JEE Main 2022 · July session

JEE Main 27 July 2022, Shift 2

88 questions (2 more dropped by NTA): 29 numerical-answer and 59 multiple choice. 13 were rated hard and 17 easy. Its hard-question count was the joint 9th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 88; 2 dropped by NTA
Numerical answer: 29; 33% of the shift
Hard: 13; 15% of the shift
Chapters asked: 66; 15 questions with a figure

Key findings · 27 Jul 2022, Shift 2

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 12 of 28 rated hard; Chemistry had the most easy questions (11 of 30).
3
29 questions tested a new idea, one no earlier year had asked: 40% of the 72 questions tagged to an idea.
4
35 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 (60% 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 6Medium 24Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 11Medium 18Hard 1

Top chapters

Maths

28 Q · 9 numerical

Easy 0Medium 16Hard 12

Top chapters

Question format

Single correct38 Q
Numerical value29 Q
Diagram based7 Q
Match the list5 Q
Other4 Q
Two statements3 Q
Assertion–reason2 Q

What each question asks you to do

Multi-step31 Q
Calculation22 Q
Application11 Q
Conceptual11 Q
Recall10 Q
Data or graph3 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
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

6 easy24 medium0 hard

Chemistry30 questions

11 easy18 medium1 hard

Q61
The correct decreasing order of energy for the orbitals having, following set of quantum numbers : (A) $n=3$ , $l=0$ , $m=0$ (B) $n=4$ , $l=0$ , $m=0$ (C) $n=3$ , $l=1$ , $m=0$ (D) $n=3$ , $l=2$ , $m=1$ is :
Structure of Atom Quantum Numbers Aufbau Principle and n+l Rule
EasySingle correctIdea asked in 5 yearsAsked the year before
Q62
Match **List - I** with **List - II**. List - I (A) $\psi_{MO}=\psi_A-\psi_B$ (B) $\mu=Q\times r$ (C) $\frac{N_b-N_a}{2}$ (D) $\psi_{MO}=\psi_A+\psi_B$ List - II (I) Dipole moment (II) Bonding molecular orbital (III) Anti-bonding molecular orbital (IV) Bond…
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
EasyMatch the listIdea asked in 3 yearsAsked the year before
Q63
The plot of pH-metric titration of weak base $\mathrm{NH_4OH}$ vs strong acid HCl looks like :
Equilibrium
MediumDiagram based · figure
Q64
Given below are two statements : **Statement I :** For KI, molar conductivity increases steeply with dilution **Statement II :** For carbonic acid, molar conductivity increases slowly with dilution In the light of the above statements, choose the **correct**…
Electrochemistry
MediumTwo statements
Q65
Given below are two statements : one is labelled as **Assertion (A)** and the other is labelled as **Reason (R)**. **Assertion (A) :** Dissolved substances can be removed from a colloidal solution by diffusion through a parchment paper. **Reason (R) :**…
Surface Chemistry Colloids Peptization and Dialysis
MediumAssertion–reasonNew idea
Q66
Outermost electronic configurations of four elements A, B, C, D are given below : (A) $3s^2$ (B) $3s^23p^1$ (C) $3s^23p^3$ (D) $3s^23p^4$ The **correct** order of first ionization enthalpy for them is :
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q67
An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is :
The s-Block Elements s-Block Elements Diagonal Relationship
EasySingle correctIdea asked in 3 years
Q68
Given below are two statements : one is labelled as **Assertion (A)** and the other is labelled as **Reason (R)**. **Assertion (A) :** Boron is unable to form $\mathrm{BF_6^{3-}}$ . **Reason (R) :** Size of B is very small. In the light of the above…
The p-Block Elements
MediumAssertion–reason
Q69
In neutral or alkaline solution, $\mathrm{MnO_4^-}$ oxidises thiosulphate to :
The d- and f-Block Elements d-Block Elements Specific KMnO4 Oxidations in Neutral/Alkaline Medium
MediumSingle correctNew ideaIdea asked in 2 years
Q70
Low oxidation state of **metals** in their complexes are common when ligands :
Coordination Compounds Crystal Field Theory Pi-Bonding and the Spectrochemical Series
MediumSingle correctNew idea
Q71
Given below are two statements : **Statement I :** The non bio-degradable fly ash and slag from steel industry can be used by cement industry. **Statement II :** The fuel obtained from plastic waste is lead free. In the light of the above statements, choose…
Environmental Chemistry Non-Biodegradable Industrial Solid Wastes
EasyTwo statementsNew ideaIdea asked in 2 years
Q72
The structure of A in the given reaction is : [figure: R-C(=O)-CH3 treated with NaOH and CH3CH2-Br (drawn as zigzag line with Br); product A (major product)]
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Alpha-Hydrogen Acidity
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q73
Major product ‘B’ of the following reaction sequence is : $\mathrm{CH_3-C(CH_3)=CH-CH_3}$ $\xrightarrow[\mathrm{CH_3OH}]{\mathrm{Br_2}}$ A $\xrightarrow{\mathrm{HI}}$ B (major product)
Hydrocarbons Alkenes and Alkynes Halohydrin Formation Regiochemistry
HardDiagram based · figureIdea asked in 2 yearsAsked the year before
Q74
Match **List - I** with **List - II**. List - I (A) $\mathrm{C_6H_5COCl}$ $\xrightarrow[\mathrm{Pd-BaSO_4}]{\mathrm{H_2}}$ $\mathrm{C_6H_5CHO}$ (B) $\mathrm{CH_3-CN}$ $\xrightarrow[\mathrm{H_3O^+}]{\mathrm{SnCl_2/HCl}}$ $\mathrm{CH_3-CHO}$ (C)…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Rosenmund Reduction
MediumMatch the list · figureIdea asked in 4 yearsAsked the year before
Q75
Match List - I with List - II. List - I (Polymer) (A) Neoprene (B) Teflon (C) Acrilan (D) Natural rubber List - II (Monomer) (I) Acrylonitrile (II) Chloroprene (III) Tetrafluoroethene (IV) Isoprene Choose the **correct** answer from the options given below :
Polymers Neoprene Synthesis
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q76
An organic compound ‘A’ contains nitrogen and chlorine. It dissolves readily in water to give a solution that turns litmus red. Titration of compound ‘A’ with standard base indicates that the molecular weight of ‘A’ is $131\pm2$ . When a sample of ‘A’ is…
Amines Diazotization of Primary Aromatic Amines
MediumDiagram based · figureNew idea
Q77
Match **List - I** with **List - II**. List - I (A) Glucose + HI (B) Glucose + $\mathrm{Br_2}$ water (C) Glucose + acetic anhydride (D) Glucose + $\mathrm{HNO_3}$ List - II (I) Gluconic acid (II) Glucose pentacetate (III) Saccharic acid (IV) Hexane Choose…
Biomolecules Carbohydrates Reduction with HI and Red Phosphorus
MediumMatch the listNew ideaIdea asked in 2 years
Q78
Which of the following enhances the lathering property of soap ?
Chemistry in Everyday Life Soaps and Detergents
EasySingle correctNew idea
Q79
Match **List - I** with **List - II**. List - I (Mixture) (A) Chloroform & Aniline (B) Benzoic acid & Napthalene (C) Water & Aniline (D) Napthalene & Sodium chloride List - II (Purification Process) (I) Steam distillation (II) Sublimation (III) Distillation…
Organic Chemistry: Some Basic Principles and Techniques
EasyMatch the list
Q80
$\mathrm{Fe^{3+}}$ cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of :
The d- and f-Block Elements Cation Analysis Confirmatory Tests
EasySingle correctIdea asked in 4 yearsAsked the year before
Q81
The normality of $\mathrm{H_2SO_4}$ in the solution obtained on mixing 100 mL of 0.1 M $\mathrm{H_2SO_4}$ with 50 mL of 0.1 M NaOH is ________ $\times10^{-1}$ N. (Nearest Integer)
Some Basic Concepts of Chemistry Mole Concept Normality and n-factor Calculation
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q82
For a real gas at 25°C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal’s constant ‘b’ should be __________ $\times10^{-2}$ L $\mathrm{mol^{-1}}$ (Nearest integer) (Given…
States of Matter Real Gases Compressibility Factor Z
MediumNumerical valueNew ideaIdea asked in 2 years
Q83
A gas (Molar mass=280 g $\mathrm{mol^{-1}}$ ) was burnt in excess $\mathrm{O_2}$ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bomb Calorimetry Calculations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q84
When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of…
Solutions Colligative Properties RLVP to Molality Approximation Formula
MediumNumerical valueNew idea
Q85
[A] $\rightarrow$ [B] Reactant Product If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half of its initial concentration. Then the rate constant of the reaction is…
Chemical Kinetics Integrated Rate Equations First Order Half-Life
EasyNumerical valueNew ideaIdea asked in 3 years
Q86
Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of principal ores if iron is __________.
General Principles and Processes of Isolation of Elements
EasyNumerical value
Q87
The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic medium is __________.
The d- and f-Block Elements d-Block Elements Specific KMnO4 Oxidations in Neutral/Alkaline Medium
MediumNumerical valueNew ideaIdea asked in 2 years
Q88
The number of molecule(s) or ion(s) from the following having non-planar structure is __________. $\mathrm{NO_3^-}$ , $\mathrm{H_2O_2}$ , $\mathrm{BF_3}$ , $\mathrm{PCl_3}$ , $\mathrm{XeF_4}$ , $\mathrm{SF_4}$ , $\mathrm{XeO_3}$ , $\mathrm{PH_4^+}$ ,…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 4 Shapes
MediumNumerical valueNew ideaIdea asked in 3 years
Q89
The spin only magnetic moment of the complex present in Fehling’s reagent is __________ B.M. (Nearest integer).
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q90
In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is __________ $\times10^{-2}$ g. (Nearest integer) [figure: toluene (CH3 on benzene ring), 5 g, arrow to benzaldehyde (CHO on benzene…
Some Basic Concepts of Chemistry Stoichiometry Theoretical and Percent Yield
EasyNumerical value · figureIdea asked in 2 yearsAsked the year before

Maths28 questions

0 easy16 medium12 hard

Q1
The domain of the function $f(x) = \sin^{-1}[2x^2 - 3] + \log_2\left(\log_{\frac{1}{2}}(x^2 - 5x + 5)\right)$ , where [t] is the greatest integer function, is :
Relations and Functions Functions and Domain Inverse Trig Function Domain
HardSingle correctNew ideaIdea asked in 4 years
Q2
Let S be the set of all $(\alpha, \beta)$ , $\pi < \alpha, \beta < 2\pi$ , for which the complex number $\frac{1 - i\sin\alpha}{1 + 2i\sin\alpha}$ is purely imaginary and $\frac{1 + i\cos\beta}{1 - 2i\cos\beta}$ is purely real. Let…
Complex Numbers and Quadratic Equations
HardSingle correct
Q4
Let $A = \begin{pmatrix} 4 & -2 \\ \alpha & \beta \end{pmatrix}$ . If $A^2 + \gamma A + 18I = O$ , then det (A) is equal to __________.
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q5
If for $p \neq q \neq 0$ , the function $f(x) = \frac{\sqrt[7]{p(729 + x)} - 3}{\sqrt[3]{729 + qx} - 9}$ is continuous at $x = 0$ , then :
Continuity and Differentiability Continuity at a Point
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q6
Let $f(x) = 2 + |x| - |x - 1| + |x + 1|$ , $x \in \mathbf{R}$ . Consider (S1) : $f'\left(-\frac{3}{2}\right) + f'\left(-\frac{1}{2}\right) + f'\left(\frac{1}{2}\right) + f'\left(\frac{3}{2}\right) = 2$ (S2) : $\int_{-2}^{2} f(x)\,dx = 12$ Then,
Continuity and Differentiability Differentiability of Modulus Functions
MediumTwo statementsIdea asked in 5 yearsAsked the year before
Q7
Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be $\frac{98}{25}$ . Then the sum of the first 21 terms of an AP, whose first term is 10ar, $n^{th}$ term is $a_n$ and the common…
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q8
The area of the region enclosed by $y \leq 4x^2$ , $x^2 \leq 9y$ and $y \leq 4$ , is equal to :
Application of Integrals Area Under Curves Area Between Curves
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q9
$\int_0^2 \left(\left|2x^2 - 3x\right| + \left[x - \frac{1}{2}\right]\right) dx$ , where [t] is the greatest integer function, is equal to :
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q10
Consider a curve $y = y(x)$ in the first quadrant as shown in the figure. Let the area $A_1$ is twice the area $A_2$ . Then the normal to the curve perpendicular to the line $2x - 12y = 15$ does NOT pass through the point.
Differential Equations Area Under Curves Curves from Area Properties
HardDiagram based · figureNew ideaIdea asked in 2 years
Q11
The equations of the sides AB, BC and CA of a triangle ABC are $2x + y = 0$ , $x + py = 39$ and $x - y = 3$ respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true ?
Straight Lines
HardSingle correct
Q12
A circle $C_1$ passes through the origin O and has diameter 4 on the positive $x$ -axis. The line $y = 2x$ gives a chord OA of circle $C_1$ . Let $C_2$ be the circle with OA as a diameter. If the tangent to $C_2$ at the point A meets the $x$ -axis at P and…
Conic Sections Circle Tangents Tangent at a point (T=0)
MediumSingle correctNew idea
Q13
If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is $x + y = a$ , is 16, then $|a|$ is equal to :
Conic Sections
MediumSingle correct
Q14
If the length of the perpendicular drawn from the point P(a, 4, 2), a > 0 on the line $\frac{x+1}{2} = \frac{y-3}{3} = \frac{z-1}{-1}$ is $2\sqrt{6}$ units and $Q(\alpha_1, \alpha_2, \alpha_3)$ is the image of the point P in this line, then…
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q15
If the line of intersection of the planes $ax + by = 3$ and $ax + by + cz = 0$ , a > 0 makes an angle $30^\circ$ with the plane $y - z + 2 = 0$ , then the direction cosines of the line are :
Three Dimensional Geometry Planes in 3D Direction of Line of Intersection
MediumSingle correctNew idea
Q16
Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $P(X > n - 3) = \frac{k}{2^n}$ , then k is equal to :
Probability
MediumSingle correct
Q17
A six faced die is biased such that $3 \times P(\text{a prime number}) = 6 \times P(\text{a composite number}) = 2 \times P(1)$ . Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is…
Probability
MediumSingle correct
Q18
The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $45^\circ$ . Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is $60^\circ$ . If…
Trigonometric Functions
MediumSingle correct
Q19
Let $S = \left\{\theta \in \left(0, \frac{\pi}{2}\right) : \sum_{m=1}^{9} \sec\left(\theta + (m-1)\frac{\pi}{6}\right)\sec\left(\theta + \frac{m\pi}{6}\right) = -\frac{8}{\sqrt{3}}\right\}$ . Then
Trigonometric Functions Trigonometric Identities Telescopic Trigonometric Series
HardSingle correctNew idea
Q20
If the truth value of the statement $(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q)$ is F, then the truth value of which of the following is F ?
Mathematical Reasoning
MediumSingle correct
Q21
Consider a matrix $A = \begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^2 & \beta^2 & \gamma^2 \\ \beta + \gamma & \gamma + \alpha & \alpha + \beta \end{bmatrix}$ , where $\alpha, \beta, \gamma$ are three distinct natural numbers. If…
Determinants Matrix Inverse Inverse Relation to Double Adjoint
HardNumerical valueIdea asked in 6 years
Q22
The number of functions f, from the set $A = \{x \in \mathbf{N} : x^2 - 10x + 9 \leq 0\}$ to the set $B = \{n^2 : n \in \mathbf{N}\}$ such that $f(x) \leq (x - 3)^2 + 1$ , for every $x \in A$ , is __________.
Relations and Functions Permutations and Combinations Total Number of Functions
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q23
Let for the $9^{th}$ term in the binomial expansion of $(3 + 6x)^n$ , in the increasing powers of $6x$ , to be the greatest for $x = \frac{3}{2}$ , the least value of n is $n_0$ . If k is the ratio of the coefficient of $x^6$ to the coefficient of $x^3$ , then…
Binomial Theorem Binomial Coefficients Ratio of Consecutive Coefficients
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q24
$\frac{2^3 - 1^3}{1 \times 7} + \frac{4^3 - 3^3 + 2^3 - 1^3}{2 \times 11} + \frac{6^3 - 5^3 + 4^3 - 3^3 + 2^3 - 1^3}{3 \times 15} + \cdots + \frac{30^3 - 29^3 + 28^3 - 27^3 + \ldots + 2^3 - 1^3}{15 \times 63}$ is equal to __________.
Sequences and Series AP and GP Method of Differences for Telescoping Series
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q25
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $\tan^{-1}\frac{3}{4}$ . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which…
Application of Derivatives Chain Rule Chain Rule in Related Rates
MediumNumerical valueIdea asked in 2 years
Q26
For the curve $C : (x^2 + y^2 - 3) + (x^2 - y^2 - 1)^5 = 0$ , the value of $3y' - y^3 y''$ , at the point $(\alpha, \alpha)$ , $\alpha > 0$ , on C, is equal to __________.
Continuity and Differentiability Chain Rule Implicit Chain Rule
HardNumerical valueIdea asked in 2 years
Q27
Let $f(x) = \min\{[x - 1], [x - 2], \ldots, [x - 10]\}$ where [t] denotes the greatest integer $\leq$ t. Then $\int_0^{10} f(x)\,dx + \int_0^{10} (f(x))^2\,dx + \int_0^{10} |f(x)|\,dx$ is equal to __________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q28
Let f be a differentiable function satisfying $f(x) = \frac{2}{\sqrt{3}} \int_0^{\sqrt{3}} f\left(\frac{\lambda^2 x}{3}\right) d\lambda$ , $x > 0$ and $f(1) = \sqrt{3}$ . If $y = f(x)$ passes through the point $(\alpha, 6)$ , then $\alpha$ is equal to __________.
Differential Equations Leibniz Rule Solving Integral Equations
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q29
A common tangent T to the curves $C_1 : \frac{x^2}{4} + \frac{y^2}{9} = 1$ and $C_2 : \frac{x^2}{42} - \frac{y^2}{143} = 1$ does not pass through the fourth quadrant. If T touches $C_1$ at $(x_1, y_1)$ and $C_2$ at $(x_2, y_2)$ , then $|2x_1 + x_2|$ is equal…
Conic Sections Tangents and Normals Common Tangents to Two Curves
HardNumerical valueNew idea

Dropped from the final key and left out of every count: Q3, Q30.

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.