JEE Main 2022 · June session

JEE Main 29 June 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 37 easy. Its hard-question count was the 22nd highest of the 24 2022 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: 72; 9 questions with a figure

Key findings · 29 Jun 2022, Shift 1

1
10 hard questions (11%): the 22nd 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 7 of 30 rated hard; Physics had the most easy questions (18 of 30).
3
27 questions tested a new idea, one no earlier year had asked: 36% of the 76 questions tagged to an idea.
4
44 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
47 shared an idea with another 2022 shift (62% 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 Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 18Medium 11Hard 1

Top chapters

Current Electricity3 Q
System of Particles and Rotational Motion2 Q
Thermodynamics2 Q
Alternating Current1 Q
Atoms1 Q
Communication Systems1 Q

Chemistry

30 Q · 10 numerical

Easy 15Medium 13Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 4Medium 19Hard 7

Top chapters

Question format

Single correct50 Q
Numerical value30 Q
Other5 Q
Match the list2 Q
Two statements2 Q
Assertion–reason1 Q

What each question asks you to do

Calculation33 Q
Multi-step27 Q
Application11 Q
Recall9 Q
Conceptual8 Q
Data or graph1 Q
Diagram reading1 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

18 easy11 medium1 hard

Chemistry30 questions

15 easy13 medium2 hard

Q61
Production of iron in blast furnace follows the following equation $\mathrm{Fe_3O_4(s) + 4CO(g) \rightarrow 3Fe(l) + 4CO_2(g)}$ when 4.640 kg of $\mathrm{Fe_3O_4}$ and 2.520 kg of CO are allowed to react then the amount of iron (in g) produced is : [Given :…
Some Basic Concepts of Chemistry Stoichiometry Limiting Reagent Identification
EasySingle correctIdea asked in 4 yearsAsked the year before
Q62
Which of the following statements are correct ? (A) The electronic configuration of Cr is [Ar] $3d^5\,4s^1$ . (B) The magnetic quantum number may have a negative value. (C) In the ground state of an atom, the orbitals are filled in order of their increasing…
Structure of Atom Quantum Numbers Anomalous Electron Configurations
EasyOtherNew ideaIdea asked in 4 years
Q63
Arrange the following in the decreasing order of their covalent character : (A) LiCl (B) NaCl (C) KCl (D) CsCl Choose the most appropriate answer from the options given below :
Chemical Bonding and Molecular Structure s-Block Elements Covalent Character in Halides
EasyOtherNew ideaIdea asked in 2 years
Q64
The solubility of AgCl will be maximum in which of the following ?
Equilibrium Solubility Product Common Ion Effect
EasySingle correctIdea asked in 4 yearsAsked the year before
Q65
Which of the following is a correct statement ?
Surface Chemistry Colloids Lyophilic and Lyophobic Sols
EasySingle correctIdea asked in 3 yearsAsked the year before
Q66
The electronic configuration of Pt (atomic number 78) is :
The d- and f-Block Elements d-Block Elements Electronic Configuration
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q67
In isolation of which one of the following metals from their ores, the use of cyanide salt is not commonly involved ?
General Principles and Processes of Isolation of Elements Metallurgical Extraction MacArthur-Forrest Cyanide Process
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q68
Which one of the following reactions indicates the reducing ability of hydrogen peroxide in basic medium ?
Hydrogen Hydrogen and Hydrides Redox Behavior of Hydrogen Peroxide
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q69
Match List - I with List - II. List - I (Metal) (A) Li (B) Na (C) Rb (D) Cs List - II (Emitted light wavelength (nm)) (I) 670.8 (II) 589.2 (III) 780.0 (IV) 455.5 Choose the most appropriate answer from the options given below :
The s-Block Elements s-Block Elements Flame Coloration
HardMatch the listIdea asked in 4 yearsAsked the year before
Q70
Match List - I with List - II. List - I (Metal) (A) Cs (B) Ga (C) B (D) Si List - II (Application) (I) High temperature thermometer (II) Water repellent sprays (III) Photoelectric cells (IV) Bullet proof vest Choose the most appropriate answer from the…
The p-Block Elements Group 13 & 14 Silicones and Zeolites
MediumMatch the listIdea asked in 2 yearsAsked the year before
Q71
The oxoacid of phosphorus that is easily obtained from a reaction of alkali and white phosphorus and has two P-H bonds, is :
The p-Block Elements Group 15 & 16 Phosphorus Oxoacids
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q72
The acid that is believed to be mainly responsible for the damage of Taj Mahal is
Environmental Chemistry Acid Rain Mechanism
EasySingle correctIdea asked in 4 yearsAsked the year before
Q73
Two isomers 'A' and 'B' with molecular formula $\mathrm{C_4H_8}$ give different products on oxidation with $\mathrm{KMnO_4}$ in acidic medium. Isomer 'A' on reaction with $\mathrm{KMnO_4/H^+}$ results in effervescence of a gas and gives ketone. The compound…
Hydrocarbons Alkenes and Alkynes Oxidative Cleavage with Hot KMnO4
MediumSingle correctNew idea
Q74
[reaction scheme: 2-bromophenol $\xrightarrow{(\mathrm{CH_3})_3\mathrm{CLi}}$ [A] $\xrightarrow{\text{(i) } \mathrm{CO_2}\text{, (ii) } \mathrm{H_3O^+}}$ salicylic acid (2-hydroxybenzoic acid)] In the given conversion the compound A is :
Haloalkanes and Haloarenes
HardOther · figure
Q75
Given below are two statements : Statement I : The esterification of carboxylic acid with an alcohol is a nucleophilic acyl substitution. Statement II : Electron withdrawing groups in the carboxylic acid will increase the rate of esterification reaction.…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Fischer Esterification
MediumTwo statementsIdea asked in 3 years
Q76
[reactions: aniline $\xrightarrow[\mathrm{H_2O}]{\mathrm{Br_2\,(excess)}}$ A (Major Product); aniline $\xrightarrow{\text{(i) }(\mathrm{CH_3CO})_2\mathrm{O}\text{; (ii) }\mathrm{Br_2,\,CH_3COOH}\text{; (iii) HCl}}$ B (Major Product)] Consider the above…
Amines Aqueous Bromination of Aniline
EasyOther · figureNew idea
Q77
The polymer, which can be stretched and retains its original status on releasing the force is
Polymers Polymer Classification
EasySingle correctIdea asked in 3 yearsAsked the year before
Q78
Sugar moiety in DNA and RNA molecules respectively are
Biomolecules
EasySingle correct
Q79
Which of the following compound does not contain sulfur atom ?
Chemistry in Everyday Life
EasySingle correct
Q80
Given below are two statements. Statement I : Phenols are weakly acidic. Statement II : Therefore they are freely soluble in NaOH solution and are weaker acids than alcohols and water. Choose the most appropriate option :
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
EasyTwo statementsNew ideaIdea asked in 3 years
Q81
Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is $0.46\ \mathrm{gL^{-1}}$ at $257^\circ\mathrm{C}$ and 100 mm Hg. The molar mass of geraniol is ____________ $\mathrm{g\ mol^{-1}}$ . (Nearest Integer) [Given :…
States of Matter Ideal Gas Laws Gas Density and Molar Mass
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q82
17.0 g of $\mathrm{NH_3}$ completely vapourises at $-33.42^\circ\mathrm{C}$ and 1 bar pressure and the enthalpy change in the process is $23.4\ \mathrm{kJ\ mol^{-1}}$ . The enthalpy change for the vapourisation of 85 g of $\mathrm{NH_3}$ under the same…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy of Phase Transitions
EasyNumerical valueNew ideaIdea asked in 2 years
Q83
1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in freezing point observed for this strength of acid is $0.0198^\circ\mathrm{C}$ . The percentage of dissociation of the acid is ____________. (Nearest integer) [Given :…
Solutions Colligative Properties Calculating Ka from Freezing Point Depression
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q84
A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced at STP is ____________ $\mathrm{cm^3}$ . (Nearest integer) [Given : Faraday constant…
Electrochemistry Faraday's Laws of Electrolysis Gas Evolution Volume
MediumNumerical valueIdea asked in 3 years
Q85
The activation energy of one of the reactions in a biochemical process is $532611\ \mathrm{J\ mol^{-1}}$ . When the temperature falls from 310 K to 300 K, the change in rate constant observed is $k_{300} = x \times 10^{-3}\ k_{310}$ . The value of $x$ is…
Chemical Kinetics Arrhenius Equation Two-Point Arrhenius Equation
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q86
The number of terminal oxygen atoms present in the product B obtained from the following reaction is ____________. $\mathrm{FeCr_2O_4 + Na_2CO_3 + O_2 \rightarrow A + Fe_2O_3 + CO_2}$ $\mathrm{A + H^+ \rightarrow B + H_2O + Na^+}$
The d- and f-Block Elements d-Block Elements Preparation Steps of Potassium Dichromate
MediumNumerical valueNew ideaIdea asked in 3 years
Q87
An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation state is ____________ B.M. (Nearest integer)
The d- and f-Block Elements d-Block Elements Disproportionation of Manganate(VI)
MediumNumerical valueNew ideaIdea asked in 2 years
Q88
Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from 0.55 g of the compound neutralised 12.5 mL of 1 M $\mathrm{H_2SO_4}$ solution. The percentage of nitrogen in the compound is ____________. (Nearest…
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q89
Observe structures of the following compounds [figure: five structures] The total number of structures/compounds which possess asymmetric carbon atoms is ____________.
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Chiral Centers
EasyNumerical value · figureIdea asked in 5 years
Q90
$\mathrm{C_6H_{12}O_6 \xrightarrow{Zymase} A \xrightarrow[\Delta]{NaOI} B + CHI_3}$ The number of carbon atoms present in the product B is ____________.
Alcohols, Phenols and Ethers Alcohols and Phenols Iodoform Test for Specific Alcohols
EasyNumerical valueNew ideaIdea asked in 4 years

Maths30 questions

4 easy19 medium7 hard

Q1
The probability that a randomly chosen $2\times 2$ matrix with all the entries from the set of first 10 primes, is singular, is equal to :
Probability
HardSingle correct
Q2
Let the solution curve of the differential equation $x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}$ , $y(1) = 3$ be $y = y(x)$ . Then $y(2)$ is equal to :
Differential Equations Homogeneous Equations Substitution y = vx
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
If the mirror image of the point $(2, 4, 7)$ in the plane $3x - y + 4z = 2$ is $(a, b, c)$ , then $2a + b + 2c$ is equal to :
Three Dimensional Geometry Point-Plane Distance Image of a Point
EasySingle correctIdea asked in 4 yearsAsked the year before
Q4
Let $f: \mathbf{R} \to \mathbf{R}$ be a function defined by : $f(x) = \begin{cases} \max_{t \le x}\{t^3 - 3t\} & ; \; x \le 2 \\ x^2 + 2x - 6 & ; \; 2 < x < 3 \\ [x - 3] + 9 & ; \; 3 \le x \le 5 \\ 2x + 1 & ; \; x > 5 \end{cases}$ where $[t]$ is the greatest…
Continuity and Differentiability Piecewise Differentiability
HardSingle correctIdea asked in 4 yearsAsked the year before
Q5
Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$ , $\vec{b} = 3\hat{i} - \beta\hat{j} + 4\hat{k}$ and $\vec{c} = \hat{i} + 2\hat{j} - 2\hat{k}$ where $\alpha, \beta \in \mathbf{R}$ , be three vectors. If the projection of $\vec{a}$ on $\vec{c}$ is…
Vector Algebra Dot Product Scalar and Vector Projection
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q6
The area enclosed by $y^2 = 8x$ and $y = \sqrt{2}\,x$ that lies outside the triangle formed by $y = \sqrt{2}\,x$ , $x = 1$ , $y = 2\sqrt{2}$ , is equal to :
Application of Integrals Area Under Curves Area Between Curves
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q7
If the system of linear equations $2x + y - z = 7$ $x - 3y + 2z = 1$ $x + 4y + \delta z = k$ , where $\delta, k \in \mathbf{R}$ has infinitely many solutions, then $\delta + k$ is equal to :
Determinants Cramer's Rule Evaluating Parameters for Consistency
EasySingle correctIdea asked in 6 yearsAsked the year before
Q8
Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + (2i - 1) = 0$ . Then, the value of $|\alpha^8 + \beta^8|$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q9
Let $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q)\,\Delta\,((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to :
Mathematical Reasoning
EasySingle correct
Q10
Let $A = [a_{ij}]$ be a square matrix of order 3 such that $a_{ij} = 2^{j-i}$ , for all $i, j = 1, 2, 3$ . Then, the matrix $A^2 + A^3 + \ldots + A^{10}$ is equal to :
Matrices Matrix Multiplication Powers of Square Matrices
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q11
Let a set $A = A_1 \cup A_2 \cup \ldots \cup A_k$ , where $A_i \cap A_j = \phi$ for $i \ne j$ , $1 \le i, j \le k$ . Define the relation R from A to A by $R = \{(x, y) : y \in A_i$ if and only if $x \in A_i$ , $1 \le i \le k\}$ . Then, R is :
Relations and Functions Sets and Relations Equivalence Relations
EasySingle correctIdea asked in 4 yearsAsked the year before
Q12
Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0 = a_1 = 0$ and $a_{n+2} = 2a_{n+1} - a_n + 1$ for all $n \ge 0$ . Then, $\sum_{n=2}^{\infty} \frac{a_n}{7^n}$ is equal to :
Sequences and Series Arithmetico-Geometric Series AGP Recurrence Relation
MediumSingle correctNew ideaIdea asked in 2 years
Q13
The distance between the two points A and A' which lie on $y = 2$ such that both the line segments AB and A'B (where B is the point $(2, 3)$ ) subtend angle $\frac{\pi}{4}$ at the origin, is equal to :
Straight Lines
MediumSingle correct
Q14
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the…
Application of Derivatives Maxima and Minima Optimization Problems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q15
The domain of the function $\cos^{-1}\left(\frac{2\sin^{-1}\left(\frac{1}{4x^2 - 1}\right)}{\pi}\right)$ is :
Inverse Trigonometric Functions Inverse Trig Domains Domain of Rational Composite Inverse Trig
MediumSingle correctNew idea
Q16
If the constant term in the expansion of $\left(3x^3 - 2x^2 + \frac{5}{x^5}\right)^{10}$ is $2^k \cdot l$ , where $l$ is an odd integer, then the value of $k$ is equal to :
Binomial Theorem
HardSingle correct
Q17
$\int_0^5 \cos\left(\pi\left(x - \left[\frac{x}{2}\right]\right)\right)dx$ , where $[t]$ denotes greatest integer less than or equal to $t$ , is equal to :
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q18
Let PQ be a focal chord of the parabola $y^2 = 4x$ such that it subtends an angle of $\frac{\pi}{2}$ at the point $(3, 0)$ . Let the line segment PQ be also a focal chord of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ , $a^2 > b^2$ . If $e$ is the…
Conic Sections Parabola Focal Chords Equation of focal chord
HardSingle correctNew ideaIdea asked in 2 years
Q19
Let the tangent to the circle $C_1: x^2 + y^2 = 2$ at the point $M(-1, 1)$ intersect the circle $C_2: (x - 3)^2 + (y - 2)^2 = 5$ , at two distinct points A and B. If the tangents to $C_2$ at the points A and B intersect at N, then the area of the triangle ANB…
Conic Sections Circle Tangents Area of Tangent-Chord Triangle
HardSingle correctIdea asked in 2 yearsAsked the year before
Q20
Let the mean and the variance of 5 observations $x_1, x_2, x_3, x_4, x_5$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first 4 observation are $\frac{7}{2}$ and $a$ respectively, then $(4a + x_5)$ is equal to :
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q21
Let $S = \{z \in \mathbf{C} : |z - 2| \le 1, z(1 + i) + \bar{z}(1 - i) \le 2\}$ . Let $|z - 4i|$ attains minimum and maximum values, respectively, at $z_1 \in S$ and $z_2 \in S$ . If $5(|z_1|^2 + |z_2|^2) = \alpha + \beta\sqrt{5}$ , where $\alpha$ and $\beta$ …
Complex Numbers and Quadratic Equations
HardNumerical value
Q22
Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + \frac{\sqrt{2}y}{2\cos^4 x - \cos 2x} = xe^{\tan^{-1}(\sqrt{2}\cot 2x)}$ , $0 < x < \frac{\pi}{2}$ with $y\left(\frac{\pi}{4}\right) = \frac{\pi^2}{32}$ . If…
Differential Equations Linear Differential Equations Inverse Trigonometric Integrating Factors
HardNumerical valueNew idea
Q23
Let $d$ be the distance between the foot of perpendiculars of the points $P(1, 2, -1)$ and $Q(2, -1, 3)$ on the plane $-x + y + z = 1$ . Then $d^2$ is equal to ____________.
Three Dimensional Geometry Point-Plane Distance Foot of Perpendicular
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q24
The number of elements in the set $S = \{\theta \in [-4\pi, 4\pi] : 3\cos^2 2\theta + 6\cos 2\theta - 10\cos^2\theta + 5 = 0\}$ is ____________.
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q25
The number of solutions of the equation $2\theta - \cos^2\theta + \sqrt{2} = 0$ in $\mathbf{R}$ is equal to ____________.
Trigonometric Functions General Solutions Graphical Root Counting for Mixed Equations
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q26
$50\tan\left(3\tan^{-1}\left(\frac{1}{2}\right) + 2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right) + 4\sqrt{2}\tan\left(\frac{1}{2}\tan^{-1}(2\sqrt{2})\right)$ is equal to ____________.
Inverse Trigonometric Functions Inverse Trig Identities Trig of Sum of Inverse Trig Functions
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q27
Let $c, k \in \mathbf{R}$ . If $f(x) = (c + 1)x^2 + (1 - c^2)x + 2k$ and $f(x + y) = f(x) + f(y) - xy$ , for all $x, y \in \mathbf{R}$ , then the value of $|2(f(1) + f(2) + f(3) + \ldots\ldots + f(20))|$ is equal to ____________.
Relations and Functions
MediumNumerical value
Q28
Let $H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , $a > 0, b > 0$ , be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt{2} + \sqrt{14})$ . If the eccentricity H is $\frac{\sqrt{11}}{2}$ , then the value of $a^2 + b^2$ …
Conic Sections
MediumNumerical value
Q29
Let $P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4$ be a plane. Let $P_2$ be another plane which passes through the points $(2, -3, 2)$ , $(2, -2, -3)$ and $(1, -4, 2)$ . If the direction ratios of the line of intersection of $P_1$ and $P_2$ be…
Three Dimensional Geometry Planes in 3D Direction of Line of Intersection
MediumNumerical valueNew idea
Q30
Let $b_1b_2b_3b_4$ be a 4-element permutation with $b_i \in \{1, 2, 3, \ldots\ldots, 100\}$ for $1 \le i \le 4$ and $b_i \ne b_j$ for $i \ne j$ , such that either $b_1, b_2, b_3$ are consecutive integers or $b_2, b_3, b_4$ are consecutive integers. Then the…
Permutations and Combinations Permutations of Distinct Objects
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 2022 shifts.