JEE Main 2022 · July session

JEE Main 29 July 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 35 easy. Its hard-question count was the joint 19th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Complex Numbers and Quadratic Equations, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 65; 9 questions with a figure

Key findings · 29 Jul 2022, Shift 2

1
11 hard questions (12%): the joint 19th 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 10 of 30 rated hard; Chemistry had the most easy questions (17 of 30).
3
39 questions tested a new idea, one no earlier year had asked: 48% of the 81 questions tagged to an idea.
4
38 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
43 shared an idea with another 2022 shift (53% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Alternating Current in Physics (2), The p-Block Elements in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 15Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 17Medium 12Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 17Hard 10

Top chapters

Complex Numbers and Quadratic Equations3 Q
Conic Sections2 Q
Continuity and Differentiability2 Q
Differential Equations2 Q
Integrals2 Q
Matrices2 Q

Question format

Single correct51 Q
Numerical value30 Q
Diagram based3 Q
Assertion–reason2 Q
Two statements2 Q
Match the list1 Q
Other1 Q

What each question asks you to do

Calculation30 Q
Multi-step29 Q
Recall11 Q
Conceptual10 Q
Application8 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
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

15 easy15 medium0 hard

Chemistry30 questions

17 easy12 medium1 hard

Q61
Consider the reaction $4\ \mathrm{HNO_3(l)} + 3\ \mathrm{KCl(s)} \rightarrow \mathrm{Cl_2(g)} + \mathrm{NOCl(g)} + 2\ \mathrm{H_2O(g)} + 3\ \mathrm{KNO_3(s)}$ The amount of $\mathrm{HNO_3}$ required to produce 110.0 g of $\mathrm{KNO_3}$ is (Given: Atomic…
Some Basic Concepts of Chemistry Stoichiometry Mass-Mass Stoichiometry
EasySingle correctIdea asked in 3 years
Q62
Given below are the quantum numbers for 4 electrons. A. $n = 3, l = 2, m_l = 1, m_s = +1/2$ B. $n = 4, l = 1, m_l = 0, m_s = +1/2$ C. $n = 4, l = 2, m_l = -2, m_s = -1/2$ D. $n = 3, l = 1, m_l = -1, m_s = +1/2$ The correct order of increasing energy is
Structure of Atom Quantum Numbers Aufbau Principle and n+l Rule
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q63
$\mathrm{C(s)} + \mathrm{O_2(g)} \rightarrow \mathrm{CO_2(g)} + 400\ \mathrm{kJ}$ $\mathrm{C(s)} + \frac{1}{2}\mathrm{O_2(g)} \rightarrow \mathrm{CO(g)} + 100\ \mathrm{kJ}$ When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Formation and Combustion
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q64
200 mL of 0.01 M HCl is mixed with 400 mL of 0.01M $\mathrm{H_2SO_4}$ . The pH of the mixture is __. Given: log 2 = 0.30, log 3 = 0.48, log 5 = 0.70, log 7 = 0.84, log 11 = 1.04
Equilibrium pH and Buffers pH of Mixed Strong Acids
MediumSingle correctNew idea
Q65
Given below are the critical temperatures of some of the gases: | Gas | Critical temperature (K) | | He | 5.2 | | $\mathrm{CH_4}$ | 190.0 | | $\mathrm{CO_2}$ | 304.2 | | $\mathrm{NH_3}$ | 405.5 | The gas showing least adsorption on a definite amount of…
Surface Chemistry Adsorption Critical Temperature and Extent of Adsorption
EasySingle correctNew ideaIdea asked in 2 years
Q66
In liquation process used for tin (Sn), the metal
General Principles and Processes of Isolation of Elements Metallurgical Extraction Liquation Refining Principle
EasySingle correctIdea asked in 2 yearsAsked the year before
Q67
Given below are two statements. Statement I: Stannane is an example of a molecular hydride. Statement II: Stannane is a planar molecule. In the light of the above statement, choose the most appropriate answer from the options given below.
Hydrogen Hydrogen and Hydrides Covalent Hydride Types
EasyTwo statementsNew ideaIdea asked in 2 years
Q68
Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?
The p-Block Elements
EasySingle correct
Q69
When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to
The p-Block Elements Group 13 & 14 Borax Bead Test Chemistry
EasySingle correctNew idea
Q70
Which of the following 3d-metal ion will give the lowest enthalpy of hydration ( $\Delta_{hyd}H$ ) when dissolved in water ?
The d- and f-Block Elements Crystal Field Theory CFSE and Hydration Enthalpy Double-Hump
MediumSingle correctNew idea
Q71
Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion?(en – ethylenediamine; $\mathrm{H_2N\text{-}CH_2\text{-}CH_2\text{-}NH_2}$ )
Coordination Compounds Crystal Field Theory Jahn-Teller Distortion
MediumSingle correctNew idea
Q72
Dinitrogen is a robust compound, but reacts at high altitudes to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is
Environmental Chemistry NO2 and Traffic Red Haze
EasySingle correctNew idea
Q73
Correct structure of $\gamma$ -methylcyclohexane carbaldehyde is
Aldehydes, Ketones and Carboxylic Acids
EasySingle correct · figure
Q74
Compound ‘A’ undergoes following sequence of reactions to give compound ‘B’. The correct structure and chirality of compound ‘B’ is [where Et is $\mathrm{-C_2H_5}$ ] [figure: Compound 'A' skeletal alkyl bromide drawn with a bold central bond and a Br…
Haloalkanes and Haloarenes Alkanes and Free Radicals Hydrolysis of Grignard Reagents
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q75
Given below are two statements. Statement I: The compound [figure: compound (A), a drawn structure with a stereocentre bearing $\mathrm{NO_2}$ (bold wedge), H (hashed), a $\mathrm{CH{=}CH{-}CH_3}$ chain on one side and a $\mathrm{CH{=}CH{-}CH_3}$ chain on…
Haloalkanes and Haloarenes Stereoisomerism Chiral Centers
MediumTwo statements · figureIdea asked in 5 years
Q76
When enthanol is heated with conc. $\mathrm{H_2SO_4}$ , a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is
Alcohols, Phenols and Ethers Alcohols and Phenols Alcohol Dehydration Ease
EasySingle correctIdea asked in 6 yearsAsked the year before
Q77
The Hinsberg reagent is
Amines Hinsberg Test
EasySingle correct · figureIdea asked in 5 yearsAsked the year before
Q78
Which of the following is NOT a natural polymer?
Polymers Polymer Classification
EasySingle correctIdea asked in 3 yearsAsked the year before
Q79
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Amylose is insoluble in water. Reason R: Amylose is a long linear molecule with more than 200 glucose units. In the light of the above…
Biomolecules Carbohydrates Structure of Amylose
MediumAssertion–reasonNew idea
Q80
A compound ‘X’ is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with $\mathrm{CH_3COOH}$ . Compound ‘X’ exists in ionized form in basic medium. The compound ‘X’ is
Equilibrium pH and Buffers Acid-Base Indicator Transition Range
EasySingle correctNew idea
Q81
‘x’ g of molecular oxygen ( $\mathrm{O_2}$ ) is mixed with 200 g of neon (Ne). The total pressure of the non-reactive mixture of $\mathrm{O_2}$ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value…
States of Matter Ideal Gas Laws Dalton's Law
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q82
Consider, $\mathrm{PF_5}$ , $\mathrm{BrF_5}$ , $\mathrm{PCl_3}$ , $\mathrm{SF_6}$ , $\mathrm{[ICl_4]^{-}}$ , $\mathrm{ClF_3}$ and $\mathrm{IF_5}$ . Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having $\mathrm{sp^3d^2}$ hybridisation is ___.
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q83
1.80 g of solute A was dissolved in 62.5 $\mathrm{cm^3}$ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is __ g $\mathrm{mol^{-1}}$ . [Given: Freezing point of ethanol is 156.0 K. Density of ethanol is 0.80 g…
Solutions Colligative Properties Molar Mass Determination
MediumNumerical valueNew idea
Q84
For a cell, $\mathrm{Cu(s) \mid Cu^{2+}(0.001M) \mid\mid Ag^{+}(0.01M) \mid Ag(s)}$ the cell potential is found to be 0.43 V at 298 K. The magnitude of standard electrode potential for $\mathrm{Cu^{2+}/Cu}$ is ____ $\times\ 10^{-2}$ V. [Given :…
Electrochemistry Nernst Equation Full Cell Nernst Equation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q85
Assuming 1µg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ____ $\times\ 10^{-1}\ \mu$ g. [Given: ln 10 = 2.303; log 2 = 0.30]
Chemical Kinetics Integrated Rate Equations Concentration After N Half-Lives
EasyNumerical valueNew idea
Q86
Sum of oxidation state (magnitude) and coordination number of cobalt in $\mathrm{Na[Co(bpy)Cl_4]}$ is ____. (Given: bpy = [figure: 2,2'-bipyridine, two pyridine rings joined by a single bond, with the two N atoms on the same side])
Coordination Compounds Coordination Nomenclature Oxidation State Calculation
EasyNumerical value · figureIdea asked in 4 yearsAsked the year before
Q87
Consider the following sulphur based oxoacids. $\mathrm{H_2SO_3}$ , $\mathrm{H_2SO_4}$ , $\mathrm{H_2S_2O_8}$ and $\mathrm{H_2S_2O_7}$ . Amongst these oxoacids, the number of those with peroxo (O-O) bond is ______
The p-Block Elements Group 15 & 16 Sulfur Oxoacids
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q88
A 1.84 mg sample of polyhydric alcoholic compound ‘X’ of molar mass 92.0 g/mol gave 1.344 mL of $\mathrm{H_2}$ gas at STP. The number of alcoholic hydrogens present in compound ‘X’ is ______.
Alcohols, Phenols and Ethers Stoichiometry Mass-Volume Stoichiometry at STP
MediumNumerical valueNew ideaIdea asked in 3 years
Q89
The number of stereoisomers formed in a reaction of $(\pm)$ Ph(C=O)C(OH)(CN)Ph with HCN is _________ . [where Ph is - $\mathrm{C_6H_5}$ ]
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Stereochemistry of Nucleophilic Addition
HardNumerical valueNew idea
Q90
The number of chlorine atoms in bithionol is ______ .
Chemistry in Everyday Life Bithionol in Medicated Soaps
EasyNumerical valueNew idea

Maths30 questions

3 easy17 medium10 hard

Q1
If $z\neq 0$ be a complex number such that $\left|z-\frac{1}{z}\right|=2$ , then the maximum value of $|z|$ is :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Triangle Inequality Extrema
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q2
Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix}-1 & 2\\ 1 & -1\end{bmatrix}$ by a single elementary row operation ?
Matrices Matrix Inverse Elementary Row Transformations
EasySingle correctNew idea
Q3
If the system of equations $x+y+z=6$ $2x+5y+\alpha z=\beta$ $x+2y+3z=14$ has infinitely many solutions, then $\alpha+\beta$ is equal to
Determinants Cramer's Rule Condition for Infinite Solutions
EasySingle correctIdea asked in 7 yearsAsked the year before
Q4
Let the function $f(x)=\begin{cases}\dfrac{\log_e(1+5x)-\log_e(1+\alpha x)}{x} & ;\ if\ x\neq 0\\ 10 & ;\ if\ x=0\end{cases}$ be continuous at $x=0$ . Then $\alpha$ is equal to
Continuity and Differentiability Finding Unknown Constants for Continuity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q5
If $[t]$ denotes the greatest integer $\leq t$ , then the value of $\int_0^1\left[2x-\left|3x^2-5x+2\right|+1\right]dx$ is :
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardSingle correctIdea asked in 7 yearsAsked the year before
Q6
Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0=a_1=0$ and $a_{n+2}=3a_{n+1}-2a_n+1,\ \forall n\geq 0$ . Then $a_{25}a_{23}-2a_{25}a_{22}-2a_{23}a_{24}+4a_{22}a_{24}$ is equal to
Sequences and Series Arithmetico-Geometric Series AGP Recurrence Relation
HardSingle correctNew ideaIdea asked in 2 years
Q7
$\sum_{r=1}^{20}\left(r^2+1\right)(r!)$ is equal to
Permutations and Combinations AP and GP Method of Differences for Telescoping Series
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q8
For $I(x)=\int\frac{\sec^2x-2022}{\sin^{2022}x}dx$ , if $I\left(\frac{\pi}{4}\right)=2^{1011}$ , then
Integrals
HardSingle correct
Q9
If the solution curve of the differential equation $\frac{dy}{dx}=\frac{x+y-2}{x-y}$ passes through the points $(2, 1)$ and $(k+1, 2)$ , $k>0$ , then
Differential Equations Homogeneous Equations Identifying Equations Reducible to Homogeneous Form
HardSingle correctNew idea
Q10
Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx}+\left(\frac{2x^2+11x+13}{x^3+6x^2+11x+6}\right)y=\frac{(x+3)}{x+1}$ , $x>-1$ , which passes through the point $(0, 1)$ . Then $y(1)$ is equal to :
Differential Equations Linear Differential Equations Particular Solution Solving
HardSingle correctIdea asked in 4 yearsAsked the year before
Q11
Let $m_1$ , $m_2$ be the slopes of two adjacent sides of a square of side a such that $a^2+11a+3\left(m_1^2+m_2^2\right)=220$ . If one vertex of the square is $(10(\cos\alpha-\sin\alpha),\ 10\,(\sin\alpha+\cos\alpha))$ , where…
Straight Lines Straight Line Distance Square Area from Vertex and Diagonal
HardSingle correctNew ideaIdea asked in 2 years
Q12
The number of elements in the set $S=\left\{x\in\mathbb{R}:2\cos\left(\frac{x^2+x}{6}\right)=4^x+4^{-x}\right\}$ is :
Trigonometric Functions General Solutions AM-GM Inequality Bounds in Trig Equations
MediumSingle correctNew idea
Q13
Let A $(\alpha,-2)$ , B $(\alpha, 6)$ and C $\left(\frac{\alpha}{4},-2\right)$ be vertices of a $\Delta$ ABC. If $\left(5,\frac{\alpha}{4}\right)$ is the circumcentre of $\Delta$ ABC, then which of the following is NOT correct about $\Delta$ ABC ?
Straight Lines Properties of Triangles Inradius and Circumradius
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q14
Let $Q$ be the foot of perpendicular drawn from the point $P\,(1, 2, 3)$ to the plane $x+2y+z=14$ . If $R$ is a point on the plane such that $\angle PRQ=60^{\mathrm{o}}$ , then the area of $\Delta PQR$ is equal to :
Three Dimensional Geometry Point-Plane Distance Foot of Perpendicular
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q15
If $(2, 3, 9)$ , $(5, 2, 1)$ , $(1, \lambda, 8)$ and $(\lambda, 2, 3)$ are coplanar, then the product of all possible values of $\lambda$ is :
Three Dimensional Geometry Triple Products Coplanarity of Four Points
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability,…
Probability Bayes' Theorem Urn and Ball Transfer Problems
MediumSingle correctNew idea
Q17
Let S $=\left\{z=x+iy:|z-1+i|\geq|z|,|z|<2,|z+i|=|z-1|\right\}$ . Then the set of all values of $x$ , for which $w=2x+iy\in$ S for some $y\in\mathbb{R}$ , is
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Locus of Full Line via Argument
HardSingle correctNew idea
Q18
Let $\vec{a},\vec{b},\vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and…
Vector Algebra Cross Product Lagrange's Identity
HardSingle correctIdea asked in 5 yearsAsked the year before
Q19
The domain of the function $f(x)=\sin^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$ is :
Relations and Functions Inverse Trig Domains Domain of Rational Composite Inverse Trig
MediumSingle correctNew idea
Q20
The statement $(p\Rightarrow q)\vee(p\Rightarrow r)$ is NOT equivalent to
Mathematical Reasoning
MediumSingle correct
Q21
The sum and product of the mean and variance of a binomial distribution are 82·5 and 1350 respectively. Then the number of trials in the binomial distribution is ________.
Probability
MediumNumerical value
Q22
Let $\alpha,\beta\ (\alpha>\beta)$ be the roots of the quadratic equation $x^2-x-4=0$ . If $P_n=\alpha^n-\beta^n$ , $n\in\mathbb{N}$ , then $\frac{P_{15}P_{16}-P_{14}P_{16}-P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}$ is equal to ________.
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q23
Let $X=\begin{bmatrix}1\\1\\1\end{bmatrix}$ and $A=\begin{bmatrix}-1 & 2 & 3\\ 0 & 1 & 6\\ 0 & 0 & -1\end{bmatrix}$ . For $k\in\mathbb{N}$ , if $X'A^kX=33$ , then k is equal to ________.
Matrices Matrix Multiplication Powers of Square Matrices
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q24
The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is ________.
Permutations and Combinations Permutations with Repetition
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q25
If $\sum_{k=1}^{10}K^2\left({}^{10}C_K\right)^2=22000L$ , then $L$ is equal to ________.
Binomial Theorem Binomial Coefficients r-Weighted Sum of Squares
MediumNumerical valueNew idea
Q26
If $[t]$ denotes the greatest integer $\leq t$ , then the number of points, at which the function $f(x)=4\,|2x+3|+9\left[x+\frac{1}{2}\right]-12\,[x+20]$ is not differentiable in the open interval $(-20, 20)$ , is ________.
Continuity and Differentiability Continuity involving GIF and Fractional Part
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q27
If the tangent to the curve $y=x^3-x^2+x$ at the point $(a, b)$ is also tangent to the curve $y=5x^2+2x-25$ at the point $(2,-1)$ , then $|2a+9b|$ is equal to ________
Application of Derivatives Tangents and Normals Common Tangents to Two Curves
MediumNumerical valueNew idea
Q28
Let $AB$ be a chord of length 12 of the circle $(x-2)^2+(y+1)^2=\frac{169}{4}$ . If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$ , then five times the distance of point $P$ from chord $AB$ is equal to ________.
Conic Sections Circle Tangents Chord of contact
MediumNumerical valueNew idea
Q29
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|^2=|\vec{a}|^2+2|\vec{b}|^2$ , $\vec{a}\cdot\vec{b}=3$ and $|\vec{a}\times\vec{b}|^2=75$ . Then $|\vec{a}|^2$ is equal to ________.
Vector Algebra Cross Product Lagrange's Identity
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q30
Let $S=\left\{(x,y)\in\mathbb{N}\times\mathbb{N}:9(x-3)^2+16(y-4)^2\leq144\right\}$ and $T=\left\{(x,y)\in\mathbb{R}\times\mathbb{R}:(x-7)^2+(y-4)^2\leq 36\right\}$ . Then $n(S\cap T)$ is equal to ________
Conic Sections
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.