JEE Main 2021 · July session

JEE Main 3 August 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 29 easy. Its hard-question count was the joint 8th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Ray Optics and Optical Instruments, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 10; 11% of the shift
Chapters asked: 61; 17 questions with a figure

Key findings · 3 Aug 2021, Shift 1

1
10 hard questions (11%): the joint 8th highest count of the 24 2021 shifts Lumi analysed. Across those shifts the hard share ran from 3% to 17%.
2
Maths was the hardest section, with 7 of 30 rated hard; Chemistry had the most easy questions (12 of 30).
3
51 questions tested a new idea, one no earlier year had asked: 68% of the 75 questions tagged to an idea.
4
24 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
37 shared an idea with another 2021 shift (49% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Ray Optics and Optical Instruments in Physics (4), The d- and f-Block Elements in Chemistry (4) and Three Dimensional Geometry in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 11Medium 18Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 6Medium 17Hard 7

Top chapters

Question format

Single correct41 Q
Numerical value30 Q
Diagram based12 Q
Two statements3 Q
Match the list3 Q
Other1 Q

What each question asks you to do

Calculation31 Q
Multi-step19 Q
Application17 Q
Conceptual9 Q
Recall7 Q
Data or graph5 Q
Diagram reading2 Q

Most common: Calculation.

Against the other 2021 shifts

This shift next to the 23 other 2021 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
24 Feb, Shift 1	90	36%	7%	33%	68%	24%
24 Feb, Shift 2	88	43%	5%	32%	63%	21%
25 Feb, Shift 1	90	23%	11%	33%	65%	30%
25 Feb, Shift 2	89	35%	10%	34%	67%	24%
26 Feb, Shift 1	88	50%	3%	33%	78%	17%
26 Feb, Shift 2	90	27%	12%	33%	80%	29%
16 Mar, Shift 2	90	31%	7%	33%	69%	33%
17 Mar, Shift 1	89	39%	8%	34%	61%	26%
17 Mar, Shift 2	89	36%	17%	34%	66%	32%
18 Mar, Shift 1	90	40%	9%	33%	74%	24%
18 Mar, Shift 2	90	34%	9%	33%	63%	28%
22 Jul, Shift 2	90	40%	12%	33%	67%	28%
25 Jul, Shift 1	90	31%	13%	33%	56%	34%
25 Jul, Shift 2	90	48%	3%	33%	63%	27%
3 Aug, Shift 1	90	32%	11%	33%	68%	21%
3 Aug, Shift 2	90	32%	7%	33%	61%	24%
4 Aug, Shift 1	90	40%	8%	33%	62%	29%
4 Aug, Shift 2	90	32%	7%	33%	65%	41%
26 Aug, Shift 1	89	27%	15%	34%	66%	30%
26 Aug, Shift 2	89	21%	9%	34%	60%	28%
27 Aug, Shift 1	90	27%	13%	33%	63%	34%
27 Aug, Shift 2	90	29%	9%	33%	72%	29%
31 Aug, Shift 1	90	27%	11%	33%	70%	24%
31 Aug, Shift 2	90	30%	13%	33%	72%	31%

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

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open30 this shift3084 · 33%33%8/830298716720359538199224
Open30 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 90 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

90 of 90 questions

Physics30 questions

11 easy18 medium1 hard

Chemistry30 questions

12 easy16 medium2 hard

Q31
The true value of a result is 5.0g and a student ‘A’ takes two measurements and reports the result as 5.3 and 5.4g. Another student ‘B’ repeats the measurement and reports 4.6 and 4.7g. Pick the statement from below that correctly describes the reports of A…
Some Basic Concepts of Chemistry
EasySingle correct
Q32
Given below are two statements : Statement I : In $\mathrm{CH_2F_2}$ molecule $\angle$ FCF is less than 109.5º Statement II : In $\mathrm{CH_2F_2}$ molecule both $\angle$ FCF and $\angle$ HCH are equal In the light of the above statements, choose the most…
Chemical Bonding and Molecular Structure VSEPR Theory Surrounding Atom Electronegativity Effect
MediumTwo statementsNew idea
Q33
The correct order of second ionization enthalpy is
The d- and f-Block Elements d-Block Elements Ionization Enthalpy Irregularities
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q34
Ellingham diagram does not predict the
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Basics
EasySingle correctIdea asked in 3 yearsAsked the year before
Q35
Sodium chromate reacts with hydrogen peroxide ( $\mathrm{H_2O_2}$ ) in the presence of dilute sulphuric acid to yield
The d- and f-Block Elements d-Block Elements Chromate-Dichromate pH Equilibrium
MediumSingle correctNew idea
Q36
The percentage of oxides in Portland Cement decreases in the order
The p-Block Elements
EasySingle correct
Q37
Select from the following, the correct order of reducing property
The p-Block Elements Group 15 & 16 Group 16 Hydrides Trends
EasySingle correctNew ideaIdea asked in 4 years
Q38
Identify the actinoid which shows +5 oxidation state :
The d- and f-Block Elements
MediumSingle correct
Q39
The correct statement for permanganate ion is
The d- and f-Block Elements d-Block Elements Permanganate Reactions
MediumSingle correctNew ideaIdea asked in 3 years
Q40
Match List I with List II : List I : A. ‘Blue baby’ syndrome ; B. Eutrophication ; C. Minimata disease ; D. Itai-Itai disease List II : I. Mercury ; II. Cadmium ; III. Nitrate ; IV. Phosphate Choose the correct answer from the options given below :
Environmental Chemistry Nitrate Limit and Blue Baby Syndrome
EasyMatch the listNew idea
Q41
Given below are two statements : Statement I : Histamine on Lassaigne’s test gives blue colour. Statement II : Pencillin on Lassaigne’s test gives blue colour. In the light of the above statements, choose the most appropriate answer from the options given…
Organic Chemistry: Some Basic Principles and Techniques
MediumTwo statements
Q42
Find out the correct major product from the following reaction (Me = – $\mathrm{CH_3}$ )
Amines Hofmann Elimination of Quaternary Salts
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q43
Find out the major product of the following reaction
Alcohols, Phenols and Ethers Alcohols and Phenols Oxymercuration-Demercuration Regioselectivity
EasyDiagram based · figureNew idea
Q44
The correct arrangement of the following compounds in the order of increasing difficulty towards nucleophilic substitution is
Haloalkanes and Haloarenes Aromatic Hydrocarbons SNAr and Meisenheimer Complex
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q45
Product [A] obtained in the following transformation is
Alcohols, Phenols and Ethers Alcohols and Phenols Concentration-Dependent Phenol Nitration
MediumDiagram based · figureNew idea
Q46
Sulphanilic acid on diazotisation and then reaction with N,N–dimethylaniline gives which of the following? Mark if their common name is correctly matched.
Amines Diazonium Salts Azo Coupling Reactions
MediumDiagram based · figureNew ideaIdea asked in 5 years
Q47
Match List I with List II : List I - Polymer : A. Bakelite ; B. HDP ; C. LDP ; D. Rayon List II - Type : I. Branched chain ; II. Linear ; III. Network ; IV. Semi-synthetic Choose the correct answer from the options given below :
Polymers Polymer Classification
EasyMatch the listNew ideaIdea asked in 3 years
Q48
The correct structure of β-D-deoxyribose present in DNA is
Biomolecules
MediumDiagram based · figure
Q49
Match List I with List II : List I : A. Hell-Volhard-Zelinsky reaction ; B. Hinsberg’s reagent ; C. Isocyanide test ; D. Hoffmann bromamide degradation List II : I. Test for primary amines ; II. Preparation of α-halocarboxylic acids ; III. Preparation of…
Amines Hinsberg Test
EasyMatch the listIdea asked in 5 yearsAsked the year before
Q50
Which of the following is the most stable conformer?
Organic Chemistry: Some Basic Principles and Techniques Alkanes and Free Radicals Ethane and Butane Conformers
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q51
Assuming $\mathrm{H_2}$ is an ideal gas, consider the quantity “P. $d$ ”, where ‘P’ is the pressure in atm and ‘ $d$ ’ is the density in g $\mathrm{L^{-1}}$ . For P = 8.21 atm, it is observed that $\left(\frac{\partial (Pd)}{\partial P}\right)_T$ = 10.0 g…
States of Matter Ideal Gas Laws Gas Density and Molar Mass
MediumNumerical valueNew ideaIdea asked in 2 years
Q52
A graph of the uncertainty in position against the inverse of the uncertainty in wavelength of an electron is shown. The wavelength of the electron in Å is ________. (Nearest integer) [Assume minimum uncertainty product. Use π = 3.142, Use Δ(g(y)) = | g′(y)…
Structure of Atom
HardNumerical value · figure
Q53
An ideal monoatomic gas traverses the cycle ABCD as shown below in the figure. The work done during the cycle is $x$ PV. The value of $x$ is ________. (Nearest integer)
Thermodynamics (Chemistry)Thermodynamic Processes Cyclic Process Work
EasyNumerical value · figureNew ideaIdea asked in 4 years
Q54
The amount of ethyl alcohol ( $\mathrm{C_2H_5OH}$ ) that should be added to 1kg of water so that the solution does not freeze at –4ºF ( $\mathrm{K_f}$ = 1.86 K kg $\mathrm{mol^{-1}}$ ) in g is ________. (Nearest integer) (Given Atomic mass C=12.0, H=1.0, O=16.0 u)
Solutions Colligative Properties Antifreeze Mass Calculations
MediumNumerical valueNew ideaIdea asked in 2 years
Q55
If 1 M solution of acetic acid is diluted $x$ times so that pH of the solution is doubled. The value of of $x$ is ( $\mathrm{K_a}$ = 1.8× $10^{-5}$ ) ________. (Nearest integer)
Equilibrium pH and Buffers pH of Weak Acids and Bases
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q56
The logarithm of equilibrium constant ( $\log_{10}$ K) for the reaction $\mathrm{Pd^{2+}_{(aq)} + 4Cl^{-}_{(aq)} \rightleftharpoons PdCl_4^{2-}{}_{(aq)}}$ is $x$ × $10^{-1}$ . The value of $x$ is ________. (Nearest integer) [Given emf for the half-cell at 25ºC…
Electrochemistry Nernst Equation E°cell and Equilibrium
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q57
The following results have been obtained during the kinetic studies of the reaction. A + 2B ⟶ 2C Experiment | [A], mol $\mathrm{L^{-1}}$ | [B], mol $\mathrm{L^{-1}}$ | Initial rate of formation of [C], mol $\mathrm{L^{-1}}$ $\mathrm{min^{-1}}$ 1 | 0.60 |…
Chemical Kinetics Rate Laws Initial Rates Method
EasyNumerical value · figureIdea asked in 5 yearsAsked the year before
Q58
200 mL of 0.85M acetic acid is shaken with 2g activated charcoal. The final concentration of the solution after adsorption is 0.75M. The mass of acetic acid in grams adsorbed per gram of charcoal is equal to ________× $10^{-1}$ . (Nearest integer) (Given…
Surface Chemistry Adsorption Adsorption from Solutions
EasyNumerical valueNew idea
Q59
The number of ions produced in an aqueous solution from the octahedral complex with stoichiometry $\mathrm{CoCl_3.5H_2O}$ , is ________.
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q60
The strength of 25 volume solution of hydrogen peroxide in percentage is ________ × $10^{-1}$ . (Nearest integer)
Hydrogen Mole Concept Volume Strength of H2O2
EasyNumerical valueNew idea

Maths30 questions

6 easy17 medium7 hard

Q61
If $S_1 = \{x \in \mathbb{R} : x^2 + |x| - 2 = 0\}$ and $S_2 = \{x \in \mathbb{R} : x^2 + x - 2 = 0\}$ , then
Relations and Functions Sets and Relations Set Operations
EasySingle correctNew idea
Q62
Let $A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$ . Then the set $\{n \in \mathbb{N} \mid A^n + A^{n+1} + A^{n+2} = B\}$ is
Matrices Matrix Multiplication Powers of Square Matrices
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q63
Let A be a square matrix of order 3 and $|A| = 3$ . If $|\mathrm{Adj}\,(3\,\mathrm{Adj}\,(4A))| = 2^m \cdot 3^n$ , then the ordered pair $(m, n)$ is equal to
Determinants Matrix Inverse Determinant of Adjoint of Inverse
MediumSingle correctNew ideaIdea asked in 3 years
Q64
For the system of linear equations $x + 3y + 2z = 7$ $x + \lambda y + 3z = 8$ $x - 2y + 7z = \mu$ , which of the following statements is NOT true?
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
The value of the limit : $\lim_{x \to 4} \left(2^x + 2^{5-x} - 17\right)^{\frac{1}{8 - 2^{3x/4}}}$ is equal to
Limits and Derivatives L'Hopital's Rule Indeterminate Power Forms
HardSingle correctNew ideaIdea asked in 3 years
Q66
Suppose that the function $f(x) = \begin{cases} x^2 - [x] + 2a; & x < -1 \\ 4x + 5 - b; & -1 \leq x < 2 \\ 3x^2 + 6[x] - 2a; & x \geq 2 \end{cases}$ is continuous on $(-2, 3)$ for some values of $a$ and $b$ where $[x]$ denotes the greatest integer function.…
Continuity and Differentiability Finding Unknowns using Continuity
MediumSingle correctNew ideaIdea asked in 3 years
Q67
The sum of the intercepts on the coordinate axes made by the tangent at any point on the curve, $\sqrt{x} + \sqrt{y} = 3$ is
Application of Derivatives Tangents and Normals Constant Sum of Intercepts
MediumSingle correctNew idea
Q68
A plane passes through the points A(1, 2, 3), B(3, 5, 2) and C(2, 1, 5). If P( $a$ , $b$ , $c$ ) be a point such that $a(b + c) = bc$ , then the acute angle which the line OP (O is the origin and $P \neq O$ ) makes with the plane is
Three Dimensional Geometry Planes in 3D Plane Through Three Points
HardSingle correctNew ideaIdea asked in 2 years
Q69
If $\int \frac{4x + 13}{\sqrt{x^2 + 5x + 6}}\,dx = A\sqrt{x^2 + 5x + 6} + B\log_e \left|\left(x + \frac{5}{2}\right) + \sqrt{x^2 + 5x + 6}\right| + C$ (C is a constant of integration), then the ordered pair (A, B) is equal to
Integrals Integration by Substitution General Linear Outside, Quadratic Inside Root Substitution
MediumSingle correctNew idea
Q70
$\int_1^2 [x^2 - 1] + [x^2 + 1]\, dx$ is equal to ( $[t]$ denotes the greatest integer $\leq t$ )
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q71
If $x = x(y)$ is the solution of the differential equation, $2 \cdot \sqrt{\sin x + \tan^{-1} y} \cdot \frac{dy}{dx} = \left(\cos x + \frac{1}{1 + y^2}\frac{dy}{dx}\right)$ satisfying $x(0) = 0$ and $x(1) = b$ , then
Differential Equations Variable Separable Form Exact Differential Grouping
HardSingle correctNew idea
Q72
The sum of the values of 'a' for which circles of radius $\frac{\sqrt{5}}{3}$ , touch the straight lines, $x - 2y - a = 0$ and $3x - 6y + 7 = 0$ , is
Straight Lines Straight Line Distance Distance between parallel lines
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q73
If the line $\alpha x + \beta y = 1$ touches the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , then the locus of the point $(\alpha, \beta)$ is
Conic Sections General Conic Section Condition for Line to be Tangent
MediumSingle correctNew ideaIdea asked in 3 years
Q74
If the tangents at the points $(2, y)$ on the ellipse, $\frac{x^2}{16} + \frac{y^2}{4} = 1$ meet the tangent at $(4, y_1)$ on it at the points A and B, then the length of the line segment AB is
Conic Sections Ellipse Eccentricity Intersection of Tangents at Focal Chord Extremities
HardSingle correctNew idea
Q75
The distance of the origin from the point of intersection of the line, $\frac{x}{2} = \frac{y + 1}{3} = \frac{z - 1}{-1}$ and the plane, $2x + y + 6z + 1 = 0$ is
Three Dimensional Geometry Planes in 3D Intersection Point of Line and Plane
MediumSingle correctNew ideaIdea asked in 2 years
Q76
The plane which is parallel to $\vec{r} \cdot (\hat{i} + 2\hat{j} + 3\hat{k}) = 6$ and passes through (1, 2, 3), also passes through the point
Three Dimensional Geometry Planes in 3D Equation of a Parallel Plane
EasySingle correctNew idea
Q77
If $\sum_{i=1}^{16} a_i - 6 = 8$ and $\sum_{i=1}^{16} a_i - 6^{\,2} = 40$ , then the standard deviation of $a_1, a_2, \ldots, a_{16}$ is
Statistics Variance and SD Variance via Arbitrary Point Deviations
EasySingle correctIdea asked in 3 yearsAsked the year before
Q78
Let $A = \{0, 1, 2, 3, 4, 5\}$ . Then the probability that a randomly selected onto function $f$ from A to A satisfies $f(1) + f(2) = f(3)$ is
Probability Permutations and Combinations Number of Surjective (Onto) Functions
HardSingle correctNew ideaIdea asked in 4 years
Q79
A vertical pole consists of two portions, the lower being $\frac{1}{3}$ rd of the whole. If the upper portion subtends an angle $\tan^{-1}\left(\frac{1}{2}\right)$ at a point on a horizontal plane drawn through the foot of the pole and at a distance 40 m from…
Trigonometric Functions
MediumSingle correct
Q80
If □, ◊ $\in \{\wedge, \vee\}$ such that $(\sim q \wedge p)$ □ $(q$ ◊ $\sim p)$ is a tautology, then
Mathematical Reasoning
MediumSingle correct
Q81
If $x^2 - x + 1 = 0$ , then the value of $\sum_{n=1}^{5}\left(x^n + \frac{1}{x^n}\right)^2$ is ________.
Complex Numbers and Quadratic Equations Roots of Unity Cyclic Powers of Omega Modulo 3
MediumNumerical valueNew ideaIdea asked in 2 years
Q82
The sum of modulus of all non-real roots of the equation, $(x^2 + 4x + 6)(2x^2 + 8x + 14) = 12$ is equal to ______ .
Complex Numbers and Quadratic Equations Quadratic Roots Reducible Biquadratics
MediumNumerical valueNew idea
Q83
If the number of permutations of the word “STATISTICS” in which all ‘S’ do not come together, is $(56)^2 k$ , then ‘ $k$ ’ is equal to ________.
Permutations and Combinations Permutations with Repetition
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q84
The remainder when $(2020)^{2022}$ is divided by 337 is ________.
Binomial Theorem
MediumNumerical value
Q85
Let $n \geq 1$ be an odd integer and $S_n = n^3 - (n-1)^3 + (n-2)^3 - \ldots + (-1)^{n-1} 1^3$ . If $S_{199} - 4 S_{99} = 10^6 \lambda$ , then the value of $\lambda$ is ________.
Sequences and Series
HardNumerical value
Q86
Let $f(x) = x + 1$ and $g$ be maps on $\mathbb{R}$ and $h(n) = (g \circ f)(n+1) - (g \circ f)(n)$ , $n \in \mathbb{N}$ . Further, $h(1), h(2), h(3), h(4), \ldots\ldots$ , is an A.P. and $h(25) = 53$ , $h(101) = 205$ . If $g(48) - g(2) = 100k$ , then ‘ $k$ ’ is equal…
Sequences and Series AP and GP AP General Term
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q87
If the area of the region enclosed by the curve $y = x^2$ and the line $y = ax$ is 36 sq. units, then $|a|$ is equal to ________.
Application of Integrals Area Under Curves Area Between Parabola and Line
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q88
If the area of $\Delta$ ABC with vertices A(0, 1), B(2, 3) and C(4, $b$ ) is 6 sq. units, then the positive value of ‘ $b$ ’ is ________.
Straight Lines
EasyNumerical value
Q89
If $f(x)$ be a differentiable function such that $f(9) = 9$ and $f\,'(9) = 4$ , then $\lim_{x \to 9} \frac{\sqrt{f(x)} - 3}{\sqrt{x} - 3}$ is ________.
Continuity and Differentiability L'Hopital's Rule Recognizing the Derivative Definition
EasyNumerical valueNew idea
Q90
The number of solutions of the equation $x^2 = \cot x$ in $[0, 2\pi]$ is ________.
Trigonometric Functions General Solutions Graphical Root Counting
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 2021 shifts.