JEE Main 2022 · June session

JEE Main 28 June 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 15 were rated hard and 27 easy. Its hard-question count was the joint 2nd 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: 15; 17% of the shift
Chapters asked: 69; 16 questions with a figure

Key findings · 28 Jun 2022, Shift 2

1
15 hard questions (17%): the joint 2nd 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 12 of 30 rated hard; Physics had the most easy questions (12 of 30).
3
26 questions tested a new idea, one no earlier year had asked: 33% of the 79 questions tagged to an idea.
4
42 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
41 shared an idea with another 2022 shift (52% 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), Coordination Compounds in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 12Medium 17Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 11Medium 17Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 4Medium 14Hard 12

Top chapters

Conic Sections3 Q
Complex Numbers and Quadratic Equations2 Q
Differential Equations2 Q
Integrals2 Q
Relations and Functions2 Q
Sequences and Series2 Q

Question format

Single correct46 Q
Numerical value30 Q
Diagram based8 Q
Other3 Q
Match the list2 Q
Assertion–reason1 Q

What each question asks you to do

Calculation34 Q
Multi-step28 Q
Application10 Q
Recall9 Q
Conceptual8 Q
Data or graph1 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

12 easy17 medium1 hard

Chemistry30 questions

11 easy17 medium2 hard

Q61
Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is, Given : Atomic masses of C, H and N are 12, 1 and 14 amu respectively. The molar mass of the compound A is 162 g mol $^{-1}$ .
Some Basic Concepts of Chemistry Mole Concept Empirical Formula from Mass Percentage
MediumSingle correctIdea asked in 3 years
Q62
Consider the following statements : (A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ $=1, 2, 3, ...$ (B) The azimuthal quantum number ‘ $l$ ’ for a given ‘n’ (principal quantum number) can have values as ‘ $l=0, 1, 2, ....$ n (C)…
Structure of Atom Quantum Numbers Validity of Quantum Number Sets
EasyOtherNew idea
Q63
In the structure of $\mathrm{SF_4}$ , the lone pair of electrons on S is in.
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 5 Derivative Shapes
EasySingle correctIdea asked in 3 years
Q64
A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of $\frac{[\mathrm{CH_3CH_2COO^-}]}{[\mathrm{CH_3CH_2COOH}]}$ required to make buffer is __________. Given : $\mathrm{K_a(CH_3CH_2COOH)} = 1.3\times10^{-5}$
Equilibrium pH and Buffers Acidic Buffer pH Calculation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q65
Match List - I with List - II : List - I | List - II (A) negatively charged sol | (I) $\mathrm{Fe_2O_3\cdot xH_2O}$ (B) macromolecular colloid | (II) CdS sol (C) positively charged sol | (III) Starch (D) Cheese | (IV) a gel Choose the correct answer from the…
Surface Chemistry Colloids Macromolecular Colloids
EasyMatch the listNew idea
Q66
Match List - I with List - II : List - I (Oxide) | List - II (Nature) (A) $\mathrm{Cl_2O_7}$ | (I) Amphoteric (B) $\mathrm{Na_2O}$ | (II) Basic (C) $\mathrm{Al_2O_3}$ | (III) Neutral (D) $\mathrm{N_2O}$ | (IV) Acidic Choose the correct answer from the…
Classification of Elements and Periodicity in Properties Periodic Trends Acidic and Basic Character of Oxides
EasyMatch the listIdea asked in 4 years
Q67
In the metallurgical extraction of copper, following reaction is used : $\mathrm{FeO + SiO_2 \rightarrow FeSiO_3}$ $\mathrm{FeO}$ and $\mathrm{FeSiO_3}$ respectively are.
General Principles and Processes of Isolation of Elements Metallurgical Extraction Acidic vs Basic Flux Selection
EasySingle correctNew idea
Q68
Hydrogen has three isotopes : protium ( $^1$ H) , deuterium ( $^2$ H or D) and tritium ( $^3$ H or T) . They have nearly same chemical properties but different physical properties. They differ in
Hydrogen Hydrogen and Hydrides Isotopes of Hydrogen
EasySingle correctIdea asked in 4 yearsAsked the year before
Q69
Among the following, basic oxide is :
The s-Block Elements Periodic Trends Acidic and Basic Character of Oxides
EasySingle correctIdea asked in 4 years
Q70
Among the given oxides of nitrogen ; $\mathrm{N_2O}$ , $\mathrm{N_2O_3}$ , $\mathrm{N_2O_4}$ and $\mathrm{N_2O_5}$ , the number of compound/(s) having $\mathrm{N-N}$ bond is :
The p-Block Elements Group 15 & 16 Nitrogen Oxides Structure
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q71
Which of the following oxoacids of sulphur contains “S” in two different oxidation states ?
The p-Block Elements Group 15 & 16 Sulfur Oxoacids
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q72
Correct statement about photo-chemical smog is :
Environmental Chemistry Classical vs Photochemical Smog
EasySingle correctIdea asked in 3 yearsAsked the year before
Q73
The correct IUPAC name of the following compound is :
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Oxo vs Formyl Prefix for Aldehydes
MediumDiagram based · figureNew idea
Q74
The major product (P) of the given reaction is (where, Me is $-\mathrm{CH_3}$ ) [reaction: reactant $\xrightarrow{\mathrm{H^+}}$ P (Major Product)]
Alcohols, Phenols and Ethers Alkenes and Alkynes Acid-Catalyzed Dehydration of Alcohols
MediumDiagram based · figureNew idea
Q75
A $\xrightarrow[\text{(ii) CN}^-\text{; (iii) H}_2\text{O/H}^+]{\text{(i) Cl}_2,\ \Delta}$ 4-Bromophenyl acetic acid. In the above reaction ‘A’ is
Haloalkanes and Haloarenes Alkanes and Free Radicals Halogenation Chain Mechanism
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q76
Isobutyraldehyde on reaction with formaldehyde and $\mathrm{K_2CO_3}$ gives compound ‘A’. Compound ‘A’ reacts with KCN and yields compound ‘B’, which on hydrolysis gives a stable compound ‘C’. The compound ‘C’ is
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cross-Aldol Condensation
HardDiagram based · figureIdea asked in 3 yearsAsked the year before
Q77
With respect to the following reaction, consider the given statements : [reaction: aniline (benzene ring with $\mathrm{NH_2}$ ) $\xrightarrow[\mathrm{H_2SO_4,\ 288\ k}]{\mathrm{HNO_3}}$ products] (A) o-Nitroaniline and p-nitroaniline are the predominant…
Amines Direct Nitration of Aniline
MediumOther · figureIdea asked in 2 yearsAsked the year before
Q78
Given below are two statements, one is Assertion (A) and other is Reason (R). Assertion (A) : Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties . Reason (R) : The cis-polyisoprene molecules consist of various…
Polymers Natural and Synthetic Rubber
EasyAssertion–reasonNew idea
Q79
When sugar ‘X’ is boiled with dilute $\mathrm{H_2SO_4}$ in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’ on oxidation with $\mathrm{HNO_3}$ yields saccharic acid where as ‘B’ is laevorotatory. The compound ‘X’ is :
Biomolecules Carbohydrates Sucrose Structure and Linkage
EasySingle correctIdea asked in 2 yearsAsked the year before
Q80
The drug tegamet is :
Chemistry in Everyday Life Therapeutic Drug Classes
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q81
100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is __________ g mol $^{-1}$ . (Nearest integer) (Given : R=0.083 L bar K $^{-1}$ mol $^{-1}$ )
States of Matter Mole Concept Molar Mass and Gas Volume
MediumNumerical valueIdea asked in 3 years
Q82
For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, $\Delta_C H^{\ominus} = -601.70$ kJ mol $^{-1}$ , the magnitude of change in internal energy for the reaction is __________ kJ . (Nearest integer) (Given : R=8.3 J…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
2.5 g of protein containing only glycine ( $\mathrm{C_2H_5NO_2}$ ) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be $5.03\times10^{-3}$ bar. The total number of glycine units present in the protein…
Solutions Colligative Properties Osmometry for Macromolecule Molar Mass
MediumNumerical valueNew ideaIdea asked in 2 years
Q84
For the given reactions $\mathrm{Sn^{2+} + 2e^- \rightarrow Sn}$ $\mathrm{Sn^{4+} + 4e^- \rightarrow Sn}$ the electrode potentials are ; $\mathrm{E^o_{Sn^{2+}/Sn}} = -0.140$ V and $\mathrm{E^o_{Sn^{4+}/Sn}} = 0.010$ V. The magnitude of standard electrode…
Electrochemistry Nernst Equation Additivity of Delta G0 for E0 Calculation
HardNumerical valueNew ideaIdea asked in 2 years
Q85
A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is __________ . (Nearest integer) (Given : antilog 0.125 =1.333, antilog 0.693 =4.93)
Chemical Kinetics Integrated Rate Equations First Order Half-Life
MediumNumerical valueNew ideaIdea asked in 3 years
Q86
$\mathrm{[Fe(CN)_6]^{4-}}$ $\mathrm{[Fe(CN)_6]^{3-}}$ $\mathrm{[Ti(CN)_6]^{3-}}$ $\mathrm{[Ni(CN)_4]^{2-}}$ $\mathrm{[Co(CN)_6]^{3-}}$ Among the given complexes, number of paramagnetic complexes is __________ .
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q87
(a) $\mathrm{CoCl_3.4\ NH_3}$ , (b) $\mathrm{CoCl_3\cdot5NH_3}$ , (c) $\mathrm{CoCl_3\cdot6NH_3}$ and (d) $\mathrm{CoCl(NO_3)_2\cdot5NH_3}$ . Number of complex(es) which will exist in cis-trans form is/are __________.
Coordination Compounds Coordination Isomerism Total Isomer Calculation
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q88
The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793g of $\mathrm{CO_2}$ and 0.442 g of $\mathrm{H_2O}$ . The percentage of oxygen composition in the organic compound is __________. (nearest integer)
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry POAC in Combustion Analysis
MediumNumerical valueNew ideaIdea asked in 3 years
Q89
The major product of the following reaction contains __________ bromine atom(s). [reaction: structure $\xrightarrow[h\nu]{\mathrm{Br_2}}$ Major Product]
Haloalkanes and Haloarenes Alkenes and Alkynes Allylic Halogenation with NBS
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q90
0.01 M $\mathrm{KMnO_4}$ solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of $\mathrm{KMnO_4}$ solution left in the burette after the end point is __________ mL. (nearest…
Redox Reactions Mohr's Salt Redox Titrations
MediumNumerical valueIdea asked in 2 yearsAsked the year before

Maths30 questions

4 easy14 medium12 hard

Q1
Let $R_1 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \leq 13\}$ and $R_2 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \neq 13\}$ . Then on $\mathbf{N}$ :
Relations and Functions Sets and Relations Equivalence Relations
EasySingle correctIdea asked in 4 yearsAsked the year before
Q2
Let $f(x)$ be a quadratic polynomial such that $f(-2)+f(3)=0$ . If one of the roots of $f(x)=0$ is $-1$ , then the sum of the roots of $f(x)=0$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
MediumSingle correctIdea asked in 6 years
Q3
The number of ways to distribute 30 identical candies among four children $C_1, C_2, C_3$ and $C_4$ so that $C_2$ receives atleast 4 and atmost 7 candies, $C_3$ receives atleast 2 and atmost 6 candies, is equal to :
Permutations and Combinations Distribution of Identical Objects
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q4
The term independent of $x$ in the expansion of $(1-x^2+3x^3)\left(\frac{5}{2}x^3-\frac{1}{5x^2}\right)^{11}$ , $x \neq 0$ is :
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
MediumSingle correctNew ideaIdea asked in 2 years
Q5
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is $1:7$ and $a+n=33$ , then the value of n is :
Sequences and Series AP and GP Arithmetic and Geometric Means
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q6
Let $f, g : \mathbf{R} \to \mathbf{R}$ be functions defined by $f(x) = \begin{cases} [x] , & x < 0 \\ |1-x| , & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} e^x - x , & x < 0 \\ (x-1)^2 - 1 , & x \geq 0 \end{cases}$ where $[x]$ denote the greatest integer…
Continuity and Differentiability Continuity and Differentiability of Composite Functions
HardSingle correctIdea asked in 5 yearsAsked the year before
Q7
Let $f : \mathbf{R} \to \mathbf{R}$ be a differentiable function such that $f\left(\frac{\pi}{4}\right)=\sqrt{2}$ , $f\left(\frac{\pi}{2}\right)=0$ and $f'\left(\frac{\pi}{2}\right)=1$ and let…
Integrals
HardSingle correct
Q8
Let $f : \mathbf{R} \to \mathbf{R}$ be a continuous function satisfying $f(x)+f(x+k)=n$ , for all $x \in \mathbf{R}$ where $k>0$ and n is a positive integer. If $I_1=\int_0^{4nk} f(x)dx$ and $I_2=\int_{-k}^{3k} f(x)dx$ , then :
Integrals Definite Integral Properties Periodic Function Property
HardSingle correctIdea asked in 3 yearsAsked the year before
Q9
The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x$ -axis is :
Application of Integrals Area Under Curves Area with Modulus
MediumSingle correctNew ideaIdea asked in 4 years
Q10
Let $x=x(y)$ be the solution of the differential equation $2y\,e^{x/y^2}\,dx+\left(y^2-4xe^{x/y^2}\right)dy=0$ such that $x(1)=0$ . Then, $x(e)$ is equal to :
Differential Equations Variable Separable Form Exponential and Logarithmic Substitutions
HardSingle correctNew idea
Q11
Let the slope of the tangent to a curve $y=f(x)$ at $(x, y)$ be given by $2\tan x(\cos x-y)$ . If the curve passes through the point $(\pi/4, 0)$ , then the value of $\int_0^{\pi/2} y\,dx$ is equal to :
Differential Equations Linear Differential Equations Forming LDEs from Geometric Conditions
HardSingle correctNew ideaIdea asked in 2 years
Q12
Let a triangle be bounded by the lines $L_1 : 2x+5y=10$ ; $L_2 : -4x+3y=12$ and the line $L_3$ , which passes through the point P(2, 3), intersects $L_2$ at A and $L_1$ at B. If the point P divides the line-segment AB, internally in the ratio $1:3$ , then the…
Straight Lines Straight Line Distance Section Ratio by a Line
MediumSingle correctNew ideaIdea asked in 3 years
Q13
Let $a>0$ , $b>0$ . Let e and $l$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ . Let e' and $l'$ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola.…
Conic Sections
MediumSingle correct
Q14
Let $\vec{a}=\alpha\hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}=-2\hat{i}+\alpha\hat{j}+\hat{k}$ , where $\alpha \in \mathbf{R}$ . If the area of the parallelogram whose adjacent sides are represented by the vectors $\vec{a}$ and $\vec{b}$ is…
Vector Algebra Cross Product Area of Triangles and Parallelograms
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q15
If vertex of a parabola is $(2, -1)$ and the equation of its directrix is $4x-3y=21$ , then the length of its latus rectum is :
Conic Sections General Conic Section Latus Rectum of a General Parabola
EasySingle correctNew idea
Q16
Let the plane $ax+by+cz=d$ pass through $(2, 3, -5)$ and is perpendicular to the planes $2x+y-5z=10$ and $3x+5y-7z=12$ . If a, b, c, d are integers $d>0$ and $\gcd(|a|, |b|, |c|, d)=1$ , then the value of $a+7b+c+20d$ is equal to :
Three Dimensional Geometry Planes in 3D Plane Perpendicular to Two Planes
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q17
The probability that a randomly chosen one-one function from the set $\{a, b, c, d\}$ to the set $\{1, 2, 3, 4, 5\}$ satisfies $f(a)+2f(b)-f(c)=f(d)$ is :
Probability Permutations and Combinations Number of Injective Functions
HardSingle correctIdea asked in 4 yearsAsked the year before
Q18
The value of $\lim_{n\to\infty} 6\tan\left\{\sum_{r=1}^{n}\tan^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\}$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Telescoping Inverse Trig Series
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q19
Let $\vec{a}$ be a vector which is perpendicular to the vector $3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}$ . If $\vec{a}\times\left(2\hat{i}+\hat{k}\right)=2\hat{i}-13\hat{j}-4\hat{k}$ , then the projection of the vector $\vec{a}$ on the vector…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
HardSingle correctIdea asked in 6 yearsAsked the year before
Q20
If $\cot\alpha=1$ and $\sec\beta=-\frac{5}{3}$ , where $\pi<\alpha<\frac{3\pi}{2}$ and $\frac{\pi}{2}<\beta<\pi$ , then the value of $\tan(\alpha+\beta)$ and the quadrant in which $\alpha+\beta$ lies, respectively are :
Trigonometric Functions Trigonometric Identities Compound Angle Formulas
EasySingle correctIdea asked in 5 yearsAsked the year before
Q21
Let the image of the point P(1, 2, 3) in the line L : $\frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3}$ be Q. Let R $(\alpha, \beta, \gamma)$ be a point that divides internally the line segment PQ in the ratio $1:3$ . Then the value of $22\,(\alpha+\beta+\gamma)$ …
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is…
Statistics Variance and SD Maximum Variance of Bounded Data
MediumNumerical valueIdea asked in 2 years
Q23
If one of the diameters of the circle $x^2+y^2-2\sqrt{2}x-6\sqrt{2}y+14=0$ is a chord of the circle $\left(x-2\sqrt{2}\right)^2+\left(y-2\sqrt{2}\right)^2=r^2$ , then the value of $r^2$ is equal to __________.
Conic Sections Power of a Point Length of Common Chord via Radical Axis
MediumNumerical valueIdea asked in 3 years
Q24
If $\lim_{x\to1}\frac{\sin(3x^2-4x+1)-x^2+1}{2x^3-7x^2+ax+b}=-2$ , then the value of $(a-b)$ is equal to __________.
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Let for $n=1, 2, \ldots, 50$ , $S_n$ be the sum of the infinite geometric progression whose first term is $n^2$ and whose common ratio is $\frac{1}{(n+1)^2}$ . Then the value of $\frac{1}{26}+\sum_{n=1}^{50}\left(S_n+\frac{2}{n+1}-n-1\right)$ is equal to…
Sequences and Series AP and GP Infinite GP Sum
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q26
If the system of linear equations $2x-3y=\gamma+5$ , $\alpha x+5y=\beta+1$ , where $\alpha, \beta, \gamma \in \mathbf{R}$ has infinitely many solutions, then the value of $|9\alpha+3\beta+5\gamma|$ is equal to __________.
Determinants Cramer's Rule Condition for Infinite Solutions
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q27
Let $A=\begin{pmatrix}1+i & 1\\ -i & 0\end{pmatrix}$ where $i=\sqrt{-1}$ . Then, the number of elements in the set $\{n \in \{1, 2, \ldots, 100\} : A^n = A\}$ is __________.
Matrices Matrix Multiplication Periodic Matrices
HardNumerical valueNew idea
Q28
Sum of squares of modulus of all the complex numbers $z$ satisfying $\bar{z}=iz^2+z^2-z$ is equal to __________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Conjugate and Inverse
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q29
Let $S=\{1, 2, 3, 4\}$ . Then the number of elements in the set $\{f : S\times S\to S : f \text{ is onto and } f(a, b)=f(b, a) \geq a\ \forall\ (a, b) \in S\times S\}$ is __________.
Relations and Functions Permutations and Combinations Number of Surjective (Onto) Functions
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q30
The maximum number of compound propositions, out of $p\vee r\vee s$ , $p\vee r\vee\sim s$ , $p\vee\sim q\vee s$ , $\sim p\vee\sim r\vee s$ , $\sim p\vee\sim r\vee\sim s$ , $\sim p\vee q\vee\sim s$ , $q\vee r\vee\sim s$ , $q\vee\sim r\vee\sim s$ ,…
Mathematical Reasoning
HardNumerical 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.