JEE Main 2021 · July session

JEE Main 4 August 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 7 were rated hard and 36 easy. Its hard-question count was the joint 16th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 7; 8% of the shift
Chapters asked: 65; 12 questions with a figure

Key findings · 4 Aug 2021, Shift 1

1
7 hard questions (8%): the joint 16th 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
47 questions tested a new idea, one no earlier year had asked: 62% of the 76 questions tagged to an idea.
4
26 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
41 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: System of Particles and Rotational Motion in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 15Hard 2

Top chapters

System of Particles and Rotational Motion3 Q
Atoms2 Q
Current Electricity2 Q
Electromagnetic Induction2 Q
Moving Charges and Magnetism2 Q
Oscillations2 Q

Chemistry

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 8Medium 18Hard 4

Top chapters

Application of Derivatives3 Q
Conic Sections3 Q
Trigonometric Functions3 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Integrals2 Q

Question format

Single correct50 Q
Numerical value30 Q
Diagram based5 Q
Match the list4 Q
Two statements1 Q

What each question asks you to do

Multi-step26 Q
Calculation24 Q
Application21 Q
Recall13 Q
Conceptual3 Q
Diagram reading2 Q
Data or graph1 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

13 easy15 medium2 hard

Chemistry30 questions

15 easy14 medium1 hard

Q31
Match List I with List II List I List II A. Frenkel defect I. CsCl B. Schottky defect II. Pink LiCl C. Impurity defect III. ZnS D. Metal excess defect IV. Solid solution of CdCl $_2$ and AgCl Choose the correct answer from the options given below :
The Solid State Solid State Defects Frenkel Defect
MediumMatch the listNew idea
Q32
Consider the following species $\mathrm{B_2, C_2, S_2, NO, O_2^{2-}}$ Which set represents all paramagnetic species?
Chemical Bonding and Molecular Structure Molecular Orbital Theory Magnetic Property Prediction
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q33
For a gaseous reaction, $\mathrm{A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}}$ , the rate of decomposition of $\mathrm{A_{(g)}}$ may be studied by measuring the pressure (P) in a system at constant volume (V) and temperature (T). If all the gaseous species follow…
Chemical Kinetics Rate Laws Rate and Stoichiometry
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q34
Graph between $\log\frac{x}{m}$ , ('x' is mass of gas adsorbed and 'm' is the mass of adsorbent) versus log P (P-pressure of gas adsorbed) is a straight line (as depicted in the figure). It is applicable when
Surface Chemistry Adsorption Limits of Freundlich Exponent (1/n)
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q35
The correct order of first ionization enthalpy is :
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
EasySingle correctNew ideaIdea asked in 4 years
Q36
The concentrated ores siderite and copper glance are converted to their oxides by
General Principles and Processes of Isolation of Elements Metallurgical Extraction Calcination vs. Roasting
EasySingle correctIdea asked in 3 yearsAsked the year before
Q37
Naturally occurring hydrogen contains three isotopes, protium (H), deuterium (D) and tritium (T). What is correct order of heat of dissociation for $\mathrm{H_2}$ , $\mathrm{D_2}$ and $\mathrm{T_2}$ ?
Hydrogen Hydrogen and Hydrides H-H Bond Dissociation Enthalpy
EasySingle correctNew idea
Q38
Choose the correct statement from the following :
The s-Block Elements s-Block Elements Formation of Oxides, Peroxides, and Superoxides
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q39
Which among the following cannot be prepared from Diborane?
The p-Block Elements Group 13 & 14 Preparation of Diborane
MediumSingle correctNew idea
Q40
Match List I with List II List I List II A. Gadolinium (At. No. 64) I. $5f^7, 6d^1, 7s^2$ B. Holmium (At. No. 67) II. $5f^4, 6d^1, 7s^2$ C. Neptunium (At. No. 93) III. $4f^{11}, 6s^2$ D. Curium (At. No. 96) IV. $4f^7, 5d^1, 6s^2$ Choose the correct answer…
The d- and f-Block Elements f-Block Elements Lanthanide Electronic Configuration
MediumMatch the listIdea asked in 5 yearsAsked the year before
Q41
In stratosphere, chlorofluorocarbon compounds break down by UV radiations, releasing 'X' free radical, which further causes ozone layer depletion. Identify 'X'.
Environmental Chemistry Ozone Layer Depletion
EasySingle correctIdea asked in 4 yearsAsked the year before
Q42
In Carius method of halogen estimation, the halogen containing compound is heated with
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q43
Select the most suitable reagent for the following reduction reaction
Hydrocarbons Alkenes and Alkynes Stereoselective Alkyne Reduction
EasySingle correct · figureNew ideaIdea asked in 3 years
Q44
Identify the reagent in the following reaction. $\mathrm{CH_3-CH_2-C(=O)-OH \xrightarrow{Reagent} CH_3-CH(X)-C(=O)-OH}$ (X = Cl, – Br)
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Hell-Volhard-Zelinsky Reaction
EasySingle correct · figureNew ideaIdea asked in 4 years
Q45
Identify P in the given chemical reaction i) $\mathrm{KMnO_4}$ , KOH, heat ii) $\mathrm{H_3O^+}$
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Side-chain Oxidation
EasyDiagram based · figureNew ideaIdea asked in 5 years
Q46
Match List I with List II List I List II A. Kolbe's Reaction I. [structure: benzene ring with a CHO substituent] B. Gatterman-Koch Reaction II. [structure: benzene ring with OH and COOH on adjacent ring carbons] C. Reimer-Tiemann Reaction III. [structure:…
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
MediumMatch the list · figureIdea asked in 4 yearsAsked the year before
Q47
Given below are two statements : Statement I : Benzenediazonium chloride is a colored crystalline solid. Statement II : Benzenediazonium fluoroborate is water soluble and stable at room temperature. In the light of the above statements, choose the most…
Amines Diazonium Salts Isolation of Diazonium Fluoroborate
MediumTwo statementsNew idea
Q48
Which one of the following compound gives Biuret Test?
Biomolecules
MediumSingle correct
Q49
Which C-atom in α-D-glucopyranose is attached with two oxygens?
Biomolecules Carbohydrates Cyclic Structure of Glucose
EasySingle correctNew idea
Q50
Match List I with List II List I (Metal salt) List II (Colour to the flame) A. $\mathrm{Cu^{2+}}$ I. Brick Red B. $\mathrm{Sr^{2+}}$ II. Apple Green C. $\mathrm{Ba^{2+}}$ III. Green Flame with blue center D. $\mathrm{Ca^{2+}}$ IV. Crimson Red. Choose the…
The s-Block Elements s-Block Elements Flame Coloration
EasyMatch the listNew ideaIdea asked in 4 years
Q51
A solution of $\mathrm{H_2SO_4}$ has 30% $\mathrm{H_2SO_4}$ by mass and a density of 1.25 g mL $^{-1}$ . The molarity of the solution is ________ M. (Nearest integer)
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q52
The wavelength of a tennis ball of mass 57 g travelling at 80 km h $^{-1}$ is ________ $\times 10^{-34}$ m. (Nearest integer) [Use : h = $6.6 \times 10^{-34}$ J s]
Structure of Atom Matter Waves Basic Wavelength-Momentum Relation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q53
A lead bullet weighing 18 g and travelling with a velocity of 500 m/s $^{-1}$ is embedded in a wooden block weighing 1 kg. If both the block and the bullet were initially at 25°C, the final temperature of the block containing the bullet is ________ °C.…
Thermodynamics (Chemistry)First Law of Thermodynamics Mechanical Energy to Internal Energy Conversion
MediumNumerical valueNew idea
Q54
One mole of glucose was added to 1.0L of water (density = 1 g mL $^{-1}$ ). The elevation in boiling point is $x$ K $_b$ . The value of $x$ is ________. (Nearest integer) (K $_b$ is molal elevation constant for water.)
Solutions Colligative Properties Boiling Point Elevation
EasyNumerical valueNew ideaIdea asked in 6 years
Q55
If K $_{SP}$ of $\mathrm{CaSO_4}$ is $9.0\times10^{-6}$ at 298K, the molar solubility of $\mathrm{CaSO_4}$ in 0.2M $\mathrm{Ca(NO_3)_2}$ is ________ $\times10^{-6}$ M. (Nearest integer)
Equilibrium Solubility Product Common Ion Effect
MediumNumerical valueNew ideaIdea asked in 4 years
Q56
For the reaction, $\mathrm{6I^-_{(aq)} + Cr_2O_7^{2-}{}_{(aq)} + 14H^+ \longrightarrow 3I_{2(aq)} + 2Cr^{3+}{}_{(aq)} + 7H_2O_{(aq)}}$ ; $\mathrm{E^0_{cell} = 0.79V}$ The standard reduction potential for $\mathrm{I_{2(aq)}}$ is $x \times10^{-2}$ V. The value…
Electrochemistry Nernst Equation Standard Cell Potential
EasyNumerical valueIdea asked in 7 years
Q57
Among the following species, the number of species with oxidation state of Fe in +3 is ________. A. $\mathrm{[(H_2O)_4(CN)Fe(\mu\text{-}OH)_2Fe(CN)(H_2O)_4]^{2+}}$ [drawn structure, see figure_note] B. $\mathrm{[Fe_3O(CH_3COO)_6(H_2O)_3]^{+}}$ C.…
Coordination Compounds Coordination Nomenclature Oxidation State Calculation
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q58
Sum of unpaired electrons in $\mathrm{[NiCl_4]^{2-}}$ and $\mathrm{[Ni(CN)_4]^{2-}}$ is ________.
Coordination Compounds Crystal Field Theory d8 Square Planar Preference
MediumNumerical valueNew ideaIdea asked in 2 years
Q59
From the following compounds, the total number of compound(s) which will show Geometrical isomerism is ________.
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Counting Geometrical Isomers
HardNumerical value · figureNew idea
Q60
Number of isomeric compounds with molecular formula $\mathrm{C_4H_{11}N}$ that will give carbylamine test is ________.
Amines Carbylamine Reaction
EasyNumerical valueIdea asked in 4 yearsAsked the year before

Maths30 questions

8 easy18 medium4 hard

Q61
The number of roots of the equation $\left(3+\sqrt{5}\right)^{|x^2-4|}+4\left(\frac{3-\sqrt{5}}{4}\right)^{|x^2-4|}=6$ is
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q62
If $z=x+iy$ and $\omega=\frac{z-1}{3(z-2)}$ , then the set of points $z$ satisfying $|z|=1=|\omega|$ contains
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q63
Let $A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}$ , $xyz=60$ and $8x+4y+3z=20$ . If $A(adj\ A)=k\,I$ , then $k$ is equal to
Determinants Matrix Inverse Cofactor Matrix and Adjoint
MediumSingle correctIdea asked in 5 years
Q64
If the system of linear equations $x+y+z=3$ $x+by+b^2z=7$ and $ax+a^2y+a^3z=1$ has infinitely many solutions, then the ordered pair $(a, b)$ is
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q65
If $(1+x+x^2)^4=a_0+a_1x+a_2x^2+\ldots\ldots+a_8x^8$ , then the value of $a_0+4a_2+16a_4+\ldots.+2^8a_8$ is equal to
Binomial Theorem Binomial Coefficients Sum of Even and Odd Coefficients
MediumSingle correctNew ideaIdea asked in 3 years
Q66
The value of $\frac{\sum_{k=1}^{22}(-1)^{k-1}\cos k^{\circ}+\sum_{k=23}^{44}(-1)^{k}\cos k^{\circ}}{\sum_{k=1}^{22}(-1)^{k-1}\sin k^{\circ}+\sum_{k=23}^{44}(-1)^{k}\sin k^{\circ}}$ , where $k^{\circ}$ denotes $k$ degree, is
Trigonometric Functions Trigonometric Identities Trigonometric Series with Angles in AP
HardSingle correctNew idea
Q67
$\lim_{x\to 2}\left(x^3-x^2-8x+13\right)^{\frac{1}{x^3-3x^2+4}}$
Limits and Derivatives L'Hopital's Rule e-Power Shortcut for 1^infinity Forms
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q68
The equation of the normal to the curve $y=e^{-|x|}$ at a point, where the curve cuts the line $x=-1$ is
Application of Derivatives Tangents and Normals Equation of Normal
EasySingle correctIdea asked in 3 yearsAsked the year before
Q69
If $I_1=\int_0^{\pi}xe^{\mathrm{cosec}\,x}dx$ and $I_2=\int_0^{\pi}e^{\mathrm{cosec}\,x}dx$ , then the ratio $I_1:I_2$ is equal to
Integrals Definite Integral Properties King's Property
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q70
The equation of the tangent to the curve $y=\int_{x^2}^{x^3}\frac{dt}{\sqrt{1+t^2}}$ at the point whose abscissa is 1, is
Application of Derivatives Tangents and Normals Equation of Tangent
MediumSingle correctNew ideaIdea asked in 2 years
Q71
If $y=y(x)$ is the solution of the differential equation, $\sqrt{1-e^{2x}}\,dy-\sqrt{4-y^2}\cdot e^{x}dx=0$ such that $y(0)=1$ , then $y(-\log_e 2)$ is equal to
Differential Equations Variable Separable Form Inverse Trigonometric Form Simplification
MediumSingle correctNew idea
Q72
If $(k, 3)$ is an interior point of the triangle formed by the lines, $x+y=4$ , $x-y=5$ and $x-2y+2=0$ , then the set of all values of k is the internal
Straight Lines Straight Line Distance Position of points relative to line
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q73
Consider a family of circles which pass through the point $(1, 1)$ and touch the axis of $y$ . If the centre of such a circle is at $(h, k)$ , then the set of all values of $h$ is the interval
Conic Sections Circle Tangents Family of Circles Touching a Line
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q74
The locus of the mid-points of the perpendiculars to the directrix of the parabola, $y^2=2x$ from points on it, is
Conic Sections
EasySingle correct
Q75
If the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the circle $x^2+y^2=4b$ intersect at an angle $\frac{\pi}{3}$ , then a value of 'b' is
Conic Sections Tangents and Normals Angle Between Curves
HardSingle correctNew idea
Q76
If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ , $\vec{b}=4\hat{i}-2\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$ are three vectors, then a vector of magnitude 6 units, which is parallel to the vector $2\vec{a}-\vec{b}+3\vec{c}$ , is
Vector Algebra
EasySingle correct
Q77
Four persons work independtly of each other on a task. If the probabilities that they will complete the task are : $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$ , then the probability, that at least one of them will complete it, is
Probability Conditional Probability Independence Criterion
EasySingle correctNew ideaIdea asked in 3 years
Q78
Two players A and B play a game. Player A first throws a fair die and if 5 or 6 appears, he wins; otherwise player B throws a fair coin and wins if head comes. The process continues till someone wins. The probability that B wins after completion of 3 or more…
Probability Conditional Probability Conditional Probability in Infinite Games
MediumSingle correctNew idea
Q79
Ten vertical poles of different height standing at equal distances on a straight line, subtend the same angle $30^{\mathrm{o}}$ at a point O on the line. If the height of the tallest pole is 12 units and the distance of the foot of the shortest pole from O…
Trigonometric Functions
HardSingle correct
Q80
If $r\in\{p, q, \sim p, \sim q\}$ such that the Boolean expression $(\sim(p\vee q))\vee(p\wedge r)$ is equivalent to $r$ , then $r$ is equal to
Mathematical Reasoning
MediumSingle correct
Q81
Let $p, q$ and $r$ be the first three terms of a G.P. such that $|p+q+r|=15$ , and the common ratio of this G.P. is negative. If $p<r$ and $q=10$ , then the product of the second and the fourth terms in it is ________.
Sequences and Series AP and GP GP General Term
MediumNumerical valueNew ideaIdea asked in 5 years
Q82
Let $M=(a_{ij})_{3\times3}$ , where $a_{ij}=\begin{cases}-1, & i=j\\ i^2-j^2, & i<j\\ 2i-j, & i>j\end{cases}$ $(i, j=1,2,3)$ If $X=\begin{bmatrix}1\\1\\1\end{bmatrix}$ , then value of $-X^TMX$ is ________. (Here, $X^T$ denotes transpose of $X$ ).
Matrices Matrix Multiplication Row-by-Column Multiplication
EasyNumerical valueNew ideaIdea asked in 2 years
Q83
Each of the numbers 1, 0, -1 is written on two different opposite faces of a six foces fair die. This die is thrown three times. The number of ways in which the sum of the numbers appearing is zero, is ________.
Permutations and Combinations Permutations with Repetition
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q84
If $f(x)=|3-x|+|2+x|+|5-x|$ , $x\in\mathbb{R}$ , then the minimum value of $f(x)$ is ______.
Relations and Functions Functions and Domain Range of Sum of Modulus Functions
EasyNumerical valueNew idea
Q85
The local minimum value of $\frac{(5+x)(2+x)}{(1+x)}$ , $(x\neq-1)$ , is ________.
Application of Derivatives Maxima and Minima Second Derivative Test
EasyNumerical valueNew idea
Q86
If $\int\left(\sqrt{\tan x}+\sqrt{\cot x}\right)dx=a\tan^{-1}\left(\frac{\tan x-1}{\sqrt{b\tan x}}\right)+\mathrm{C}$ , then the value of $a^4+b^5$ is ________. (Here, C is a constant of integration).
Integrals Integration by Substitution Twin Trigonometric Integrals Substitution
HardNumerical valueNew ideaIdea asked in 2 years
Q87
Maximum number of lines, through the origin which make equal angles with the three coordinate axes in XYZ-space, is ________.
Three Dimensional Geometry Angle Between Lines Angle with Coordinate Axes
EasyNumerical valueNew idea
Q88
If the distance between the point $(a, -1, 1)$ $(a>0)$ and the plane passing through the points $(1, -2, 1)$ , $(3, 1, 0)$ and $(2, 0, 1)$ is $\frac{7}{\sqrt{6}}$ , then the value of 'a' is ________.
Three Dimensional Geometry Planes in 3D Plane Through Three Points
MediumNumerical valueNew ideaIdea asked in 2 years
Q89
The number of points in $(0, 2\pi)$ , where the function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x)=|\sin x|+|\cos x|$ is NOT differentiable, is ________.
Continuity and Differentiability Differentiability of Modulus Functions
MediumNumerical valueNew ideaIdea asked in 5 years
Q90
If $\tan A$ is equal to the integral solution of the inequality $4x^2-24x+35<0$ and $\sin B$ is equal to the slope of the angle bisector of the second quadrant, then $40\sin(A+B)\sin(B-A)$ is ________.
Trigonometric Functions Trigonometric Identities Compound Angle Formulas
MediumNumerical valueIdea asked in 5 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.