JEE Main 2024 · April session

JEE Main 5 April 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 7 were rated hard and 36 easy. Its hard-question count was the joint 17th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 7; 8% of the shift
Chapters asked: 57; 17 questions with a figure

Key findings · 5 Apr 2024, Shift 1

1
7 hard questions (8%): the joint 17th highest count of the 18 2024 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 5 of 30 rated hard; Chemistry had the most easy questions (21 of 30).
3
16 questions tested a new idea, one no earlier year had asked: 22% of the 73 questions tagged to an idea.
4
30 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
43 shared an idea with another 2024 shift (59% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Gravitation in Physics (3), Haloalkanes and Haloarenes in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Gravitation3 Q
Moving Charges and Magnetism3 Q
Electrostatic Potential and Capacitance2 Q
Laws of Motion2 Q
Units and Measurements2 Q
Wave Optics2 Q

Chemistry

30 Q · 10 numerical

Easy 21Medium 8Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 23Hard 5

Top chapters

Question format

Single correct40 Q
Numerical value30 Q
Two statements7 Q
Diagram based7 Q
Other3 Q
Assertion–reason2 Q
Match the list1 Q

What each question asks you to do

Multi-step24 Q
Calculation23 Q
Conceptual16 Q
Application14 Q
Recall10 Q
Data or graph3 Q

Most common: Multi-step.

Against the other 2024 shifts

This shift next to the 17 other 2024 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
27 Jan, Shift 1	90	50%	9%	33%	29%	29%
29 Jan, Shift 1	89	38%	10%	34%	28%	34%
30 Jan, Shift 1	90	37%	11%	33%	22%	17%
30 Jan, Shift 2	89	42%	10%	34%	32%	29%
31 Jan, Shift 1	90	39%	12%	33%	31%	34%
31 Jan, Shift 2	89	28%	13%	34%	23%	30%
1 Feb, Shift 1	90	36%	11%	33%	21%	19%
1 Feb, Shift 2	88	40%	8%	34%	19%	21%
4 Apr, Shift 1	89	26%	20%	33%	26%	36%
4 Apr, Shift 2	90	33%	18%	33%	13%	26%
5 Apr, Shift 1	90	40%	8%	33%	22%	27%
5 Apr, Shift 2	90	37%	10%	33%	23%	32%
6 Apr, Shift 1	88	43%	11%	34%	18%	22%
6 Apr, Shift 2	89	35%	15%	33%	28%	33%
8 Apr, Shift 1	90	31%	9%	33%	19%	37%
8 Apr, Shift 2	90	33%	12%	33%	19%	28%
9 Apr, Shift 1	90	31%	11%	33%	20%	50%
9 Apr, Shift 2	90	31%	16%	33%	27%	39%

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

13 easy16 medium1 hard

Chemistry30 questions

21 easy8 medium1 hard

Q61
The incorrect postulates of the Dalton's atomic theory are : (A) Atoms of different elements differ in mass. (B) Matter consists of divisible atoms. (C) Compounds are formed when atoms of different element combine in a fixed ratio. (D) All the atoms of given…
Some Basic Concepts of Chemistry
EasyOther
Q62
Number of $\sigma$ and $\pi$ bonds present in ethylene molecule is respectively :
Chemical Bonding and Molecular Structure
EasySingle correct
Q63
The following reaction occurs in the Blast furnace where iron ore is reduced to iron metal $\mathrm{Fe_2O_{3(s)} + 3CO_{(g)} \rightleftharpoons Fe_{(l)} + 3CO_{2(g)}}$ Using the Le-chatelier's principle, predict which one of the following will not disturb…
Equilibrium Chemical Equilibrium Adding Pure Solid or Liquid
EasySingle correctNew idea
Q64
The reaction at cathode in the cells commonly used in clocks involves.
Electrochemistry
EasySingle correct
Q65
Molar ionic conductivities of divalent cation and anion are 57 S cm $^2$ mol $^{-1}$ and 73 S cm $^2$ mol $^{-1}$ respectively. The molar conductivity of solution of an electrolyte with the above cation and anion will be :
Electrochemistry
EasySingle correct
Q66
The statement(s) that are correct about the species $\mathrm{O^{2-}}$ , $\mathrm{F^-}$ , $\mathrm{Na^+}$ and $\mathrm{Mg^{2+}}$ . (A) All are isoelectronic (B) All have the same nuclear charge (C) $\mathrm{O^{2-}}$ has the largest ionic radii (D)…
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasyOtherIdea asked in 5 yearsAsked the year before
Q67
Given below are two statements : Statement I : In group 13, the stability of $+1$ oxidation state increases down the group. Statement II : The atomic size of gallium is greater than that of aluminium. In the light of the above statements, choose the most…
The p-Block Elements Periodic Trends Inert Pair Effect and Oxidation State Stability
EasyTwo statementsIdea asked in 2 yearsAsked the year before
Q68
The number of neutrons present in the more abundant isotope of boron is 'x'. Amorphous boron upon heating with air forms a product, in which the oxidation state of boron is 'y'. The value of $x+y$ is ________.
The p-Block Elements
EasySingle correct
Q69
The metal that shows highest and maximum number of oxidation state is :
The d- and f-Block Elements d-Block Elements Oxidation State Trends
EasySingle correctIdea asked in 4 yearsAsked the year before
Q70
The correct order of ligands arranged in increasing field strength.
Coordination Compounds Crystal Field Theory Spectrochemical Series
EasySingle correctIdea asked in 4 years
Q71
Which one of the following complexes will exhibit the least paramagnetic behaviour ? [Atomic number, Cr = 24, Mn = 25, Fe = 26, Co = 27]
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
EasySingle correctIdea asked in 7 yearsAsked the year before
Q72
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $-57$ kJ mol $^{-1}$ Reason (R) : Enthalpy of…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Constant Enthalpy of Neutralization
EasyAssertion–reasonIdea asked in 3 years
Q73
An organic compound has 42.1% carbon, 6.4% hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is :
Some Basic Concepts of Chemistry Mole Concept Molecular Formula Determination
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q74
Given below are two statements : Statement I : Nitration of benzene involves the following step - $\mathrm{H{-}\underset{\cdot\cdot}{O}^{\oplus}(H){-}NO_2 \rightleftharpoons H_2O + \overset{\oplus}{N}O_2}$ Statement II : Use of Lewis base promotes the…
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Nitrating Mixture and Nitronium Ion Generation
EasyTwo statements · figureIdea asked in 3 years
Q75
For the Compounds : (A) $\mathrm{H_3C-CH_2-O-CH_2-CH_2-CH_3}$ (B) $\mathrm{H_3C-CH_2-CH_2-CH_2-CH_3}$ (C) $\mathrm{CH_3-CH_2-C(=O)-CH_2-CH_3}$ (D) $\mathrm{H_3C-CH(OH)-CH_2-CH_2-CH_3}$ The increasing order of boiling point is : Choose the correct answer from…
Haloalkanes and Haloarenes Alcohols and Phenols Hydrogen Bonding Trends in Alcohols
EasyOtherIdea asked in 3 yearsAsked the year before
Q76
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Cis form of alkene is found to be more polar than the trans form. Reason (R) : Dipole moment of trans isomer of 2-butene is zero. In…
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Physical Properties of Cis/Trans Isomers
EasyAssertion–reasonNew idea
Q77
Given below are two statement : Statements I : Bromination of phenol in solvent with low polarity such as $\mathrm{CHCl_3}$ or $\mathrm{CS_2}$ requires Lewis acid catalyst. Statements II : The Lewis acid catalyst polarises the bromine to generate…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Bromination Solvent Effect
EasyTwo statementsIdea asked in 3 years
Q78
Identify compound (Z) in the following reaction sequence. chlorobenzene $+ \mathrm{NaOH} \xrightarrow[\text{300 atm}]{\text{623 K}} X \xrightarrow{\mathrm{HCl}} Y \xrightarrow{\text{Conc. } \mathrm{HNO_3}} Z$
Haloalkanes and Haloarenes Alcohols and Phenols Dow Process for Phenol
EasyDiagram based · figureIdea asked in 2 years
Q79
Identify 'A' in the following reaction : butan-2-one ( $\mathrm{CH_3-C(=O)-CH_2-CH_3}$ ) $\xrightarrow[\text{(ii) ethylene glycol/KOH}]{\text{(i) } \mathrm{N_2H_4}}$ 'A'
Aldehydes, Ketones and Carboxylic Acids Alkanes and Free Radicals Wolff-Kishner Reduction to Alkanes
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q80
Which of the following gives a positive test with ninhydrin ?
Biomolecules
EasySingle correct
Q81
The value of Rydberg constant ( $\mathrm{R_H}$ ) is $2.18 \times 10^{-18}$ J. The velocity of electron having mass $9.1 \times 10^{-31}$ kg in Bohr's first orbit of hydrogen atom = ________ $\times 10^5$ ms $^{-1}$ (nearest integer).
Structure of Atom Bohr's Atomic Theory Electron Velocity in Orbit
MediumNumerical valueIdea asked in 2 years
Q82
In the lewis dot structure for $\mathrm{NO_2^-}$ , total number of valence electrons around nitrogen is ________.
Chemical Bonding and Molecular Structure
EasyNumerical value
Q83
The heat of combustion of solid benzoic acid at constant volume is $-321.30$ kJ at $27^\circ$ C. The heat of combustion at constant pressure is $(-321.30 - xR)$ kJ, the value of $x$ is ________.
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bomb Calorimetry Calculations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q84
An artificial cell is made by encapsulating 0.2 M glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell is placed within a 0.05 M solution of NaCl at 300 K is ________ $\times 10^{-1}$ bar. (nearest…
Solutions Colligative Properties Osmotic Pressure
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
During Kinetic study of reaction $2\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} + \mathrm{D}$ , the following results were obtained : A [M] B [M] initial rate of formation of D I 0.1 0.1 $6.0 \times 10^{-3}$ II 0.3 0.2 $7.2 \times 10^{-2}$ III 0.3 0.4…
Chemical Kinetics Rate Laws Initial Rates Method
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q86
The spin-only magnetic moment value of the ion among $\mathrm{Ti^{2+}}$ , $\mathrm{V^{2+}}$ , $\mathrm{Co^{3+}}$ and $\mathrm{Cr^{2+}}$ , that acts as strong oxidising agent in aqueous solution is ________ BM (Near integer). (Given atomic numbers : Ti : 22, V :…
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumNumerical valueIdea asked in 6 years
Q87
In a borax bead test under hot condition, a metal salt (one from the given) is heated at point B of the flame, resulted in green colour salt bead. The spin-only magnetic moment value of the salt is ________ BM (Nearest integer) [Given atomic number of Cu =…
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
HardNumerical value · figureIdea asked in 6 years
Q88
The number of halobenzenes from the following that can be prepared by Sandmeyer's reaction is ________. [figure: five monohalobenzenes I-V with substituents F (I), Cl (II), Br (III), I (IV), At (V)]
Haloalkanes and Haloarenes Diazonium Salts Sandmeyer Reaction
EasyNumerical value · figureIdea asked in 4 yearsAsked the year before
Q89
Consider the given chemical reaction sequence : phenol $\xrightarrow{\text{Conc. } \mathrm{H_2SO_4}}$ Product A $\xrightarrow{\text{Conc. } \mathrm{HNO_3}}$ Product B Total sum of oxygen atoms in Product A and Product B are ________.
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Nitration Reagent Effects
MediumNumerical value · figureIdea asked in 2 years
Q90
9.3 g of pure aniline is treated with bromine water at room temperature to give a white precipitate of the product 'P'. The mass of product 'P' obtaind is 26.4 g. The percentage yield is ________%.
Amines Direct Bromination of Aniline
MediumNumerical valueNew idea

Maths30 questions

2 easy23 medium5 hard

Q1
Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$ . Then the total number of one-one maps $f:A\to B$ , such that $f(1)+f(3)=14$ , is :
Relations and Functions Permutations and Combinations Number of Injective Functions
MediumSingle correctIdea asked in 4 years
Q2
Consider the following two statements : Statement I : For any two non-zero complex numbers $z_1, z_2$ , $(|z_1|+|z_2|)\left|\frac{z_1}{|z_1|}+\frac{z_2}{|z_2|}\right| \le 2(|z_1|+|z_2|)$ , and Statement II : If $x, y, z$ are three distinct complex numbers and…
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
HardTwo statementsIdea asked in 5 yearsAsked the year before
Q3
Let A and B be two square matrices of order 3 such that $|A|=3$ and $|B|=2$ . Then $|A^{T}A(\mathrm{adj}(2A))^{-1}(\mathrm{adj}(4B))(\mathrm{adj}(AB))^{-1}AA^{T}|$ is equal to :
Determinants Matrix Inverse Determinant of Adjoint of Inverse
MediumSingle correctIdea asked in 3 years
Q4
If the system of equations $11x+y+\lambda z=-5$ $2x+3y+5z=3$ $8x-19y-39z=\mu$ has infinitely many solutions, then $\lambda^4-\mu$ is equal to :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q5
For the function $f(x)=\sin x+3x-\frac{2}{\pi}(x^2+x)$ , where $x\in\left[0,\frac{\pi}{2}\right]$ , consider the following two statements : (I) $f$ is increasing in $\left(0,\frac{\pi}{2}\right)$ . (II) $f'$ is decreasing in $\left(0,\frac{\pi}{2}\right)$ .…
Application of Derivatives Monotonicity Monotonicity of the Derivative Function
MediumTwo statementsNew idea
Q6
If $\frac{1}{\sqrt1+\sqrt2}+\frac{1}{\sqrt2+\sqrt3}+\ldots+\frac{1}{\sqrt{99}+\sqrt{100}}=m$ and $\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\ldots+\frac{1}{99\cdot100}=n$ , then the point $(m,n)$ lies on the line
Sequences and Series AP and GP Method of Differences for Telescoping Series
EasySingle correctIdea asked in 6 yearsAsked the year before
Q7
If the function $f(x)=\frac{\sin3x+\alpha\sin x-\beta\cos3x}{x^3}$ , $x\in\mathbb{R}$ , is continuous at $x=0$ , then $f(0)$ is equal to :
Continuity and Differentiability Limits via Series Expansion for Continuity
MediumSingle correctIdea asked in 3 years
Q8
Let $f(x)=x^5+2x^3+3x+1$ , $x\in\mathbb{R}$ , and $g(x)$ be a function such that $g(f(x))=x$ for all $x\in\mathbb{R}$ . Then $\frac{g(7)}{g'(7)}$ is equal to :
Continuity and Differentiability Chain Rule Derivative of Inverse Functions via Chain Rule
MediumSingle correctIdea asked in 3 years
Q9
Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let $a$ and $b$ be the sides of the rectangle PQRS when its area is maximum. Then $(a+b)^2$ is…
Application of Derivatives Maxima and Minima Max/Min of Inscribed Geometric Figures
HardSingle correctNew idea
Q10
The value of $\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy$ is :
Integrals Definite Integral Properties King's Property
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q11
The integral $\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx$ is equal to :
Integrals Integration by Substitution Numerator-Denominator Derivative Matching
MediumSingle correctIdea asked in 2 years
Q12
If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+2y=\sin(2x)$ , $y(0)=\frac34$ , then $y\left(\frac{\pi}{8}\right)$ is equal to :
Differential Equations Linear Differential Equations Integrating Factor Calculation
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q13
Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point $(3, 2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point $(5, 5)$ is :
Conic Sections Circle Tangents Maximum and Minimum Distance to a Circle
MediumSingle correctIdea asked in 2 years
Q14
Let two straight lines drawn from the origin O intersect the line $3x+4y=12$ at the points P and Q such that $\triangle OPQ$ is an isosceles triangle and $\angle POQ=90^\circ$ . If $l=OP^2+PQ^2+QO^2$ , then the greatest integer less than or equal to $l$ is :
Straight Lines Straight Line Distance Altitude Length of a Triangle
MediumSingle correctIdea asked in 2 years
Q15
Let the line $2x+3y-k=0$ , $k>0$ , intersect the $x$ -axis and $y$ -axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is $x^2+y^2-3x-2y=0$ and the length of the latus rectum of the ellipse…
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q16
If the line $\frac{2-x}{3}=\frac{3y-2}{4\lambda+1}=4-z$ makes a right angle with the line $\frac{x+3}{3\mu}=\frac{1-2y}{6}=\frac{5-z}{7}$ , then $4\lambda+9\mu$ is equal to :
Three Dimensional Geometry Lines in 3D Condition for Perpendicular Lines
MediumSingle correctNew idea
Q17
Let d be the distance of the point of intersection of the lines $\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}$ and $\frac{x-7}{4}=\frac{y-9}{3}=\frac{z-4}{2}$ from the point $(7, 8, 9)$ . Then $d^2+6$ is equal to :
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q18
If $A(1,-1,2)$ , $B(5,7,-6)$ , $C(3,4,-10)$ and $D(-1,-4,-2)$ are the vertices of a quadrilateral ABCD, then its area is :
Vector Algebra Cross Product Area of Quadrilateral via Diagonals
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q19
The coefficients $a, b, c$ in the quadratic equation $ax^2+bx+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$ . The probability of this equation having repeated roots is :
Probability
MediumSingle correct
Q20
Suppose $\theta\in\left[0,\frac{\pi}{4}\right]$ is a solution of $4\cos\theta-3\sin\theta=1$ . Then $\cos\theta$ is equal to :
Trigonometric Functions
MediumSingle correct
Q21
If $S=\{a\in\mathbb{R}:|2a-1|=3[a]+2\{a\}\}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$ , then $72\sum_{a\in S}a$ is equal to ________.
Relations and Functions
HardNumerical value
Q22
The number of distinct real roots of the equation $|x||x+2|-5|x+1|-1=0$ is ________.
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q23
The number of ways of getting a sum 16 on throwing a dice four times is ________.
Permutations and Combinations Distribution of Identical Objects
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q24
If the constant term in the expansion of $(1+2x-3x^3)\left(\frac{3}{2}x^2-\frac{1}{3x}\right)^9$ is $p$ , then $108p$ is equal to ________.
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
MediumNumerical valueIdea asked in 2 years
Q25
Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let $A_k=a_1^2-a_2^2+a_3^2-a_4^2+\ldots+a_{2k-1}^2-a_{2k}^2$ . If $A_3=-153$ , $A_5=-435$ and $a_1^2+a_2^2+a_3^2=66$ , then $a_{17}-A_7$ is equal to ________.
Sequences and Series AP and GP AP Sum of n terms
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q26
Let $f$ be a differentiable function in the interval $(0,\infty)$ such that $f(1)=1$ and $\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1$ for each $x>0$ . Then $2f(2)+3f(3)$ is equal to ________.
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q27
The area of the region enclosed by the parabolas $y=x^2-5x$ and $y=7x-x^2$ is ________.
Application of Integrals Area Under Curves Area Between Two Standard Parabolas
EasyNumerical valueIdea asked in 4 years
Q28
Suppose AB is a focal chord of the parabola $y^2=12x$ of length $l$ and slope $m<\sqrt3$ . If the distance of the chord AB from the origin is $d$ , then $ld^2$ is equal to ________.
Conic Sections Parabola Focal Chords Focal Chord Length via Slope
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q29
Let $\vec a=\hat i-3\hat j+7\hat k$ , $\vec b=2\hat i-\hat j+\hat k$ and $\vec c$ be a vector such that $(\vec a+2\vec b)\times\vec c=3(\vec c\times\vec a)$ . If $\vec a\cdot\vec c=130$ , then $\vec b\cdot\vec c$ is equal to ________.
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q30
From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is $\sigma^2$ , then $96\sigma^2$ is equal to ________.
Probability
MediumNumerical 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 2024 shifts.