JEE Main 2021 · August session

JEE Main 26 August 2021, Shift 1

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 13 were rated hard and 24 easy. Its hard-question count was the 2nd highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Complex Numbers and Quadratic Equations, with 3 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 13; 15% of the shift
Chapters asked: 66; 12 questions with a figure

Key findings · 26 Aug 2021, Shift 1

1
13 hard questions (15%): the 2nd 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 10 of 29 rated hard; Physics had the most easy questions (12 of 30).
3
49 questions tested a new idea, one no earlier year had asked: 66% of the 74 questions tagged to an idea.
4
24 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
40 shared an idea with another 2021 shift (54% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (3), The d- and f-Block Elements in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 10Medium 19Hard 1

Top chapters

The d- and f-Block Elements3 Q
Aldehydes, Ketones and Carboxylic Acids2 Q
Biomolecules2 Q
Electrochemistry2 Q
Equilibrium2 Q
Hydrocarbons2 Q

Maths

29 Q · 10 numerical

Easy 2Medium 17Hard 10

Top chapters

Question format

Single correct44 Q
Numerical value30 Q
Diagram based7 Q
Two statements6 Q
Other2 Q

What each question asks you to do

Calculation28 Q
Multi-step27 Q
Conceptual13 Q
Application12 Q
Recall6 Q
Data or graph2 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
Open29 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 89 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

89 of 89 questions

Physics30 questions

12 easy16 medium2 hard

Chemistry30 questions

10 easy19 medium1 hard

Q31
Given below are two statements : Statement I : Frenkel defects are vacancy as well as interstitial defects. Statement II : Frenkel defect leads to colour in ionic solids due to presence of F-centres. Choose the most appropriate answer for the statements from…
The Solid State Solid State Defects Frenkel Defect
EasyTwo statementsNew idea
Q32
Given below are two statements : Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.…
Structure of Atom Bohr's Atomic Theory Electron Velocity in Orbit
MediumTwo statementsNew ideaIdea asked in 2 years
Q33
Given below are two statements : Statement I : The limiting molar conductivity of KCl (strong electrolyte) is higher compared to that of $\mathrm{CH_3COOH}$ (weak electrolyte). Statement II : Molar conductivity decreases with decrease in concentration of…
Electrochemistry
MediumTwo statements
Q34
Which one of the following is correct for the adsorption of a gas at a given temperature on a solid surface ?
Surface Chemistry Adsorption Thermodynamics of Adsorption
EasySingle correctNew ideaIdea asked in 2 years
Q35
Given below are two statements. Statement I : The choice of reducing agents for metals extraction can be made by using Ellingham diagram, a plot of $\Delta \mathrm{G}$ vs temperature. Statement II : The value of $\Delta \mathrm{S}$ increases from left to…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Basics
MediumTwo statementsIdea asked in 3 yearsAsked the year before
Q36
Which one of the following methods is most suitable for preparing deionized water ?
Hydrogen Hydrogen and Hydrides Ion-Exchange Resins for Water Softening
EasySingle correctNew ideaIdea asked in 2 years
Q37
What are the products formed in sequence when excess of $\mathrm{CO_2}$ is passed in slaked lime ?
The s-Block Elements Anion Analysis Carbonate Lime Water Test
EasySingle correctNew idea
Q38
The incorrect statement is :
The p-Block Elements Group 17 & 18 Halogen Reactivity Trends
MediumSingle correctNew ideaIdea asked in 2 years
Q39
Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere ?
The d- and f-Block Elements d-Block Elements Color and Catalysis
EasySingle correctNew ideaIdea asked in 4 years
Q40
The conversion of hydroxyapatite occurs due to presence of $\mathrm{F^-}$ ions in water. The correct formula of hydroxyapatite is :
Environmental Chemistry Drinking Water Standards: Fluoride Limits
MediumSingle correctNew ideaIdea asked in 3 years
Q41
Which one of the following complexes is violet in colour ?
Coordination Compounds Anion Analysis Sulfide Sodium Nitroprusside Test
MediumSingle correctNew ideaIdea asked in 3 years
Q42
Excess of isobutane on reaction with $\mathrm{Br_2}$ in presence of light at 125℃ gives which one of the following, as the major product ?
Hydrocarbons Alkanes and Free Radicals Reactivity-Selectivity Principle
EasySingle correct · figureNew idea
Q43
The major product formed in the following reaction is : [figure: reactant, arrow labelled HBr above, "Major Product" after the arrow; "(excess)" printed beneath the reactant]
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
MediumSingle correct · figureIdea asked in 6 yearsAsked the year before
Q44
Among the following compounds I-IV, which one forms a yellow precipitate on reacting sequentially with (i) NaOH (ii) dil. $\mathrm{HNO_3}$ (iii) $\mathrm{AgNO_3}$ ? [figure: four hexagonal-ring structures labelled I, II, III, IV]
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Reactivity of Allylic and Benzylic Halides
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q45
The major products formed in the following reaction sequence A and B are : [figure: hexagonal ring joined to a carbonyl carbon (C=O) which carries $\mathrm{CH_3}$ ; arrow with $\mathrm{Br_2}$ above and KOH below, giving A + B]
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Haloform Interference with Aldol
MediumOther · figureNew idea
Q46
The correct options for the products A and B of the following reactions are : [figure: hexagonal ring (inner circle) with OH at top; left arrow labelled $\mathrm{Br_2}$ (Excess) / $\mathrm{H_2O}$ gives A; right arrow labelled $\mathrm{Br_2}$ /…
Alcohols, Phenols and Ethers Aromatic Hydrocarbons Ortho-Para vs Meta Directing
MediumDiagram based · figureNew ideaIdea asked in 5 years
Q47
The major product formed in the following reaction is : [figure: ring system of a hexagonal ring fused to a five-membered ring containing NH; the five-membered ring carries a side chain $\mathrm{CH_2}$ -CH(COOH)(NH $_2$ ); arrow labelled $\mathrm{SOCl_2}$ ,…
Biomolecules
MediumDiagram based · figure
Q48
The correct sequential addition of reagents in the preparation of 3-nitrobenzoic acid from benzene is :
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Carboxylic Acid Synthesis via Grignard and CO2
MediumSingle correctNew ideaIdea asked in 3 years
Q49
The polymer formed on heating Novolac with formaldehyde is :
Polymers Novolac Intermediate Formation
EasySingle correctNew ideaIdea asked in 2 years
Q50
Given below are two statements : Statement I : In the titration between strong acid and weak base methyl orange is suitable as an indicator. Statement II : For titration of acetic acid with NaOH phenolphthalein is not a suitable indicator. In the light of…
Equilibrium pH and Buffers Indicator Selection for Titrations
MediumTwo statementsNew ideaIdea asked in 2 years
Q51
An aqueous KCl solution of density 1.20 g mL $^{-1}$ has a molality of 3.30 mol kg $^{-1}$ . The molarity of the solution in mol L $^{-1}$ is __________. (Nearest integer) [ Molar mass of KCl = 74.5 ]
Some Basic Concepts of Chemistry Mole Concept Molarity and Molality Interconversion
MediumNumerical valueNew ideaIdea asked in 3 years
Q52
$\mathrm{AB_3}$ is an interhalogen T-shaped molecule. The number of lone pairs of electrons on A is ___________. (Integer answer)
The p-Block Elements Group 17 & 18 Interhalogen Compounds
EasyNumerical valueNew ideaIdea asked in 3 years
Q53
The Born-Haber cycle for KCl is evaluated with the following data : $\Delta_f \mathrm{H}^{\ominus}$ for KCl $= -436.7$ kJ mol $^{-1}$ ; $\Delta_{sub} \mathrm{H}^{\ominus}$ for K $= 89.2$ kJ mol $^{-1}$ ; $\Delta_{ionization} \mathrm{H}^{\ominus}$ for K $= 419.0$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Born-Haber Cycle for Lattice Enthalpy
MediumNumerical valueNew idea
Q54
Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of 0.10 M $\mathrm{C_2H_5OH}$ is __________. (Integer answer) (i) 0.10 M $\mathrm{Ba_3(PO_4)_2}$ (ii) 0.10 M $\mathrm{Na_2SO_4}$ (iii) 0.10 M KCl…
Solutions Colligative Properties Van't Hoff Factor (i)
EasyNumerical valueNew ideaIdea asked in 4 years
Q55
The $\mathrm{OH^-}$ concentration in a mixture of 5.0 mL of 0.0504 M $\mathrm{NH_4Cl}$ and 2 mL of 0.0210 M $\mathrm{NH_3}$ solution is $x \times 10^{-6}$ M. The value of $x$ is __________. (Nearest integer) [Given $\mathrm{K_w} = 1 \times 10^{-14}$ and…
Equilibrium pH and Buffers Basic Buffer pH Calculation
MediumNumerical valueNew ideaIdea asked in 3 years
Q56
The following data was obtained for chemical reaction given below at 975 K. $2\mathrm{NO_{(g)}} + 2\mathrm{H_{2(g)}} \rightarrow \mathrm{N_{2(g)}} + 2\mathrm{H_2O_{(g)}}$ [NO] mol L $^{-1}$ | [ $\mathrm{H_2}$ ] mol L $^{-1}$ | Rate mol L $^{-1}$ s $^{-1}$ (A)…
Chemical Kinetics Rate Laws Initial Rates Method
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q57
These are physical properties of an element (A) Sublimation enthalpy (B) Ionisation enthalpy (C) Hydration enthalpy (D) Electron gain enthalpy The total number of above properties that affect the reduction potential is __________. (Integer answer)
Electrochemistry
MediumNumerical value
Q58
The number of 4 $f$ electrons in the ground state electronic configuration of $\mathrm{Gd^{2+}}$ is __________. [Atomic number of Gd = 64]
The d- and f-Block Elements f-Block Elements Anomalous Electronic Configuration of Gadolinium
MediumNumerical valueNew idea
Q59
The ratio of number of water molecules in Mohr's salt and potash alum is __________ $\times 10^{-1}$ . (Integer answer)
The d- and f-Block Elements
MediumNumerical value
Q60
The total number of negative charge in the tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12.5 will be ___________. (Integer answer)
Biomolecules
HardNumerical value

Maths29 questions

2 easy17 medium10 hard

Q61
Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :
Relations and Functions Sets and Relations Venn Diagrams
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q62
The equation $\arg\left(\frac{z-1}{z+1}\right) = \frac{\pi}{4}$ represents a circle with :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Locus of Argument Ratio (Circular Arc)
MediumSingle correctNew ideaIdea asked in 3 years
Q63
If $A = \begin{pmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{pmatrix}$ , $B = \begin{pmatrix} 1 & 0 \\ i & 1 \end{pmatrix}$ , $i = \sqrt{-1}$ , and $Q = A^T B A$ , then the inverse of the matrix…
Matrices Matrix Inverse Properties of Matrix Inverses
MediumSingle correctNew idea
Q64
Let $\theta \in \left(0, \frac{\pi}{2}\right)$ . If the system of linear equations. $(1+\cos^2\theta)\,x + \sin^2\theta\,y + 4\sin 3\theta\,z = 0$ $\cos^2\theta\,x + (1+\sin^2\theta)\,y + 4\sin 3\theta\,z = 0$ …
Determinants Cramer's Rule Parameter Evaluation in Homogeneous Systems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q66
If $^{20}C_r$ is the co-efficient of $x^r$ in the expansion of $(1+x)^{20}$ , then the value of $\sum_{r=0}^{20} r^2\,{}^{20}C_r$ is equal to :
Binomial Theorem Binomial Coefficients Second Derivative Method for Sums
MediumSingle correctNew ideaIdea asked in 3 years
Q67
If the sum of an infinite GP $a, ar, ar^2, ar^3, \ldots$ is 15 and the sum of the squares of its each term is 150, then the sum of $ar^2, ar^4, ar^6, \ldots$ is :
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q68
Let $f(x) = \cos\left(2\tan^{-1}\sin\left(\cot^{-1}\sqrt{\frac{1-x}{x}}\right)\right)$ , $0 < x < 1$ . Then :
Inverse Trigonometric Functions Inverse Trig Identities Multiple Angle Inverse ID
HardSingle correctNew ideaIdea asked in 2 years
Q69
The value of $\int_{-1/\sqrt{2}}^{1/\sqrt{2}} \left(\left(\frac{x+1}{x-1}\right)^2 + \left(\frac{x-1}{x+1}\right)^2 - 2\right)^{1/2} dx$ is :
Integrals Definite Integral Properties Modulus Function Interval Splitting
HardSingle correctIdea asked in 3 yearsAsked the year before
Q70
The value of $\lim_{n\to\infty} \frac{1}{n}\sum_{r=0}^{2n-1} \frac{n^2}{n^2+4r^2}$ is :
Integrals Integral as Limit of Sum Fractional or Multiple Upper Bounds
MediumSingle correctNew idea
Q71
The sum of solutions of the equation $\frac{\cos x}{1+\sin x} = |\tan 2x|$ , $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) - \left\{\frac{\pi}{4}, -\frac{\pi}{4}\right\}$ is :
Trigonometric Functions General Solutions Modulus Trigonometric Equations
HardSingle correctNew ideaIdea asked in 2 years
Q72
Let ABC be a triangle with A $(-3, 1)$ and $\angle ACB = \theta$ , $0 < \theta < \frac{\pi}{2}$ . If the equation of the median through B is $2x+y-3=0$ and the equation of angle bisector of C is $7x-4y-1=0$ , then $\tan\theta$ is equal to :
Straight Lines Straight Line Distance Angle Bisector Locus via Distances
HardSingle correctNew ideaIdea asked in 3 years
Q73
If a line along a chord of the circle $4x^2+4y^2+120x+675=0$ , passes through the point $(-30, 0)$ and is tangent to the parabola $y^2=30x$ , then the length of this chord is :
Conic Sections Circle Tangents Tangent in slope form
HardSingle correctNew idea
Q74
On the ellipse $\frac{x^2}{8}+\frac{y^2}{4}=1$ let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line $x+2y=0$ . Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the…
Conic Sections Ellipse Eccentricity Area of Foci-Minor Axis Triangle
HardSingle correctNew idea
Q75
A plane P contains the line $x+2y+3z+1=0=x-y-z-6$ , and is perpendicular to the plane $-2x+y+z+8=0$ . Then which of the following points lies on P ?
Three Dimensional Geometry Planes in 3D Family of Planes
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q76
Let $y=y(x)$ be a solution curve of the differential equation $(y+1)\tan^2 x\,dx+\tan x\,dy+y\,dx=0$ , $x \in \left(0, \frac{\pi}{2}\right)$ . If $\lim_{x\to 0+} xy(x)=1$ , then the value of $y\left(\frac{\pi}{4}\right)$ is :
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q77
Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{j}-\hat{k}$ . If $\vec{c}$ is a vector such that $\vec{a}\times\vec{c}=\vec{b}$ and $\vec{a}\cdot\vec{c}=3$ , then $\vec{a}\cdot(\vec{b}\times\vec{c})$ is equal to :
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q78
If the truth value of the Boolean expression $((p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)) \rightarrow (p \wedge q)$ is false, then the truth values of the statements p, q, r respectively can be :
Mathematical Reasoning
EasySingle correct
Q79
Let A and B be independent events such that P(A) $=p$ , P(B) $=2p$ . The largest value of p, for which P (exactly one of A, B occurs) $=\frac{5}{9}$ , is :
Probability
MediumSingle correct
Q80
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If $\alpha$ and $\sqrt{\beta}$ are the mean and standard deviation respectively for…
Statistics Variance and SD Correcting Incorrect Variance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q81
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is __________.
Permutations and Combinations Permutations of Distinct Objects
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q82
Let a, b $\in$ $\mathbf{R}$ , b $\neq$ 0. Define a function $f(x)=\begin{cases} a\sin\frac{\pi}{2}(x-1), & \text{for } x \leq 0 \\ \frac{\tan 2x-\sin 2x}{b\,x^3}, & \text{for } x>0. \end{cases}$ If $f$ is continuous at $x=0$ , then $10-ab$ is equal to…
Continuity and Differentiability Continuity at a Point
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
The sum of all integral values of k (k $\neq$ 0) for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots, is __________.
Complex Numbers and Quadratic Equations Quadratic Roots Nature of Roots
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q84
A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then…
Application of Derivatives Maxima and Minima Optimization Problems
MediumNumerical valueIdea asked in 5 years
Q85
The area of the region S $=\{(x, y) : 3x^2 \leq 4y \leq 6x+24\}$ is __________.
Application of Integrals Area Under Curves Area Between Parabola and Line
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q86
If $y=y(x)$ is an implicit function of $x$ such that $\log_e(x+y)=4xy$ , then $\frac{d^2y}{dx^2}$ at $x=0$ is equal to __________.
Continuity and Differentiability Chain Rule Second Order Implicit Chain Rule
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q87
If $^1P_1+2\cdot{}^2P_2+3\cdot{}^3P_3+\ldots+15\cdot{}^{15}P_{15}={}^qP_r-s$ , $0 \leq s \leq 1$ , then $^{q+s}C_{r-s}$ is equal to __________.
Permutations and Combinations
HardNumerical value
Q88
Let the line L be the projection of the line $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}$ in the plane $x-2y-z=3$ . If d is the distance of the point $(0, 0, 6)$ from L, then $d^2$ is equal to __________.
Three Dimensional Geometry
HardNumerical value
Q89
Let $z=\frac{1-i\sqrt{3}}{2}$ , $i=\sqrt{-1}$ . Then the value of $21+\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{21}+\frac{1}{z^{21}}\right)^3$ is __________.
Complex Numbers and Quadratic Equations Roots of Unity De Moivre's Theorem
HardNumerical valueNew idea
Q90
The locus of a point, which moves such that the sum of squares of its distances from the points $(0, 0)$ , $(1, 0)$ , $(0, 1)$ $(1, 1)$ is 18 units, is a circle of diameter d. Then $d^2$ is equal to __________.
Conic Sections
MediumNumerical value

Dropped from the final key and left out of every count: Q65.

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.