JEE Main 2022 · June session

JEE Main 29 June 2022, Shift 2

88 questions (2 more dropped by NTA): 29 numerical-answer and 59 multiple choice. 8 were rated hard and 31 easy. Its hard-question count was the 23rd highest of the 24 2022 shifts Lumi analysed. The biggest chapter was The p-Block Elements, with 3 questions.

Questions: 88; 2 dropped by NTA
Numerical answer: 29; 33% of the shift
Hard: 8; 9% of the shift
Chapters asked: 71; 9 questions with a figure

Key findings · 29 Jun 2022, Shift 2

1
8 hard questions (9%): the 23rd 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 28 rated hard; Physics had the most easy questions (15 of 30).
3
31 questions tested a new idea, one no earlier year had asked: 41% of the 75 questions tagged to an idea.
4
40 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
42 shared an idea with another 2022 shift (56% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), The p-Block Elements in Chemistry (3) and Application of Derivatives in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 15Hard 0

Top chapters

Current Electricity2 Q
Electrostatic Potential and Capacitance2 Q
Laws of Motion2 Q
Moving Charges and Magnetism2 Q
Nuclei2 Q
Alternating Current1 Q

Chemistry

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Maths

28 Q · 9 numerical

Easy 1Medium 20Hard 7

Top chapters

Question format

Single correct48 Q
Numerical value29 Q
Diagram based6 Q
Two statements2 Q
Assertion–reason2 Q
Match the list1 Q

What each question asks you to do

Calculation29 Q
Multi-step26 Q
Application14 Q
Conceptual11 Q
Recall6 Q
Data or graph2 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
Open28 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 88 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

88 of 88 questions

Physics30 questions

15 easy15 medium0 hard

Chemistry30 questions

15 easy14 medium1 hard

Q61
Using the rules for significant figures, the correct answer for the expression $\frac{0.02858 \times 0.112}{0.5702}$ will be
Some Basic Concepts of Chemistry
EasySingle correct
Q62
Which of the following is the correct plot for the probability density $\Psi^2$ $(r)$ as a function of distance 'r' of the electron from the nucleus for 2s orbital?
Structure of Atom Quantum Numbers Interpreting Radial Wavefunction Graphs
MediumDiagram based · figureNew idea
Q63
Consider the species $\mathrm{CH_4}$ , $\mathrm{NH_4^{+}}$ and $\mathrm{BH_4^{-}}$ . Choose the correct option with respect to the there species.
Chemical Bonding and Molecular Structure VSEPR Theory Isoelectronic and Isostructural Principle
EasySingle correctNew ideaIdea asked in 2 years
Q64
4.0 moles of argon and 5.0 moles of $\mathrm{PCl_5}$ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The $\mathrm{K_p}$ for…
Equilibrium Chemical Equilibrium Kp Expression via Partial Pressures
MediumSingle correctNew ideaIdea asked in 2 years
Q65
A 42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol is [Given: Molar mass : Na = 23.0 g $\mathrm{mol^{-1}}$ ; Cl = 35.5 g $\mathrm{mol^{-1}}$ ]
Surface Chemistry Colloids Flocculation Value Calculation
MediumSingle correctNew ideaIdea asked in 2 years
Q66
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The first ionization enthalpy for oxygen is lower than that of nitrogen. Reason R: The four electrons in 2p orbitals of oxygen experience more…
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
EasyAssertion–reasonIdea asked in 4 yearsAsked the year before
Q67
Match List I with List II. List I Ore | List II Composition A. Siderite | I. $\mathrm{FeCO_3}$ B. Malachite | II. $\mathrm{CuCO_3.Cu(OH)_2}$ C. Sphalerite | III. ZnS D. Calamine | IV. $\mathrm{ZnCO_3}$ Choose the correct answer from the options given below:
General Principles and Processes of Isolation of Elements
EasyMatch the list
Q68
Given below are two statements. • Statement I: In $\mathrm{CuSO_4{\cdot}5H_2O}$ , Cu-O bonds are present. • Statement II: In $\mathrm{CuSO_4{\cdot}5H_2O}$ , ligands coordinating with Cu(II) ion are O-and S-based ligands. In the light of the above statements,…
Coordination Compounds Hydrogen and Hydrides Classification of Hydrates
MediumTwo statementsIdea asked in 2 yearsAsked the year before
Q69
Amongst baking soda, caustic soda and washing soda, carbonate anion is present in
The s-Block Elements
EasySingle correct
Q70
Number of lone pair(s) of electrons on central atom and the shape of $\mathrm{BrF_3}$ molecule respectively, are
The p-Block Elements VSEPR Theory T-Shaped Geometry (SN=5, 2 LP)
EasySingle correctIdea asked in 2 yearsAsked the year before
Q71
Aqueous solution of which of the following boron compounds will be strongly basic in nature?
The p-Block Elements Group 13 & 14 Borax and Boric Acid
MediumSingle correctNew ideaIdea asked in 2 years
Q72
Sulphur dioxide is one of the components of polluted air. $\mathrm{SO_2}$ is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by $\mathrm{SO_2}$ is
Environmental Chemistry Acid Rain Mechanism
EasySingle correctIdea asked in 4 yearsAsked the year before
Q73
Which of the following carbocations is most stable?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Relative Stability
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q74
[figure: six-membered ring drawn with alternating double bonds] + $\mathrm{CH_3CH_2CH_2Cl}$ → 'A' Major Product (reagent over the arrow: Anhydrous, $\mathrm{AlCl_3}$ ) The stable carbocation formed in the above reaction is
Hydrocarbons Aromatic Hydrocarbons Friedel-Crafts Alkylation
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q75
Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2% ; H, 4.9 % and Br 42.9%, respectively on oxidation with $\mathrm{KMnO_4}$ . Isomer ‘A’ is optically active and gives a pale yellow precipitate when warmed with alcoholic…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN1
HardDiagram based · figureIdea asked in 5 yearsAsked the year before
Q76
In Friedel-Crafts alkylation of aniline, one gets
Amines Aromatic Hydrocarbons Friedel-Crafts Failure with Aniline
EasySingle correctNew ideaIdea asked in 2 years
Q77
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Dacron is an example of polyester polymer. Reason R: Dacron is made up of ethylene glycol and terephthalic acid monomers. In the light of the…
Polymers Terylene (Dacron) Monomers
EasyAssertion–reasonNew idea
Q78
The structure of protein that is unaffected by heating is
Biomolecules
EasySingle correct
Q79
The mixture of chloroxylenol and terpineol is an example of
Chemistry in Everyday Life Chemical Composition of Dettol
EasySingle correctNew idea
Q80
A white precipitate was formed when $\mathrm{BaCl_2}$ was added to water extract of an inorganic salt. Further, a gas ‘X’ with characteristic odour was released when the formed white precipitate was dissolved in dilute HCl. The anion present in the inorganic…
The p-Block Elements Anion Analysis Sulfate vs Sulfite Barium Test
EasySingle correctNew idea
Q81
A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure.…
States of Matter Ideal Gas Laws Ideal Gas Equation
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q82
2.2 g of nitrous oxide ( $\mathrm{N_2O}$ ) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ΔU is '−x' J. The value of ‘x’ is ___.…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant ( $\mathrm{K_b/K_f}$ ) is ___.
Solutions Colligative Properties Boiling Point Elevation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q84
The cell potential for the given cell at 298 K $\mathrm{Pt|H_2\,(g,1\ bar)|H^{+}\,(aq)||Cu^{2+}\,(aq)|Cu(s)}$ is 0.31V. The pH of the acidic solution is found to be 3, whereas the concentration of $\mathrm{Cu^{2+}}$ is $10^{-x}$ M. The value of $x$ is ___.…
Electrochemistry Nernst Equation pH Dependence of Electrode Potential
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
The equation $k = (6.5\times10^{12}\ \mathrm{s^{-1}})\,e^{-26000\,\mathrm{K}/T}$ is followed for the decomposition of compound A. The activation energy for the reaction is ___ kJ $\mathrm{mol^{-1}}$ . [nearest integer] (Given: R = 8.314 J $\mathrm{K^{-1}}$ …
Chemical Kinetics Arrhenius Equation Activation Energy Calculation
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q86
Spin only magnetic moment of $[\mathrm{MnBr_6}]^{4-}$ is ___ B.M. (round off to the closest integer)
The d- and f-Block Elements Crystal Field Theory Spin-only Magnetic Moment
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q87
For the reaction given below : $\mathrm{CoCl_3\cdot}\,x\,\mathrm{NH_3 + AgNO_3}$ (aq) → If two equivalents of AgCl precipitate out, then the value of $x$ will be ________.
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q88
The number of chiral alcohol(s) with molecular formula $\mathrm{C_4H_{10}O}$ is _____.
Haloalkanes and Haloarenes Stereoisomerism Chiral Centers
MediumNumerical valueIdea asked in 5 years
Q89
In the given reaction, [figure: six-membered ring of single bonds with an HO group attached; reagents over the arrow: (i) $\mathrm{K_2Cr_2O_7}$ , (ii) $\mathrm{C_6H_5MgBr}$ , (iii) $\mathrm{H_2O}$ , (iv) $\mathrm{H^{+}}$ , heat; product 'X' Major Product] the…
Alcohols, Phenols and Ethers Alcohols and Phenols Selective Alcohol Oxidation
MediumNumerical value · figureIdea asked in 2 yearsAsked the year before
Q90
In the given reaction, [figure: six-membered ring with a carbonyl oxygen (O double bonded to a ring carbon); reagents over the arrow: (i) ⁻OH, (ii) heat; product 'P' Major Product] The number of π electrons present in the product ‘P’ is ____.
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Self-Aldol Condensation
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before

Maths28 questions

1 easy20 medium7 hard

Q1
Let $\alpha$ be a root of the equation $1 + x^2 + x^4 = 0$ . Then the value of $\alpha^{1011} + \alpha^{2022} - \alpha^{3033}$ is equal to :
Complex Numbers and Quadratic Equations Roots of Unity Equations Reducible to Roots of Unity
MediumSingle correctNew idea
Q2
Let $\arg(z)$ represent the principal argument of the complex number $z$ . Then, $|z| = 3$ and $\arg(z - 1) - \arg(z + 1) = \frac{\pi}{4}$ intersect
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Locus of Argument Ratio (Circular Arc)
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q3
Let $A = \begin{pmatrix} 2 & -1 \\ 0 & 2 \end{pmatrix}$ . If $B = I - {}^5C_1\,(adjA) + {}^5C_2\,(adjA)^2 - \ldots - {}^5C_5\,(adjA)^5$ , then the sum of all elements of the matrix $B$ is
Determinants Matrix Multiplication Binomial Expansion for Commuting Matrices
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q4
The sum of the infinite series $1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \frac{51}{6^5} + \frac{70}{6^6} + \ldots$ is equal to:
Sequences and Series Arithmetico-Geometric Series Second-Order AGP Summation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q5
The value of $\lim_{x \to 1} \frac{(x^2 - 1)\sin^2(\pi x)}{x^4 - 2x^3 + 2x - 1}$ is equal to:
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q6
Let $f : \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = (x - 3)^{n_1}(x - 5)^{n_2}$ , $n_1, n_2 \in \mathbb{N}$ . Then, which of the following is NOT true?
Application of Derivatives Maxima and Minima First Derivative Test
MediumSingle correctIdea asked in 3 years
Q7
Let $f$ be a real valued continuous function on $[0, 1]$ and $f(x) = x + \int_0^1 (x - t) f(t)\,dt$ . Then, which of the following points $(x, y)$ lies on the curve $y = f(x)$ ?
Integrals Leibniz Rule Solving Integral Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q8
If $\int_0^2 \left(\sqrt{2x} - \sqrt{2x - x^2}\right) dx = \int_0^1 \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) dy + \int_1^2 \left(2 - \frac{y^2}{2}\right) dy + I$ then $I$ equals
Application of Integrals Area Under Curves Optimal Strip Selection (dx vs dy)
MediumSingle correctNew idea
Q9
If $y = y\,(x)$ is the solution of the differential equation $\left(1 + e^{2x}\right)\frac{dy}{dx} + 2\left(1 + y^2\right)e^x = 0$ and $y\,(0) = 0$ , then $6\left\{y'(0) + \left(y\left(\log_e \sqrt{3}\right)\right)^2\right\}$ is equal to
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q10
Let P : $y^2 = 4ax$ , $a > 0$ be a parabola with focus S. Let the tangents to the parabola P make an angle of $\frac{\pi}{4}$ with the line $y = 3x + 5$ touch the parabola P at A and B. Then the value of $a$ for which A, B and S are collinear is
Conic Sections Parabola Focal Chords Chord of Contact from Directrix is Focal
HardSingle correctNew idea
Q12
Let $\frac{x - 2}{3} = \frac{y + 1}{-2} = \frac{z + 3}{-1}$ lie on the plane $px - qy + z = 5$ , for some $p, q \in \mathbb{R}$ . The shortest distance of the plane from the origin is:
Three Dimensional Geometry Planes in 3D Condition for Line to Lie in Plane
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q13
The distance of the origin from the centroid of the triangle whose two sides have the equations $x - 2y + 1 = 0$ and $2x - y - 1 = 0$ and whose orthocenter is $\left(\frac{7}{3}, \frac{7}{3}\right)$ is:
Straight Lines Pair of Straight Lines Orthocenter of Triangle with Pair of Lines
HardSingle correctNew idea
Q14
Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane $x + 2y + 2z = 16$ . Let T be a plane passing through the point Q and contains the line $\vec{r} = -\hat{k} + \lambda\left(\hat{i} + \hat{j} + 2\hat{k}\right)$ ,…
Three Dimensional Geometry Planes in 3D Plane Containing a Line and a Point
HardSingle correctIdea asked in 3 yearsAsked the year before
Q15
Let $A, B, C$ be three points whose position vectors respectively are $\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$ $\vec{b} = 2\hat{i} + \alpha\hat{j} + 4\hat{k}, \alpha \in \mathbb{R}$ $\vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}$ If $\alpha$ is the smallest…
Vector Algebra Linear Independence Collinearity of Three Position Vectors
EasySingle correctNew ideaIdea asked in 2 years
Q16
The probability that a relation R from $\{x, y\}$ to $\{x, y\}$ is both symmetric and transitive, is equal to
Probability Sets and Relations Counting Relations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
The number of values of $a \in \mathbb{N}$ such that the variance of $3, 7, 12, a, 43 - a$ is a natural number is:
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q18
From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is $60^\circ$ . The pole subtends an angle $30^\circ$ at the top of the tower. Then the height of the tower is:
Trigonometric Functions
MediumSingle correct
Q19
Negation of the Boolean statement $(p \vee q) \Rightarrow ((\sim r) \vee p)$ is equivalent to
Mathematical Reasoning
MediumSingle correct
Q20
Let $n \geq 5$ be an integer. If $9^n - 8n - 1 = 64\alpha$ and $6^n - 5n - 1 = 25\beta$ , then $\alpha - \beta$ is equal to
Binomial Theorem
HardSingle correct
Q22
Let $y = y(x)$ , $x > 1$ , be the solution of the differential equation $(x - 1)\frac{dy}{dx} + 2xy = \frac{1}{x - 1}$ , with $y(2) = \frac{1 + e^4}{2e^4}$ . If $y(3) = \frac{e^{\alpha} + 1}{\beta e^{\alpha}}$ , then the value of $\alpha + \beta$ is equal to ___.
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q23
Let $3, 6, 9, 12, \ldots$ upto 78 terms and $5, 9, 13, 17, \ldots$ upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to___.
Sequences and Series AP and GP Common Terms of Two APs
MediumNumerical valueNew ideaIdea asked in 2 years
Q24
The number of solutions of the equation $\sin x = \cos^2 x$ in the interval $(0, 10)$ is ___.
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q25
For real numbers $a, b$ ( $a > b > 0$ ), let Area $\left\{(x, y) : x^2 + y^2 \leq a^2 \text{ and } \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1\right\} = 30\pi$ and Area…
Application of Integrals Area Under Curves Area of Ellipse and Sectors
MediumNumerical valueIdea asked in 2 years
Q26
Let $f$ and $g$ be twice differentiable even functions on $(-2, 2)$ such that $f\left(\frac{1}{4}\right) = 0$ , $f\left(\frac{1}{2}\right) = 0$ , $f(1) = 1$ and $g\left(\frac{3}{4}\right) = 0$ , $g(1) = 2$ Then, the minimum number of solutions of…
Application of Derivatives Rolle's Theorem Auxiliary Functions: Product and Quotient Rules
HardNumerical valueNew idea
Q27
Let the coefficients of $x^{-1}$ and $x^{-3}$ in the expansion of $\left(2x^{\frac{1}{5}} - \frac{1}{x^{\frac{1}{5}}}\right)^{15}$ , $x > 0$ , be $m$ and $n$ respectively. If $r$ is a positive integer such that $mn^2 = {}^{15}C_r \cdot 2^r$ , then the value of…
Binomial Theorem
MediumNumerical value
Q28
The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ________.
Permutations and Combinations
HardNumerical value
Q29
Let $M = \begin{bmatrix} 0 & -\alpha \\ \alpha & 0 \end{bmatrix}$ , where $\alpha$ is a non-zero real number an $N = \sum_{k=1}^{49} M^{2k}$ . If $(I - M^2)N = -2I$ , then the positive integral value of $\alpha$ is ___.
Matrices Matrix Multiplication Square of Skew-Symmetric Matrix
MediumNumerical valueNew idea
Q30
Let $f(x)$ and $g(x)$ be two real polynomials of degree 2 and 1 respectively. If $f(g(x)) = 8x^2 - 2x$ , and $g(f(x)) = 4x^2 + 6x + 1$ , then the value of $f(2) + g(2)$ is ___.
Relations and Functions
MediumNumerical value

Dropped from the final key and left out of every count: Q11, Q21.

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.