JEE Main 2021 · July session

JEE Main 22 July 2021, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 36 easy. Its hard-question count was the joint 6th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 63; 12 questions with a figure

Key findings · 22 Jul 2021, Shift 2

1
11 hard questions (12%): the joint 6th highest count of the 24 2021 shifts Lumi analysed. Across those shifts the hard share ran from 3% to 17%.
2
Maths was the hardest section, with 9 of 30 rated hard; Chemistry had the most easy questions (17 of 30).
3
49 questions tested a new idea, one no earlier year had asked: 67% of the 73 questions tagged to an idea.
4
23 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
42 shared an idea with another 2021 shift (58% 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), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 14Medium 14Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 17Medium 13Hard 0

Top chapters

Organic Chemistry: Some Basic Principles and Techniques3 Q
Alcohols, Phenols and Ethers2 Q
Amines2 Q
Hydrocarbons2 Q
Solutions2 Q
The p-Block Elements2 Q

Maths

30 Q · 10 numerical

Easy 5Medium 16Hard 9

Top chapters

Question format

Single correct48 Q
Numerical value30 Q
Diagram based5 Q
Match the list4 Q
Other2 Q
Two statements1 Q

What each question asks you to do

Calculation28 Q
Multi-step25 Q
Application16 Q
Recall10 Q
Conceptual9 Q
Diagram reading1 Q
Data or graph1 Q

Most common: Calculation.

Against the other 2021 shifts

This shift next to the 23 other 2021 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 Feb, Shift 1	90	36%	7%	33%	68%	24%
24 Feb, Shift 2	88	43%	5%	32%	63%	21%
25 Feb, Shift 1	90	23%	11%	33%	65%	30%
25 Feb, Shift 2	89	35%	10%	34%	67%	24%
26 Feb, Shift 1	88	50%	3%	33%	78%	17%
26 Feb, Shift 2	90	27%	12%	33%	80%	29%
16 Mar, Shift 2	90	31%	7%	33%	69%	33%
17 Mar, Shift 1	89	39%	8%	34%	61%	26%
17 Mar, Shift 2	89	36%	17%	34%	66%	32%
18 Mar, Shift 1	90	40%	9%	33%	74%	24%
18 Mar, Shift 2	90	34%	9%	33%	63%	28%
22 Jul, Shift 2	90	40%	12%	33%	67%	28%
25 Jul, Shift 1	90	31%	13%	33%	56%	34%
25 Jul, Shift 2	90	48%	3%	33%	63%	27%
3 Aug, Shift 1	90	32%	11%	33%	68%	21%
3 Aug, Shift 2	90	32%	7%	33%	61%	24%
4 Aug, Shift 1	90	40%	8%	33%	62%	29%
4 Aug, Shift 2	90	32%	7%	33%	65%	41%
26 Aug, Shift 1	89	27%	15%	34%	66%	30%
26 Aug, Shift 2	89	21%	9%	34%	60%	28%
27 Aug, Shift 1	90	27%	13%	33%	63%	34%
27 Aug, Shift 2	90	29%	9%	33%	72%	29%
31 Aug, Shift 1	90	27%	11%	33%	70%	24%
31 Aug, Shift 2	90	30%	13%	33%	72%	31%

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

14 easy14 medium2 hard

Chemistry30 questions

17 easy13 medium0 hard

Q31
Match List - I with List - II : List - I (Species) List - II (Hybrid Orbitals) (a) $\mathrm{SF_4}$ (i) $sp^3d^2$ (b) $\mathrm{IF_5}$ (ii) $d^2sp^3$ (c) $\mathrm{NO_2^+}$ (iii) $sp^3d$ (d) $\mathrm{NH_4^+}$ (iv) $sp^3$ (v) $sp$ Choose the correct answer from…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumMatch the listNew ideaIdea asked in 6 years
Q32
Which one of the following 0.06 M aqueous solutions has lowest freezing point ?
Solutions Colligative Properties Freezing Point Depression
EasySingle correctIdea asked in 4 yearsAsked the year before
Q33
When silver nitrate solution is added to potassium iodide solution then the sol produced is :
Surface Chemistry Colloids Predicting Sol Charge via Excess Reagent
MediumSingle correctNew idea
Q34
Which one of the following statements for D.I. Mendeleeff, is incorrect ?
Classification of Elements and Periodicity in Properties
EasySingle correct
Q35
Sulphide ion is soft base and its ores are common for metals. (a) Pb (b) Al (c) Ag (d) Mg Choose the correct answer from the options given below :
General Principles and Processes of Isolation of Elements
EasyOther
Q36
Isotope(s) of hydrogen which emits low energy $\beta^-$ particles with $t_{1/2}$ value $>$ 12 years is/are :
Hydrogen Hydrogen and Hydrides Radioactive Decay of Tritium
EasySingle correctNew idea
Q37
Match List - I with List - II : List - I (Elements) List - II (Properties) (a) Ba (i) Organic solvent soluble compounds (b) Ca (ii) Outer electronic configuration $6s^2$ (c) Li (iii) Oxalate insoluble in water (d) Na (iv) Formation of very strong monoacidic…
The s-Block Elements s-Block Elements Solubility of Salts
MediumMatch the listNew idea
Q38
Which one of the following group-15 hydride is the strongest reducing agent ?
The p-Block Elements Group 15 & 16 Group 15 Hydrides Trends
EasySingle correctNew ideaIdea asked in 3 years
Q39
Given below are the statements about diborane. (a) Diborane is prepared by the oxidation of $\mathrm{NaBH_4}$ with $\mathrm{I_2}$ . (b) Each boron atom is in $sp^2$ hybridized state. (c) Diborane has one bridged 3 centre-2-electron bond. (d) Diborane is a…
The p-Block Elements Group 13 & 14 Diborane Structure
MediumOtherNew ideaIdea asked in 2 years
Q40
The set having ions which are coloured and paramagnetic both is :
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q41
The water having more dissolved $\mathrm{O_2}$ is :
Environmental Chemistry Eutrophication and Dissolved Oxygen Limits
EasySingle correctIdea asked in 3 yearsAsked the year before
Q42
Which purification technique is used for high boiling organic liquid compound (decomposes near its boiling point) ?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q43
Which one of the following compounds does not exhibit resonance ?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Resonance Structures
MediumSingle correct · figureNew idea
Q44
Which one of the following molecules does not show stereo isomerism ?
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Geometrical Isomerism
MediumSingle correctNew idea
Q45
An organic compound A ( $\mathrm{C_6H_6O}$ ) gives dark green colouration with ferric chloride. On treatment with $\mathrm{CHCl_3}$ and KOH, followed by acidification gives compound B. Compound B can also be obtained from compound C on reaction with pyridinium…
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q46
Which one of the following compounds will provide a tertiary alcohol on reaction with excess of $\mathrm{CH_3MgBr}$ followed by hydrolysis ?
Alcohols, Phenols and Ethers Carboxylic Acids and Derivatives Reaction of Esters with Grignard Reagents
MediumDiagram based · figureIdea asked in 3 years
Q47
In the chemical reactions given above A and B respectively are :
Amines Diazonium Salts Deamination Byproducts: Hypophosphorous Acid
EasyDiagram based · figureNew ideaIdea asked in 2 years
Q48
Which one of the following reactions does not occur ?
Amines Aromatic Hydrocarbons Friedel-Crafts Failure with Aniline
EasyDiagram based · figureNew idea
Q49
Match List - I with List - II : List - I List - II (a) Chloroprene (i) [figure: skeletal structure drawn in lines only: a vertical stub line (no atom label) on a carbon that has a double bond to the left and a single bond to the right, followed by a further…
Polymers Neoprene Synthesis
MediumMatch the list · figureNew ideaIdea asked in 2 years
Q50
Thiamine and pyridoxine are also known respectively as :
Biomolecules
EasySingle correct
Q51
If the concentration of glucose ( $\mathrm{C_6H_{12}O_6}$ ) in blood is 0.72 g L $^{-1}$ , the molarity of glucose in blood is ________ $\times 10^{-3}$ M. (Nearest integer) (Given : Atomic mass of C=12, H=1, O=16 u)
Solutions Mole Concept Molarity Calculation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q52
A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.62 g cm $^{-3}$ . The molar mass of copper complex is ________ g…
The Solid State Crystal Lattices Unit Cell Density
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q53
Number of electrons that Vanadium (Z=23) has in p-orbitals is equal to ________.
Structure of Atom Quantum Numbers Aufbau Principle and n+l Rule
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q54
If the standard molar enthalpy change for combustion of graphite powder is $-2.48 \times 10^2$ kJ mol $^{-1}$ , the amount of heat generated on combustion of 1 g of graphite powder is ________ kJ. (Nearest integer)
Thermodynamics (Chemistry)Enthalpy and Hess's Law Formation and Combustion
EasyNumerical valueNew ideaIdea asked in 5 years
Q55
Value of $\mathrm{K_p}$ for the equilibrium reaction $\mathrm{N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}}$ at 288 K is 47.9. The $\mathrm{K_c}$ for this reaction at same temperature is ________. (Nearest integer) (R=0.083 L bar K $^{-1}$ mol $^{-1}$ )
Equilibrium Chemical Equilibrium Kc and Kp Relationship
EasyNumerical valueNew ideaIdea asked in 2 years
Q56
Assume a cell with the following reaction $\mathrm{Cu_{(s)} + 2Ag^+ (1\times10^{-3}\ M) \rightarrow Cu^{2+} (0.250\ M) + 2\ Ag_{(s)}}$ $\mathrm{E^{\ominus}_{cell}}$ = 2.97 V $\mathrm{E_{cell}}$ for the above reaction is ________ V. (Nearest integer) [Given :…
Electrochemistry Nernst Equation Full Cell Nernst Equation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q57
$\mathrm{N_2O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2} O_{2(g)}}$ In the above first order reaction the initial concentration of $\mathrm{N_2O_5}$ is $2.40\times10^{-2}$ mol L $^{-1}$ at 318 K. The concentration of $\mathrm{N_2O_5}$ after 1 hour was…
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q58
The total number of unpaired electrons present in $\mathrm{[Co(NH_3)_6]Cl_2}$ and $\mathrm{[Co(NH_3)_6]Cl_3}$ is ________.
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q59
The number of acyclic structural isomers (including geometrical isomers) for pentene are ________.
Hydrocarbons Structural Isomerism Enumeration of Structural Isomers
MediumNumerical valueNew ideaIdea asked in 4 years
Q60
Methylation of 10 g of benzene gave 9.2 g of toluene. Calculate the percentage yield of toluene ________. (Nearest integer)
Hydrocarbons Stoichiometry Theoretical and Percent Yield
EasyNumerical valueNew ideaIdea asked in 2 years

Maths30 questions

5 easy16 medium9 hard

Q61
If the domain of the function $f(x)=\frac{\cos^{-1}\sqrt{x^2-x+1}}{\sqrt{\sin^{-1}\left(\frac{2x-1}{2}\right)}}$ is the interval $(\alpha, \beta]$ , then $\alpha+\beta$ is equal to :
Inverse Trigonometric Functions Inverse Trig Domains Domain Intersection of Multiple Inverse Trig Functions
MediumSingle correctNew idea
Q62
The number of solutions of $\sin^7 x+\cos^7 x=1$ , $x\in[0, 4\pi]$ is equal to :
Trigonometric Functions General Solutions Boundedness and Range Analysis
MediumSingle correctNew ideaIdea asked in 2 years
Q63
If the shortest distance between the straight lines $3(x-1)=6(y-2)=2(z-1)$ and $4(x-2)=2(y-\lambda)=(z-3)$ , $\lambda\in\mathbf{R}$ is $\frac{1}{\sqrt{38}}$ , then the integral value of $\lambda$ is equal to :
Three Dimensional Geometry Skew Lines Finding an Unknown Parameter from Shortest Distance
MediumSingle correctNew ideaIdea asked in 3 years
Q64
Let $\mathrm{A}=[\mathrm{a}_{ij}]$ be a real matrix of order $3\times3$ , such that $\mathrm{a}_{i1}+\mathrm{a}_{i2}+\mathrm{a}_{i3}=1$ , for $i=1, 2, 3$ . Then, the sum of all the entries of the matrix $\mathrm{A}^3$ is equal to :
Matrices Matrix Multiplication Powers of Square Matrices
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=\begin{cases}\frac{x^3}{(1-\cos2x)^2}\log_e\left(\frac{1+2xe^{-2x}}{(1-xe^{-x})^2}\right), & x\neq0\\ \alpha, & x=0\end{cases}$ . If $f$ is continuous at $x=0$ , then $\alpha$ is equal to :
Continuity and Differentiability Limits via Series Expansion for Continuity
HardSingle correctNew ideaIdea asked in 3 years
Q66
Which of the following Boolean expressions is not a tautology ?
Mathematical Reasoning
EasySingle correct
Q67
Let $\mathrm{E}_1:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ . Let $\mathrm{E}_2$ be another ellipse such that it touches the end points of major axis of $\mathrm{E}_1$ and the foci of $\mathrm{E}_2$ are the end points of minor axis of $\mathrm{E}_1$ . If…
Conic Sections Ellipse Eccentricity Similarity of Ellipses
MediumSingle correctNew idea
Q68
Let a line $\mathrm{L}:2x+y=k$ , $k>0$ be a tangent to the hyperbola $x^2-y^2=3$ . If $\mathrm{L}$ is also a tangent to the parabola $y^2=\alpha x$ , then $\alpha$ is equal to :
Conic Sections General Conic Section Condition for Line to be Tangent
MediumSingle correctNew ideaIdea asked in 3 years
Q69
Let $\mathrm{L}$ be the line of intersection of planes $\vec{\mathrm{r}}\cdot(\hat{i}-\hat{j}+2\hat{k})=2$ and $\vec{\mathrm{r}}\cdot(2\hat{i}+\hat{j}-\hat{k})=2$ . If $\mathrm{P}(\alpha, \beta, \gamma)$ is the foot of perpendicular on $\mathrm{L}$ from the…
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q70
Let $y=y(x)$ be the solution of the differential equation $\mathrm{cosec}^2x\,dy+2dx=(1+y\cos2x)\,\mathrm{cosec}^2x\,dx$ , with $y\left(\frac{\pi}{4}\right)=0$ . Then, the value of $(y(0)+1)^2$ is equal to :
Differential Equations Linear Differential Equations Particular Solution Solving
MediumSingle correctNew ideaIdea asked in 4 years
Q71
Let the circle $\mathrm{S}:36x^2+36y^2-108x+120y+\mathrm{C}=0$ be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, $x-2y=4$ and $2x-y=5$ lies inside the circle $\mathrm{S}$ , then :
Conic Sections Power of a Point Point position relative to circle
MediumSingle correctNew idea
Q72
Let three vectors $\vec{a}$ , $\vec{b}$ and $\vec{c}$ be such that $\vec{a}\times\vec{b}=\vec{c}$ , $\vec{b}\times\vec{c}=\vec{a}$ and $|\vec{a}|=2$ . Then which one of the following is not true ?
Vector Algebra Cross Product Orthogonal Triad Expansion
MediumSingle correctNew idea
Q73
Four dice are thrown simultaneously and the numbers shown on these dice are recorded in $2\times2$ matrices. The probability that such formed matrices have all different entries and are non-singular, is :
Probability
HardSingle correct
Q74
Let $\mathrm{S}_\mathrm{n}$ denote the sum of first n-terms of an arithmetic progression. If $\mathrm{S}_{10}=530$ , $\mathrm{S}_5=140$ , then $\mathrm{S}_{20}-\mathrm{S}_6$ is equal to :
Sequences and Series AP and GP AP Sum of n terms
EasySingle correctIdea asked in 7 yearsAsked the year before
Q75
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=\begin{cases}-\frac{4}{3}x^3+2x^2+3x, & x>0\\ 3xe^x, & x\leq0\end{cases}$ Then $f$ is increasing function in the interval.
Application of Derivatives Monotonicity Monotonicity in Piecewise Functions
MediumSingle correctNew idea
Q76
If $\int_0^{100\pi}\frac{\sin^2x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}}dx=\frac{\alpha\pi^3}{1+4\pi^2}$ , $\alpha\in\mathbf{R}$ , where $[x]$ is the greatest integer less than or equal to $x$ , then the value of $\alpha$ is :
Integrals Definite Integral Properties Periodic Function Property
HardSingle correctNew ideaIdea asked in 3 years
Q77
The values of $\lambda$ and $\mu$ such that the system of equations $x+y+z=6$ , $3x+5y+5z=26$ , $x+2y+\lambda z=\mu$ has no solution, are :
Determinants Cramer's Rule Condition for No Solution
EasySingle correctIdea asked in 6 yearsAsked the year before
Q78
Let n denote the number of solutions of the equation $z^2+3\bar{z}=0$ , where $z$ is a complex number. Then the value of $\sum_{k=0}^{\infty}\frac{1}{\mathrm{n}^k}$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Conjugate and Inverse
MediumSingle correctNew ideaIdea asked in 3 years
Q79
Let $[x]$ denote the greatest integer less than or equal to $x$ . Then, the values of $x\in\mathbf{R}$ satisfying the equation $[e^x]^2+[e^x+1]-3=0$ lie in the interval :
Relations and Functions Functions and Domain Domain Constraints of Greatest Integer Function
MediumSingle correctNew ideaIdea asked in 2 years
Q80
Let a vector $\vec{\mathrm{a}}$ be coplanar with vectors $\vec{\mathrm{b}}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{\mathrm{c}}=\hat{i}-\hat{j}+\hat{k}$ . If $\vec{\mathrm{a}}$ is perpendicular to $\vec{\mathrm{d}}=3\hat{i}+2\hat{j}+6\hat{k}$ , and…
Vector Algebra Triple Products STP Algebraic Properties
HardSingle correctNew idea
Q81
Let $\mathrm{A}=\{0, 1, 2, 3, 4, 5, 6, 7\}$ . Then the number of bijective functions $f:\mathrm{A}\to\mathrm{A}$ such that $f(1)+f(2)=3-f(3)$ is equal to ________.
Relations and Functions Permutations and Combinations Number of Injective Functions
MediumNumerical valueNew ideaIdea asked in 4 years
Q82
Let $\mathrm{A}=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}$ . Then the number of $3\times3$ matrices $\mathrm{B}$ with entries from the set $\{1, 2, 3, 4, 5\}$ and satisfying $\mathrm{AB}=\mathrm{BA}$ is ________.
Matrices Matrix Multiplication Non-commutativity Property
HardNumerical valueNew idea
Q83
The area (in sq. units) of the region bounded by the curves $x^2+2y-1=0$ , $y^2+4x-4=0$ and $y^2-4x-4=0$ , in the upper half plane is ________.
Application of Integrals Area Under Curves Regions with Multiple Bounding Curves
HardNumerical valueNew ideaIdea asked in 3 years
Q84
If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$ , then the number of all numbers greater than $10{,}000$ is equal to ________.
Permutations and Combinations Fundamental Counting Principle
EasyNumerical valueNew ideaIdea asked in 5 years
Q85
Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined as $f(x)=\begin{cases}3\left(1-\frac{|x|}{2}\right) & \text{if } |x|\leq2\\ 0 & \text{if } |x|>2\end{cases}$ Let $g:\mathbf{R}\to\mathbf{R}$ be given by $g(x)=f(x+2)-f(x-2)$ . If n and m denote the number…
Continuity and Differentiability Piecewise Differentiability
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q86
The sum of all the elements in the set $\{\mathrm{n}\in\{1, 2, .........., 100\}\mid\mathrm{H.C.F.}$ of n and $2040$ is $1\}$ is equal to ________.
Relations and Functions Sets and Relations Inclusion-Exclusion for Three Sets
MediumNumerical valueNew ideaIdea asked in 4 years
Q87
If the constant term, in binomial expansion of $\left(2x^{\mathrm{r}}+\frac{1}{x^2}\right)^{10}$ is $180$ , then r is equal to ________.
Binomial Theorem
EasyNumerical value
Q88
The number of elements in the set $\{\mathrm{n}\in\{1, 2, 3, .........., 100\}\mid(11)^\mathrm{n}>(10)^\mathrm{n}+(9)^\mathrm{n}\}$ is ________.
Binomial Theorem
HardNumerical value
Q89
Consider the following frequency distribution : Class : 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 Frequency : a | b | 12 | 9 | 5 If mean $=\frac{309}{22}$ and median $=14$ , then the value $(\mathrm{a}-\mathrm{b})^2$ is equal to ________.
Statistics Variance and SD Mean of Discrete Data
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q90
Let $y=y(x)$ be the solution of the differential equation $\left((x+2)\,e^{\left(\frac{y+1}{x+2}\right)}+(y+1)\right)dx=(x+2)\,dy$ , $y(1)=1$ . If the domain of $y=y(x)$ is an open interval $(\alpha, \beta)$ , then $|\alpha+\beta|$ is equal to ________.
Differential Equations Homogeneous Equations Domain Restrictions from Initial Value Problems
HardNumerical valueNew idea

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 2021 shifts.