JEE Main 2021 · July session

JEE Main 4 August 2021, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 6 were rated hard and 29 easy. Its hard-question count was the joint 18th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Integrals, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 6; 7% of the shift
Chapters asked: 66; 17 questions with a figure

Key findings · 4 Aug 2021, Shift 2

1
6 hard questions (7%): the joint 18th 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 4 of 30 rated hard; Chemistry had the most easy questions (15 of 30).
3
51 questions tested a new idea, one no earlier year had asked: 65% of the 79 questions tagged to an idea.
4
27 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 (47% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: System of Particles and Rotational Motion in Physics (3), Amines in Chemistry (3) and Integrals in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 9Medium 20Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 5Medium 21Hard 4

Top chapters

Integrals4 Q
Conic Sections3 Q
Determinants3 Q
Application of Derivatives2 Q
Complex Numbers and Quadratic Equations2 Q
Probability2 Q

Question format

Single correct44 Q
Numerical value30 Q
Diagram based9 Q
Other3 Q
Two statements2 Q
Match the list2 Q

What each question asks you to do

Multi-step37 Q
Calculation24 Q
Recall10 Q
Application8 Q
Conceptual7 Q
Data or graph3 Q
Diagram reading1 Q

Most common: Multi-step.

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 easy20 medium1 hard

Chemistry30 questions

15 easy14 medium1 hard

Q31
Match List-I with List-II : List-I : Examples of Colloids A. Paints B. Hair cream C. Whipped cream D. Cheese List-II : Type of Colloid I. Emulsion II. Gel III. Sol IV. Foam Choose the most appropriate answer from the options given below :
Surface Chemistry Colloids Colloid Classification by State
EasyMatch the list · figureIdea asked in 4 yearsAsked the year before
Q32
Identify the element with positive value of electron gain enthalpy
Classification of Elements and Periodicity in Properties Periodic Trends Positive Electron Gain Enthalpy of Noble Gases
EasySingle correctNew idea
Q33
During the isolation of copper from copper matte, $\mathrm{SiO_2}$ is added to
General Principles and Processes of Isolation of Elements Metallurgical Extraction Silica Flux in Copper Smelting
EasySingle correctNew idea
Q34
$\mathrm{H_2O_2}$ reacts with $\mathrm{MnO_4^-}$ in basic medium to produce
Hydrogen Hydrogen and Hydrides Reducing Action of H2O2
MediumSingle correctNew ideaIdea asked in 2 years
Q35
Given below are two statements : Statement-I : The chlorides of both beryllium and aluminium have structures in which chlorobridges are present in vapour phase. Statement-II : Chlorides of both beryllium and aluminium are insoluble in organic solvents and…
The s-Block Elements s-Block Elements Phase-Dependent Structure of BeCl2
MediumTwo statementsNew ideaIdea asked in 2 years
Q36
The number of $\sigma$ (sigma) bond present in chloric acid, chlorous acid and perchloric acid are, respectively,
Chemical Bonding and Molecular Structure Group 17 & 18 Structures of Halogen Oxoacids
MediumSingle correctNew idea
Q37
Ruby and emerald are coloured due to the presence of
The d- and f-Block Elements d-Block Elements Color and Catalysis
EasySingle correctNew ideaIdea asked in 4 years
Q38
The oxidation states of Mn in $\mathrm{Mn_2(CO)_{10}}$ , $\left[\mathrm{Mn(CO)_5Br}\right]$ and $\mathrm{K}\left[\mathrm{Mn(CN)_6}\right]$ are, respectively,
Coordination Compounds Coordination Nomenclature Oxidation State Calculation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q39
The set in which both ligands generally behave in a bidentate chelating mode is
Coordination Compounds
EasySingle correct
Q40
The INCORRECT statement among those given below regarding smog is
Environmental Chemistry Classical vs Photochemical Smog
EasySingle correctNew ideaIdea asked in 3 years
Q41
In the reaction given below, [reaction scheme: drawn structure → A + B, see figure_note] the products A and B formed are
Alcohols, Phenols and Ethers Alcohols and Phenols Alcohol Dehydration Ease
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q42
Reaction of $\mathrm{CH_3-CH=CH_2}$ with different reagents (List-I) yield different products (List-II). Match List-I with List-II : List-I : Reagents A. $\mathrm{O_3/Zn,\ H_2O}$ B. $\mathrm{KMnO_4/H_2SO_4}$ C. $\mathrm{KMnO_4/NaOH}$ D. $\mathrm{H_3O^+}$ …
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
MediumMatch the list · figureIdea asked in 7 yearsAsked the year before
Q43
Neopentyl bromide on reaction with ethyl alcohol gives, as the major product,
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Neopentyl Halide Exceptions
MediumOther · figureNew idea
Q44
The major products A and B in the following reaction sequence are [reaction scheme: see figure_note] (Ph = - $\mathrm{C_6H_5}$ )
Alcohols, Phenols and Ethers Nucleophilic Addition Grignard Reagent Addition
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q45
Cannizzaro reaction cannot be given by
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cannizzaro Reaction
EasyOther · figureIdea asked in 4 yearsAsked the year before
Q46
For the compounds below given [structures I, II, III, IV: see figure_note] the correct order of basicity is
Amines Basicity of Nitrogen Heterocycles
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q47
The major products A and B in the following reaction sequence are [reaction scheme: see figure_note] (Ph = - $\mathrm{C_6H_5}$ )
Amines
MediumDiagram based · figure
Q48
The drug that is used as an antacid is
Chemistry in Everyday Life Evolution of Antacids: Neutralizers vs Receptor Blockers
EasySingle correctNew ideaIdea asked in 2 years
Q49
The evidence about the cyclic structure of glucose appears from the fact that
Biomolecules Carbohydrates Chemical Evidence for the Cyclic Structure
MediumSingle correctNew idea
Q50
The reagent that gives purple coloured complex with $\mathrm{S^{2-}}$ ion is
Coordination Compounds Anion Analysis Sulfide Sodium Nitroprusside Test
EasySingle correctNew ideaIdea asked in 3 years
Q51
The amount of potassium chlorate ( $\mathrm{KClO_3}$ ) that needs to be completely decomposed in order to liberate 40 $\mathrm{dm^3}$ of oxygen gas at STP is ________ g. (Nearest integer) [Atomic Masses : K = 39.0 u; Cl = 35.5 u; O = 16.0 u, R = 0.0831 L bar…
Some Basic Concepts of Chemistry Stoichiometry Stoichiometry of Thermal Decomposition
EasyNumerical valueNew ideaIdea asked in 2 years
Q52
A gaseous mixture of helium and oxygen contains 20% helium by weight. If the partial pressure of oxygen in the mixture is 5 atm, the partial pressure of helium is ________ atm. (Nearest integer) [Atomic Masses : He : 4.0 u; O : 16.0 u]
Thermodynamics (Chemistry)Ideal Gas Laws Dalton's Law
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q53
The number of photons emitted by a 800 nm lamp having an average power of 5 mW in 10 s is ________ $\times\ 10^{17}$ . (Nearest integer) [Given : h = 6.626 $\times$ $10^{-34}$ Js; C = 3.0 $\times$ $10^{8}$ $\mathrm{ms^{-1}}$ ]
Structure of Atom Photoelectric Effect Photon Flux and Beam Power
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q54
The bond order in $\mathrm{NO^+}$ is ________ . ( integer answer)
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
EasyNumerical valueNew ideaIdea asked in 3 years
Q55
The standard reaction enthalpy for hydrogenation of propene is $-124\ \mathrm{kJ\ mol^{-1}}$ . Additionally, standard heat of combustion $\Delta_c H^{\ominus}$ (propane) = $-2220\ \mathrm{kJ\ mol^{-1}}$ . and standard heat of formation…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Hess's Law
MediumNumerical valueIdea asked in 5 years
Q56
0.7 $\mathrm{cm^3}$ of compound A (molar mass = 70 $\mathrm{g\ mol^{-1}}$ , density = 1.024 $\mathrm{g\ cm^{-3}}$ ) is dissolved in 1 $\mathrm{dm^3}$ of water. If the depression in freezing point of water is 0.02 $^{\mathrm{o}}$ C, the van't Hoff factor for the…
Solutions Colligative Properties Van't Hoff Factor (i)
MediumNumerical valueNew ideaIdea asked in 4 years
Q57
$x \times 10^{-5}$ g of $\mathrm{Ca(OH)_2}$ are required to produce 200 $\mathrm{cm^3}$ of an aqueous solution of pH 10.0. The value of $x$ is ________ . (Nearest integer) [Given : Atomic masses : Ca : 40.0 u; H : 1.0 u; O : 16.0 u]
Equilibrium pH and Buffers pH of Strong Acids and Bases
MediumNumerical valueNew ideaIdea asked in 4 years
Q58
The standard electrode potentials of the reactions are given below. $\mathrm{MnO_4^-} + 8\mathrm{H^+} + 5\mathrm{e^-} \rightleftharpoons \mathrm{Mn^{2+}} + 4\mathrm{H_2O}$ $\mathrm{E^\circ} = 1.51\ \mathrm{V}$ …
Electrochemistry Nernst Equation E°cell and Equilibrium
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q59
$\mathrm{N_2O_5}$ decomposes following first order kinetics according to the reaction $2\mathrm{N_2O_5(g)} \rightarrow 4\mathrm{NO_2(g)} + \mathrm{O_2(g)}$ $\mathrm{N_2O_5}$ is introduced in a closed vessel. After 46 minutes, the pressure in the vessel is…
Chemical Kinetics Integrated Rate Equations Gas Kinetics with Complex Stoichiometry
HardNumerical valueNew ideaIdea asked in 5 years
Q60
[reaction scheme: see figure_note] In the reactions above, yield of the first step is 90% and that of the second step is 80%. The overall yield of the reaction is ________ %.
Amines Stoichiometry Overall Yield of Sequential Reactions
EasyNumerical value · figureNew idea

Maths30 questions

5 easy21 medium4 hard

Q61
The domain of the function $f(x)=\frac{\log_2(x+3)}{(x+1)(x+2)}$ is
Relations and Functions Functions and Domain Intersection of Domains
EasySingle correctNew ideaIdea asked in 2 years
Q62
If A is a $3\times3$ matrix and $|A|=\frac{1}{36}$ , then the value of $|2\cdot adj(3\cdot adj(6A))|$ is
Determinants Matrix Inverse Determinant of Adjoint of Inverse
MediumSingle correctNew ideaIdea asked in 3 years
Q63
The system of equations $x+2y+pz=4$ $x+qy+z=5$ $2x+4y+z=8$ has
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q64
If $C_r$ ( $r=0,1,2,\ldots,11$ ) are the Binomial coefficients in the expansion of $(1+x)^{11}$ , then the value of $C_0+(C_0+C_1)+(C_0+C_1+C_2)+\ldots..+(C_0+C_1+\ldots.+C_{11})$ is
Binomial Theorem Binomial Coefficients Double Summation of Coefficients
MediumSingle correctNew ideaIdea asked in 2 years
Q65
A fair coin is tossed $n$ times. If the probability of getting 6 heads is equal to that of getting 8 tails, then the probability of getting 2 heads, is
Probability
MediumSingle correct
Q66
The value of $\lim_{x\to2}\left(2-\cos\left(2x^2-5x+2\right)\right)^{\frac{1}{\left(x^2-4x+4\right)}}$ is equal to
Limits and Derivatives L'Hopital's Rule e-Power Shortcut for 1^infinity Forms
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q67
Let $f:\mathbb{R}\to\mathbb{R}$ be twice differentiable and satisfy $f(x+y)=f(x)+f(y)$ . If $f'(0)=1$ , then which of the following is true?
Continuity and Differentiability Differentiability via Functional Equations
EasySingle correctIdea asked in 6 yearsAsked the year before
Q68
Equation of a tangent to the curve, $y=2\int_0^x|t|\,dt$ which is parallel to the line, $2x-y=13$ is
Application of Derivatives Tangents and Normals Tangents to Piecewise/Modulus Functions
MediumSingle correctNew idea
Q69
If $\int\sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx=A\tan^{-1}\left(\frac{2x+2}{3}\right)+B\log_e\left(4x^2+8x+13\right)+C$ (C is a constant of integration), then the ordered pair (A, 4B) is equal to
Integrals Integration by Parts Inverse Trig Simplification Before Parts
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q70
The value of the integral $\int_1^6\frac{\log_e x\,dx}{\log_e x^2+\log_e(x^2-14x+49)}$ is
Integrals Definite Integral Properties King's Property
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q71
If $u+v+w=91$ , and $2u=3v=4w$ , then the value of $\int_{u-v+w}^{2u+v+4w}e^{(x-[x])}\,dx$ , where $[x]$ denotes the greatest integer $\le x$ , is equal to
Integrals Definite Integral Properties Fractional Part Function Integrals
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q72
If two distinct chords, drawn from the point $(\alpha,\beta)$ on the circle $x^2+y^2=\alpha x+\beta y$ (where $\alpha\beta\neq0$ ) are bisected by the $y$ -axis, then
Conic Sections Circle Tangents Equation of Chord with Given Midpoint (T = S1)
HardSingle correctNew idea
Q73
If the area of the triangle formed by the tangent at a point in the first quadrant on the ellipse, $4x^2+3y^2=12$ and its axes is 4 sq. units, then one such point is
Conic Sections Tangents and Normals Intercepts of Tangent and Normal
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q74
Let the normal at any point of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ intersect the coordinate axes at points P and Q. Then the locus of the mid-point of PQ is :
Conic Sections Normals to Conics Hyperbola Normal Parametric Form
HardSingle correctNew idea
Q75
The equation of a line passing through the point $(2,-1,1)$ and the point of intersection of the lines $2x-y-4=0=y+2z$ and $x+3z=0=2x+5z-1$ , is
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
MediumSingle correctNew ideaIdea asked in 6 years
Q76
The distance of the point $(5,6,9)$ from the plane, which passes through the line of intersection of the planes $x+y-z=1$ and $2x+3y+4z=5$ , and is perpendicular to the plane $x-y+z=0$ is
Three Dimensional Geometry Planes in 3D Family of Planes Perpendicular to a Third Plane
MediumSingle correctNew ideaIdea asked in 3 years
Q77
The mean and the variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12 and 14, then the absolute difference of the remaining two observations is
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q78
A bag contains four bulbs. Some of these bulbs are defective. Two bulbs are drawn at random and it is found that both the bulbs are defective. What is the probability that the bag contains exactly 3 defective bulbs?
Probability Bayes' Theorem Implicit Equally Likely Priors
MediumSingle correctNew ideaIdea asked in 2 years
Q79
The number of solutions of the equation $|\cos x|=\cos x-2\sin x,\,-2\pi\le x\le2\pi$ , is
Trigonometric Functions General Solutions Modulus Trigonometric Equations
MediumSingle correctNew ideaIdea asked in 2 years
Q80
Consider the following statements : p : Amit plays cricket q : Amit is out of Delhi. r : It is Sunday Then the statement “Amit plays cricket only if he is in Delhi and it is Sunday” can be expressed as :
Mathematical Reasoning
EasySingle correct
Q81
If $z=\frac{\sqrt3-i}{2}$ and $(z^{95}+i^{95})^{94}=z^n$ , then the minimum positive integral value of ‘ $n$ ’ is ________ .
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form De Moivre's Theorem for Integer Powers
MediumNumerical valueNew idea
Q82
The integral value of $a$ , for which the equation $(x^2+x+2)^2-(a-3)(x^2+x+2)(x^2+x+1)+(a-4)(x^2+x+1)^2=0$ has real roots, is ________.
Complex Numbers and Quadratic Equations Quadratic Roots Resolution into Two Linear Factors
HardNumerical valueNew idea
Q83
If $A=\begin{bmatrix}1&0&0\\1&1&0\\1&1&1\end{bmatrix}$ , the sum of the entries of $A^{20}$ is ________ .
Matrices Matrix Multiplication Powers of Square Matrices
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q84
The unit digit in the sum of $1!+2!+3!+\ldots.+2021!$ is ________ .
Permutations and Combinations
EasyNumerical value
Q85
Let $\vec a=-\hat i+\hat j$ and $\vec b=\hat i+\hat j-\hat k$ be two given vectors. If a vector $\vec c$ satisfies $(\vec a\times\vec c)+\vec b=\vec 0$ and $\vec a.\vec c=3$ , then $10\,|\,\vec c\,|^2$ is equal to ________.
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
MediumNumerical valueNew ideaIdea asked in 5 years
Q86
If 32, $5x$ and $y$ are in A.P., and 2, $x$ and $y$ are in G.P., then the positive common difference of the A.P. is ________.
Sequences and Series AP and GP Conditions for Three Terms in AP or GP
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q87
If $f$ be a twice differentiable function satisfying $f(x)=x^4+x^2f''(1)+f''(2)$ , then the modulus of the minimum value of $f(x)$ is equal to ________.
Application of Derivatives Maxima and Minima Second Derivative Test
MediumNumerical valueNew idea
Q88
If $\frac{dw(t)}{dt}=t\sqrt{121-t^2}$ and $w(0)=0$ , then the value of $3w(\sqrt{21})$ is ________.
Integrals Integration by Substitution Square Root Derivative Integration Rule
EasyNumerical valueNew idea
Q89
One side of a square lies along the line $x-3y+1=0$ and its one vertex is $(1,4)$ . If $(a,b)$ and $(c,d)$ are its two vertices on the line $x-3y+1=0$ , then $|a-2|+|c-2|+|b-1|+|d-1|$ is equal to ________.
Straight Lines Straight Line Distance Foot of the perpendicular
MediumNumerical valueNew ideaIdea asked in 2 years
Q90
The number of real solutions of the equation $\begin{vmatrix}x^2+\sin x\cos x&x(1+\sin x)\\x+\cos x&x+1\end{vmatrix}=0$ is ________.
Determinants
HardNumerical 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 2021 shifts.