JEE Main 2021 · August session

JEE Main 31 August 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 24 easy. Its hard-question count was the joint 8th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 10; 11% of the shift
Chapters asked: 66; 15 questions with a figure

Key findings · 31 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
Physics was the hardest section, with 4 of 30 rated hard; Chemistry had the most easy questions (12 of 30).
3
52 questions tested a new idea, one no earlier year had asked: 70% of the 74 questions tagged to an idea.
4
19 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
38 shared an idea with another 2021 shift (51% 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), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 9Medium 17Hard 4

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 23Hard 4

Top chapters

Conic Sections3 Q
Integrals3 Q
Complex Numbers and Quadratic Equations2 Q
Continuity and Differentiability2 Q
Determinants2 Q
Differential Equations2 Q

Question format

Single correct43 Q
Numerical value30 Q
Diagram based11 Q
Assertion–reason4 Q
Match the list1 Q
Two statements1 Q

What each question asks you to do

Calculation30 Q
Multi-step22 Q
Recall13 Q
Conceptual11 Q
Application8 Q
Data or graph5 Q
Diagram reading1 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

9 easy17 medium4 hard

Chemistry30 questions

12 easy16 medium2 hard

Q31
Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas ? (P and V stand for pressure and volume of the gas respectively)
States of Matter Ideal Gas Laws Graphical Analysis of Boyle's Law
EasyDiagram based · figureNew idea
Q32
In the structure of the dichromate ion, there is a :
The d- and f-Block Elements
MediumSingle correct
Q33
Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression ?
Solutions Colligative Properties Van't Hoff Factor (i)
EasySingle correctNew ideaIdea asked in 4 years
Q34
Select the graph that correctly describes the adsorption isotherms at two temperatures $\mathrm{T_1}$ and $\mathrm{T_2}$ ( $\mathrm{T_1} > \mathrm{T_2}$ ) for a gas : ( $x-$ mass of the gas adsorbed $\mathrm{m}-$ mass of adsorbent $\mathrm{P}-$ pressure)
Surface Chemistry Adsorption Factors Affecting Adsorption
MediumDiagram based · figureNew idea
Q35
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Metallic character decreases and non-metallic character increases on moving from left to right in a period. Reason (R) : It is due to…
Classification of Elements and Periodicity in Properties Periodic Trends Metallic and Non-Metallic Character Trends
EasyAssertion–reasonNew ideaIdea asked in 3 years
Q36
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Aluminium is extracted from bauxite by the electrolysis of molten mixture of $\mathrm{Al_2O_3}$ with cryolite. Reason (R) : The…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Hall-Heroult Process
EasyAssertion–reasonNew ideaIdea asked in 3 years
Q37
Given below are two statements : Statement I : The process of producing syn-gas is called gasification of coal. Statement II : The composition of syn-gas is $\mathrm{CO + CO_2 + H_2}$ (1 : 1 : 1). In the light of the above statements, choose the most…
Hydrogen Hydrogen and Hydrides Syngas Production via Reforming
EasyTwo statementsNew ideaIdea asked in 2 years
Q38
The major component/ingredient of Portland Cement is :
The s-Block Elements s-Block Elements Portland Cement Composition and Setting
EasySingle correctNew ideaIdea asked in 2 years
Q39
Which one of the following lanthanides exhibits $+2$ oxidation state with diamagnetic nature ? (Given Z for Nd $=60$ , Yb $=70$ , La $=57$ , Ce $=58$ )
The d- and f-Block Elements f-Block Elements Identifying Diamagnetic Lanthanide Ions
MediumSingle correctNew idea
Q40
The denticity of an organic ligand, biuret is :
Coordination Compounds
MediumSingle correct
Q41
BOD values (in ppm) for clean water (A) and polluted water (B) are expected respectively as :
Environmental Chemistry BOD Values for Clean vs Polluted Water
EasySingle correctNew ideaIdea asked in 2 years
Q42
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple distillation can be used to separate a mixture of propanol and propanone. Reason (R) : Two liquids with a difference of more…
Organic Chemistry: Some Basic Principles and Techniques
EasyAssertion–reason
Q43
Choose the correct name for compound given below :
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Alkene vs Alkyne Numbering Tiebreaker
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q44
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Treatment of bromine water with propene yields 1-bromopropan-2-ol. Reason (R) : Attack of water on bromonium ion follows Markovnikov…
Hydrocarbons Alkenes and Alkynes Halohydrin Formation Regiochemistry
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q45
The correct order of reactivity of the given chlorides with acetate in acetic acid is :
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN1
HardDiagram based · figureIdea asked in 5 years
Q46
The major product formed in the following reaction is :
Alcohols, Phenols and Ethers Alcohols and Phenols Alcohol Dehydration Ease
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q47
The structure of product C, formed by the following sequence of reactions is : $\mathrm{CH_3COOH + SOCl_2} \longrightarrow \mathrm{A} \xrightarrow[\mathrm{AlCl_3}]{\text{Benzene}} \mathrm{B} \xrightarrow[{}^{-}\mathrm{OH}]{\mathrm{KCN}} \mathrm{C}$
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Cyanohydrin Formation
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q48
The major products A and B in the following set of reactions are :
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Reduction of Cyanohydrins
MediumDiagram based · figureNew idea
Q49
Monomer of Novolac is :
Polymers Novolac Structure and Role
EasySingle correctNew ideaIdea asked in 2 years
Q50
Which one of the following compounds contains $\beta$ - $\mathrm{C_1}$ - $\mathrm{C_4}$ glycosidic linkage ?
Biomolecules Carbohydrates Glycosidic Linkage
EasySingle correctNew idea
Q51
The molarity of the solution prepared by dissolving 6.3 g of oxalic acid ( $\mathrm{H_2C_2O_4\cdot 2H_2O}$ ) in 250 mL of water in mol $\mathrm{L^{-1}}$ is $x\times10^{-2}$ . The value of $x$ is __________. (Nearest integer) [Atomic mass : H : 1.0, C : 12.0, O :…
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q52
Ge ( $\mathrm{Z}=32$ ) in its ground state electronic configuration has $x$ completely filled orbitals with $\mathrm{m}_l=0$ . The value of $x$ is __________ .
Structure of Atom Quantum Numbers Magnetic Quantum Number
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q53
According to the following figure, the magnitude of the enthalpy change of the reaction $\mathrm{A+B\rightarrow M+N}$ in kJ mol $^{-1}$ is equal to __________. (Integer answer)
Chemical Kinetics Arrhenius Equation Reaction Energy Profiles
MediumNumerical value · figureNew ideaIdea asked in 3 years
Q54
$\mathrm{A_3B_2}$ is a sparingly soluble salt of molar mass M ( $\mathrm{g\,mol^{-1}}$ ) and solubility $x$ g $\mathrm{L^{-1}}$ . The solubility product satisfies $\mathrm{K_{sp}}=a\left(\frac{x}{\mathrm{M}}\right)^5$ . The value of $a$ is __________ . (Integer…
Equilibrium Solubility Product Solubility-Ksp Relationship
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q55
Consider the following cell reaction $\mathrm{Cd_{(s)}+Hg_2SO_{4(s)}+\frac{9}{5}H_2O_{(\mathit{l})}\rightleftharpoons CdSO_4\cdot\frac{9}{5}H_2O_{(s)}+2Hg_{(\mathit{l})}}$ . The value of $\mathrm{E^0_{cell}}$ is 4.315 V at 25°C. If…
Electrochemistry Nernst Equation Temperature Coefficient of Cell EMF
MediumNumerical valueNew ideaIdea asked in 2 years
Q56
For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is __________. (Integer answer)
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q57
The number of halogen/(s) forming halic (V) acid is __________.
The p-Block Elements Group 17 & 18 Nomenclature of Halogen Oxoacids
MediumNumerical valueNew idea
Q58
The number of hydrogen bonded water molecule(s) associated with stoichiometry $\mathrm{CuSO_4\cdot 5H_2O}$ is __________.
Hydrogen Hydrogen and Hydrides Classification of Hydrates
MediumNumerical valueNew ideaIdea asked in 2 years
Q59
The total number of reagents from those given below, that can convert nitrobenzene into aniline is __________. (Integer answer) I. Sn $-$ HCl II. Sn $-$ $\mathrm{NH_4OH}$ III. Fe $-$ HCl IV. Zn $-$ HCl V. $\mathrm{H_2}$ $-$ Pd VI. $\mathrm{H_2}$ $-$ Raney…
Amines Reduction of Nitro Compounds with Iron
MediumNumerical valueNew idea
Q60
Consider the sulphides HgS, PbS, CuS, $\mathrm{Sb_2S_3}$ , $\mathrm{As_2S_3}$ and CdS. Number of these sulphides soluble in 50% $\mathrm{HNO_3}$ is __________.
Equilibrium
HardNumerical value

Maths30 questions

3 easy23 medium4 hard

Q61
Which of the following is not correct for relation R on the set of real numbers ?
Relations and Functions Sets and Relations Relation Types
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q62
The number of real roots of the equation $\mathrm{e}^{4x}+2\mathrm{e}^{3x}-\mathrm{e}^{x}-6=0$ is :
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q63
If $\mathrm{a_r}=\cos\frac{2\mathrm{r}\pi}{9}+i\sin\frac{2\mathrm{r}\pi}{9}$ , $\mathrm{r}=1, 2, 3, ..., i=\sqrt{-1}$ , then the determinant…
Determinants Roots of Unity Evaluating Determinants with Cube Roots
HardSingle correctIdea asked in 2 years
Q64
If the following system of linear equations $2x+y+z=5$ $x-y+z=3$ $x+y+\mathrm{a}z=\mathrm{b}$ has no solution, then :
Determinants Cramer's Rule Condition for No Solution
EasySingle correctIdea asked in 6 yearsAsked the year before
Q65
Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is $3\mathrm{r}^2$ , then…
Sequences and Series AP and GP GP General Term
MediumSingle correctNew ideaIdea asked in 5 years
Q66
The sum of 10 terms of the series $\frac{3}{1^2\times2^2}+\frac{5}{2^2\times3^2}+\frac{7}{3^2\times4^2}+...$ is :
Sequences and Series AP and GP Method of Differences for Telescoping Series
MediumSingle correctNew ideaIdea asked in 6 years
Q67
$\lim_{x\to0}\frac{\sin^2(\pi\cos^4x)}{x^4}$ is equal to :
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctNew ideaIdea asked in 6 years
Q68
If the function $f(x)=\begin{cases}\frac{1}{x}\log_e\left(\frac{1+\frac{x}{\mathrm{a}}}{1-\frac{x}{\mathrm{b}}}\right) & , \quad x<0\\ \mathrm{k} & , \quad x=0\\ \frac{\cos^2x-\sin^2x-1}{\sqrt{x^2+1}-1} & , \quad x>0\end{cases}$ is continuous at $x=0$ , then…
Continuity and Differentiability Finding Unknown Constants for Continuity
MediumSingle correctNew ideaIdea asked in 3 years
Q69
The function $f(x)=|x^2-2x-3|\cdot\mathrm{e}^{|9x^2-12x+4|}$ is not differentiable at exactly :
Continuity and Differentiability Differentiability of Modulus Functions
MediumSingle correctNew ideaIdea asked in 5 years
Q70
The integral $\int\frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}}\,dx$ is equal to : (where C is a constant of integration)
Integrals Integration by Substitution Rational Powers Summing to Two Substitution
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q71
If $\frac{dy}{dx}=\frac{2^{x+y}-2^x}{2^y}$ , $y(0)=1$ , then $y(1)$ is equal to :
Differential Equations Variable Separable Form Exponential Sum/Difference Separation
MediumSingle correctNew ideaIdea asked in 2 years
Q72
Let $f$ be a non-negative function in $[0, 1]$ and twice differentiable in $(0, 1)$ . If $\int_0^x\sqrt{1-(f'(\mathrm{t}))^2}\,\mathrm{dt}=\int_0^x f(\mathrm{t})\,\mathrm{dt}$ , $0\leq x\leq1$ and $f(0)=0$ , then…
Integrals Leibniz Rule Constant Limit Leibniz
HardSingle correctNew idea
Q73
If p and q are the lengths of the perpendiculars from the origin on the lines, $x\,\mathrm{cosec}\,\alpha-y\sec\alpha=\mathrm{k}\cot2\alpha$ and $x\sin\alpha+y\cos\alpha=\mathrm{k}\sin2\alpha$ respectively, then $\mathrm{k}^2$ is equal to :
Straight Lines Straight Line Distance Distance from Origin to a Line
MediumSingle correctNew idea
Q74
The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$ -axis at a distance R and S ( $>$ R) respectively from the origin, is :
Conic Sections
EasySingle correct
Q75
The line $12x\cos\theta+5y\sin\theta=60$ is tangent to which of the following curves ?
Conic Sections
MediumSingle correct
Q76
Let the equation of the plane, that passes through the point $(1, 4, -3)$ and contains the line of intersection of the planes $3x-2y+4z-7=0$ and $x+5y-2z+9=0$ , be $\alpha x+\beta y+\gamma z+3=0$ , then $\alpha+\beta+\gamma$ is equal to :
Three Dimensional Geometry Planes in 3D Family of Planes
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q77
$\mathrm{cosec}18^\circ$ is a root of the equation :
Trigonometric Functions Trigonometric Identities Values of Non-Standard Specific Angles
MediumSingle correctNew ideaIdea asked in 3 years
Q78
Let $\vec{\mathrm{a}}$ and $\vec{\mathrm{b}}$ be two vectors such that $|2\vec{\mathrm{a}}+3\vec{\mathrm{b}}|=|3\vec{\mathrm{a}}+\vec{\mathrm{b}}|$ and the angle between $\vec{\mathrm{a}}$ and $\vec{\mathrm{b}}$ is $60^\circ$ . If…
Vector Algebra Dot Product Expansion of Sum of Vectors Squared
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q79
A vertical pole fixed to the horizontal ground is divided in the ratio $3:7$ by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of…
Trigonometric Functions
MediumSingle correct
Q80
Let $*, ▯ \in \{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p}*\sim\mathrm{q})\Rightarrow(\mathrm{p}\,▯\,\mathrm{q})$ is a tautology. Then :
Mathematical Reasoning
MediumSingle correct
Q81
If $\left(\frac{3^6}{4^4}\right)\mathrm{k}$ is the term, independent of $x$ , in the binomial expansion of $\left(\frac{x}{4}-\frac{12}{x^2}\right)^{12}$ , then k is equal to __________.
Binomial Theorem
MediumNumerical value
Q82
A point $z$ moves in the complex plane such that $\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{4}$ , then the minimum value of $|z-9\sqrt{2}-2i|^2$ is equal to __________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Locus of Argument Ratio (Circular Arc)
HardNumerical valueNew ideaIdea asked in 3 years
Q83
If ‘R’ is the least value of ‘a’ such that the function $f(x)=x^2+\mathrm{a}x+1$ is increasing on $[1, 2]$ and ‘S’ is the greatest value of ‘a’ such that the function $f(x)=x^2+\mathrm{a}x+1$ is decreasing on $[1, 2]$ , then the value of…
Application of Derivatives Monotonicity Parameter Range for Localized Monotonicity
EasyNumerical valueNew idea
Q84
Let [t] denote the greatest integer $\leq$ t. Then the value of $8\cdot\int_{-\frac{1}{2}}^{1}([2x]+|x|)\,dx$ is __________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q85
If $x\,\phi(x)=\int_5^x(3t^2-2\phi'(\mathrm{t}))\,\mathrm{dt}$ , $x>-2$ , and $\phi(0)=4$ , then $\phi(2)$ is __________.
Differential Equations Leibniz Rule Solving Integral Equations
MediumNumerical valueNew ideaIdea asked in 6 years
Q86
If the variable line $3x+4y=\alpha$ lies between the two circles $(x-1)^2+(y-1)^2=1$ and $(x-9)^2+(y-1)^2=4$ , without intercepting a chord on either circle, then the sum of all the integral values of $\alpha$ is __________.
Conic Sections Circle Tangents Condition of tangency
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q87
The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2x-y+z=6$ from the point $(-1, -1, 2)$ is __________.
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
MediumNumerical valueNew ideaIdea asked in 6 years
Q88
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate.…
Probability Conditional Probability Conditional Probability Definition
MediumNumerical valueNew ideaIdea asked in 2 years
Q89
The number of six letter words (with or without meaning), formed using all the letters of the word ‘VOWELS’, so that all the consonants never come together, is __________.
Permutations and Combinations The Block/Tie Method
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q90
The mean of 10 numbers $7\times8,\ 10\times10,\ 13\times12,\ 16\times14,\ ...$ is __________.
Statistics Variance and SD Mean of Discrete Data
MediumNumerical valueIdea asked in 4 yearsAsked the year before

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.