JEE Main 2022 · July session

JEE Main 27 July 2022, Shift 1

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 13 were rated hard and 26 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: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 13; 15% of the shift
Chapters asked: 67; 9 questions with a figure

Key findings · 27 Jul 2022, Shift 1

1
13 hard questions (15%): 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 29 rated hard; Physics had the most easy questions (13 of 30).
3
21 questions tested a new idea, one no earlier year had asked: 30% of the 71 questions tagged to an idea.
4
46 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
39 shared an idea with another 2022 shift (55% 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 (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 11Medium 18Hard 1

Top chapters

Maths

29 Q · 10 numerical

Easy 2Medium 16Hard 11

Top chapters

Conic Sections4 Q
Complex Numbers and Quadratic Equations2 Q
Differential Equations2 Q
Integrals2 Q
Relations and Functions2 Q
Sequences and Series2 Q

Question format

Single correct42 Q
Numerical value30 Q
Two statements4 Q
Match the list4 Q
Diagram based3 Q
Other3 Q
Assertion–reason3 Q

What each question asks you to do

Multi-step28 Q
Calculation27 Q
Conceptual15 Q
Application8 Q
Recall8 Q
Data or graph2 Q
Diagram reading1 Q

Most common: Multi-step.

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
Open29 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 89 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

89 of 89 questions

Physics30 questions

13 easy16 medium1 hard

Chemistry30 questions

11 easy18 medium1 hard

Q61
250 g solution of D-glucose in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, H,1 u; C,12 u; O,16 u)
Solutions Mole Concept Molality Calculation
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q62
Given below are two statements. Statement I: $\mathrm{O_2}$ , $\mathrm{Cu^{2+}}$ , and $\mathrm{Fe^{3+}}$ are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field. Statement II: NaCl and $\mathrm{H_2O}$ are weakly…
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
EasyTwo statementsIdea asked in 6 yearsAsked the year before
Q63
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium. Reason R: Energies of the orbitals in the same subshell…
Structure of Atom
MediumAssertion–reason
Q64
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Activated charcoal adsorbs $\mathrm{SO_2}$ more efficiently than $\mathrm{CH_4}$ . Reason R: Gases with lower critical temperatures are readily…
Surface Chemistry Adsorption Critical Temperature and Extent of Adsorption
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q65
Boiling point of a 2% aqueous solution of a non-volatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is
Solutions Colligative Properties Boiling Point Elevation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q66
The incorrect statement is
Classification of Elements and Periodicity in Properties Periodic Trends Ionization Enthalpy Trends
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q67
Which of the following methods are not used to refine any metal? A. Liquation B. Calcination C. Electrolysis D. Leaching E. Distillation Choose the correct answer from the options given below:
General Principles and Processes of Isolation of Elements Metallurgical Extraction Metal Refining Techniques
EasyOtherIdea asked in 4 yearsAsked the year before
Q68
Given below are two statements. Statement I: Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions. Statement II: Density of hydrogen peroxide at 298 K is lower than that of $\mathrm{D_2O}$ . In the light of the above statements,…
Hydrogen Hydrogen and Hydrides Oxidizing Action of H2O2
MediumTwo statementsIdea asked in 2 yearsAsked the year before
Q69
Given below are two statements. Statement I: The chlorides of Be and Al have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases. Statement II: Hydroxides of Be and Al dissolve in excess alkali to give beryllate and aluminate…
The s-Block Elements s-Block Elements Amphoterism of Beryllium Compounds
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q70
Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?
The p-Block Elements Group 15 & 16 Phosphorus Oxoacids
EasySingle correctIdea asked in 4 yearsAsked the year before
Q71
Given below are two statements. Statement I: Iron (III) catalyst, acidified $\mathrm{K_2Cr_2O_7}$ and neutral $\mathrm{KMnO_4}$ have the ability to oxidise $\mathrm{I^-}$ to $\mathrm{I_2}$ independently. Statement II: Manganate ion is paramagnetic in nature…
The d- and f-Block Elements d-Block Elements Permanganate Reactions
HardTwo statementsIdea asked in 3 yearsAsked the year before
Q72
The total number of Mn=O bonds in $\mathrm{Mn_2O_7}$ is ____.
The d- and f-Block Elements
MediumSingle correct
Q73
Match List I with List II. List I (Pollutant) | List II (Disease/sickness) A. Sulphate (>500 ppm) | I. Methemoglobinemia B. Nitrate (>50 ppm) | II. Brown mottling of teeth C. Lead (>50 ppb) | III. Laxative effect D. Fluoride (> 2ppm) | IV. Kidney damage…
Environmental Chemistry Fluoride Limits in Drinking Water
MediumMatch the listIdea asked in 3 yearsAsked the year before
Q74
Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R. Assertion A: [6] Annulene, [8] Annulene and cis-[10] Annulene, are respectively aromatic, not-aromatic and aromatic. [6] Annulene [8] Annulene cis - [10]…
Hydrocarbons Aromatic Hydrocarbons Annulene Planarity and Aromaticity
MediumAssertion–reason · figureNew ideaIdea asked in 2 years
Q75
[figure: benzene ring (hexagon with inner circle) with CH2OH at the top and OH at the bottom (para)] $+$ HCl $\xrightarrow{\Delta}$ A $\xrightarrow{\text{NaI}}$ B In the above reaction product B is: Product B is
Alcohols, Phenols and Ethers SN1 and SN2 Mechanisms Finkelstein Reaction
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q76
Match List I with List II. List I (Polymers) | List II (Commercial names) A. Phenol-formaldehyde resin | I. Glyptal B. Copolymer of 1,3-butadiene and styrene | II. Novolac C. Polyester of glycol and phthalic acid | III. Buna-S D. Polyester of glycol and…
Polymers Novolac Intermediate Formation
MediumMatch the listIdea asked in 2 yearsAsked the year before
Q77
A sugar ‘X’ dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol gives the coloured product after sometime. Sugar ‘X’ is
Biomolecules
MediumSingle correct
Q78
Match List I with List II. List I | List II A. [structure drawn, see figure_note] | I. Anti-depressant B. [structure drawn, see figure_note] | II. 550 times sweeter than cane sugar. C. [structure drawn, see figure_note] | III. Narcotic analgesic D.…
Chemistry in Everyday Life Drug Classification
MediumMatch the list · figureIdea asked in 2 yearsAsked the year before
Q79
In Carius method of estimation of halogen, 0.45 g of an organic compound gave 0.36 g of AgBr. Find out the percentage of bromine in the compound. (Molar masses : AgBr = 188 g mol $^{-1}$ ; Br = 80 g mol $^{-1}$ )
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q80
Match List I with List II. List I | List II A. Benzenesulphonyl chloride | I. Test for primary amines B. Hoffmann bromamide reaction | II. Anti Saytzeff C. Carbylamine reaction | III. Hinsberg reagent D. Hoffmann orientation | IV. Known reaction of…
Amines Hinsberg Test
MediumMatch the listIdea asked in 5 yearsAsked the year before
Q81
20 mL of 0.02 M $\mathrm{K_2Cr_2O_7}$ solution is used for the titration of 10 mL of $\mathrm{Fe^{2+}}$ solution in the acidic medium. The molarity of $\mathrm{Fe^{2+}}$ solution is ____ $\times 10^{-2}$ M. (Nearest Integer)
Redox Reactions Law of Chemical Equivalence in Redox
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q82
$\mathrm{2NO + 2H_2 \rightarrow N_2 + 2H_2O}$ The above reaction has been studied at $800^\circ$ C. The related data are given in the table below Reaction serial number | Initial Pressure of $\mathrm{H_2}$ / kPa | Initial Pressure of NO/kPa | Initial rate…
Chemical Kinetics Rate Laws Initial Rates Method
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q83
Amongst the following, the number of oxide(s) which are paramagnetic in nature is $\mathrm{Na_2O, KO_2, NO_2, N_2O, ClO_2, NO, SO_2, Cl_2O}$
The p-Block Elements Group 15 & 16 Nitrogen Oxides Structure
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q84
The molar heat capacity for an ideal gas at constant pressure is 20.785 J K $^{-1}$ mol $^{-1}$ . The change in internal energy is 5000 J upon heating from 300 K to 500 K. The number of moles of the gas at constant volume is __. [Nearest integer] (Given: R =…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Heat Capacity Relation in Enthalpy
MediumNumerical valueIdea asked in 3 years
Q85
According to MO theory, number of species/ions from the following having identical bond order is__. $\mathrm{CN^-, NO^+, O_2, O_2^+, O_2^{2+}}$
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q86
At 310 K, the solubility of $\mathrm{CaF_2}$ in water is $2.34 \times 10^{-3}$ g/100 mL. The solubility product of $\mathrm{CaF_2}$ is _____ $\times 10^{-8}$ (mol/L) $^3$ . (Give molar mass : $\mathrm{CaF_2}$ = 78 g mol $^{-1}$ )
Equilibrium Solubility Product Solubility-Ksp Relationship
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q87
The conductivity of a solution of complex with formula $\mathrm{CoCl_3(NH_3)_4}$ corresponds to 1:1 electrolyte, then the primary valency of central metal ion is ____
Coordination Compounds
MediumNumerical value
Q88
In the titration of $\mathrm{KMnO_4}$ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is _____
Redox Reactions Oxidation Number Assignment
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q89
Optical activity of an enantiomeric mixture is $+12.6^\circ$ and the specific rotation of (+) isomer is $+30^\circ$ . The optical purity is _____%.
Haloalkanes and Haloarenes Stereoisomerism Enantiomeric Excess and Specific Rotation
EasyNumerical valueNew idea
Q90
In the following reaction [figure: benzene $\xrightarrow{\text{Oleum}}$ (I) benzene bearing $\mathrm{SO_3H}$ $\xrightarrow{\text{NaOH (excess)/H}^+}$ (II) benzene bearing OH] The % yield for reaction I is 60% and that of reaction II is 50%. The overall yield…
Alcohols, Phenols and Ethers Stoichiometry Stoichiometry of Sequential Reactions
EasyNumerical value · figureNew idea

Maths29 questions

2 easy16 medium11 hard

Q1
Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $a\,R_1\,b \Leftrightarrow ab \ge 0$ and $a\,R_2\,b \Leftrightarrow a \ge b$ Then,
Relations and Functions Sets and Relations Equivalence Relations
EasySingle correctIdea asked in 4 yearsAsked the year before
Q2
Let $f, g : \mathbb{N}-\{1\} \rightarrow \mathbb{N}$ be functions defined by $f(a) = \alpha$ , where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^{\alpha}$ divides $a$ , and $g(a) = a + 1$ , for all $a \in \mathbb{N}-\{1\}$ . Then, the…
Relations and Functions
MediumSingle correct
Q3
Let the minimum value $v_0$ of $v = |z|^2 + |z-3|^2 + |z-6i|^2$ , $z \in \mathbb{C}$ is attained at $z = z_0$ . Then $\left|2z_0^2 - \bar{z}_0^3 + 3\right|^2 + v_0^2$ is equal to
Complex Numbers and Quadratic Equations
HardSingle correct
Q4
Let $A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}$ . Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^2 + \beta A = 2I$ . Then $\alpha + \beta$ is equal to
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q5
The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by 7 is
Binomial Theorem
MediumSingle correct
Q6
Suppose $a_1, a_2, ..., a_n, ...$ be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is 5 : 17 and $110 < a_{15} < 120$ , then the sum of the first ten terms of the…
Sequences and Series AP and GP AP Ratio Conversion: Sum to General Term
MediumSingle correctNew idea
Q7
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined as $f(x) = a\sin\left(\dfrac{\pi[x]}{2}\right) + [2-x]$ , $a \in \mathbb{R}$ , where $[t]$ is the greatest integer less than or equal to $t$ . If $\lim_{x \to -1} f(x)$ exists, then the value of…
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q8
Let $I = \int_{\pi/4}^{\pi/3} \left(\dfrac{8\sin x - \sin 2x}{x}\right) dx$ . Then
Integrals Definite Integral Properties Bounding and Estimation Property
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q9
The area of the smaller region enclosed by the curves $y^2 = 8x + 4$ and $x^2 + y^2 + 4\sqrt{3}x - 4 = 0$ is equal to
Application of Integrals Area Under Curves Area Between Curves
HardSingle correctIdea asked in 7 yearsAsked the year before
Q10
Let $y = y_1(x)$ and $y = y_2(x)$ be two distinct solutions of the differential equation $\dfrac{dy}{dx} = x + y$ , with $y_1(0) = 0$ and $y_2(0) = 1$ respectively. Then, the number of points of intersection of $y = y_1(x)$ and $y = y_2(x)$ is
Differential Equations Linear Differential Equations Analyzing Roots of LDE Solutions
HardSingle correctNew idea
Q11
Let $P(a, b)$ be a point on the parabola $y^2 = 8x$ such that the tangent at $P$ passes through the centre of the circle $x^2 + y^2 - 10x - 14y + 65 = 0$ . Let $A$ be the product of all possible values of $a$ and $B$ be the product of all possible values of…
Conic Sections General Conic Section Tangent to General Conic (T=0)
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q13
Let $\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ . If $\left(\left(\vec{a} \times \vec{b}\right) \times \hat{i}\right) \cdot \hat{k} = \dfrac{23}{2}$ , then $\left|\vec{b} \times 2\hat{j}\right|$ is equal to
Vector Algebra Triple Products VTP BAC-CAB Expansion
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q14
Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$ , is a multiple of 7 but not divisible by 5, then $9p$ is equal to
Probability
MediumSingle correct
Q15
Let a vertical tower $AB$ of height $2h$ stands on a horizontal ground. Let from a point $P$ on the ground a man can see upto height $h$ of the tower with an angle of elevation $2\alpha$ . When from $P$ , he moves a distance $d$ in the direction of…
Trigonometric Functions
HardSingle correct
Q16
$(p \wedge r) \Leftrightarrow (p \wedge (\sim q))$ is equivalent to $(\sim p)$ when $r$ is
Mathematical Reasoning
MediumSingle correct
Q17
If the plane $P$ passes through the intersection of two mutually perpendicular planes $2x + ky - 5z = 1$ and $3kx - ky + z = 5$ , $k < 3$ and intercepts a unit length on positive $x$ -axis, then the intercept made by the plane $P$ on the $y$ -axis is
Three Dimensional Geometry Planes in 3D Family of Planes
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q18
Let $A(1, 1)$ , $B(-4, 3)$ , $C(-2, -5)$ be vertices of a triangle $ABC$ , $P$ be a point on side $BC$ , and $\Delta_1$ and $\Delta_2$ be the areas of triangles $APB$ and $ABC$ , respectively. If $\Delta_1 : \Delta_2 = 4 : 7$ , then the area enclosed by the lines…
Straight Lines Straight Line Distance Section Ratio by a Line
MediumSingle correctNew ideaIdea asked in 3 years
Q19
If the circle $x^2 + y^2 - 2gx + 6y - 19c = 0$ , $g, c \in \mathbb{R}$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2cy = 8$ , then the length of intercept made by the circle on $x$ -axis is
Conic Sections General Conic Section Length of Intercept on a Line
MediumSingle correctNew idea
Q20
Let a function $f : \mathbb{R} \rightarrow \mathbb{R}$ be defined as : $f(x) = \begin{cases} \int_0^x (5 - |t-3|)\,dt, & x > 4 \\ x^2 + bx, & x \le 4 \end{cases}$ where $b \in \mathbb{R}$ . If $f$ is continuous at $x = 4$ , then which of the following…
Continuity and Differentiability Piecewise Differentiability
HardSingle correctIdea asked in 4 yearsAsked the year before
Q21
For $k \in \mathbb{R}$ , let the solutions of the equation $\cos\left(\sin^{-1}\left(x\cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}x\right)\right)\right)\right)\right) = k$ , $0 < |x| < \dfrac{1}{\sqrt{2}}$ be $\alpha$ and $\beta$ , where the inverse…
Inverse Trigonometric Functions Inverse Trig Identities Evaluating Trig of Inverse Trig
HardNumerical valueNew ideaIdea asked in 2 years
Q22
The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ________.
Statistics Variance and SD Correcting Incorrect Variance
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q23
Let the line $\dfrac{x-3}{7} = \dfrac{y-2}{-1} = \dfrac{z-3}{-4}$ intersect the plane containing the lines $\dfrac{x-4}{1} = \dfrac{y+1}{-2} = \dfrac{z}{1}$ and $4ax - y + 5z - 7a = 0 = 2x - 5y - z - 3$ , $a \in \mathbb{R}$ at the point…
Three Dimensional Geometry Planes in 3D Intersection Point of Line and Plane
HardNumerical valueIdea asked in 2 yearsAsked the year before
Q24
An ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ passes through the vertices of the hyperbola $H : \dfrac{x^2}{49} - \dfrac{y^2}{64} = -1$ . Let the major and minor axes of the ellipse $E$ coincide with the transverse and conjugate axes of the…
Conic Sections Ellipse Eccentricity Length of Latus Rectum
HardNumerical valueIdea asked in 6 years
Q25
Let $y = y(x)$ be the solution curve of the differential equation $\sin\left(2x^2\right)\log_e\left(\tan x^2\right)dy + \left(4xy - 4\sqrt{2}\,x\sin\left(x^2 - \dfrac{\pi}{4}\right)\right)dx = 0$ , $0 < x < \sqrt{\dfrac{\pi}{2}}$ , which passes through the…
Differential Equations Linear Differential Equations Particular Solution Solving
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q26
Let $M$ and $N$ be the number of points on the curve $y^5 - 9xy + 2x = 0$ , where the tangents to the curve are parallel to $x$ -axis and $y$ -axis, respectively. Then the value of $M + N$ equals ________.
Application of Derivatives Tangents and Normals Tangents Parallel to Coordinate Axes
MediumNumerical valueNew idea
Q27
Let $f(x) = 2x^2 - x - 1$ and $S = \{n \in \mathbb{Z} : |f(n)| \le 800\}$ . Then, the value of $\sum_{n \in S} f(n)$ is equal to ________.
Sequences and Series
HardNumerical value
Q28
Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{-1, 0, 1\}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{\mathrm{T}}A$ is 6 is ________.
Permutations and Combinations Fundamental Counting Principle
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q29
If the length of the latus rectum of the ellipse $x^2 + 4y^2 + 2x + 8y - \lambda = 0$ is 4, and $l$ is the length of its major axis, then $\lambda + l$ is equal to ________.
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumNumerical valueIdea asked in 6 years
Q30
Let $S = \{z \in \mathbb{C} : z^2 + \bar{z} = 0\}$ . Then $\sum_{z \in S}\left(\mathrm{Re}(z) + \mathrm{Im}(z)\right)$ is equal to ________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Conjugate and Inverse
MediumNumerical valueIdea asked in 3 yearsAsked the year before

Dropped from the final key and left out of every count: Q12.

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.