JEE Main 2020 · September session

JEE Main 3 September 2020, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 12 were rated hard and 16 easy. Its hard-question count was the joint highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 12; 16% of the shift
Chapters asked: 56; 12 questions with a figure

Key findings · 3 Sep 2020, Shift 2

1
12 hard questions (16%): the joint highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
Chemistry was the hardest section, with 5 of 25 rated hard; Physics had the most easy questions (6 of 25).
3
63 questions tested a new idea, one no earlier year had asked: 98% of the 64 questions tagged to an idea.
4
1 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
5
18 shared an idea with another 2020 shift (28% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Alcohols, Phenols and Ethers in Chemistry (2) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 6Medium 17Hard 2

Top chapters

Chemistry

25 Q · 5 numerical

Easy 6Medium 14Hard 5

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 16Hard 5

Top chapters

Application of Derivatives3 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Determinants2 Q
Integrals2 Q
Sequences and Series2 Q

Question format

Single correct48 Q
Numerical value15 Q
Diagram based9 Q
Other2 Q
Match the list1 Q

What each question asks you to do

Calculation27 Q
Multi-step22 Q
Conceptual12 Q
Application9 Q
Data or graph3 Q
Recall2 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 easy17 medium2 hard

Chemistry25 questions

6 easy14 medium5 hard

Q26
An ionic micelle is formed on the addition of :
Surface Chemistry Colloids Micelle Formation and CMC
MediumSingle correct · figureNew ideaIdea asked in 3 years
Q27
100 mL of 0.1 M $\mathrm{HCl}$ is taken in a beaker and to it 100 mL of 0.1 M $\mathrm{NaOH}$ is added in steps of 2 mL and the pH is continuously measured. Which of the following graphs correctly depicts the change in pH ?
Equilibrium pH and Buffers pH of Strong Acid and Strong Base Mixtures
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q28
Consider the following molecules and statements related to them : (A) [figure] (B) [figure] (a) (B) is more likely to be crystalline than (A) (b) (B) has higher boiling point than (A) (c) (B) dissolves more readily than (A) in water Identify the correct…
Alcohols, Phenols and Ethers Organic Acidity and Basicity Intramolecular H-Bonding in Phenols
MediumOther · figureNew ideaIdea asked in 2 years
Q29
For the reaction $2\mathrm{A} + 3\mathrm{B} + \frac{3}{2}\mathrm{C} \rightarrow 3\mathrm{P}$ , which statement is correct ?
Chemical Kinetics Rate Laws Rate and Stoichiometry
EasySingle correctNew ideaIdea asked in 5 years
Q30
Consider the hypothetical situation where the azimuthal quantum number, $l$ , takes values 0, 1, 2, ...... n + 1, where n is the principal quantum number. Then, the element with atomic number :
Structure of Atom Quantum Numbers Azimuthal Quantum Number
HardSingle correctNew idea
Q31
A mixture of one mole each of $\mathrm{H_2}$ , He and $\mathrm{O_2}$ each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of $\mathrm{H_2}$ is 2 atm, the total pressure of the gases in the cylinder is :
States of Matter Ideal Gas Laws Dalton's Law
EasySingle correctNew ideaIdea asked in 4 years
Q32
The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 $\mathrm{kJ\ mol^{-1}}$ . The number of valence electrons in the element is :
Classification of Elements and Periodicity in Properties Periodic Trends Successive Ionization Enthalpy Jumps
EasySingle correctNew ideaIdea asked in 3 years
Q33
The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity (M), respectively, are : (Take molar mass of hydrogen peroxide as 34 g/mol)
Hydrogen Hydrogen and Hydrides Volume Strength of H2O2
MediumSingle correctNew idea
Q34
Among the statements (I $-$ IV), the correct ones are : (I) Be has smaller atomic radius compared to Mg. (II) Be has higher ionization enthalpy than Al. (III) Charge/radius ratio of Be is greater than that of Al. (IV) Both Be and Al form mainly covalent…
The s-Block Elements s-Block Elements Diagonal Relationship
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q35
The incorrect statement is :
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumSingle correctNew ideaIdea asked in 6 years
Q36
Complex A has a composition of $\mathrm{H_{12}O_6Cl_3Cr}$ . If the complex on treatment with conc. $\mathrm{H_2SO_4}$ loses 13.5% of its original mass, the correct molecular formula of A is : [Given : atomic mass of Cr=52 amu and Cl=35 amu]
Coordination Compounds Coordination Isomerism Dehydration of Hydrate Isomers
MediumSingle correctNew idea
Q37
The d-electron configuration of $\mathrm{[Ru(en)_3]Cl_2}$ and $\mathrm{[Fe(H_2O)_6]Cl_2}$ , respectively are :
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumSingle correctNew ideaIdea asked in 7 years
Q38
The incorrect statement(s) among (a) $-$ (d) regarding acid rain is (are) : (a) It can corrode water pipes. (b) It can damage structures made up of stone. (c) It cannot cause respiratory ailments in animals (d) It is not harmful for trees
Environmental Chemistry Acid Rain Mechanism
EasyOtherNew ideaIdea asked in 4 years
Q39
The increasing order of the reactivity of the following compounds in nucleophilic addition reaction is : Propanal, Benzaldehyde, Propanone, Butanone
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Aldehyde vs Ketone Reactivity
MediumSingle correctNew ideaIdea asked in 2 years
Q40
Consider the following reaction : [figure] $\xrightarrow[\text{anhydride}]{\text{Chromic}}$ ‘P’ The product ‘P’ gives positive ceric ammonium nitrate test. This is because of the presence of which of these $-$ OH group(s) ?
Alcohols, Phenols and Ethers
HardDiagram based · figure
Q41
Three isomers A, B and C (mol. formula $\mathrm{C_8H_{11}N}$ ) give the following results : A and C $\xrightarrow{\text{Diazotization}}$ P + Q $\xrightarrow[\text{(ii) oxidation }(\mathrm{KMnO_4+H^+})]{\text{(i) Hydrolysis}}$ R (product of A) + S (product of…
Amines Hinsberg Test
HardDiagram based · figureNew ideaIdea asked in 5 years
Q42
The decreasing order of reactivity of the following compounds towards nucleophilic substitution ( $\mathrm{S_N2}$ ) is : (I) [figure] (II) [figure] (III) [figure] (IV) [figure]
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN2
HardDiagram based · figureNew ideaIdea asked in 2 years
Q43
Match the following drugs with their therapeutic actions : (i) Ranitidine (a) Antidepressant (ii) Nardil (Phenelzine) (b) Antibiotic (iii) Chloramphenicol (c) Antihistamine (iv) Dimetane (Brompheniramine) (d) Antacid (e) Analgesic
Chemistry in Everyday Life Therapeutic Drug Classes
EasyMatch the listNew ideaIdea asked in 3 years
Q44
The compound A in the following reactions is : A $\xrightarrow[\text{(ii) Conc. }\mathrm{H_2SO_4}/\Delta]{\text{(i) }\mathrm{CH_3MgBr/H_2O}}$ B $\xrightarrow[\text{(ii) Zn/}\mathrm{H_2O}]{\text{(i) }\mathrm{O_3}}$ C + D C…
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cannizzaro Reaction
HardDiagram based · figureNew ideaIdea asked in 4 years
Q45
The major product in the following reaction is : [figure] $\xrightarrow[\text{Heat}]{\text{t-BuOH}}$
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Temperature Effects on Substitution vs Elimination
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q46
$6.023\times10^{22}$ molecules are present in 10 g of a substance ‘ $x$ ’. The molarity of a solution containing 5 g of substance ‘ $x$ ’ in 2 L solution is __________ $\times10^{-3}$ .
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasyNumerical valueNew ideaIdea asked in 5 years
Q47
If 250 $\mathrm{cm^3}$ of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of another aqueous solution containing 1.65 g of a protein B, at 298 K, the ratio of the molecular masses of A and B is __________ $\times10^{-2}$ (to…
Solutions Colligative Properties Isotonic Solutions
MediumNumerical valueNew ideaIdea asked in 3 years
Q48
An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation $\mathrm{Cr_2O_7^{2-} + 14\ H^+ + 6\ e^- \rightarrow 2\ Cr^{3+} + 7\ H_2O}$ The amount of $\mathrm{Cr^{3+}}$ obtained was 0.104 g. The efficiency…
Electrochemistry Faraday's Laws of Electrolysis Current Efficiency
MediumNumerical valueNew idea
Q49
The volume (in mL) of 0.1 N $\mathrm{NaOH}$ required to neutralise 10 mL of 0.1 N phosphinic acid is __________.
Some Basic Concepts of Chemistry Mole Concept Normality and n-factor Calculation
MediumNumerical valueNew ideaIdea asked in 4 years
Q50
The number of $>\mathrm{C=O}$ groups present in a tripeptide Asp $-$ Glu $-$ Lys is __________.
Biomolecules
MediumNumerical value

Maths25 questions

4 easy16 medium5 hard

Q51
Let $R_1$ and $R_2$ be two relations defined as follows : $R_1 = \{(a, b) \in \mathbf{R}^2 : a^2 + b^2 \in Q\}$ and $R_2 = \{(a, b) \in \mathbf{R}^2 : a^2 + b^2 \notin Q\}$ , where Q is the set of all rational numbers. Then :
Relations and Functions Sets and Relations Relation Types
MediumSingle correctNew ideaIdea asked in 5 years
Q52
The set of all real values of $\lambda$ for which the quadratic equations, $(\lambda^2 + 1)x^2 - 4\lambda x + 2 = 0$ always have exactly one root in the interval (0, 1) is :
Complex Numbers and Quadratic Equations Location of Roots Exactly one root in interval
MediumSingle correctNew idea
Q53
If $z_1$ , $z_2$ are complex numbers such that $\mathrm{Re}(z_1) = |z_1 - 1|$ , $\mathrm{Re}(z_2) = |z_2 - 1|$ and $\arg(z_1 - z_2) = \frac{\pi}{6}$ , then $\mathrm{Im}(z_1 + z_2)$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Principal Argument Arithmetic
HardSingle correctNew ideaIdea asked in 2 years
Q54
Let A be a $3 \times 3$ matrix such that $\mathrm{adj}\, A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix}$ and $B = \mathrm{adj}(\mathrm{adj}\, A)$ . If $|A| = \lambda$ and $|(B^{-1})^T| = \mu$ , then the ordered pair,…
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumSingle correctNew ideaIdea asked in 6 years
Q55
If the term independent of $x$ in the expansion of $\left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9$ is k, then 18 k is equal to :
Binomial Theorem
MediumSingle correct
Q56
If the sum of the series $20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5} + \ldots$ upto $n^{th}$ term is 488 and the $n^{th}$ term is negative, then :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctNew ideaIdea asked in 7 years
Q57
$\lim_{x \to a} \frac{(a + 2x)^{\frac{1}{3}} - (3x)^{\frac{1}{3}}}{(3a + x)^{\frac{1}{3}} - (4x)^{\frac{1}{3}}}$ $(a \neq 0)$ is equal to :
Limits and Derivatives L'Hopital's Rule Fractional Power Substitution
MediumSingle correctNew idea
Q58
Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1$ , 0, 1. If $T = \{x \in \mathbf{R} \mid f(x) = f(0)\}$ , then the sum of squares of all the elements of T is :
Application of Derivatives Maxima and Minima Analyzing Polynomial Roots via Extrema
MediumSingle correctNew ideaIdea asked in 4 years
Q59
If the surface area of a cube is increasing at a rate of 3.6 cm $^2$ /sec, retaining its shape; then the rate of change of its volume (in cm $^3$ /sec.), when the length of a side of the cube is 10 cm, is :
Application of Derivatives Chain Rule Chain Rule in Related Rates
EasySingle correctNew ideaIdea asked in 2 years
Q60
If $\int \sin^{-1}\left(\sqrt{\frac{x}{1+x}}\right) dx = A(x)\tan^{-1}(\sqrt{x}) + B(x) + C$ , where C is a constant of integration, then the ordered pair $(A(x), B(x))$ can be :
Integrals Integration by Parts Inverse Trig Simplification Before Parts
HardSingle correctNew ideaIdea asked in 2 years
Q61
If the value of the integral $\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx$ is $\frac{k}{6}$ , then k is equal to :
Integrals Integration by Substitution Trigonometric Substitution
MediumSingle correctNew ideaIdea asked in 3 years
Q62
If $x^3 dy + xy\, dx = x^2 dy + 2y\, dx$ ; $y(2) = e$ and $x > 1$ , then $y(4)$ is equal to :
Differential Equations Variable Separable Form Separability Check
MediumSingle correctNew ideaIdea asked in 2 years
Q63
If a $\Delta$ ABC has vertices A $(-1, 7)$ , B $(-7, 1)$ and C $(5, -5)$ , then its orthocentre has coordinates :
Straight Lines
MediumSingle correct
Q64
Let the latus ractum of the parabola $y^2 = 4x$ be the common chord to the circles $C_1$ and $C_2$ each of them having radius $2\sqrt{5}$ . Then, the distance between the centres of the circles $C_1$ and $C_2$ is :
Conic Sections Power of a Point Length of Common Chord via Radical Axis
MediumSingle correctNew ideaIdea asked in 3 years
Q65
Let $e_1$ and $e_2$ be the eccentricities of the ellipse, $\frac{x^2}{25} + \frac{y^2}{b^2} = 1$ $(b < 5)$ and the hyperbola, $\frac{x^2}{16} - \frac{y^2}{b^2} = 1$ respectively satisfying $e_1 e_2 = 1$ . If $\alpha$ and $\beta$ are the distances between the…
Conic Sections Ellipse Eccentricity Distance Between Foci
MediumSingle correctNew ideaIdea asked in 2 years
Q66
The plane which bisects the line joining the points $(4, -2, 3)$ and $(2, 4, -1)$ at right angles also passes through the point :
Three Dimensional Geometry Planes in 3D Perpendicular Bisector Plane
EasySingle correctNew ideaIdea asked in 3 years
Q67
Let $x_i$ $(1 \leq i \leq 10)$ be ten observations of a random variable X. If $\sum_{i=1}^{10}(x_i - p) = 3$ and $\sum_{i=1}^{10}(x_i - p)^2 = 9$ where $0 \neq p \in \mathbf{R}$ , then the standard deviation of these observations is :
Statistics Variance and SD Variance via Arbitrary Point Deviations
EasySingle correctNew ideaIdea asked in 3 years
Q68
The probability that a randomly chosen 5-digit number is made from exactly two digits is :
Probability
HardSingle correct
Q69
Let a, b, $c \in \mathbf{R}$ be such that $a^2 + b^2 + c^2 = 1$ . If $a\cos\theta = b\cos\left(\theta + \frac{2\pi}{3}\right) = c\cos\left(\theta + \frac{4\pi}{3}\right)$ , where $\theta = \frac{\pi}{9}$ , then the angle between the vectors…
Vector Algebra Dot Product Angle Between Vectors
HardSingle correctNew ideaIdea asked in 4 years
Q70
Let p, q, r be three statements such that the truth value of $(p \wedge q) \rightarrow (\sim q \vee r)$ is F. Then the truth values of p, q, r are respectively :
Mathematical Reasoning
EasySingle correct
Q71
Let S be the set of all integer solutions, $(x, y, z)$ , of the system of equations $x - 2y + 5z = 0$ $-2x + 4y + z = 0$ $-7x + 14y + 9z = 0$ such that $15 \leq x^2 + y^2 + z^2 \leq 150$ . Then, the number of elements in the set S is equal to __________.
Determinants Cramer's Rule Variable Ratios in Homogeneous Systems
HardNumerical valueNew idea
Q72
The total number of 3 - digit numbers, whose sum of digits is 10, is __________.
Permutations and Combinations Distribution of Identical Objects
MediumNumerical valueNew ideaIdea asked in 6 years
Q73
If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $4^{th}$ A.M. is equal to $2^{nd}$ G.M., then m is equal to __________.
Sequences and Series AP and GP Arithmetic and Geometric Means
MediumNumerical valueNew ideaIdea asked in 4 years
Q74
If the tangent to the curve, $y = e^x$ at a point $(c, e^c)$ and the normal to the parabola, $y^2 = 4x$ at the point $(1, 2)$ intersect at the same point on the $x$ -axis, then the value of c is __________.
Application of Derivatives Tangents and Normals Intercepts of Tangent and Normal
MediumNumerical valueNew ideaIdea asked in 3 years
Q75
Let a plane P contain two lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$ , $\lambda \in \mathbf{R}$ and $\vec{r} = -\hat{j} + \mu(\hat{j} - \hat{k})$ , $\mu \in \mathbf{R}$ . If $Q(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from the…
Three Dimensional Geometry Planes in 3D Plane Containing Two Lines
MediumNumerical valueNew ideaIdea asked in 2 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.