JEE Main 2020 · September session

JEE Main 4 September 2020, Shift 1

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

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 12; 16% of the shift
Chapters asked: 59; 18 questions with a figure

Key findings · 4 Sep 2020, Shift 1

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
59 questions tested a new idea, one no earlier year had asked: 98% of the 60 questions tagged to an idea.
3
1 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
4
21 shared an idea with another 2020 shift (35% of tagged questions). Shifts in the same year can test the same idea in a new setting.
5
Biggest chapters: Dual Nature of Radiation and Matter in Physics (2), Alcohols, Phenols and Ethers in Chemistry (2) and Integrals 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 6Medium 17Hard 2

Top chapters

Maths

25 Q · 5 numerical

Easy 2Medium 18Hard 5

Top chapters

Question format

Single correct40 Q
Diagram based15 Q
Numerical value15 Q
Match the list2 Q
Other2 Q
Two statements1 Q

What each question asks you to do

Multi-step28 Q
Calculation17 Q
Recall8 Q
Application8 Q
Conceptual7 Q
Data or graph4 Q
Diagram reading3 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

6 easy17 medium2 hard

Q26
Match the following : (i) Foam (a) smoke (ii) Gel (b) cell fluid (iii) Aerosol (c) jellies (iv) Emulsion (d) rubber (e) froth (f) milk
Surface Chemistry Colloids Colloid Classification by State
EasyMatch the listNew ideaIdea asked in 4 years
Q27
$E^\circ_{\mathrm{Cu^{2+}|Cu}} = +0.34\ \mathrm{V}$ $E^\circ_{\mathrm{Zn^{2+}|Zn}} = -0.76\ \mathrm{V}$ Identify the incorrect statement from the options below for the above cell :
Electrochemistry
MediumDiagram based · figure
Q28
For the equilibrium $\mathrm{A \rightleftharpoons B}$ , the variation of the rate of the forward (a) and reverse (b) reaction with time is given by :
Equilibrium Chemical Equilibrium Rate-Time Graph Analysis
EasyDiagram based · figureNew idea
Q29
For one mole of an ideal gas, which of these statements must be true ? (a) U and H each depends only on temperature (b) Compressibility factor $z$ is not equal to 1 (c) $\mathrm{C_{P,m} - C_{V,m} = R}$ (d) $\mathrm{dU = C_V dT}$ for any process
Thermodynamics (Chemistry)Enthalpy and Hess's Law Heat Capacity Relation in Enthalpy
MediumOtherNew ideaIdea asked in 3 years
Q30
The intermolecular potential energy for the molecules A, B, C and D given below suggests that :
Chemical Bonding and Molecular Structure
MediumDiagram based · figure
Q31
The region in the electromagnetic spectrum where the Balmer series lines appear is :
Structure of Atom Bohr's Atomic Theory Electromagnetic Regions of Spectral Series
EasySingle correctNew idea
Q32
The ionic radii of $\mathrm{O^{2-}}$ , $\mathrm{F^-}$ , $\mathrm{Na^+}$ and $\mathrm{Mg^{2+}}$ are in the order :
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasySingle correctNew ideaIdea asked in 5 years
Q33
Among statements (a) - (d), the correct ones are : (a) Lime stone is decomposed to CaO during the extraction of iron from its oxides. (b) In the extraction of silver, silver is extracted as an anionic complex. (c) Nickel is purified by Mond's process. (d) Zr…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Metal Refining Techniques
MediumOtherNew ideaIdea asked in 4 years
Q34
On combustion of Li, Na and K in excess of air, the major oxides formed, respectively, are :
The s-Block Elements s-Block Elements Formation of Oxides, Peroxides, and Superoxides
EasySingle correctNew ideaIdea asked in 4 years
Q35
On heating, lead(II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid (C) is :
The p-Block Elements
MediumSingle correct
Q36
The elements with atomic numbers 101 and 104 belong to, respectively, :
Classification of Elements and Periodicity in Properties
MediumSingle correct
Q37
The number of isomers possible for $\mathrm{[Pt(en)(NO_2)_2]}$ is :
Coordination Compounds Coordination Isomerism Ambidentate Ligands in Linkage Isomerism
MediumSingle correctNew ideaIdea asked in 2 years
Q38
The pair in which both the species have the same magnetic moment (spin only) is :
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumSingle correctNew ideaIdea asked in 7 years
Q39
An organic compound (A) (molecular formula $\mathrm{C_6H_{12}O_2}$ ) was hydrolysed with dil. $\mathrm{H_2SO_4}$ to give a carboxylic acid (B) and an alcohol (C). 'C' gives white turbidity immediately when treated with anhydrous $\mathrm{ZnCl_2}$ and conc.…
Alcohols, Phenols and Ethers Alcohols and Phenols Lucas Test Differentiation
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q40
The IUPAC name of the following compound is :
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Special Suffixes for Ring-Attached Functional Groups
MediumDiagram based · figureNew idea
Q41
The decreasing order of reactivity of the following organic molecules towards $\mathrm{AgNO_3}$ solution is :
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Substrate Steric Effects
HardDiagram based · figureNew ideaIdea asked in 3 years
Q42
What are the functional groups present in the structure of maltose ?
Biomolecules Carbohydrates Maltose Structure and Linkage
MediumSingle correctNew ideaIdea asked in 3 years
Q43
[P] on treatment with $\mathrm{Br_2/FeBr_3}$ in $\mathrm{CCl_4}$ produced a single isomer $\mathrm{C_8H_7O_2Br}$ while heating [P] with sodalime gave toluene. The compound [P] is :
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Decarboxylation Reactions
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q44
When neopentyl alcohol is heated with an acid, it slowly converted into an 85 : 15 mixture of alkenes A and B, respectively. What are these alkenes ?
Alcohols, Phenols and Ethers Alcohols and Phenols Alcohol Dehydration Ease
MediumDiagram based · figureNew ideaIdea asked in 6 years
Q45
Which of the following will react with $\mathrm{CHCl_3}$ + alc. KOH ?
Amines Carbylamine Reaction
MediumSingle correctNew ideaIdea asked in 4 years
Q46
The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is __________.
Some Basic Concepts of Chemistry Mole Concept Limiting Reagent and Reaction Yield
EasyNumerical valueNew ideaIdea asked in 4 years
Q47
At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of…
Solutions Colligative Properties Relative Lowering of VP
MediumNumerical valueNew ideaIdea asked in 7 years
Q48
If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed in approximately (in minutes) __________. (Take : log 2=0.30; log 2.5=0.40)
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
MediumNumerical valueNew ideaIdea asked in 6 years
Q49
A 20.0 mL solution containing 0.2 g impure $\mathrm{H_2O_2}$ reacts completely with 0.316 g of $\mathrm{KMnO_4}$ in acid solution. The purity of $\mathrm{H_2O_2}$ (in %) is __________ (mol. wt. of $\mathrm{H_2O_2}$ =34; mol. wt. of $\mathrm{KMnO_4}$ =158)
Redox Reactions Law of Chemical Equivalence in Redox
MediumNumerical valueNew ideaIdea asked in 5 years
Q50
The number of chiral centres present in [B] is __________.
Aldehydes, Ketones and Carboxylic Acids Stereoisomerism Chiral Centers
HardNumerical value · figureNew ideaIdea asked in 5 years

Maths25 questions

2 easy18 medium5 hard

Q51
A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If $x$ % of the people read both the newspapers, then a possible value of $x$ can be :
Relations and Functions Sets and Relations Venn Diagrams
EasySingle correctNew ideaIdea asked in 3 years
Q52
Let [t] denote the greatest integer $\le$ t. Then the equation in $x$ , $[x]^2 + 2[x+2] - 7 = 0$ has :
Relations and Functions
MediumSingle correct
Q53
Let u $= \frac{2z+i}{z-ki}$ , $z = x+iy$ and k $> 0$ . If the curve represented by Re(u) + Im(u) = 1 intersects the $y$ -axis at the points P and Q where PQ = 5, then the value of k is :
Complex Numbers and Quadratic Equations
HardSingle correct
Q54
If A $= \begin{bmatrix} \cos\theta & i\sin\theta \\ i\sin\theta & \cos\theta \end{bmatrix}$ , $\left(\theta = \frac{\pi}{24}\right)$ and A $^5 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ , where $i = \sqrt{-1}$ , then which one of the following is not true ?
Matrices Matrix Multiplication Powers of Square Matrices
MediumSingle correctNew ideaIdea asked in 6 years
Q55
The value of $\sum_{r=0}^{20} {}^{50-r}C_6$ is equal to :
Binomial Theorem Binomial Coefficients Hockey Stick Identity
MediumSingle correctNew ideaIdea asked in 4 years
Q56
Let $\alpha$ and $\beta$ be the roots of $x^2 - 3x + p = 0$ and $\gamma$ and $\delta$ be the roots of $x^2 - 6x + q = 0$ . If $\alpha, \beta, \gamma, \delta$ form a geometric progression. Then ratio $(2q+p) : (2q-p)$ is :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctNew ideaIdea asked in 6 years
Q57
If $1 + (1 - 2^2 \cdot 1) + (1 - 4^2 \cdot 3) + (1 - 6^2 \cdot 5) + \ldots\ldots + (1 - 20^2 \cdot 19) = \alpha - 220\beta$ , then an ordered pair $(\alpha, \beta)$ is equal to :
Sequences and Series
MediumSingle correct
Q58
Let $f$ be a twice differentiable function on $(1, 6)$ . If $f(2) = 8$ , $f'(2) = 5$ , $f'(x) \ge 1$ and $f''(x) \ge 4$ , for all $x \in (1, 6)$ , then :
Application of Derivatives Mean Value Theorem Proving Inequalities via LMVT
HardSingle correctNew idea
Q59
If $(a + \sqrt{2}\, b\cos x)(a - \sqrt{2}\, b\cos y) = a^2 - b^2$ , where $a > b > 0$ , then $\frac{dx}{dy}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is :
Continuity and Differentiability Chain Rule Implicit Chain Rule
MediumSingle correctNew ideaIdea asked in 2 years
Q60
Let $f(x) = |x-2|$ and $g(x) = f(f(x))$ , $x \in [0, 4]$ . Then $\int_0^3 (g(x) - f(x))\,\mathrm{d}x$ is equal to :
Integrals Definite Integral Properties Geometric Area for Piecewise Linear Integrals
MediumSingle correctNew idea
Q61
The integral $\int \left(\frac{x}{x\sin x + \cos x}\right)^2 \mathrm{d}x$ is equal to (where C is a constant of integration) :
Integrals Integration by Parts Integrability over ILATE
HardSingle correctNew idea
Q62
Let $f(x) = \int \frac{\sqrt{x}}{(1+x)^2}\,\mathrm{d}x$ $(x \ge 0)$ . Then $f(3) - f(1)$ is equal to :
Integrals Integration by Substitution Fractional Powers LCM Substitution
MediumSingle correctNew ideaIdea asked in 4 years
Q63
Let $y = y(x)$ be the solution of the differential equation, $xy' - y = x^2(x\cos x + \sin x)$ , $x > 0$ . If $y(\pi) = \pi$ , then $y''\left(\frac{\pi}{2}\right) + y\left(\frac{\pi}{2}\right)$ is equal to :
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctNew ideaIdea asked in 7 years
Q64
A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If $\angle BAC = 90^\circ$ , and ar( $\Delta$ ABC) $= 5\sqrt{5}$ sq. units, then the abscissa of the vertex C is :
Straight Lines
MediumSingle correct
Q65
Let $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b)$ be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, $\phi(t) = \frac{5}{12} + t - t^2$ , then $a^2 + b^2$ is equal to :
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumSingle correctNew ideaIdea asked in 6 years
Q66
Let P(3, 3) be a point on the hyperbola, $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ . If the normal to it at P intersects the $x$ -axis at (9, 0) and e is its eccentricity, then the ordered pair $(a^2, e^2)$ is equal to :
Conic Sections Normals to Conics Hyperbola Normal Point Form
MediumSingle correctNew ideaIdea asked in 3 years
Q67
Let $x_0$ be the point of local maxima of $f(x) = \vec{a} \cdot (\vec{b} \times \vec{c})$ , where $\vec{a} = x\hat{i} - 2\hat{j} + 3\hat{k}$ , $\vec{b} = -2\hat{i} + x\hat{j} - \hat{k}$ and $\vec{c} = 7\hat{i} - 2\hat{j} + x\hat{k}$ . Then the value of…
Vector Algebra Triple Products STP Definition and Determinant
MediumSingle correctNew ideaIdea asked in 2 years
Q68
The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctNew ideaIdea asked in 7 years
Q69
Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :
Straight Lines
MediumSingle correct
Q70
Given the following two statements : $(S_1) : (q \vee p) \to (p \leftrightarrow \sim q)$ is a tautology. $(S_2) : \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy. Then :
Mathematical Reasoning
MediumTwo statements
Q71
If the system of equations $x - 2y + 3z = 9$ $2x + y + z = b$ $x - 7y + az = 24$ , has infinitely many solutions, then $a - b$ is equal to ________.
Determinants Cramer's Rule Condition for Infinite Solutions
MediumNumerical valueNew ideaIdea asked in 7 years
Q72
Let $(2x^2 + 3x + 4)^{10} = \sum_{r=0}^{20} a_r x^r$ . Then $\frac{a_7}{a_{13}}$ is equal to ________.
Binomial Theorem
HardNumerical value
Q73
Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) = f(x) + f(y) + xy^2 + x^2y$ , for all real $x$ and $y$ . If $\lim_{x \to 0} \frac{f(x)}{x} = 1$ , then $f'(3)$ is equal to ________.
Continuity and Differentiability Differentiability via Functional Equations
MediumNumerical valueNew ideaIdea asked in 6 years
Q74
If the equation of a plane P, passing through the intersection of the planes, $x + 4y - z + 7 = 0$ and $3x + y + 5z = 8$ is $ax + by + 6z = 15$ for some $a, b \in \mathbf{R}$ , then the distance of the point $(3, 2, -1)$ from the plane P is ________.
Three Dimensional Geometry Planes in 3D Family of Planes
MediumNumerical valueNew ideaIdea asked in 4 years
Q75
The probability of a man hitting a target is $\frac{1}{10}$ . The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$ , is ________.
Probability
EasyNumerical value

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.