JEE Main 2022 · June session

JEE Main 24 June 2022, Shift 1

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 15 were rated hard and 26 easy. Its hard-question count was the joint 2nd highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 4 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 15; 17% of the shift
Chapters asked: 68; 8 questions with a figure

Key findings · 24 Jun 2022, Shift 1

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 29 rated hard; Chemistry had the most easy questions (13 of 30).
3
22 questions tested a new idea, one no earlier year had asked: 31% of the 71 questions tagged to an idea.
4
42 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
42 shared an idea with another 2022 shift (59% 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), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Application of Derivatives in Maths (4).

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 13Medium 15Hard 2

Top chapters

Maths

29 Q · 10 numerical

Easy 1Medium 16Hard 12

Top chapters

Application of Derivatives4 Q
Conic Sections3 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Integrals2 Q
Probability2 Q

Question format

Single correct51 Q
Numerical value30 Q
Other3 Q
Match the list2 Q
Two statements2 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step33 Q
Calculation27 Q
Application11 Q
Recall10 Q
Conceptual7 Q
Data or graph1 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

12 easy17 medium1 hard

Chemistry30 questions

13 easy15 medium2 hard

Q61
If a rocket runs on a fuel ( $\mathrm{C_{15}H_{30}}$ ) and liquid oxygen, the weight of oxygen required and $\mathrm{CO_2}$ released for every litre of fuel respectively are : (Given : density of the fuel is 0.756 g/mL)
Some Basic Concepts of Chemistry Stoichiometry Hydrocarbon Combustion General Equation
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q62
Consider the following pairs of electrons (A) (a) $n=3, l=1, m_l=1, m_s=+\frac{1}{2}$ (b) $n=3, l=2, m_l=1, m_s=+\frac{1}{2}$ (B) (a) $n=3, l=2, m_l=-2, m_s=-\frac{1}{2}$ (b) $n=3, l=2, m_l=-1, m_s=-\frac{1}{2}$ (C) (a) $n=4, l=2, m_l=2, m_s=+\frac{1}{2}$ …
Structure of Atom Quantum Numbers Hydrogen vs Multi-Electron Degeneracy
EasyOtherNew idea
Q63
Match List - I with List - II : List - I (A) $[\mathrm{PtCl_4}]^{2-}$ (B) $\mathrm{BrF_5}$ (C) $\mathrm{PCl_5}$ (D) $[\mathrm{Co(NH_3)_6}]^{3+}$ List - II (I) $sp^3d$ (II) $d^2sp^3$ (III) $dsp^2$ (IV) $sp^3d^2$ Choose the most appropriate answer from the…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumMatch the listIdea asked in 6 yearsAsked the year before
Q64
For a reaction at equilibrium $\mathrm{A(g)} \rightleftharpoons \mathrm{B(g)}+\frac{1}{2}\mathrm{C(g)}$ the relation between dissociation constant (K), degree of dissociation ( $\alpha$ ) and equilibrium pressure (p) is given by :
Equilibrium Chemical Equilibrium Degree of Dissociation
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q65
Given below are two statements : Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing. Statement II : For stabilisation of an emulsion, excess of electrolyte is added. In the light of the above…
Surface Chemistry Colloids Role of Emulsifying Agents
MediumTwo statementsNew idea
Q66
Given below are the oxides : $\mathrm{Na_2O,\ As_2O_3,\ N_2O,\ NO}$ and $\mathrm{Cl_2O_7}$ Number of amphoteric oxides is :
The p-Block Elements Periodic Trends Acidic and Basic Character of Oxides
MediumSingle correctIdea asked in 4 years
Q67
Match List - I with List - II : List - I (A) Sphalerite (B) Calamine (C) Galena (D) Siderite List - II (I) $\mathrm{FeCO_3}$ (II) $\mathrm{PbS}$ (III) $\mathrm{ZnCO_3}$ (IV) $\mathrm{ZnS}$ Choose the most appropriate answer from the options given below :
General Principles and Processes of Isolation of Elements
EasyMatch the list
Q68
The highest industrial consumption of molecular hydrogen is to produce compounds of element :
Hydrogen
EasySingle correct
Q69
Which of the following statements are correct ? (A) Both LiCl and $\mathrm{MgCl_2}$ are soluble in ethanol. (B) The oxides $\mathrm{Li_2O}$ and MgO combine with excess of oxygen to give superoxide. (C) LiF is less soluble in water than other alkali metal…
The s-Block Elements s-Block Elements Covalent Character in Halides
MediumOtherNew idea
Q70
Identify the correct statement for $\mathrm{B_2H_6}$ from those given below. (A) In $\mathrm{B_2H_6}$ , all B-H bonds are equivalent. (B) In $\mathrm{B_2H_6}$ , there are four 3-centre-2-electron bonds. (C) $\mathrm{B_2H_6}$ is a Lewis acid. (D)…
The p-Block Elements Group 13 & 14 Diborane Structure
MediumOtherIdea asked in 2 yearsAsked the year before
Q71
The most stable trihalide of nitrogen is :
The p-Block Elements
EasySingle correct
Q72
Which one of the following elemental forms is not present in the enamel of the teeth ?
Chemistry in Everyday Life
EasySingle correct
Q73
In the given reaction sequence, the major product 'C' is : $\mathrm{C_8H_{10}}\xrightarrow[\mathrm{H_2SO_4}]{\mathrm{HNO_3}}\mathrm{A}\xrightarrow[\Delta]{\mathrm{Br_2}}\mathrm{B}\xrightarrow{\text{alcoholic KOH}}\mathrm{C}$
Haloalkanes and Haloarenes Aromatic Hydrocarbons Ortho-Para vs Meta Directing
MediumSingle correct · figureIdea asked in 5 yearsAsked the year before
Q74
Two statements are given belwo : Statement I : The melting point of monocarboxylic acid with even number of carbon atoms is higher than that of with odd number of carbon atoms acid immediately below and above it in the series. Statement II : The solubility…
Aldehydes, Ketones and Carboxylic Acids
MediumTwo statements
Q75
Which of the following is an example of conjugated diketone ?
Aldehydes, Ketones and Carboxylic Acids Alcohols and Phenols Phenol Oxidation to Benzoquinone
EasySingle correct · figureNew idea
Q76
[figure: 4-methoxybenzyl bromide, i.e. 4- $\mathrm{CH_3O}$ -C6H4- $\mathrm{CH_2Br}$ ] (i) NaCN (ii) $\mathrm{OH^-}$ (iii) Cyclohexanone (iv) $\mathrm{H_2}$ , Ni $\longrightarrow$ A (Major Product) The major product of the above reactions is :
Amines Reduction of Nitriles vs Isocyanides
HardSingle correct · figureIdea asked in 2 years
Q77
Which of the following is an example of polyester ?
Polymers PHBV Monomers
EasySingle correctIdea asked in 2 years
Q78
A polysaccharide 'X' on boiling with dil $\mathrm{H_2SO_4}$ at 393 K under 2-3 atm pressure yields 'Y'. 'Y' on treatment with bromine water gives gluconic acid. 'X' contains $\beta$ -glycosidic linkages only. Compound 'X' is :
Biomolecules Carbohydrates Structure of Cellulose
EasySingle correctNew idea
Q79
Which of the following is not a broad spectrum antibiotic ?
Chemistry in Everyday Life Broad vs Narrow Spectrum Antibiotics
EasySingle correctNew idea
Q80
During the qualitative analysis of salt with cation $y^{2+}$ , addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation ( $y^{2+}$ ) present respectively are :
Organic Chemistry: Some Basic Principles and Techniques Cation Analysis Nickel DMG Complex
EasySingle correctNew ideaIdea asked in 2 years
Q81
Atoms of element X form hcp lattice and those of element Y occupy $\frac{2}{3}$ of its tetrahedral voids. The percentage of element X in the lattice is ______. (Nearest integer)
The Solid State Crystal Lattices Empirical Formula from Void Occupancy
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q82
$\mathrm{2O_3(g)\rightleftharpoons 3O_2(g)}$ At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is $(-)$ ______ $\mathrm{J\ mol^{-1}}$ . (Nearest integer) [Given : $\ln 1.35=0.3$ and…
Thermodynamics (Chemistry)Gibbs Free Energy Gibbs Energy and Equil
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q83
The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in $\mathrm{gL^{-1}}$ is ______. (Molar mass of glucose $=180\ \mathrm{g\ mol^{-1}}$ …
Solutions Colligative Properties Isotonic Solutions
EasyNumerical valueIdea asked in 3 years
Q84
The cell potential for the following cell $\mathrm{Pt\,|H_2(g)|H^+(aq)\|\ Cu^{2+}(0.01\ M)|Cu(s)}$ is 0.576 V at 298 K. The pH of the solution is ______. (Nearest integer) (Given : $E^\circ_{\mathrm{Cu^{2+}/Cu}}=0.34$ V and $\frac{2.303RT}{F}=0.06$ V)
Electrochemistry Nernst Equation Full Cell Nernst Equation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q85
The rate constants for decomposition of acetaldehyde have been measured over the temperature range $700-1000$ K. The data has been analysed by plotting $\ln k$ vs $\frac{10^3}{T}$ graph. The value of activation energy for the reaction is ______…
Chemical Kinetics Arrhenius Equation Activation Energy Calculation
EasyNumerical value · figureIdea asked in 3 yearsAsked the year before
Q86
The difference in oxidation state of chromium in chromate and dichromate salts is ______.
Redox Reactions Oxidation Number Assignment
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q87
In the cobalt-carbonyl complex : $\mathrm{[Co_2(CO)_8]}$ , number of Co-Co bonds is "X" and terminal CO ligands is "Y". X + Y = ______.
Coordination Compounds
MediumNumerical value
Q88
A 0.166 g sample of an organic compound was digested with conc. $\mathrm{H_2SO_4}$ and then distilled with NaOH. The ammonia gas evolved was passed through 50.0 mL of 0.5 N $\mathrm{H_2SO_4}$ . The used acid required 30.0 mL of 0.25 N NaOH for complete…
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q89
Number of electrophilic centres in the given compound is ______.
Organic Chemistry: Some Basic Principles and Techniques Nucleophilic Addition 1,2- vs 1,4-Addition to Conjugated Carbonyls
MediumNumerical value · figureNew idea
Q90
The major product 'A' of the following given reaction has ______ $sp^2$ hybridized carbon atoms. 2,7-Dimethyl-2,6-octadiene $\xrightarrow{\mathrm{H^+}}$ A (Major Product)
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
HardNumerical valueIdea asked in 6 yearsAsked the year before

Maths29 questions

1 easy16 medium12 hard

Q1
Let $A = \{z \in \mathbb{C} : 1 \le |z-(1+i)| \le 2\}$ and $B = \{z \in A : |z-(1-i)| = 1\}$ . Then, B :
Complex Numbers and Quadratic Equations
MediumSingle correct
Q2
The remainder when $3^{2022}$ is divided by 5 is :
Binomial Theorem
EasySingle correct
Q3
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
Application of Derivatives Chain Rule Chain Rule in Related Rates
MediumSingle correctIdea asked in 2 years
Q4
Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is…
Probability Bayes' Theorem Bayes' Theorem Application
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0, 6)$ and touching the parabola $y=x^2$ at $(2, 4)$ . Then $A+C$ is equal to ______.
Conic Sections Circle Tangents Common Tangent to Circle and Conic
HardSingle correctIdea asked in 3 yearsAsked the year before
Q6
The number of values of $\alpha$ for which the system of equations : $x+y+z=\alpha$ $\alpha x+2\alpha y+3z=-1$ $x+3\alpha y+5z=4$ is inconsistent, is
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q7
If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^2+\lambda x-1=0$ is 15, then $6(\alpha^3+\beta^3)^2$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q8
The set of all values of k for which $(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}$ , is the interval :
Inverse Trigonometric Functions Inverse Trig Identities Complementary Identities
HardSingle correctIdea asked in 3 yearsAsked the year before
Q9
Let $S = \{\sqrt{n} : 1 \le n \le 50$ and n is odd $\}$ . Let $a \in S$ and $A = \begin{bmatrix} 1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1 \end{bmatrix}$ . If $\sum_{a \in S} \det(\mathrm{adj}\,A) = 100\lambda$ , then $\lambda$ is equal to :
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q10
For the function $f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1$ , which one of the following is NOT correct ?
Application of Derivatives Monotonicity First Derivative Test
HardSingle correctIdea asked in 3 yearsAsked the year before
Q11
If the tangent at the point $(x_1, y_1)$ on the curve $y=x^3+3x^2+5$ passes through the origin, then $(x_1, y_1)$ does NOT lie on the curve :
Application of Derivatives Tangents and Normals Tangents Passing Through Origin
MediumSingle correctNew idea
Q12
The sum of absolute maximum and absolute minimum values of the function $f(x)=|2x^2+3x-2|+\sin x\cos x$ in the interval $[0, 1]$ is :
Application of Derivatives Maxima and Minima Closed Interval Extrema
HardSingle correctIdea asked in 6 yearsAsked the year before
Q13
If $\{a_i\}_{i=1}^{n}$ , where n is an even integer, is an arithmetic progression with common difference 1, and $\sum_{i=1}^{n} a_i = 192$ , $\sum_{i=1}^{n/2} a_{2i} = 120$ , then n is equal to :
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q14
If $x=x(y)$ is the solution of the differential equation $y\frac{dx}{dy}=2x+y^3(y+1)e^y,\ x(1)=0$ ; then $x(e)$ is equal to :
Differential Equations Linear Differential Equations Linear in x Form
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q15
Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2x^2-y^2=b^2$ . Then $\left(\frac{\lambda}{a}\right)^2-\left(\frac{\mu}{b}\right)^2$ is equal to :
Conic Sections General Conic Section Condition for Line to be Tangent
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
Let $\hat{a}, \hat{b}$ be unit vectors. If $\vec{c}$ be a vector such that the angle between $\hat{a}$ and $\vec{c}$ is $\frac{\pi}{12}$ , and $\hat{b}=\vec{c}+2(\vec{c}\times\hat{a})$ , then $\left|6\vec{c}\right|^2$ is equal to :
Vector Algebra Cross Product Solving Vector Equations with Cross Products
HardSingle correctIdea asked in 6 yearsAsked the year before
Q17
If a random variable X follows the Binomial distribution B(33, p) such that $3P(X=0)=P(X=1)$ , then the value of $\frac{P(X=15)}{P(X=18)}-\frac{P(X=16)}{P(X=17)}$ is equal to :
Probability
MediumSingle correct
Q19
Let $S=\left\{\theta\in[-\pi, \pi]-\left\{\pm\frac{\pi}{2}\right\}: \sin\theta\tan\theta+\tan\theta=\sin 2\theta\right\}$ . If $T=\sum_{\theta\in S}\cos 2\theta$ , then $T+n(S)$ is equal to :
Trigonometric Functions General Solutions Domain Restricted Solutions
MediumSingle correctNew idea
Q20
The number of choices for $\Delta\in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ , such that $(p\ \Delta\ q)\Rightarrow((p\ \Delta\ \sim q)\vee((\sim p)\ \Delta\ q))$ is a tautology, is :
Mathematical Reasoning
MediumSingle correct
Q21
The number of one-one functions $f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\}$ such that $2f(a)-f(b)+3f(c)+f(d)=0$ is ______.
Relations and Functions Permutations and Combinations Number of Injective Functions
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q22
In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, $-2$ marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a…
Permutations and Combinations Permutations with Repetition
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q23
Let $A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right)$ , $a>0$ , be a fixed point in the $xy$ -plane. The image of A in $y$ -axis be B and the image of B in $x$ -axis be C. If $D(3\cos\theta, a\sin\theta)$ is a point in the fourth quadrant such that the maximum area of…
Straight Lines
HardNumerical value
Q24
Let a line having direction ratios $1, -4, 2$ intersect the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the points A and B. Then $(AB)^2$ is equal to ______.
Three Dimensional Geometry Lines in 3D General Point Parameterization
MediumNumerical valueNew ideaIdea asked in 2 years
Q25
The number of points where the function $f(x)=\begin{cases}|2x^2-3x-7| & \text{if } x\le -1\\ [4x^2-1] & \text{if } -1<x<1\\ |x+1|+|x-2| & \text{if } x\ge 1,\end{cases}$ $[t]$ denotes the greatest integer $\le t$ , is discontinuous is ______.
Continuity and Differentiability Continuity involving GIF and Fractional Part
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q26
Let $f(\theta)=\sin\theta+\int_{-\pi/2}^{\pi/2}(\sin\theta+t\cos\theta)f(t)\,dt$ . Then the value of $\left|\int_0^{\pi/2}f(\theta)\,d\theta\right|$ is ______.
Integrals
HardNumerical value
Q27
Let $\max_{0\le x\le 2}\left\{\frac{9-x^2}{5-x}\right\}=\alpha$ and $\min_{0\le x\le 2}\left\{\frac{9-x^2}{5-x}\right\}=\beta$ . If…
Integrals Definite Integral Properties Max/Min Function Integrals
HardNumerical valueNew idea
Q28
If two tangents drawn from a point $(\alpha, \beta)$ lying on the ellipse $25x^2+4y^2=1$ to the parabola $y^2=4x$ are such that the slope of one tangent is four times the other, then the value of $(10\alpha+5)^2+(16\beta^2+50)^2$ equals ______.
Conic Sections General Conic Section Condition for Line to be Tangent
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q29
Let S be the region bounded by the curves $y=x^3$ and $y^2=x$ . The curve $y=2|x|$ divides S into two regions of areas $R_1$ and $R_2$ . If $\max\{R_1, R_2\}=R_2$ , then $\frac{R_2}{R_1}$ is equal to ______.
Application of Integrals Area Under Curves Ratio of Divided Areas
HardNumerical valueNew ideaIdea asked in 2 years
Q30
If the shortest distance between the lines $\vec{r}=(-\hat{i}+3\hat{k})+\lambda(\hat{i}-a\hat{j})$ and $\vec{r}=(-\hat{j}+2\hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is $\sqrt{\frac{2}{3}}$ , then the integral value of a is equal to ______.
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
MediumNumerical valueIdea asked in 5 yearsAsked the year before

Dropped from the final key and left out of every count: Q18.

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.