JEE Main 2020 · September session

JEE Main 4 September 2020, Shift 2

75 questions: 15 numerical-answer and 60 multiple choice. 10 were rated hard and 24 easy. Its hard-question count was the joint 4th highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 10; 13% of the shift
Chapters asked: 59; 12 questions with a figure

Key findings · 4 Sep 2020, Shift 2

1
10 hard questions (13%): the joint 4th 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 4 of 25 rated hard; Physics had the most easy questions (11 of 25).
3
64 questions tested a new idea, one no earlier year had asked: 97% of the 66 questions tagged to an idea.
4
2 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 (27% 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), Haloalkanes and Haloarenes in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 11Medium 11Hard 3

Top chapters

Chemistry

25 Q · 5 numerical

Easy 9Medium 12Hard 4

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 18Hard 3

Top chapters

Question format

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

What each question asks you to do

Multi-step29 Q
Calculation25 Q
Conceptual8 Q
Application6 Q
Recall4 Q
Data or graph2 Q
Diagram reading1 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

11 easy11 medium3 hard

Chemistry25 questions

9 easy12 medium4 hard

Q26
A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, HCHO and water. The component which ensures stability of the ink sample is :
Surface Chemistry Colloids Protective Colloids and Gold Number
EasySingle correctNew idea
Q27
250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M $\mathrm{AgNO_3}$ and 0.1 M AuCl. The solution was electrolyzed at 2 V by passing a current of 1 A for 15 minutes. The metal/metals electrodeposited will be :…
Electrochemistry Faraday's Laws of Electrolysis Predicting Products
MediumSingle correctNew ideaIdea asked in 2 years
Q28
If the equilibrium constant for $\mathrm{A \rightleftharpoons B + C}$ is $K_{eq}^{(1)}$ and that of $\mathrm{B + C \rightleftharpoons P}$ is $K_{eq}^{(2)}$ , the equilibrium constant for $\mathrm{A \rightleftharpoons P}$ is :
Equilibrium Chemical Equilibrium Equilibrium Constant for Modified Equations
EasySingle correctNew ideaIdea asked in 4 years
Q29
Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is :
Thermodynamics (Chemistry)
EasySingle correct
Q30
The molecule in which hybrid MOs involve only one d-orbital of the central atom is :
Chemical Bonding and Molecular Structure VSEPR Theory Octahedral and Square Planar
MediumSingle correctNew ideaIdea asked in 3 years
Q31
The shortest wavelength of H atom in the Lyman series is $\lambda_1$ . The longest wavelength in the Balmer series of $\mathrm{He^+}$ is :
Structure of Atom Bohr's Atomic Theory Rydberg Formula and Transitions
MediumSingle correctNew ideaIdea asked in 2 years
Q32
The process that is NOT endothermic in nature is :
Classification of Elements and Periodicity in Properties Periodic Trends Positive Electron Gain Enthalpy
EasySingle correctNew ideaIdea asked in 2 years
Q33
An alkaline earth metal 'M' readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable to heat and does not have rock-salt structure. M is :
The s-Block Elements s-Block Elements Amphoterism of Beryllium Compounds
EasySingle correctNew ideaIdea asked in 4 years
Q34
The reaction in which the hybridisation of the underlined atom is affected is :
Chemical Bonding and Molecular Structure Group 17 & 18 Xenon Fluorides as Fluoride Donors
HardSingle correctNew ideaIdea asked in 2 years
Q35
The incorrect statement(s) among (a) - (c) is (are) : (a) W(VI) is more stable than Cr(VI). (b) in the presence of HCl, permanganate titrations provide satisfactory results. (c) some lanthanoid oxides can be used as phosphors.
The d- and f-Block Elements d-Block Elements HCl Limitation in KMnO4 Titrations
MediumOtherNew ideaIdea asked in 2 years
Q36
The Crystal Field Stabilization Energy (CFSE) of $[\mathrm{CoF_3(H_2O)_3}]$ ( $\Delta_0 < P$ ) is :
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumSingle correctNew ideaIdea asked in 6 years
Q37
The one that can exhibit highest paramagnetic behaviour among the following is : gly = glycinato; bpy = 2, 2′-bipyridine
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumSingle correctNew ideaIdea asked in 7 years
Q38
The processes of calcination and roasting in metallurgical industries, respectively, can lead to :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Calcination vs. Roasting
EasySingle correctNew ideaIdea asked in 3 years
Q39
Among the following compounds, which one has the shortest C $-$ Cl bond ?
Haloalkanes and Haloarenes Resonance and Hyperconjugation Mesomeric Effect
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q40
Which of the following compounds will form the precipitate with aq. $\mathrm{AgNO_3}$ solution most readily ?
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Neighboring Group Participation (NGP)
HardDiagram based · figureNew idea
Q41
The major product [B] in the following reactions is : $\mathrm{CH_3-CH_2-\underset{\underset{CH_3}{|}}{CH}-CH_2-OCH_2-CH_3 \xrightarrow[Heat]{HI} [A]\ alcohol \xrightarrow[\Delta]{H_2SO_4} [B]}$
Alcohols, Phenols and Ethers Ethers Cold HI Cleavage (SN2)
MediumOther · figureNew idea
Q42
In the following reaction sequence, [C] is : [figure: ring drawn as a hexagon with a circle inside, $\mathrm{NH_2}$ at the top and $\mathrm{CH_3}$ at the bottom (opposite positions)]…
Haloalkanes and Haloarenes Diazonium Salts Sandmeyer Reaction
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q43
The mechanism of action of “Terfenadine” (Seldane) is :
Chemistry in Everyday Life Antihistamine Receptor Specificity
EasySingle correctNew ideaIdea asked in 2 years
Q44
The major product [R] in the following sequence of reactions is : $\mathrm{HC\equiv CH} \xrightarrow[\text{(ii) } \mathrm{H_3C}\searrow\mathrm{CH-Br}\ \nearrow(\mathrm{CH_3})_2\mathrm{CH}]{\text{(i) } \mathrm{LiNH_2/ether}}$ [P]…
Hydrocarbons Alkenes and Alkynes Alkylation of Terminal Alkynes
HardDiagram based · figureNew ideaIdea asked in 2 years
Q45
The major product [C] of the following reaction sequence will be : $\mathrm{CH_2=CH-CHO} \xrightarrow[\text{(ii) } \mathrm{SOCl_2}]{\text{(i) } \mathrm{NaBH_4}}$ [A] $\xrightarrow[\mathrm{Anhy.\ AlCl_3}]{[\text{ring: hexagon with a circle inside}]}$ [B]…
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Friedel-Crafts Alkylation
HardDiagram based · figureNew ideaIdea asked in 5 years
Q46
A 100 mL solution was made by adding 1.43 g of $\mathrm{Na_2CO_3 \cdot}x\mathrm{H_2O}$ . The normality of the solution is 0.1 N. The value of $x$ is __________. (The atomic mass of Na is 23 g/mol)
Some Basic Concepts of Chemistry Mole Concept Water of Crystallization Determination
MediumNumerical valueNew idea
Q47
The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of the glucose solution is $x \times 10^{-3}$ atm. $x$ is…
Solutions Colligative Properties Osmotic Pressure of Mixed Solutions
EasyNumerical valueNew ideaIdea asked in 2 years
Q48
The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from 27 $^\circ$ C to 42 $^\circ$ C. Its energy of activation in J/mol is __________. (Take ln 5 $=1.6094$ ;…
Chemical Kinetics Arrhenius Equation Boltzmann Factor as Active Fraction
MediumNumerical valueNew idea
Q49
Consider the following equations : $2\ \mathrm{Fe^{2+} + H_2O_2} \rightarrow x\ \mathrm{A} + y\ \mathrm{B}$ (in basic medium) $2\ \mathrm{MnO_4^- + 6\ H^+ + 5\ H_2O_2} \rightarrow x'\ \mathrm{C} + y'\ \mathrm{D} + z'\ \mathrm{E}$ (in acidic medium) The sum…
Redox Reactions Oxidation State Method
MediumNumerical valueNew idea
Q50
The number of chiral centres present in threonine is __________.
Biomolecules Stereoisomerism Chiral Centers
EasyNumerical valueNew ideaIdea asked in 5 years

Maths25 questions

4 easy18 medium3 hard

Q51
Let $\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$ , where each $X_i$ contains 10 elements and each $Y_i$ contains 5 elements. If each element of the set T is an element of exactly 20 of sets $X_i$ 's and exactly 6 of sets $Y_i$ 's, then n is equal to :
Relations and Functions
MediumSingle correct
Q52
Let $\lambda \neq 0$ be in $\mathbf{R}$ . If $\alpha$ and $\beta$ are the roots of the equation, $x^2 - x + 2\lambda = 0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2 - 10x + 27\lambda = 0$ , then $\frac{\beta\gamma}{\lambda}$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctNew ideaIdea asked in 6 years
Q53
If a and b are real numbers such that $(2+\alpha)^4 = a + b\alpha$ , where $\alpha = \frac{-1+i\sqrt{3}}{2}$ , then $a+b$ is equal to :
Complex Numbers and Quadratic Equations Roots of Unity Cube Roots of Unity
MediumSingle correctNew idea
Q54
If the system of equations $x+y+z=2$ $2x+4y-z=6$ $3x+2y+\lambda z=\mu$ has infinitely many solutions, then :
Determinants Cramer's Rule Condition for Infinite Solutions
EasySingle correctNew ideaIdea asked in 7 years
Q55
Suppose the vectors $x_1$ , $x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax=b$ when the vector b on the right side is equal to $b_1$ , $b_2$ and $b_3$ respectively. If $x_1 = \begin{bmatrix}1\\1\\1\end{bmatrix}$ ,…
Determinants Matrix Multiplication Determinant of Product
MediumSingle correctNew ideaIdea asked in 4 years
Q56
If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in the ratio $5 : 10 : 14$ , then the largest coefficient in this expansion is :
Binomial Theorem Binomial Coefficients Ratio of Consecutive Coefficients
MediumSingle correctNew ideaIdea asked in 5 years
Q57
Let $a_1, a_2, \ldots, a_n$ be a given A.P. whose common difference is an integer and $S_n = a_1 + a_2 + \ldots + a_n$ . If $a_1 = 1, a_n = 300$ and $15 \leq n \leq 50$ , then the ordered pair $(S_{n-4}, a_{n-4})$ is equal to :
Sequences and Series AP and GP AP General Term
MediumSingle correctNew ideaIdea asked in 4 years
Q58
Let $f : (0, \infty) \to (0, \infty)$ be a differentiable function such that $f(1) = e$ and $\lim_{t \to x} \frac{t^2 f^2(x) - x^2 f^2(t)}{t - x} = 0$ . If $f(x) = 1$ , then $x$ is equal to :
Continuity and Differentiability Differentiability via Functional Equations
HardSingle correctNew ideaIdea asked in 6 years
Q59
The function $f(x) = \begin{cases} \frac{\pi}{4} + \tan^{-1} x, & |x| \leq 1 \\ \frac{1}{2}(|x| - 1), & |x| > 1 \end{cases}$ is :
Continuity and Differentiability Piecewise Differentiability
MediumSingle correctNew ideaIdea asked in 4 years
Q60
The minimum value of $2^{\sin x} + 2^{\cos x}$ is :
Application of Derivatives Maxima and Minima Optimization via AM-GM Inequality
MediumSingle correctNew ideaIdea asked in 4 years
Q61
The integral $\int_{\pi/6}^{\pi/3} \tan^3 x \cdot \sin^2 3x \,(2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin 6x)\,dx$ is equal to :
Integrals Integration by Substitution Implicit Derivative Recognition
HardSingle correctNew ideaIdea asked in 2 years
Q62
The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the $x$ -axis and vertices C and D lie on the parabola, $y = x^2 - 1$ below the $x$ -axis, is :
Application of Derivatives Maxima and Minima Inscribed 2D Geometry Optimization
MediumSingle correctNew idea
Q63
The solution of the differential equation $\frac{dy}{dx} - \frac{y+3x}{\log_e (y+3x)} + 3 = 0$ is : (where C is a constant of integration.)
Differential Equations Variable Separable Form Reducible to Separable
MediumSingle correctNew ideaIdea asked in 3 years
Q64
If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has $y$ -intercept equal to $-4$ , then a value of k is :
Straight Lines
MediumSingle correct
Q65
The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y=0$ , having its centre on the line, $2x-3y+12=0$ , also passes through the point :
Conic Sections Power of a Point Radical axis of two circles
MediumSingle correctNew ideaIdea asked in 3 years
Q66
Let $x=4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$ . If P(1, $\beta$ ), $\beta > 0$ is a point on this ellipse, then the equation of the normal to it at P is :
Conic Sections Normals to Conics Ellipse Normal Point Form
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q67
The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is :
Three Dimensional Geometry Point-Plane Distance Distance Along a Line
MediumSingle correctNew ideaIdea asked in 5 years
Q68
In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he…
Probability Conditional Probability Conditional Probability in Infinite Games
MediumSingle correctNew idea
Q69
The angle of elevation of a cloud C from a point P, 200 m above a still lake is $30^\circ$ . If the angle of depression of the image of C in the lake from the point P is $60^\circ$ , then PC (in m) is equal to :
Trigonometric Functions
MediumSingle correct
Q70
Contrapositive of the statement : ‘If a function $f$ is differentiable at a, then it is also continuous at a’, is :
Continuity and Differentiability
EasySingle correct
Q71
If the variance of the following frequency distribution : Class : 10-20 20-30 30-40 Frequency : 2 $x$ 2 is 50, then $x$ is equal to ________.
Statistics Variance and SD Finding Unknown Frequency via Variance
EasyNumerical valueNew ideaIdea asked in 2 years
Q72
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ________.
Permutations and Combinations Combinations of Distinct Objects
EasyNumerical valueIdea asked in 8 yearsAsked the year before
Q73
Let $\{x\}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$ . If $\int_0^n \{x\}\,dx$ , $\int_0^n [x]\,dx$ and $10(n^2-n)$ , $(n \in \mathbf{N}, n > 1)$ are three consecutive terms of a G.P., then…
Integrals Definite Integral Properties Fractional Part Function Integrals
MediumNumerical valueNew ideaIdea asked in 2 years
Q74
Let PQ be a diameter of the circle $x^2+y^2=9$ . If $\alpha$ and $\beta$ are the lengths of the perpendiculars from P and Q on the straight line, $x+y=2$ respectively, then the maximum value of $\alpha\beta$ is ________.
Conic Sections Straight Line Distance Perpendicular distance from point
HardNumerical valueNew ideaIdea asked in 3 years
Q75
If $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$ , then the value of $\left|\hat{i} \times (\vec{a} \times \hat{i})\right|^2 + \left|\hat{j} \times (\vec{a} \times \hat{j})\right|^2 + \left|\hat{k} \times (\vec{a} \times \hat{k})\right|^2$ is equal to ________.
Vector Algebra Triple Products Perpendicular Vector Component via VTP
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.