JEE Main 2022 · July session

JEE Main 28 July 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 13 were rated hard and 25 easy. Its hard-question count was the joint 9th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 13; 14% of the shift
Chapters asked: 66; 15 questions with a figure

Key findings · 28 Jul 2022, Shift 2

1
13 hard questions (14%): the joint 9th highest count of the 24 2022 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 22%.
2
Maths was the hardest section, with 11 of 30 rated hard; Chemistry had the most easy questions (13 of 30).
3
28 questions tested a new idea, one no earlier year had asked: 40% of the 70 questions tagged to an idea.
4
35 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
31 shared an idea with another 2022 shift (44% 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 (3), The p-Block Elements in Chemistry (3) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 10Medium 20Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 13Medium 15Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 17Hard 11

Top chapters

Question format

Single correct45 Q
Numerical value30 Q
Assertion–reason5 Q
Two statements4 Q
Diagram based3 Q
Match the list2 Q
Other1 Q

What each question asks you to do

Calculation33 Q
Multi-step25 Q
Conceptual11 Q
Application11 Q
Recall6 Q
Data or graph4 Q

Most common: Calculation.

Against the other 2022 shifts

This shift next to the 23 other 2022 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 Jun, Shift 1	89	29%	17%	34%	31%	37%
24 Jun, Shift 2	90	40%	14%	33%	39%	36%
25 Jun, Shift 1	90	44%	13%	33%	33%	30%
25 Jun, Shift 2	90	30%	13%	33%	34%	22%
26 Jun, Shift 1	89	34%	16%	34%	37%	32%
26 Jun, Shift 2	90	30%	13%	33%	36%	27%
27 Jun, Shift 1	90	34%	8%	33%	38%	31%
27 Jun, Shift 2	90	32%	17%	33%	34%	46%
28 Jun, Shift 1	90	32%	12%	33%	38%	27%
28 Jun, Shift 2	90	30%	17%	33%	33%	31%
29 Jun, Shift 1	90	41%	11%	33%	36%	30%
29 Jun, Shift 2	88	35%	9%	33%	41%	30%
30 Jun, Shift 1	90	36%	13%	33%	27%	27%
25 Jul, Shift 1	88	28%	15%	33%	38%	38%
25 Jul, Shift 2	90	37%	12%	33%	33%	33%
26 Jul, Shift 1	90	27%	13%	33%	34%	31%
26 Jul, Shift 2	89	37%	16%	34%	41%	38%
27 Jul, Shift 1	89	29%	15%	34%	30%	32%
27 Jul, Shift 2	88	19%	15%	33%	40%	35%
28 Jul, Shift 1	90	36%	17%	33%	36%	30%
28 Jul, Shift 2	90	28%	14%	33%	40%	28%
29 Jul, Shift 1	90	31%	22%	33%	41%	37%
29 Jul, Shift 2	90	39%	12%	33%	48%	32%
30 Jul, Shift 2	90	30%	17%	33%	36%	33%

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

10 easy20 medium0 hard

Chemistry30 questions

13 easy15 medium2 hard

Q31
Given below are two statements : One is labelled as **Assertion A** and the other is labelled as **Reason R** **Assertion A** : Zero orbital overlap is an out of phase overlap. **Reason R** : It results due to different orientation / direction of approach of…
Chemical Bonding and Molecular Structure
MediumAssertion–reason
Q32
The correct decreasing order for metallic character is
Classification of Elements and Periodicity in Properties Periodic Trends Metallic and Non-Metallic Character Trends
EasySingle correctIdea asked in 3 yearsAsked the year before
Q33
Given below are two statements : One is labelled as **Assertion A** and the other is labelled as **Reason R** **Assertion A** : The reduction of a metal oxide is easier if the metal formed is in liquid state than solid state. **Reason R** : The value of…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Role of Entropy in Ellingham Slopes
MediumAssertion–reasonNew idea
Q34
The products obtained during treatment of hard water using Clark's method are :
Hydrogen Hydrogen and Hydrides Temporary Hardness and Clark's Method
EasySingle correctIdea asked in 2 yearsAsked the year before
Q35
**Statement I** : An alloy of lithium and magnesium is used to make aircraft plates. **Statement II** : The magnesium ions are important for cell-membrane integrity. In the light the above statements, choose the *correct* answer from the options given below
The s-Block Elements s-Block Elements Biological Role of Mg2+ and Ca2+
MediumTwo statementsNew idea
Q36
White phosphorus reacts with thionyl chloride to give
The p-Block Elements
MediumSingle correct
Q37
Concentrated $\mathrm{HNO_3}$ reacts with Iodine to give
The p-Block Elements Group 17 & 18 Oxidation of Iodine by Nitric Acid
EasySingle correctNew idea
Q38
Which of the following pair is not isoelectronic species? (At. no. Sm, 62; Er, 68; Yb, 70; Lu, 71; Eu, 63; Tb, 65; Tm, 69)
Structure of Atom Quantum Numbers Configurations of Isoelectronic Species
MediumSingle correctIdea asked in 2 years
Q39
Given below are two statements : One is labelled as **Assertion A** and the other is labelled as **Reason R** **Assertion A** : Permanganate titrations are not performed in presence of hydrochloric acid. **Reason R** : Chlorine is formed as a consequence of…
The d- and f-Block Elements d-Block Elements HCl Limitation in KMnO4 Titrations
EasyAssertion–reasonIdea asked in 2 years
Q40
Match **List I** with **List II** List I (Complex) | List II (Hybridization) A. $\mathrm{Ni(CO)_4}$ | I. $sp^3$ B. $\mathrm{[Ni\,(CN)_4]^{2-}}$ | II. $sp^3d^2$ C. $\mathrm{[Co\,(CN)_6]^{3-}}$ | III. $d^2sp^3$ D. $\mathrm{[CoF_6]^{3-}}$ | IV. $dsp^2$ Choose…
Coordination Compounds
MediumMatch the list
Q41
Dinitrogen and dioxygen, the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because
The p-Block Elements
EasySingle correct
Q42
The major product in the given reaction is [reaction: line structure of an unsaturated tertiary alcohol, alkene with two methyl groups at the left end and a tertiary carbon bearing OH at the right end]…
Alcohols, Phenols and Ethers
HardDiagram based · figure
Q43
Arrange the following in increasing order of reactivity towards nitration A. p-xylene B. bromobenzene C. mesitylene D. nitrobenzene E. benzene Choose the correct answer from the options given below
Hydrocarbons Aromatic Hydrocarbons Ranking Activating Groups
MediumSingle correctNew ideaIdea asked in 3 years
Q44
Compound I is heated with Conc. HI to give a hydroxy compound A which is further heated with Zn dust to give compound B. Identify A and B. [Compound I: isopropyl phenyl ether, drawn as a benzene ring bonded to O, which is bonded to an isopropyl group]…
Alcohols, Phenols and Ethers Ethers Cleavage of Alkyl-Aryl Ethers
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q45
Given below are two statements : one is labelled as **Assertion A** and the other is labelled as **Reason R** **Assertion A** : Aniline on nitration yields ortho, meta & para nitro derivatives of aniline. **Reason R** : Nitrating mixture is a strong acidic…
Amines Direct Nitration of Aniline
MediumAssertion–reasonIdea asked in 2 yearsAsked the year before
Q46
Match **List I** with **List II** List I (Polymer) | List II (Nature) A. $-\left[\mathrm{CH_2-C(Cl)=CH-CH_2}\right]_n-$ | I. Thermosetting polymer B. $-\left[\mathrm{NH-(CH_2)_6-NH-C(=O)-(CH_2)_4-C(=O)}\right]_n-$ | II. Fibers C.…
Polymers Polymer Classification
MediumMatch the list · figureIdea asked in 3 yearsAsked the year before
Q47
Two statements in respect of drug-enzyme interaction are given below **Statement I :** Action of an enzyme can be blocked only when an inhibitor blocks the active site of the enzyme. **Statement II :** An inhibitor can form a strong covalent bond with the…
Chemistry in Everyday Life Competitive vs Allosteric Enzyme Inhibition
EasyTwo statementsIdea asked in 2 yearsAsked the year before
Q48
Given below are two statements : One is labelled as **Assertion A** and the other is labelled as **Reason R** **Assertion A** : Thin layer chromatography is an adsorption chromatography. **Reason R** : A thin layer of silica gel is spread over a glass plate…
Organic Chemistry: Some Basic Principles and Techniques Adsorption Adsorption Chromatography Principle
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q49
The formulas of A and B for the following reaction sequence Fructose $\xrightarrow[\mathrm{H_3O^+}]{\mathrm{HCN}}$ A Fructose $\xrightarrow[\text{(ii) HI/P}]{\text{(i) } \mathrm{NaBH_4}}$ B are
Biomolecules Carbohydrates Carbonyl Addition Reactions in Glucose
MediumOther · figureNew idea
Q50
[Structure: cyclohexene ring bearing a -CH2-C(=O)OH side chain on an alkene carbon (ring C=C adjacent to the CH2COOH-bearing carbon)] $\xrightarrow{(1)\ \mathrm{I_2/\,NaHCO_3};\ (2)\ \text{Pyridine},\ \Delta}$ Find out the major product for the above reaction.
Aldehydes, Ketones and Carboxylic Acids
HardDiagram based · figure
Q51
2L of 0.2M $\mathrm{H_2SO_4}$ is reacted with 2L of 0.1M NaOH solution, the molarity of the resulting product $\mathrm{Na_2SO_4}$ in the solution is ______ millimolar. (Nearest integer )
Some Basic Concepts of Chemistry Mole Concept Molarity of Diluted and Mixed Solutions
EasyNumerical valueNew ideaIdea asked in 2 years
Q52
Metal M crystallizes into a fcc lattice with the edge length of $4.0\times10^{-8}$ cm. The atomic mass of the metal is ______ g/mol. (Nearest integer) (Use : $\mathrm{N_A}=6.02\times10^{23}\ \mathrm{mol^{-1}}$ , density of metal, M $=9.03\mathrm{g\ cm^{-3}}$ )
The Solid State Crystal Lattices Unit Cell Density
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q53
If the wavelength for an electron emitted from H-atom is $3.3\times10^{-10}$ m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is ______ times. (Nearest integer) [Given : h =…
Structure of Atom Bohr's Atomic Theory Ionization and Excitation Energy
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q54
A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is…
Solutions
MediumNumerical value
Q55
At 600K, 2 mol of NO are mixed with 1 mol of $\mathrm{O_2}$ . $\mathrm{2NO_{(g)}+O_2\,(g)\rightleftharpoons 2NO_2(g)}$ The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen…
Equilibrium Chemical Equilibrium Kp Expression via Partial Pressures
MediumNumerical valueNew ideaIdea asked in 2 years
Q56
A sample of 0.125g of an organic compound when analyzed by Duma's method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is ______. (Nearest integer) Given : (a) The…
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Dumas Method
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q57
On reaction with stronger oxidizing agent like $\mathrm{KIO_4}$ , hydrogen peroxide oxidizes with the evolution of $\mathrm{O_2}$ . The oxidation number of I in $\mathrm{KIO_4}$ changes to ______.
Redox Reactions Hydrogen and Hydrides Redox Behavior of Hydrogen Peroxide
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q58
For a reaction, given below is the graph of ln k vs $\frac{1}{T}$ . The activation energy for the reaction is equal to ______ cal $\mathrm{mol^{-1}}$ . (nearest integer) (Given : R = 2 cal $\mathrm{K^{-1}\ mol^{-1}}$ )
Chemical Kinetics Arrhenius Equation Log Base 10 Arrhenius Plot Slope
EasyNumerical value · figureIdea asked in 4 yearsAsked the year before
Q59
Among the following the number of curves not in accordance with Freundlich adsorption isotherm is ________. (a) plot of log(x/m) (y-axis) against log P (x-axis) (b) plot of log(x/m) (y-axis) against P (x-axis) (c) plot of log(x/m) (y-axis) against P (x-axis)…
Surface Chemistry Adsorption Freundlich Logarithmic Plot
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q60
Among the following the number of state variables is ______. Internal energy (U) Volume (V) Heat (q) Enthalpy (H)
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy as a State Function
EasyNumerical valueNew idea

Maths30 questions

2 easy17 medium11 hard

Q61
Let $S=\left\{x\in[-6,3]-\{-2,2\}:\frac{|x+3|-1}{|x|-2}\geq 0\right\}$ and $T=\left\{x\in\mathbb{Z}:x^2-7|x|+9\leq 0\right\}$ . Then the number of elements in S $\cap$ T is :
Relations and Functions
MediumSingle correct
Q62
Let $\alpha,\beta$ be the roots of the equation $x^2-\sqrt{2}\,x+\sqrt{6}=0$ and $\frac{1}{\alpha^2}+1,\ \frac{1}{\beta^2}+1$ be the roots of the equation $x^2+ax+b=0$ . Then the roots of the equation $x^2-(a+b-2)x+(a+b+2)=0$ are :
Complex Numbers and Quadratic Equations Quadratic Roots Transformation of Roots
MediumSingle correctNew ideaIdea asked in 2 years
Q63
Let A and B be any two $3\times 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?
Matrices Matrix Multiplication Product of Symmetric Matrices
MediumSingle correctNew idea
Q64
Let $f(x)=ax^2+bx+c$ be such that $f(1)=3,\ f(-2)=\lambda$ and $f(3)=4$ . If $f(0)+f(1)+f(-2)+f(3)=14$ , then $\lambda$ is equal to :
Complex Numbers and Quadratic Equations
MediumSingle correct
Q65
The function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=\lim_{n\to\infty}\frac{\cos(2\pi x)-x^{2n}\sin(x-1)}{1+x^{2n+1}-x^{2n}}$ is continuous for all $x$ in :
Continuity and Differentiability Functions Defined by Infinite Limits
HardSingle correctNew idea
Q66
The function $f(x)=xe^{x(1-x)},\ x\in\mathbb{R}$ , is :
Application of Derivatives Monotonicity Finding Intervals
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q67
The sum of the absolute maximum and absolute minimum values of the function $f(x)=\tan^{-1}(\sin x-\cos x)$ in the interval $[0,\ \pi]$ is :
Application of Derivatives Maxima and Minima Closed Interval Extrema
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q68
Let $x(t)=2\sqrt{2}\cos t\sqrt{\sin 2t}$ and $y(t)=2\sqrt{2}\sin t\sqrt{\sin 2t},\ t\in\left(0,\frac{\pi}{2}\right)$ . Then $\frac{1+\left(\frac{dy}{dx}\right)^2}{\frac{d^2y}{dx^2}}$ at $t=\frac{\pi}{4}$ is equal to :
Continuity and Differentiability Chain Rule Chain Rule in Parametric Differentiation
HardSingle correctNew idea
Q69
Let $I_n(x)=\int_0^x\frac{1}{(t^2+5)^n}dt,\ n=1,2,3,....$ Then :
Integrals Integration by Parts Algebraic Reduction Formulas
HardSingle correctIdea asked in 3 yearsAsked the year before
Q70
The area enclosed by the curves $y=\log_e(x+e^2)$ , $x=\log_e\left(\frac{2}{y}\right)$ and $x=\log_e 2$ , above the line $y=1$ is :
Application of Integrals Area Under Curves Exponential and Logarithmic Bounded Regions
HardSingle correctNew idea
Q71
Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx}+\frac{1}{x^2-1}y=\left(\frac{x-1}{x+1}\right)^{1/2},\ x>1$ passing through the point $\left(2,\sqrt{\frac{1}{3}}\right)$ . Then $\sqrt{7}\,y(8)$ is equal to :
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q72
The differential equation of the family of circles passing through the points $(0,2)$ and $(0,-2)$ is :
Differential Equations
MediumSingle correct
Q73
Let the tangents at two points A and B on the circle $x^2+y^2-4x+3=0$ meet at origin O (0, 0). Then the area of the triangle OAB is :
Conic Sections Circle Tangents Area of Tangent-Chord Triangle
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q74
Let the hyperbola $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ pass through the point $(2\sqrt{2},-2\sqrt{2})$ . A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H.…
Conic Sections
HardSingle correct
Q75
Let the lines $\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?
Three Dimensional Geometry Skew Lines Coplanarity Determinant Test
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q76
A plane P is parallel to two lines whose direction ratios are $-2,\ 1,\ -3$ and $-1,\ 2,\ -2$ and it contains the point $(2,\ 2,\ -2)$ . Let P intersect the co-ordinate axes at the points A, B, C making the intercepts $\alpha,\ \beta,\ \gamma$ . If V is the…
Three Dimensional Geometry Planes in 3D Plane Through Point Parallel to Two Vectors
MediumSingle correctNew idea
Q77
Let S be the set of all $a\in\mathbb{R}$ for which the angle between the vectors $\vec{u}=a(\log_e b)\hat{i}-6\hat{j}+3\hat{k}$ and $\vec{v}=(\log_e b)\hat{i}+2\hat{j}+2a(\log_e b)\hat{k},\ (b>1)$ is acute. Then S is equal to :
Vector Algebra Dot Product Acute and Obtuse Angle Conditions
MediumSingle correctNew ideaIdea asked in 2 years
Q78
A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that $\angle PAO=\angle PBO=15^0$ and $\angle PCO=45^0$ , where C is the midpoint of AB.Then $(OP)^2$ is equal to
Trigonometric Functions
HardSingle correct
Q79
Let A and B be two events such that $P(B|A)=\frac{2}{5},\ P(A|B)=\frac{1}{7}$ and $P(A\cap B)=\frac{1}{9}$ . Consider (S1) $P(A'\cup B)=\frac{5}{6}$ , (S2) $P(A'\cap B')=\frac{1}{18}$ Then
Probability Conditional Probability Conditional Probability with De Morgan's Laws
MediumTwo statementsNew idea
Q80
Let p : Ramesh listens to music. q : Ramesh is out of his village. r : It is Sunday. s : It is Saturday. Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as
Mathematical Reasoning
EasySingle correct
Q81
Let the coefficients of the middle terms in the expansion of $\left(\frac{1}{\sqrt{6}}+\beta x\right)^4,\ (1-3\beta x)^2$ and $\left(1-\frac{\beta}{2}x\right)^6,\ \beta>0$ , respectively form the first three terms of an A.P. If d is the common difference of…
Binomial Theorem
MediumNumerical value
Q82
A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g is equal to _______.
Permutations and Combinations Combinations of Distinct Objects
EasyNumerical valueIdea asked in 8 yearsAsked the year before
Q83
Let the tangents at the points P and Q on the ellipse $\frac{x^2}{2}+\frac{y^2}{4}=1$ meet at the point $R(\sqrt{2},2\sqrt{2}-2)$ . If S is the focus of the ellipse on its negative major axis, then $SP^2+SQ^2$ is equal to ________.
Conic Sections Ellipse Eccentricity Focal distance property
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q84
If $1+(2+{}^{49}C_1+{}^{49}C_2+...+{}^{49}C_{49})({}^{50}C_2+{}^{50}C_4+...+{}^{50}C_{50})$ is equal to $2^n\cdot m$ , where m is odd, then n + m is equal to _______.
Binomial Theorem Binomial Coefficients Sum of all Coefficients
MediumNumerical valueIdea asked in 4 years
Q85
Two tangent lines $l_1$ and $l_2$ are drawn from the point (2, 0) to the parabola $2y^2=-x$ . If the lines $l_1$ and $l_2$ are also tangent to the circle $(x-5)^2+y^2=r$ , then 17r is equal to_______.
Conic Sections Circle Tangents Common Tangent to Circle and Conic
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q86
If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+...+\frac{10240}{3}=2^n\cdot m$ , where m is odd, then $m\cdot n$ is equal to ______.
Sequences and Series AP and GP GP Sum of n terms
MediumNumerical valueIdea asked in 5 years
Q87
Let $S=\left[-\pi,\frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3\pi}{4},\frac{\pi}{4}\right\}$ . Then the number of elements in the set $A=\left\{\theta\in S:\tan\theta\left(1+\sqrt{5}\tan(2\theta)\right)=\sqrt{5}-\tan(2\theta)\right\}$ is…
Trigonometric Functions General Solutions Tangent General Solution
HardNumerical valueNew idea
Q88
Let $z=a+ib,\ b\neq 0$ be complex numbers satisfying $z^2=\bar{z}\cdot 2^{1-|z|}$ . Then the least value of $n\in\mathbb{N}$ , such that $z^n=(z+1)^n$ , is equal to _______.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q89
A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If $\sigma^2$ is the variance of X, then $100\sigma^2$ is equal to ________.
Probability
MediumNumerical value
Q90
The value of the integral $\int_0^{\pi/2}60\frac{\sin(6x)}{\sin x}dx$ is equal to ________.
Integrals
MediumNumerical 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 2022 shifts.