JEE Main 2024 · January session

JEE Main 30 January 2024, Shift 2

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 9 were rated hard and 37 easy. Its hard-question count was the joint 12th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 9; 10% of the shift
Chapters asked: 60; 12 questions with a figure

Key findings · 30 Jan 2024, Shift 2

1
9 hard questions (10%): the joint 12th 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 6 of 29 rated hard; Physics had the most easy questions (17 of 30).
3
25 questions tested a new idea, one no earlier year had asked: 32% of the 79 questions tagged to an idea.
4
29 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
34 shared an idea with another 2024 shift (43% 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 (4) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 17Medium 11Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 16Medium 13Hard 1

Top chapters

Maths

29 Q · 10 numerical

Easy 4Medium 19Hard 6

Top chapters

Question format

Single correct47 Q
Numerical value30 Q
Diagram based5 Q
Two statements3 Q
Other2 Q
Match the list1 Q
Assertion–reason1 Q

What each question asks you to do

Calculation29 Q
Multi-step26 Q
Application12 Q
Conceptual10 Q
Recall9 Q
Data or graph3 Q

Most common: Calculation.

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
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

17 easy11 medium2 hard

Chemistry30 questions

16 easy13 medium1 hard

Q61
If a substance 'A' dissolves in solution of a mixture of 'B' and 'C' with their respective number of moles as $\mathrm{n_A}$ , $\mathrm{n_B}$ and $\mathrm{n_C}$ . Mole fraction of C in the solution is :
Solutions Mole Concept Mole Fraction Calculation
EasySingle correctIdea asked in 3 years
Q62
Given below are two statements: Statement - I: Since Fluorine is more electronegative than nitrogen, the net dipole moment of $\mathrm{NF_3}$ is greater than $\mathrm{NH_3}$ . Statement - II: In $\mathrm{NH_3}$ , the orbital dipole due to lone pair and the…
Chemical Bonding and Molecular Structure VSEPR Theory VSEPR Symmetry and Dipole Moments
MediumTwo statementsNew ideaIdea asked in 2 years
Q63
The molecule / ion with square pyramidal shape is
Chemical Bonding and Molecular Structure VSEPR Theory Square Pyramidal Geometry (SN=6, 1 LP)
EasySingle correctIdea asked in 3 yearsAsked the year before
Q64
The solution from the following with highest depression in freezing point/lowest freezing point is
Solutions Colligative Properties Ranking Solutions by Colligative Extremes
MediumSingle correctNew idea
Q65
Reduction potential of ions are given below: $\mathrm{ClO_4^-}$ $E^\circ = 1.19\ V$ ; $\mathrm{IO_4^-}$ $E^\circ = 1.65\ V$ ; $\mathrm{BrO_4^-}$ $E^\circ = 1.74\ V$ The correct order of their oxidising power is :
Electrochemistry Nernst Equation Standard Cell Potential
EasySingle correctIdea asked in 7 yearsAsked the year before
Q66
Given below are two statements: Statement - I: Along the period, the chemical reactivity of the elements gradually increases from group 1 to group 18. Statement - II: The nature of oxides formed by group 1 elements is basic while that of group 17 is acidic.…
Classification of Elements and Periodicity in Properties Periodic Trends Acidic and Basic Character of Oxides
EasyTwo statementsIdea asked in 4 years
Q67
Choose the correct statements about the hydrides of group 15 elements. A. The stability of the hydrides decreases in the order $\mathrm{NH_3} > \mathrm{PH_3} > \mathrm{AsH_3} > \mathrm{SbH_3} > \mathrm{BiH_3}$ . B. The reducing ability of the hydride…
The p-Block Elements Periodic Trends Acidic and Reducing Nature of Hydrides
MediumOtherNew idea
Q68
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: $\mathrm{H_2Te}$ is more acidic than $\mathrm{H_2S}$ . Reason R: Bond dissociation enthalpy of $\mathrm{H_2Te}$ is lower than $\mathrm{H_2S}$ .…
The p-Block Elements Periodic Trends Acidic Strength Trends of p-Block Hydrides
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q69
Alkaline oxidative fusion of $\mathrm{MnO_2}$ gives "A" which on electrolytic oxidation in alkaline solution produces B. A and B respectively are
The d- and f-Block Elements d-Block Elements Preparation Steps of Potassium Permanganate
EasySingle correctNew idea
Q70
The orange colour of $\mathrm{K_2Cr_2O_7}$ and purple colour of $\mathrm{KMnO_4}$ is due to
The d- and f-Block Elements d-Block Elements Ligand-to-Metal Charge Transfer (LMCT)
EasySingle correctNew idea
Q71
The coordination geometry around the manganese in decacarbonyldimanganese (0) is
Coordination Compounds
MediumSingle correct
Q72
Which among the following purification methods is based on the principle of "Solubility" in two different solvents?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q73
The correct stability order of carbocations is
Organic Chemistry: Some Basic Principles and Techniques Inductive and Electromeric Effects Carbocation Stability
EasySingle correctIdea asked in 4 yearsAsked the year before
Q74
IUPAC name of following compound is : $\mathrm{CH_3-CH-CH_2-CN}$ with $\mathrm{NH_2}$ on the CH carbon
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Nomenclature of Cyanides and Isocyanides
EasySingle correct · figureNew idea
Q75
Given below are two statements: Statement - I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow $\mathrm{S_N}2$ mechanism. Statement - II: A secondary alkyl halide when treated…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Solvent Effects on Substitution
MediumTwo statementsIdea asked in 3 yearsAsked the year before
Q76
Salicylaldehyde is synthesized from phenol, when reacted with
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
EasySingle correctIdea asked in 4 years
Q77
Products A and B formed in the following set of reactions are B $\xleftarrow{\mathrm{B_2H_6},\ \mathrm{H_2O_2,\ NaOH(aq)}}$ [1-methylcyclohexene] $\xrightarrow{\mathrm{H^+/H_2O}}$ A
Alcohols, Phenols and Ethers Alcohols and Phenols Hydroboration-Oxidation Regiochemistry
MediumDiagram based · figureNew idea
Q78
m-chlorobenzaldehyde on treatment with 50% KOH solution yields
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cannizzaro Reaction
EasyDiagram based · figureIdea asked in 4 years
Q79
The products A and B formed in the following reaction scheme are respectively Benzene $\xrightarrow[\text{ii) Sn / HCl}]{\text{i) con. }\mathrm{HNO_3}/\text{Con. }\mathrm{H_2SO_4},\ 323\text{--}333\ \mathrm{K}}$ A…
Amines Diazonium Salts Azo Coupling Reactions
EasyDiagram based · figureIdea asked in 5 yearsAsked the year before
Q80
A and B formed in the following reactions are: $\mathrm{CrO_2Cl_2} + 4\mathrm{NaOH} \to A + 2\mathrm{NaCl} + 2\mathrm{H_2O}$ $A + 2\mathrm{HCl} + 2\mathrm{H_2O_2} \to B + 3\mathrm{H_2O}$
The d- and f-Block Elements d-Block Elements Chromyl Chloride Test Reactions
MediumSingle correctNew idea
Q81
Number of spectral lines obtained in $\mathrm{He^+}$ spectra, when an electron makes transition from fifth excited state to first excited state will be
Structure of Atom Bohr's Atomic Theory Number of Spectral Lines in Transitions
EasyNumerical valueIdea asked in 2 years
Q82
Two reactions are given below: $2\mathrm{Fe_{(s)}} + \frac{3}{2}\mathrm{O_{2(g)}} \to \mathrm{Fe_2O_{3(s)}},\ \Delta H^\circ = -822\ \mathrm{kJ/mol}$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Hess's Law
EasyNumerical valueIdea asked in 5 years
Q83
The pH of an aqueous solution containing 1M benzoic acid ( $\mathrm{pK_a} = 4.20$ ) and 1M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ________ mL. (given : $\log 2 = 0.3$ )
Equilibrium pH and Buffers Volume Ratios for Buffer Preparation
MediumNumerical valueNew idea
Q84
Total number of species from the following which can undergo disproportionation reaction is ________. $\mathrm{H_2O_2, ClO_3^-, P_4, Cl_2, Ag, Cu^{+1}, F_2, NO_2, K^+}$
Redox Reactions Predicting Redox Feasibility via Extreme States
MediumNumerical valueNew idea
Q85
$\mathrm{NO_2}$ required for a reaction is produced by decomposition of $\mathrm{N_2O_5}$ in $\mathrm{CCl_4}$ as by equation $2\mathrm{N_2O_{5(g)}} \to 4\mathrm{NO_{2(g)}} + \mathrm{O_{2(g)}}$ The initial concetration. of $\mathrm{N_2O_5}$ is 3 mol L $^{-1}$ …
Chemical Kinetics Rate Laws Rate and Stoichiometry
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q86
Number of complexes which show optical isomerism among the following is ________. $cis\text{-}[\mathrm{Cr(ox)_2Cl_2}]^{3-}$ , $[\mathrm{Co(en)_3}]^{3+}$ , $cis\text{-}[\mathrm{Pt(en)_2Cl_2}]^{2+}$ , $cis\text{-}[\mathrm{Co(en)_2Cl_2}]^{+}$ ,…
Coordination Compounds Coordination Isomerism Optical Activity in M(AA)2B2 Complexes
MediumNumerical valueNew idea
Q87
Number. of geometrical isomers possible for the given structure is/are ________.
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Calculating Geometrical Isomers in Polyenes
MediumNumerical value · figureNew idea
Q88
2-chlorobutane + $\mathrm{Cl_2} \to \mathrm{C_4H_8Cl_2}$ (isomers) Total number of optically active isomers shown by $\mathrm{C_4H_8Cl_2}$ , obtained in the above reaction is ________.
Haloalkanes and Haloarenes Stereoisomerism Counting Optical Isomers
HardNumerical valueNew idea
Q89
The total number of correct statements, regarding the nucleic acids is ________ A. RNA is regarded as the reserve of genetic information B. DNA molecule self-duplicates during cell division C. DNA synthesizes proteins in the cell D. The message for the…
Biomolecules
EasyNumerical value
Q90
Number of metal ions characterized by flame test among the following is ________. $\mathrm{Sr^{2+}, Ba^{2+}, Ca^{2+}, Cu^{2+}, Zn^{2+}, Co^{2+}, Fe^{2+}}$
The s-Block Elements s-Block Elements Flame Coloration
MediumNumerical valueIdea asked in 4 yearsAsked the year before

Maths29 questions

4 easy19 medium6 hard

Q1
If the domain of the function $f(x) = \log_e\left(\frac{2x+3}{4x^2+x-3}\right) + \cos^{-1}\left(\frac{2x-1}{x+2}\right)$ is $(\alpha, \beta]$ , then the value of $5\beta - 4\alpha$ is equal to
Relations and Functions Functions and Domain Intersection of Domains
MediumSingle correctIdea asked in 2 years
Q2
If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$ , is equal to
Complex Numbers and Quadratic Equations Roots of Unity Roots of z^2 + z + 1 = 0
MediumSingle correctIdea asked in 2 years
Q3
Let $R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix}$ be a non-zero $3\times 3$ matrix, where $x\sin\theta = y\sin\left(\theta + \frac{2\pi}{3}\right) = z\sin\left(\theta + \frac{4\pi}{3}\right) \neq 0$ , $\theta \in (0, 2\pi)$ . For a…
Determinants Matrix Inverse Inverse Relation to Double Adjoint
HardOtherIdea asked in 6 yearsAsked the year before
Q4
Consider the system of linear equations $x + y + z = 5$ , $x + 2y + \lambda^2 z = 9$ , $x + 3y + \lambda z = \mu$ , where $\lambda, \mu \in \mathbb{R}$ . Then, which of the following statement is NOT correct?
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q6
Let $a$ and $b$ be be two distinct positive real numbers. Let $11^{\mathrm{th}}$ term of a GP, whose first term is $a$ and third term is $b$ , is equal to $p^{\mathrm{th}}$ term of another GP, whose first term is $a$ and fifth term is $b$ . Then $p$ is equal to
Sequences and Series AP and GP GP General Term
EasySingle correctIdea asked in 5 yearsAsked the year before
Q7
Let $f: \mathbb{R} - \{0\} \to \mathbb{R}$ be a function satisfying $f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)}$ for all $x, y, f(y) \neq 0$ . If $f'(1) = 2024$ , then
Continuity and Differentiability Differentiability via Functional Equations
MediumSingle correctIdea asked in 6 years
Q8
Let $a$ and $b$ be real constants such that the function $f$ defined by $f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1 \\ bx + 2, & x > 1 \end{cases}$ be differentiable on $\mathbb{R}$ . Then, the value of $\int_{-2}^{2} f(x)dx$ equals
Continuity and Differentiability Finding Unknowns using Differentiability
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q9
Let $f(x) = (x+3)^2 (x-2)^3$ , $x \in [-4, 4]$ . If $M$ and $m$ are the maximum and minimum values of $f$ , respectively in $[-4, 4]$ , then the value of $M - m$ is
Application of Derivatives Maxima and Minima Closed Interval Extrema
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q10
Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = ae^{2x} + be^x + cx$ . If $f(0) = -1$ , $f'(\log_e 2) = 21$ and $\int_0^{\log_e 4} (f(x) - cx)dx = \frac{39}{2}$ , then the value of $|a + b + c|$ equals
Integrals
MediumSingle correct
Q11
For $\alpha, \beta \in (0, \pi/2)$ , let $3\sin(\alpha + \beta) = 2\sin(\alpha - \beta)$ and a real number $k$ be such that $\tan\alpha = k\tan\beta$ . Then, the value of $k$ is equal to
Trigonometric Functions Trigonometric Identities Compound Angle Formulas
MediumSingle correctIdea asked in 5 years
Q12
Let $y = f(x)$ be a thrice differentiable function in $(-5, 5)$ . Let the tangents to the curve $y = f(x)$ at $(1, f(1))$ and $(3, f(3))$ make angles $\pi/6$ and $\pi/4$ , respectively with positive $x$ -axis. If…
Integrals Integration by Substitution Composite Function Substitution
HardSingle correctIdea asked in 3 years
Q13
Let $f: \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \frac{x}{(1+x^4)^{1/4}}$ , and $g(x) = f(f(f(f(x))))$ . Then, $18\int_0^{\sqrt{2\sqrt{5}}} x^2 g(x)dx$ is equal to
Integrals Integration by Substitution Composite Function Substitution
HardSingle correctIdea asked in 3 years
Q14
Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5x + 7y = 50$ . Let the point $P$ divide the line segment $AB$ internally in the ratio $7:3$ . Let $3x - 25 = 0$ be a directrix of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and the…
Conic Sections Ellipse Eccentricity Equations of directrices
MediumSingle correctNew idea
Q15
Let $P$ be a point on the hyperbola $H: \frac{x^2}{9} - \frac{y^2}{4} = 1$ , in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $2\sqrt{13}$ . Then, the square of the distance of $P$ from the origin is
Conic Sections
MediumSingle correct
Q16
If $x^2 - y^2 + 2hxy + 2gx + 2fy + c = 0$ is the locus of a point, which moves such that it is always equidistant from the lines $x + 2y + 7 = 0$ and $2x - y + 8 = 0$ , then the value of $g + c + h - f$ equals
Straight Lines Straight Line Distance Angle Bisector Locus via Distances
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q17
Let $L_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R}$ , $L_2: \vec{r} = (\hat{j} - \hat{k}) + \mu(3\hat{i} + \hat{j} + p\hat{k}), \mu \in \mathbb{R}$ , and…
Three Dimensional Geometry Lines in 3D Line Perpendicular to Two Given Lines
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q18
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{b}| = 1$ and $|\vec{b} \times \vec{a}| = 2$ . Then $\left|(\vec{b} \times \vec{a}) - \vec{b}\right|^2$ is equal to
Vector Algebra Dot Product Expansion of Sum of Vectors Squared
EasySingle correctIdea asked in 4 years
Q19
Let $\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}$ , $\alpha, \beta \in \mathbb{R}$ . Let a vector $\vec{b}$ be such that the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$ and $|\vec{b}|^2 = 6$ . If $\vec{a} \cdot \vec{b} = 3\sqrt{2}$ , then the…
Vector Algebra Cross Product Lagrange's Identity
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q20
Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is
Probability Bayes' Theorem Bayes' Theorem Application
EasySingle correctIdea asked in 6 yearsAsked the year before
Q21
The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is ________.
Relations and Functions Sets and Relations Counting Relations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
The number of real solutions of the equation $x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0$ is ________.
Relations and Functions Quadratic Roots Roots of Modulus Quadratics
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q23
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $A$ , $B$ and $C$ . A student is required to attempt total 15 questions taking at least 4 questions from each section. If…
Permutations and Combinations Selection of One or More Objects
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q24
Let $\alpha = \sum_{k=0}^{n} \left(\frac{({}^nC_k)^2}{k+1}\right)$ and $\beta = \sum_{k=0}^{n-1} \left(\frac{{}^nC_k\, {}^nC_{k+1}}{k+2}\right)$ . If $5\alpha = 6\beta$ , then $n$ equals ________.
Binomial Theorem Binomial Coefficients Definite Integral Method for Beta-like Sums
HardNumerical valueNew idea
Q25
Let $S_n$ be the sum to $n$ -terms of an arithmetic progression $3, 7, 11, \ldots$ . If $40 < \left(\frac{6}{n(n+1)}\sum_{k=1}^{n} S_k\right) < 42$ , then $n$ equals ________.
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q26
The area of the region enclosed by the parabola $(y-2)^2 = x - 1$ , the line $x - 2y + 4 = 0$ and the positive coordinate axes is ________.
Application of Integrals Area Under Curves Regions with Multiple Bounding Curves
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q27
Let $Y = Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y'(x)(X - x)$ and the co-ordinate axes, where $(x, y)$ is any point on the curve, is always $\frac{-y^2}{2Y'(x)} + 1$ , $Y'(x) \neq 0$ . If $Y(1) = 1$ , then…
Differential Equations Linear Differential Equations Forming LDEs from Geometric Conditions
HardNumerical valueIdea asked in 2 years
Q28
Consider two circles $C_1: x^2 + y^2 = 25$ and $C_2: (x - \alpha)^2 + y^2 = 16$ , where $\alpha \in (5, 9)$ . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_1$ and $C_2$ be…
Conic Sections Power of a Point Length of Common Chord via Radical Axis
HardNumerical valueIdea asked in 3 years
Q29
Let a line passing through the point $(-1, 2, 3)$ intersect the lines $L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}$ at $M(\alpha, \beta, \gamma)$ and $L_2: \frac{x+2}{-3} = \frac{y-2}{-2} = \frac{z-1}{4}$ at $N(a, b, c)$ . Then the value of…
Three Dimensional Geometry Lines in 3D Line Through Point Intersecting Two Skew Lines
MediumNumerical valueNew ideaIdea asked in 2 years
Q30
The variance $\sigma^2$ of the data | $x_i$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | $f_i$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 | is ________.
Statistics Variance and SD Variance of Discrete Frequency Distribution
EasyNumerical valueIdea asked in 2 yearsAsked the year before

Dropped from the final key and left out of every count: Q5.

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.