Ketones and Carboxylic Acids Organic Acidity and Basicity Acidity of Active Methylene Compounds
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q40
Glycerol is separated in soap industries by :
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q41
Which of the following compounds produces an optically inactive compound on hydrogenation ?
Hydrocarbons Stereoisomerism Chiral Centers
HardSingle correct · figureNew ideaIdea asked in 5 years
Q42
The antifertility drug “Novestrol” can react with :
Chemistry in Everyday Life Antifertility Drugs
MediumSingle correctNew ideaIdea asked in 2 years
Q43
An organic compound [A], molecular formula $\mathrm{C_{10}H_{20}O_2}$ was hydrolyzed with dilute sulphuric acid to give a carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with $\mathrm{CrO_3-H_2SO_4}$ produced [B]. Which of the following structures…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Fischer Esterification
MediumSingle correct · figureNew ideaIdea asked in 3 years
Q44
The mechanism of $\mathrm{S_N1}$ reaction is given as : $\mathrm{R-X\longrightarrow R^{\oplus}X^{\ominus}\longrightarrow R^{\oplus}\,\|\,X^{\ominus}\xrightarrow{Y^{\ominus}}R-Y+X^{\ominus}}$ Ion pair; Solvent Separated ion pair A student writes general…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms SN1 Carbocation Intermediate
MediumOther · figureNew ideaIdea asked in 2 years
Q45
The Kjeldahl method of Nitrogen estimation fails for which of the following reaction products ? (a) [figure: a six-membered ring drawn with three inner double-bond lines, bearing a substituent labelled $\mathrm{NO_2}$ on a vertical line at the top; arrow…
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
MediumOther · figureNew ideaIdea asked in 4 years
Q46
The mole fraction of glucose ( $\mathrm{C_6H_{12}O_6}$ ) in an aqueous binary solution is 0.1. The mass percentage of water in it, to the nearest integer, is __________.
Solutions Mole Concept Mole Fraction Calculation
EasyNumerical valueNew ideaIdea asked in 3 years
Q47
An element with molar mass $2.7\times10^{-2}$ $\mathrm{kg\ mol^{-1}}$ forms a cubic unit cell with edge length 405 pm. If its density is $2.7\times10^{3}$ $\mathrm{kg\ m^{-3}}$ , the radius of the element is approximately __________ $\times10^{-12}$ m (to the…
The Solid State Crystal Lattices Unit Cell Density
MediumNumerical valueNew ideaIdea asked in 4 years
Q48
The photoelectric current from Na (work function, $\mathrm{w_0}=2.3$ eV) is stopped by the output voltage of the cell $\mathrm{Pt(s)|H_2(g,\ 1\ bar)|HCl(aq.,\ pH=1)|AgCl(s)|Ag(s)}$ . The pH of aq. HCl required to stop the photoelectric current from…
Electrochemistry Nernst Equation Full Cell Nernst Equation
HardNumerical valueNew ideaIdea asked in 6 years
Q49
The volume strength of 8.9 M $\mathrm{H_2O_2}$ solution calculated at 273 K and 1 atm is __________. (R $=0.0821$ L atm $\mathrm{K^{-1}\ mol^{-1}}$ ) (rounded off to the nearest integer)
Hydrogen Hydrogen and Hydrides Volume Strength of H2O2
MediumNumerical valueNew idea
Q50
The total number of monohalogenated organic products (including stereoisomers) in the following reaction is __________. A $\xrightarrow[\mathrm{(ii)\ X_2/\Delta}]{\mathrm{(i)\ H_2/Ni/\Delta}}$ (Simplest optically active alkene)
Hydrocarbons Alkanes and Free Radicals Stereochemistry of Free Radical Halogenation
HardNumerical valueNew ideaIdea asked in 2 years

Maths25 questions

6 easy18 medium1 hard

Q51
Consider the two sets : $A=\{m\in\mathbf{R}$ : both the roots of $x^2-(m+1)x+m+4=0$ are real $\}$ and $B=[-3,5)$ . Which of the following is not true ?
Complex Numbers and Quadratic Equations Quadratic Roots Nature of Roots
MediumSingle correctNew ideaIdea asked in 3 years
Q52
If $\alpha$ and $\beta$ are the roots of the equation $x^2+px+2=0$ and $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ are the roots of the equation $2x^2+2qx+1=0$ , then…
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctNew ideaIdea asked in 6 years
Q53
The value of $(2\cdot{}^1P_0-3\cdot{}^2P_1+4\cdot{}^3P_2-\ldots$ up to $51^{th}$ term $)+(1!-2!+3!-\ldots$ up to $51^{th}$ term $)$ is equal to :
Permutations and Combinations Permutations of Distinct Objects
MediumSingle correctNew ideaIdea asked in 4 years
Q54
If $\Delta=\begin{vmatrix}x-2&2x-3&3x-4\\2x-3&3x-4&4x-5\\3x-5&5x-8&10x-17\end{vmatrix}=Ax^3+Bx^2+Cx+D$ , then $B+C$ is equal to :
Determinants
MediumSingle correct
Q55
If the number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^n$ is exactly 33, then the least value of n is :
Binomial Theorem
MediumSingle correct
Q56
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :
Sequences and Series AP and GP AP Sum of n terms
EasySingle correctNew ideaIdea asked in 7 years
Q57
If $y^2+\log_e(\cos^2x)=y$ , $x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ , then :
Continuity and Differentiability Chain Rule Second Order Implicit Chain Rule
MediumSingle correctNew ideaIdea asked in 4 years
Q58
Let $[t]$ denote the greatest integer $\le t$ . If for some $\lambda\in\mathbf{R}-\{0,1\}$ , $\lim_{x\to0}\left|\frac{1-x+|x|}{\lambda-x+[x]}\right|=L$ , then L is equal to :
Limits and Derivatives L'Hopital's Rule Handling Greatest Integer Functions
MediumSingle correctNew ideaIdea asked in 3 years
Q59
The function, $f(x)=(3x-7)x^{2/3}$ , $x\in\mathbf{R}$ , is increasing for all $x$ lying in :
Application of Derivatives Monotonicity Finding Intervals
MediumSingle correctNew ideaIdea asked in 5 years
Q60
$\int_{-\pi}^{\pi}|\pi-|x||dx$ is equal to :
Integrals Definite Integral Properties Modulus Function Interval Splitting
EasySingle correctNew ideaIdea asked in 3 years
Q61
The area (in sq. units) of the region $\{(x,y):0\le y\le x^2+1,\ 0\le y\le x+1,$ $\frac{1}{2}\le x\le2\}$ is :
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q62
The solution curve of the differential equation, $(1+e^{-x})(1+y^2)\frac{dy}{dx}=y^2$ , which passes through the point (0, 1), is :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q63
Let P be a point on the parabola, $y^2=12x$ and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the $y$ -intercept of the…
Conic Sections
MediumSingle correct
Q64
A hyperbola having the transverse axis of length $\sqrt{2}$ has the same foci as that of the ellipse $3x^2+4y^2=12$ , then this hyperbola does not pass through which of the following points ?
Conic Sections
MediumSingle correct
Q65
The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, $-2$ , 3) and (1, 1, 0) lies on the plane :
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumSingle correctNew ideaIdea asked in 6 years
Q66
The lines $\vec{r}=(\hat{i}-\hat{j})+l(2\hat{i}+\hat{k})$ and $\vec{r}=(2\hat{i}-\hat{j})+\mathrm{m}(\hat{i}+\hat{j}-\hat{k})$
Three Dimensional Geometry Lines in 3D Condition for Intersection of Two Lines
EasySingle correctNew ideaIdea asked in 3 years
Q67
For the frequency distribution : Variate ( $x$ ) : $x_1$ $x_2$ $x_3$ ... $x_{15}$ Frequency ( $f$ ) : $f_1$ $f_2$ $f_3$ ... $f_{15}$ where $0<x_1<x_2<x_3<\ldots<x_{15}=10$ and $\sum_{i=1}^{15}f_i>0$ , the standard deviation cannot be :
Statistics Variance and SD Maximum Variance of Bounded Data
HardSingle correctNew ideaIdea asked in 2 years
Q68
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
Probability Conditional Probability Conditioning on Dice Sums
EasySingle correctNew idea
Q69
$2\pi-\left(\sin^{-1}\frac{4}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{16}{65}\right)$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Sine Inverse Sum and Difference
MediumSingle correctNew ideaIdea asked in 3 years
Q70
The proposition $p\to\sim(p\wedge\sim q)$ is equivalent to :
Mathematical Reasoning
EasySingle correct
Q71
If $\left(\frac{1+i}{1-i}\right)^{m/2}=\left(\frac{1+i}{i-1}\right)^{n/3}=1$ , $(\mathrm{m},\ \mathrm{n}\in\mathbf{N})$ then the greatest common divisor of the least values of m and n is __________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Smallest Integer Power for Real/Imaginary
EasyNumerical valueNew idea
Q72
Let $A=\begin{bmatrix}x&1\\1&0\end{bmatrix}$ , $x\in\mathbf{R}$ and $A^4=[a_{ij}]$ . If $a_{11}=109$ , then $a_{22}$ is equal to __________.
Matrices Matrix Multiplication Powers of Square Matrices
MediumNumerical valueNew ideaIdea asked in 6 years
Q73
The value of $(0.16)^{\log_{2.5}\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\ldots\text{ to }\infty\right)}$ is equal to __________.
Sequences and Series AP and GP Infinite GP Sum
MediumNumerical valueNew ideaIdea asked in 6 years
Q74
If $\lim_{x\to0}\left\{\frac{1}{x^8}\left(1-\cos\frac{x^2}{2}-\cos\frac{x^2}{4}\right.\right.$ $\left.\left.+\cos\frac{x^2}{2}\cos\frac{x^2}{4}\right)\right\}=2^{-k}$ , then the value of k is __________.
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumNumerical valueNew ideaIdea asked in 7 years
Q75
The diameter of the circle, whose centre lies on the line $x+y=2$ in the first quadrant and which touches both the lines $x=3$ and $y=2$ , is __________.
Conic Sections Circle Tangents Condition of tangency
MediumNumerical valueNew ideaIdea asked in 4 years

Dropped from the final key and left out of every count: Q29.

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.