JEE Main 2024 · April session

JEE Main 4 April 2024, Shift 1

89 questions (1 more dropped by NTA): 29 numerical-answer and 60 multiple choice. 18 were rated hard and 23 easy. Its hard-question count was the highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 5 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 29; 33% of the shift
Hard: 18; 20% of the shift
Chapters asked: 56; 13 questions with a figure

Key findings · 4 Apr 2024, Shift 1

1
18 hard questions (20%): the 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 12 of 29 rated hard; Chemistry had the most easy questions (11 of 30).
3
20 questions tested a new idea, one no earlier year had asked: 26% of the 78 questions tagged to an idea.
4
30 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
36 shared an idea with another 2024 shift (46% 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), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (5) and Determinants in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 10Medium 14Hard 6

Top chapters

Chemistry

30 Q · 10 numerical

Easy 11Medium 19Hard 0

Top chapters

Maths

29 Q · 9 numerical

Easy 2Medium 15Hard 12

Top chapters

Determinants3 Q
Application of Derivatives2 Q
Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Differential Equations2 Q

Question format

Single correct46 Q
Numerical value29 Q
Diagram based6 Q
Other5 Q
Two statements2 Q
Match the list1 Q

What each question asks you to do

Multi-step32 Q
Calculation25 Q
Conceptual12 Q
Application7 Q
Recall7 Q
Data or graph4 Q
Diagram reading2 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
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

10 easy14 medium6 hard

Chemistry30 questions

11 easy19 medium0 hard

Q61
The Molarity (M) of an aqueous solution containing 5.85 g of NaCl in 500 mL water is : (Given : Molar Mass Na : 23 and Cl : 35.5 $\mathrm{gmol^{-1}}$ )
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasySingle correctIdea asked in 5 yearsAsked the year before
Q62
Which one of the following molecules has maximum dipole moment ?
Chemical Bonding and Molecular Structure VSEPR Theory Net Dipole Moment from VSEPR Symmetry
EasySingle correctIdea asked in 4 yearsAsked the year before
Q63
What will be the decreasing order of basic strength of the following conjugate bases ? $\overline{\mathrm{O}}\mathrm{H}$ , $\mathrm{R}\overline{\mathrm{O}}$ , $\mathrm{CH_3CO}\overline{\mathrm{O}}$ , $\mathrm{C}\bar{\mathrm{l}}$
Organic Chemistry: Some Basic Principles and Techniques Organic Acidity and Basicity Carboxylic Acid Acidity
EasySingle correctIdea asked in 4 years
Q64
One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode comes ?
Electrochemistry Nernst Equation Calomel Electrode Potential
EasySingle correctNew idea
Q65
What pressure (bar) of $\mathrm{H_2}$ would be required to make emf of hydrogen electrode zero in pure water at 25°C ?
Electrochemistry Nernst Equation Single Electrode Nernst
MediumSingle correctNew idea
Q66
The correct order of first ionization enthalpy values of the following elements is : (A) O (B) N (C) Be (D) F (E) B Choose the correct answer from the options given below :
Classification of Elements and Periodicity in Properties Periodic Trends Ionization Enthalpy Trends
MediumOtherIdea asked in 6 years
Q67
Number of elements from the following that CANNOT form compounds with valencies which match with their respective group valencies is ________. B, C, N, S, O, F, P, Al, Si
Classification of Elements and Periodicity in Properties Periodic Trends Valency and Oxidation States
MediumSingle correctNew idea
Q68
Number of molecules/ions from the following in which the central atom is involved in $\mathrm{sp^3}$ hybridization is ________. $\mathrm{NO_3^-}$ , $\mathrm{BCl_3}$ , $\mathrm{ClO_2^-}$ , $\mathrm{ClO_3}$
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q69
The element which shows only one oxidation state other than its elemental form 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 sequence of ligands in the order of decreasing field strength is :
Coordination Compounds Crystal Field Theory Spectrochemical Series
MediumSingle correctIdea asked in 4 years
Q71
Number of complexes from the following with even number of unpaired "d" electrons is ________. $[\mathrm{V(H_2O)_6}]^{3+}$ , $[\mathrm{Cr(H_2O)_6}]^{2+}$ , $[\mathrm{Fe(H_2O)_6}]^{3+}$ , $[\mathrm{Ni(H_2O)_6}]^{3+}$ , $[\mathrm{Cu(H_2O)_6}]^{2+}$ [Given atomic…
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q72
In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to :
Coordination Compounds Cation Analysis Group III Hydroxides
MediumSingle correctIdea asked in 2 years
Q73
Which of the following nitrogen containing compound does not give Lassaigne's test ?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q74
Match List I with List II : List - I (Mechanism steps) List - II (Effect) (A) [structure: aniline, lone pair on NH $_2$ donated into ring, resonance with $\mathrm{N^+H_2}$ = ring and carbanion] — (I) $-$ E effect (B) [structure: cyclohexene + $\mathrm{H^+}$ …
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Mesomeric Effect
MediumMatch the list · figureIdea asked in 3 years
Q75
Which among the following is incorrect statement ?
Organic Chemistry: Some Basic Principles and Techniques Inductive and Electromeric Effects Electromeric Effect
EasySingle correctNew idea
Q76
Identify (B) and (C) and how are (A) and (C) related ? (A) = 1-bromo-4-(2-bromoethyl)benzene drawn as 4-Br-C6H4-CH2CH2Br; $\xrightarrow{\mathrm{NaOH_{(alc)}}}$ (B) $\xrightarrow[\mathrm{Ether}]{\mathrm{HBr}}$ (C) (B) (C)
Haloalkanes and Haloarenes Structural Isomerism Chain vs Position Priority Resolution
MediumOther · figureNew idea
Q77
Identify the correct set of reagents or reaction conditions 'X' and 'Y' in the following set of transformation. $\mathrm{CH_3-CH_2-CH_2-Br} \xrightarrow{'X'} \mathrm{Product} \xrightarrow{'Y'} \mathrm{CH_3-CH-CH_3}$ (with Br on the middle carbon)
Haloalkanes and Haloarenes Alkenes and Alkynes Markovnikov's Rule Application
EasyOtherIdea asked in 6 years
Q78
Given below are two statements : Statements I : Acidity of $\alpha$ -hydrogens of aldehydes and ketones is responsible for Aldol reaction. Statement II : Reaction between benzaldehyde and ethanal will NOT give Cross - Aldol product. In the light of the above…
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cross-Aldol Condensation
MediumTwo statementsIdea asked in 3 years
Q79
Identify the product in the following reaction : [reactant: benzene ring with a CHO group and, meta to it, a COCH3 group (3-acetylbenzaldehyde)] $\xrightarrow[\mathrm{HCl}]{\mathrm{Zn-Hg}}$ Product
Aldehydes, Ketones and Carboxylic Acids Alkanes and Free Radicals Clemmensen Reduction to Alkanes
EasyOther · figureIdea asked in 3 yearsAsked the year before
Q80
Which of the following is the correct structure of L-Glucose ?
Biomolecules Carbohydrates D and L Configuration of Sugars
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q81
The de-Broglie's wavelength of an electron in the $4^{\mathrm{th}}$ orbit is ________ $\pi a_0$ . ( $a_0$ = Bohr's radius)
Structure of Atom Bohr's Atomic Theory Circumference and De Broglie Wavelength
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q82
Number of molecules/species from the following having one unpaired electron is ________. $\mathrm{O_2}$ , $\mathrm{O_2^{-1}}$ , NO, $\mathrm{CN^{-1}}$ , $\mathrm{O_2^{2-}}$
Chemical Bonding and Molecular Structure Molecular Orbital Theory Magnetic Property Prediction
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q83
The enthalpy of formation of ethane ( $\mathrm{C_2H_6}$ ) from ethylene by addition of hydrogen where the bond-energies of C $-$ H, C $-$ C, C $=$ C, H $-$ H are 414 kJ, 347 kJ, 615 kJ and 435 kJ respectively is $-$ ________ kJ
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bond Enthalpy Calculations
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q84
2.5 g of a non-volatile, non-electrolyte is dissolved in 100 g of water at 25°C. The solution showed a boiling point elevation by 2°C. Assuming the solute concentration is negligible with respect to the solvent concentration, the vapor pressure of the…
Solutions Colligative Properties Boiling Point Elevation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q85
Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.…
Chemical Kinetics Arrhenius Equation Effective Activation Energy for Complex Reactions
MediumNumerical valueNew idea
Q86
Consider the following reaction $\mathrm{MnO_2 + KOH + O_2 \rightarrow A + H_2O}$ . Product 'A' in neutral or acidic medium disproportionate to give products 'B' and 'C' along with water. The sum of spin-only magnetic moment values of B and C is ________ BM.…
The d- and f-Block Elements d-Block Elements Permanganate Reactions
MediumNumerical valueIdea asked in 3 years
Q87
Only 2 mL of $\mathrm{KMnO_4}$ solution of unknown molarity is required to reach the end point of a titration of 20 mL of oxalic acid (2 M) in acidic medium. The molarity of $\mathrm{KMnO_4}$ solution should be ________ M.
Redox Reactions Law of Chemical Equivalence in Redox
MediumNumerical valueIdea asked in 5 years
Q88
The number of different chain isomers for $\mathrm{C_7H_{16}}$ is ________.
Organic Chemistry: Some Basic Principles and Techniques Structural Isomerism Enumeration of Structural Isomers
MediumNumerical valueIdea asked in 4 years
Q89
The number of the correct reaction(s) among the following is ________. (A) [benzene + benzoyl chloride ( $\mathrm{C_6H_5COCl}$ ), Anhyd. $\mathrm{AlCl_3}$ $\rightarrow$ diphenylmethane ( $\mathrm{C_6H_5{-}CH_2{-}C_6H_5}$ )] (B) [benzoyl chloride, $\mathrm{H_2}$ ,…
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Friedel-Crafts Acylation and Acylium Ion
MediumNumerical value · figureIdea asked in 2 years
Q90
X g of ethylamine is subjected to reaction with $\mathrm{NaNO_2}$ /HCl followed by water; evolved dinitrogen gas which occupied 2.24 L volume at STP. X is ________ $\times 10^{-1}$ g.
Amines Reaction of Primary Aliphatic Amines with HNO2
EasyNumerical valueIdea asked in 2 years

Maths29 questions

2 easy15 medium12 hard

Q1
If the domain of the function $\sin^{-1}\left(\frac{3x-22}{2x-19}\right)+\log_e\left(\frac{3x^2-8x+5}{x^2-3x-10}\right)$ is $(\alpha, \beta]$ , then $3\alpha+10\beta$ is equal to :
Relations and Functions Functions and Domain Inverse Trig Function Domain
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q2
Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0$ , $z \in C$ . Then $4(\alpha^2+\beta^2)$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Conjugate and Inverse
MediumSingle correctIdea asked in 3 years
Q3
If 2 and 6 are the roots of the equation $ax^2+bx+1=0$ , then the quadratic equation, whose roots are $\frac{1}{2a+b}$ and $\frac{1}{6a+b}$ , is :
Complex Numbers and Quadratic Equations Quadratic Roots Transformation of Roots
EasySingle correctIdea asked in 2 years
Q4
If the system of equations $x+(\sqrt{2}\sin\alpha)y+(\sqrt{2}\cos\alpha)z=0$ $x+(\cos\alpha)y+(\sin\alpha)z=0$ $x+(\sin\alpha)y-(\cos\alpha)z=0$ has a non-trivial solution, then $\alpha \in \left(0, \frac{\pi}{2}\right)$ is equal to :
Determinants Cramer's Rule Parameter Evaluation in Homogeneous Systems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q5
Let $\alpha \in (0, \infty)$ and $A=\begin{bmatrix}1&2&\alpha\\1&0&1\\0&1&2\end{bmatrix}$ . If $\det(\mathrm{adj}(2A-A^T)\cdot \mathrm{adj}(A-2A^T))=2^8$ , then $(\det(A))^2$ is equal to :
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
HardSingle correctIdea asked in 6 yearsAsked the year before
Q6
Let $f: \mathbf{R} \to \mathbf{R}$ be a function given by $f(x)=\begin{cases}\frac{1-\cos 2x}{x^2}, & x<0\\ \alpha, & x=0,\\ \frac{\beta\sqrt{1-\cos x}}{x}, & x>0\end{cases}$ where $\alpha, \beta \in \mathbf{R}$ . If $f$ is continuous at $x=0$ , then…
Continuity and Differentiability Continuity at a Point
MediumSingle correctIdea asked in 4 years
Q7
There are 5 points $P_1, P_2, P_3, P_4, P_5$ on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points $P_6, P_7, \ldots, P_{11}$ on the side BC and 7 points $P_{12}, P_{13}, \ldots, P_{18}$ on the side CA of the triangle. The number…
Permutations and Combinations Triangles from Points with Collinearity
MediumSingle correctIdea asked in 3 years
Q8
The sum of all rational terms in the expansion of $\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$ is equal to :
Binomial Theorem
MediumSingle correct
Q9
Let the first three terms $2$ , $p$ and $q$ , with $q \neq 2$ , of a G.P. be respectively the $7^{th}$ , $8^{th}$ and $13^{th}$ terms of an A.P. If the $5^{th}$ term of the G.P. is the $n^{th}$ term of the A.P., then n is equal to :
Sequences and Series AP and GP GP General Term
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q10
Let $f(x)=\begin{cases}-2, & -2 \le x \le 0\\ x-2, & 0<x \le 2\end{cases}$ and $h(x)=f(|x|)+|f(x)|$ . Then $\int_{-2}^{2} h(x)\,dx$ is equal to :
Integrals Definite Integral Properties Interval Splitting
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q11
Let $f(x)=x^5+2e^{x/4}$ for all $x \in \mathbf{R}$ . Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x \in \mathbf{R}$ . Then the value of $8g'(2)$ is :
Application of Derivatives Chain Rule Derivative of Inverse Functions via Chain Rule
MediumSingle correctIdea asked in 3 years
Q12
Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2x^2-3x+8}{2x^2+3x+8}$ be $\frac{m}{n}$ , where $\gcd(m, n)=1$ . Then $m+n$ is equal to :
Application of Derivatives Maxima and Minima Extrema of Quadratic over Quadratic
MediumSingle correctNew idea
Q13
One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$ . Let the area of the region enclosed by these curves be $\frac{1}{24}(l\sqrt{5}+m)-n\log_e(1+\sqrt{5})$ , where $l, m, n \in \mathbf{N}$ . Then…
Application of Integrals Area Under Curves Area Between Curves
HardSingle correctIdea asked in 7 yearsAsked the year before
Q14
If the solution $y=y(x)$ of the differential equation $(x^4+2x^3+3x^2+2x+2)dy-(2x^2+2x+3)dx=0$ satisfies $y(-1)=-\frac{\pi}{4}$ , then $y(0)$ is equal to :
Differential Equations Variable Separable Form Partial Fractions in Separated Integrals
HardSingle correctNew idea
Q15
A square is inscribed in the circle $x^2+y^2-10x-6y+30=0$ . One side of this square is parallel to $y=x+3$ . If $(x_i, y_i)$ are the vertices of the square, then $\Sigma(x_i^2+y_i^2)$ is equal to :
Conic Sections
HardSingle correct
Q16
The vertices of a triangle are A $(-1, 3)$ , B $(-2, 2)$ and C $(3, -1)$ . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :
Straight Lines Straight Line Distance Distance between parallel lines
MediumSingle correctIdea asked in 4 years
Q17
Let the point, on the line passing through the points P $(1, -2, 3)$ and Q $(5, -4, 7)$ , farther from the origin and at a distance of 9 units from the point P, be $(\alpha, \beta, \gamma)$ . Then $\alpha^2+\beta^2+\gamma^2$ is equal to :
Three Dimensional Geometry Lines in 3D Parametric Points at Distance r
MediumSingle correctNew idea
Q18
Let a unit vector which makes an angle of $60^\circ$ with $2\hat{i}+2\hat{j}-\hat{k}$ and an angle of $45^\circ$ with $\hat{i}-\hat{k}$ be $\vec{C}$ . Then $\vec{C}+\left(-\frac{1}{2}\hat{i}+\frac{1}{3\sqrt{2}}\hat{j}-\frac{\sqrt{2}}{3}\hat{k}\right)$ is :
Vector Algebra Dot Product Angle Between Vectors
HardSingle correctIdea asked in 4 years
Q19
Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :
Probability Bayes' Theorem Bayes' Theorem Application
EasySingle correctIdea asked in 6 yearsAsked the year before
Q20
Let $\alpha, \beta \in \mathbf{R}$ . Let the mean and the variance of 6 observations $-3, 4, 7, -6, \alpha, \beta$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q21
In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and…
Relations and Functions Sets and Relations Min-Max Cardinality Boundaries
HardNumerical valueNew idea
Q22
Let A be a $3\times3$ matrix of non-negative real elements such that $A\begin{bmatrix}1\\1\\1\end{bmatrix}=3\begin{bmatrix}1\\1\\1\end{bmatrix}$ . Then the maximum value of $\det(A)$ is ________.
Determinants
HardNumerical value
Q23
Let $a=1+\frac{{}^2C_2}{3!}+\frac{{}^3C_2}{4!}+\frac{{}^4C_2}{5!}+\ldots$ , $b=1+\frac{{}^1C_0+{}^1C_1}{1!}+\frac{{}^2C_0+{}^2C_1+{}^2C_2}{2!}+\frac{{}^3C_0+{}^3C_1+{}^3C_2+{}^3C_3}{3!}+\ldots$ . Then $\frac{2b}{a^2}$ is equal to ________.
Binomial Theorem
HardNumerical value
Q24
If $\lim_{x\to1}\frac{(5x+1)^{1/3}-(x+5)^{1/3}}{(2x+3)^{1/2}-(x+4)^{1/2}}=\frac{m\sqrt{5}}{n(2n)^{2/3}}$ , where $\gcd(m, n)=1$ , then $8m+12n$ is equal to ________.
Limits and Derivatives L'Hopital's Rule Conjugation vs L'Hopital for Radicals
HardNumerical valueIdea asked in 3 years
Q25
If $\int_0^{\pi/4}\frac{\sin^2x}{1+\sin x\cos x}dx=\frac{1}{a}\log_e\left(\frac{a}{3}\right)+\frac{\pi}{b\sqrt{3}}$ , where $a, b \in \mathbf{N}$ , then $a+b$ is equal to ________.
Integrals Definite Integral Properties King's Property
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q26
Let the solution $y=y(x)$ of the differential equation $\frac{dy}{dx}-y=1+4\sin x$ satisfy $y(\pi)=1$ . Then $y\left(\frac{\pi}{2}\right)+10$ is equal to ________.
Differential Equations Linear Differential Equations Particular Solution Solving
MediumNumerical valueIdea asked in 4 years
Q28
Let the length of the focal chord PQ of the parabola $y^2=12x$ be 15 units. If the distance of PQ from the origin is p, then $10p^2$ is equal to ________.
Conic Sections Parabola Focal Chords Focal Chord Length via Vertex Distance
MediumNumerical valueNew idea
Q29
If the shortest distance between the lines $\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$ and $\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}$ is $\frac{38}{3\sqrt{5}}k$ , and $\int_0^k[x^2]dx=\alpha-\sqrt{\alpha}$ , where $[x]$ denotes the greatest integer function,…
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
HardNumerical valueIdea asked in 5 years
Q30
Let ABC be a triangle of area $15\sqrt{2}$ and the vectors $\overrightarrow{AB}=\hat{i}+2\hat{j}-7\hat{k}$ , $\overrightarrow{BC}=a\hat{i}+b\hat{j}+c\hat{k}$ and $\overrightarrow{AC}=6\hat{i}+d\hat{j}-2\hat{k}$ , $d>0$ . Then the square of the length of the…
Vector Algebra Cross Product Area of Triangles and Parallelograms
HardNumerical valueIdea asked in 6 yearsAsked the year before

Dropped from the final key and left out of every count: Q27.

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.