JEE Main 2020 · September session

JEE Main 2 September 2020, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 5 were rated hard and 15 easy. Its hard-question count was the joint 9th highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Alcohols, Phenols and Ethers, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 5; 7% of the shift
Chapters asked: 59; 18 questions with a figure

Key findings · 2 Sep 2020, Shift 2

1
5 hard questions (7%): the joint 9th highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
64 questions tested a new idea, one no earlier year had asked: 97% of the 66 questions tagged to an idea.
3
2 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
4
26 shared an idea with another 2020 shift (39% 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), Alcohols, Phenols and Ethers in Chemistry (3) and Application of Derivatives in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 6Medium 18Hard 1

Top chapters

Chemistry

25 Q · 5 numerical

Easy 8Medium 14Hard 3

Top chapters

Maths

25 Q · 5 numerical

Easy 1Medium 23Hard 1

Top chapters

Question format

Single correct48 Q
Numerical value15 Q
Diagram based8 Q
Other3 Q
Match the list1 Q

What each question asks you to do

Calculation27 Q
Multi-step24 Q
Application11 Q
Conceptual7 Q
Recall3 Q
Data or graph2 Q
Diagram reading1 Q

Most common: Calculation.

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

6 easy18 medium1 hard

Chemistry25 questions

8 easy14 medium3 hard

Q26
The results given in the below table were obtained during kinetic studies of the following reaction : $2\,\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} + \mathrm{D}$ Experiment | $[\mathrm{A}]/\mathrm{molL^{-1}}$ | $[\mathrm{B}]/\mathrm{molL^{-1}}$ |…
Chemical Kinetics Rate Laws Initial Rates Method
MediumSingle correct · figureNew ideaIdea asked in 5 years
Q27
The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the following processes can explain this ?
Solutions
EasySingle correct
Q28
Amongst the following statements regarding adsorption, those that are valid are : (a) $\Delta$ H becomes less negative as adsorption proceeds. (b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas. (c) On adsorption, the residual force acting…
Surface Chemistry Adsorption Physisorption vs Chemisorption
MediumOtherNew idea
Q29
The molecular geometry of $\mathrm{SF_6}$ is octahedral. What is the geometry of $\mathrm{SF_4}$ (including lone pair(s) of electrons, if any)?
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 5 Derivative Shapes
EasySingle correctNew ideaIdea asked in 3 years
Q30
The number of subshells associated with $n=4$ and $m=-2$ quantum numbers is :
Structure of Atom Quantum Numbers Magnetic Quantum Number
MediumSingle correctNew ideaIdea asked in 4 years
Q31
Match the type of interaction in column A with the distance dependence of their interaction energy in column B : A (I) ion-ion (II) dipole - dipole (III) London dispersion B (a) $\frac{1}{r}$ (b) $\frac{1}{r^2}$ (c) $\frac{1}{r^3}$ (d) $\frac{1}{r^6}$
States of Matter
MediumMatch the list
Q32
Three elements X, Y and Z are in the $3^{\mathrm{rd}}$ period of the periodic table. The oxides of X, Y and Z, respectively, are basic, amphoteric and acidic. The correct order of the atomic numbers of X, Y and Z is :
Classification of Elements and Periodicity in Properties Periodic Trends Acidic and Basic Character of Oxides
EasySingle correctNew ideaIdea asked in 4 years
Q33
Cast iron is used for the manufacture of :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Iron Extraction Chemistry
EasySingle correctNew idea
Q34
If you spill a chemical toilet cleaning liquid on your hand, your first aid would be :
Equilibrium
EasySingle correct
Q35
Two elements A and B have similar chemical properties. They don’t form solid hydrogencarbonates, but react with nitrogen to form nitrides. A and B, respectively, are :
The s-Block Elements s-Block Elements Direct Formation of Nitrides
MediumSingle correctNew idea
Q36
The shape/structure of $[\mathrm{XeF_5}]^{-}$ and $\mathrm{XeO_3F_2}$ , respectively, are :
Chemical Bonding and Molecular Structure VSEPR Theory Pentagonal Planar Geometry (SN=7, 2 LP)
MediumSingle correctNew idea
Q37
Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of $\mathrm{M^{n+}}$ ion are provided below; their $\lambda_{\max}$ values are marked as A, B and C respectively. The correct match between the complexes and their $\lambda_{\max}$ values…
Coordination Compounds Crystal Field Theory Spectrochemical Series
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q38
The one that is not expected to show isomerism is :
Coordination Compounds Coordination Isomerism Absence of Geometrical Isomerism in Tetrahedral Complexes
MediumSingle correctNew idea
Q39
Arrange the following labelled hydrogens in decreasing order of acidity :
Organic Chemistry: Some Basic Principles and Techniques Organic Acidity and Basicity Carboxylic Acid Acidity
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q40
The major product of the following reaction is : reactant (drawn structure) with the arrow labelled: conc. $\mathrm{HNO_3}$ + conc. $\mathrm{H_2SO_4}$
Alcohols, Phenols and Ethers Aromatic Hydrocarbons Nitrating Mixture and Nitronium Ion Generation
MediumSingle correct · figureNew ideaIdea asked in 3 years
Q41
The correct observation in the following reactions is : $\mathrm{Sucrose} \xrightarrow[\text{Cleavage (Hydrolysis)}]{\text{Glycosidic bond}} \mathrm{A} + \mathrm{B} \xrightarrow{\text{Seliwanoff’s reagent}} ?$
Biomolecules Carbohydrates Seliwanoff's Test
EasySingle correctNew ideaIdea asked in 2 years
Q42
Consider the reaction sequence given below : (1) [drawn structure] $-\mathrm{Br}$ $\xrightarrow[\mathrm{H_2O}]{\mathrm{OH^{\ominus}}}$ [drawn structure] $-\mathrm{OH} + \mathrm{Br^{\ominus}}$ ......... (1) rate $= k[\text{t-BuBr}]$ (2) [arrow drawn down from…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Rate Law and Concentration Dependence
MediumSingle correct · figureNew idea
Q43
An organic compound ‘A’ ( $\mathrm{C_9H_{10}O}$ ) when treated with conc. HI undergoes cleavage to yield compounds ‘B’ and ‘C’. ‘B’ gives yellow precipitate with $\mathrm{AgNO_3}$ where as ‘C’ tautomerizes to ‘D’. ‘D’ gives positive iodoform test. ‘A’ could be :
Alcohols, Phenols and Ethers Ethers Cleavage of Vinyl Ethers
HardSingle correct · figureNew idea
Q44
The major product obtained from $\mathrm{E_2}$ -elimination of 3-bromo-2-fluoropentane is :
Haloalkanes and Haloarenes Alkenes and Alkynes Saytzeff vs. Hofmann Elimination
HardSingle correct · figureIdea asked in 6 yearsAsked the year before
Q45
Two compounds A and B with same molecular formula ( $\mathrm{C_3H_6O}$ ) undergo Grignard’s reaction with methylmagnesium bromide to give products C and D. Products C and D show following chemical tests. Test | C | D Ceric ammonium nitrate Test | Positive |…
Alcohols, Phenols and Ethers Alcohols and Phenols Lucas Test Differentiation
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q46
The work function of sodium metal is $4.41\times10^{-19}$ J. If photons of wavelength 300 nm are incident on the metal, the kinetic energy of the ejected electrons will be ( $h=6.63\times10^{-34}$ J s; $c=3\times10^{8}$ m/s) __________ $\times10^{-21}$ J.
Structure of Atom Bohr's Atomic Theory Photoelectric Effect Coupling
EasyNumerical valueNew ideaIdea asked in 3 years
Q47
The heat of combustion of ethanol into carbon dioxids and water is $-327$ kcal at constant pressure. The heat evolved (in cal) at constant volume and $27^\circ$ C (if all gases behave ideally) is ( $R=2$ cal $\mathrm{mol^{-1}}$ $\mathrm{K^{-1}}$ ) __________.
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
MediumNumerical valueNew ideaIdea asked in 4 years
Q48
For the disproportionation reaction $2\,\mathrm{Cu^+(aq)} \rightleftharpoons \mathrm{Cu(s)} + \mathrm{Cu^{2+}(aq)}$ at 298 K, $\ln K$ (where K is the equilibrium constant) is __________ $\times10^{-1}$ . Given : ( $E^0_{\mathrm{Cu^{2+}/Cu^+}} = 0.16$ V…
Electrochemistry Nernst Equation Equilibrium Constant of Disproportionation
MediumNumerical valueNew idea
Q49
The oxidation states of transition metal atoms in $\mathrm{K_2Cr_2O_7}$ , $\mathrm{KMnO_4}$ and $\mathrm{K_2FeO_4}$ , respectively, are $x$ , $y$ and $z$ . The sum of $x$ , $y$ and $z$ is __________.
Redox Reactions Oxidation State Method
EasyNumerical valueNew idea
Q50
The ratio of the mass percentages of ‘C & H’ and ‘C & O’ of a saturated acyclic organic compound ‘X’ are 4 : 1 and 3 : 4 respectively. Then, the moles of oxygen gas required for complete combustion of two moles of organic compound ‘X’ is __________.
Some Basic Concepts of Chemistry Mole Concept Empirical Formula from Mass Percentage
HardNumerical valueNew ideaIdea asked in 3 years

Maths25 questions

1 easy23 medium1 hard

Q51
Let $f : \mathbf{R} \to \mathbf{R}$ be a function which satisfies $f(x+y)=f(x)+f(y)\ \forall\ x,y \in \mathbf{R}$ . If $f(1)=2$ and $g(n)=\sum_{k=1}^{(n-1)} f(k)$ , $n \in \mathbf{N}$ then the value of n, for which $g(n)=20$ , is :
Relations and Functions
MediumSingle correct
Q52
Let $f(x)$ be a quadratic polynomial such that $f(-1)+f(2)=0$ . If one of the roots of $f(x)=0$ is 3, then its other root lies in :
Complex Numbers and Quadratic Equations Quadratic Roots Equation Formation
MediumSingle correctNew ideaIdea asked in 2 years
Q53
The imaginary part of $\left(3+2\sqrt{-54}\right)^{1/2}-\left(3-2\sqrt{-54}\right)^{1/2}$ can be :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Square Root via Polar Form
MediumSingle correctNew idea
Q54
Let a, b, c $\in \mathbf{R}$ be all non-zero and satisfy $a^3+b^3+c^3=2$ . If the matrix $A=\begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \end{pmatrix}$ satisfies $A^T A=I$ , then a value of abc can be :
Matrices Matrix Multiplication Orthogonal Matrix Properties
MediumSingle correctNew idea
Q55
Let $A=\{X=(x,\ y,\ z)^T : PX=0$ and $x^2+y^2+z^2=1\}$ , where $P=\begin{bmatrix} 1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1 \end{bmatrix}$ , then the set A :
Determinants Cramer's Rule Geometric Meaning of Non-Trivial Homogeneous Solutions
MediumSingle correctNew idea
Q56
Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining…
Permutations and Combinations Number of Diagonals in a Polygon
MediumSingle correctNew idea
Q57
If the sum of first 11 terms of an A.P., $a_1$ , $a_2$ , $a_3$ , ... is 0 ( $a_1 \neq 0$ ), then the sum of the A.P., $a_1$ , $a_3$ , $a_5$ , ..., $a_{23}$ is $ka_1$ , where k is equal to :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctNew ideaIdea asked in 7 years
Q58
Let S be the sum of the first 9 terms of the series : $\{x+ka\}+\{x^2+(k+2)a\}+\{x^3+(k+4)a\}+\{x^4+(k+6)a\}+\ldots$ where $a \neq 0$ and $x \neq 1$ . If $S=\frac{x^{10}-x+45a(x-1)}{x-1}$ , then k is equal to :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctNew ideaIdea asked in 7 years
Q59
$\lim_{x \to 0}\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{1/x}$ is equal to :
Limits and Derivatives L'Hopital's Rule e-Power Shortcut for 1^infinity Forms
EasySingle correctNew ideaIdea asked in 3 years
Q60
The equation of the normal to the curve $y=(1+x)^{2y}+\cos^2(\sin^{-1}x)$ at $x=0$ is :
Application of Derivatives Tangents and Normals Equation of Normal
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q61
Let $f:(-1,\infty)\to\mathbf{R}$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x}\log_e(1+x)$ , $x\neq 0$ . Then the function $f$ :
Application of Derivatives Monotonicity First Derivative Test
MediumSingle correctNew ideaIdea asked in 3 years
Q62
Consider a region $R=\{(x,\ y)\in\mathbf{R}^2 : x^2\le y\le 2x\}$ . If a line $y=\alpha$ divides the area of region R into two equal parts, then which of the following is true ?
Application of Integrals Area Under Curves Bisection of Bounded Areas
MediumSingle correctNew ideaIdea asked in 2 years
Q63
If a curve $y=f(x)$ , passing through the point $(1,\,2)$ , is the solution of the differential equation, $2x^2\,dy=(2xy+y^2)\,dx$ , then $f\left(\frac{1}{2}\right)$ is equal to :
Differential Equations Homogeneous Equations Substitution y = vx
MediumSingle correctNew ideaIdea asked in 6 years
Q64
The set of all possible values of $\theta$ in the interval $(0,\pi)$ for which the points $(1,\,2)$ and $(\sin\theta,\cos\theta)$ lie on the same side of the line $x+y=1$ is :
Straight Lines Straight Line Distance Position of points relative to line
MediumSingle correctNew ideaIdea asked in 2 years
Q65
The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^2=8x$ , with one of its vertices on the vertex of this parabola, is :
Conic Sections
MediumSingle correct
Q66
For some $\theta\in\left(0,\frac{\pi}{2}\right)$ , if the eccentricity of the hyperbola, $x^2-y^2\sec^2\theta=10$ is $\sqrt{5}$ times the eccentricity of the ellipse, $x^2\sec^2\theta+y^2=5$ , then the length of the latus rectum of the ellipse, is :
Conic Sections Ellipse Eccentricity Eccentricity calculation
MediumSingle correctNew ideaIdea asked in 6 years
Q67
A plane passing through the point $(3,\,1,\,1)$ contains two lines whose direction ratios are $1,\,-2,\,2$ and $2,\,3,\,-1$ respectively. If this plane also passes through the point $(\alpha,\,-3,\,5)$ , then $\alpha$ is equal to :
Three Dimensional Geometry Planes in 3D Plane Containing Two Lines
MediumSingle correctNew ideaIdea asked in 2 years
Q68
Let $E^C$ denote the complement of an event E. Let $E_1$ , $E_2$ and $E_3$ be any pairwise independent events with $P(E_1)>0$ and $P(E_1\cap E_2\cap E_3)=0$ . Then $P\left(E_2^C\cap E_3^C\,/\,E_1\right)$ is equal to :
Probability Conditional Probability De Morgan's Laws in Conditional Spaces
MediumSingle correctNew idea
Q69
If the equation $\cos^4\theta+\sin^4\theta+\lambda=0$ has real solutions for $\theta$ , then $\lambda$ lies in the interval :
Trigonometric Functions General Solutions Fourth Power Identity Application
MediumSingle correctNew ideaIdea asked in 2 years
Q70
Which of the following is a tautology ?
Relations and Functions
MediumSingle correct
Q71
For a positive integer n, $\left(1+\frac{1}{x}\right)^n$ is expanded in increasing powers of $x$ . If three consecutive coefficients in this expansion are in the ratio, $2:5:12$ , then n is equal to ________.
Binomial Theorem Binomial Coefficients Ratio of Consecutive Coefficients
MediumNumerical valueNew ideaIdea asked in 5 years
Q72
If $y=\sum_{k=1}^{6} k\cos^{-1}\left\{\frac{3}{5}\cos kx-\frac{4}{5}\sin kx\right\}$ , then $\frac{dy}{dx}$ at $x=0$ is ________.
Continuity and Differentiability Chain Rule Pre-simplification via Trig Substitution
HardNumerical valueNew ideaIdea asked in 2 years
Q73
Let the position vectors of points 'A' and 'B' be $\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}+\hat{j}+3\hat{k}$ , respectively. A point 'P' divides the line segment AB internally in the ratio $\lambda:1$ ( $\lambda>0$ ). If O is the origin and…
Vector Algebra Cross Product Lagrange's Identity
MediumNumerical valueNew ideaIdea asked in 5 years
Q74
Let [t] denote the greatest integer less than or equal to t. Then the value of $\int_1^2 |2x-[3x]|\,dx$ is ________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumNumerical valueNew ideaIdea asked in 7 years
Q75
If the variance of the terms in an increasing A.P., $b_1$ , $b_2$ , $b_3$ , ...., $b_{11}$ is 90, then the common difference of this A.P. is ________.
Statistics Variance and SD Variance of an Arithmetic Progression
MediumNumerical valueNew idea

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.