JEE Main 2024 · April session

JEE Main 9 April 2024, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 14 were rated hard and 28 easy. Its hard-question count was the 3rd highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Aldehydes, Ketones and Carboxylic Acids, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 14; 16% of the shift
Chapters asked: 61; 16 questions with a figure

Key findings · 9 Apr 2024, Shift 2

1
14 hard questions (16%): the 3rd 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 9 of 30 rated hard; Physics had the most easy questions (16 of 30).
3
19 questions tested a new idea, one no earlier year had asked: 27% of the 70 questions tagged to an idea.
4
25 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
27 shared an idea with another 2024 shift (39% 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), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 16Medium 12Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 15Hard 3

Top chapters

Maths

30 Q · 10 numerical

Easy 0Medium 21Hard 9

Top chapters

Question format

Single correct53 Q
Numerical value30 Q
Match the list5 Q
Two statements2 Q

What each question asks you to do

Multi-step35 Q
Calculation25 Q
Application14 Q
Recall9 Q
Conceptual5 Q
Diagram reading1 Q
Data or graph1 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

16 easy12 medium2 hard

Q31
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/\sqrt{2mE}$ . The dimensional formula for Planck's constant is :
Units and Measurements
EasySingle correct
Q32
Two cars are travelling towards each other at speed of $20\ \mathrm{m\,s^{-1}}$ each. When the cars are $300\ \mathrm{m}$ apart, both the drivers apply brakes and the cars retard at the rate of $2\ \mathrm{m\,s^{-2}}$ . The distance between them when they…
Motion in a Straight Line Kinematics in 1D Stopping Distance Proportionality
EasySingle correctIdea asked in 2 years
Q33
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$ . After disintegration they will move :
System of Particles and Rotational Motion Collisions Momentum Conservation
EasySingle correctNew idea
Q34
A $1$ kg mass is suspended from the ceiling by a rope of length $4$ m. A horizontal force $F$ is applied at the mid point of the rope so that the rope makes an angle of $45^\circ$ with respect to the vertical axis as shown in figure. The magnitude of $F$ is…
Laws of Motion Newton's Laws of Motion Static Equilibrium
EasySingle correct · figureIdea asked in 4 yearsAsked the year before
Q35
A hydrogen atom in ground state is given an energy of $10.2$ eV. How many spectral lines will be emitted due to transition of electrons ?
Atoms Bohr's Atomic Model Number of Spectral Lines
EasySingle correctIdea asked in 3 yearsAsked the year before
Q36
A real gas within a closed chamber at $27^\circ C$ undergoes the cyclic process as shown in figure. The gas obeys $PV^3=RT$ equation for the path $A$ to $B$ . The net work done in the complete cycle is (assuming $R=8$ J/mol K) :
Thermodynamics Thermodynamic Processes Cyclic Process Work
HardSingle correct · figureIdea asked in 4 yearsAsked the year before
Q37
The energy released in the fusion of $2\ kg$ of hydrogen deep in the sun is $E_H$ and the energy released in the fission of $2\ kg$ of $^{235}\mathrm{U}$ is $E_U$ . The ratio $\frac{E_H}{E_U}$ is approximately: (Consider the fusion reaction as…
Nuclei Fission and Fusion Energy Density Comparison
MediumSingle correctNew idea
Q38
A satellite of $10^3$ kg mass is revolving in circular orbit of radius $2R$ . If $\frac{10^4R}{6}$ J energy is supplied to the satellite, it would revolve in a new circular orbit of radius : (use $g=10\ \mathrm{m/s^2}$ , $R$ = radius of earth)
Gravitation Orbital Mechanics Work Done to Shift Orbits
MediumSingle correctNew idea
Q39
The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:
Mechanical Properties of Fluids Surface Tension Excess Pressure in Soap Bubbles
EasySingle correctIdea asked in 4 years
Q40
A spherical ball of radius $1\times10^{-4}$ m and density $10^5\ \mathrm{kg/m^3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of $h$ is…
Mechanical Properties of Fluids Viscosity Terminal Velocity Calculation
HardSingle correctIdea asked in 3 yearsAsked the year before
Q41
The temperature of a gas is $-78^\circ$ C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2$ K is :
Kinetic Theory Kinetic Theory of Gases Kinetic Energy and Temp
EasySingle correctIdea asked in 7 yearsAsked the year before
Q42
Five charges $+q$ , $+5q$ , $-2q$ , $+3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is :
Electric Charges and Fields Gauss's Law Flux from External Charges
EasySingle correct · figureNew idea
Q43
The effective resistance between $A$ and $B$ , if resistance of each resistor is $R$ , will be :
Current Electricity Kirchhoff's Laws Circuit Symmetry Analysis
MediumSingle correct · figureIdea asked in 4 yearsAsked the year before
Q44
A proton and a deutron ( $q=+e$ , $m=2.0$ u) having same kinetic energies enter a region of uniform magnetic field $\vec{B}$ , moving perpendicular to $\vec{B}$ . The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is :
Moving Charges and Magnetism Lorentz Force Trajectory Radii Ratio for Same Kinetic Energy
EasySingle correctIdea asked in 3 years
Q45
A square loop of side $15$ cm being moved towards right at a constant speed of $2$ cm/s as shown in figure. The front edge enters the $50$ cm wide magnetic field at $t=0$ . The value of induced emf in the loop at $t=10$ s will be :
Electromagnetic Induction Faraday's Law EMF Profile of Loop Entering/Exiting B-Field
EasySingle correct · figureNew idea
Q46
The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length $10$ cm and $15$ cm respectively. The distance between $L_1$ & $L_2$ is :
Ray Optics and Optical Instruments Lens Maker's Formula Afocal Lens System
MediumSingle correct · figureNew idea
Q47
UV light of $4.13$ eV is incident on a photosensitive metal surface having work function $3.13$ eV. The maximum kinetic energy of ejected photoelectrons will be:
Dual Nature of Radiation and Matter Photoelectric Effect Einstein's Photoelectric Equation
EasySingle correctIdea asked in 5 years
Q48
In the truth table of the above circuit the value of X and Y are :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumSingle correct · figureIdea asked in 7 yearsAsked the year before
Q49
The $I$ - $V$ characteristics of an electronic device shown in the figure. The device is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes I-V Characteristics
EasySingle correct · figureNew idea
Q50
The magnetic field in a plane electromagnetic wave is $B_y=(3.5\times10^{-7})\sin(1.5\times10^3x+0.5\times10^{11}t)\mathrm{T}$ . The corresponding electric field will be :
Electromagnetic Waves
MediumSingle correct
Q51
A force $(3x^2+2x-5)$ N displaces a body from $x=2$ m to $x=4$ m. Work done by this force is ___________ J.
Work, Energy and Power Work and Kinetic Energy Work by Variable Force
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q52
Monochromatic light of wavelength $500$ nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index = 1.5), the central maximum is shifted to a…
Wave Optics Young's Double Slit Fringe Shift by Thin Slab
MediumNumerical valueIdea asked in 3 years
Q53
A capacitor of reactance $4\sqrt{3}\ \Omega$ and a resistor of resistance $4\ \Omega$ are connected in series with an ac source of peak value $8\sqrt{2}$ V. The power dissipation in the circuit is ___________ W.
Alternating Current Phasor Diagrams Power Factor from Phasors
MediumNumerical valueIdea asked in 5 years
Q54
A straight magnetic strip has a magnetic moment of $44\ \mathrm{Am^2}$ . If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\mathrm{Am^2}$ . (given $\pi=\frac{22}{7}$ )
Magnetism and Matter Magnetic Dipole Moment Bending a Bar Magnet into a Semicircle
EasyNumerical valueNew idea
Q55
At room temperature ( $27^\circ$ C), the resistance of a heating element is $50\ \Omega$ . The temperature coefficient of the material is $2.4\times10^{-4}\ {}^\circ C^{-1}$ . The temperature of the element, when its resistance is $62\ \Omega$ , is _________…
Current Electricity Ohm's Law and Resistance Temperature Coefficient of Resistance
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q56
An electric field $\vec{E}=(2x\hat{i})\ NC^{-1}$ exists in space. A cube of side $2$ m is placed in the space as per figure given below. The electric flux through the cube is ________ $Nm^2/C$ .
Electric Charges and Fields Gauss's Law Flux in Spatially Variable Field
MediumNumerical value · figureNew idea
Q57
A particle of mass $0.50$ kg executes simple harmonic motion under force $F=-50\ (Nm^{-1})x$ . The time period of oscillation is $\frac{x}{35}$ s. The value of $x$ is __________. (Given $\pi=\frac{22}{7}$ )
Oscillations SHM Equations SHM Definition and Force Law
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q58
A circular disc reaches from top to bottom of an inclined plane of length $l$ . When it slips down the plane, if takes $t$ s. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1/2}t$ s, where $\alpha$ is _________.
System of Particles and Rotational Motion
MediumNumerical value
Q59
The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$ . The angle between vectors $\vec{A}$ and $\vec{B}$ is _________ $^\circ$ .
Motion in a Plane
MediumNumerical value
Q60
To determine the resistance ( $R$ ) of a wire, a circuit is designed below. The $V$ - $I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is ___________ $\Omega$ .
Current Electricity Ohm's Law and Resistance Ohm's Law and V-I Graphs
MediumNumerical value · figureIdea asked in 3 years

Chemistry30 questions

12 easy15 medium3 hard

Maths30 questions

0 easy21 medium9 hard

Q1
Let the range of the function $f(x)=\frac{1}{2+\sin 3x+\cos 3x},\ x\in\mathbb{R}$ be $[a, b]$ . If $\alpha$ and $\beta$ are respectively the A.M. and the G.M. of $a$ and $b$ , then $\frac{\alpha}{\beta}$ is equal to
Sequences and Series Trigonometric Identities Extrema of Linear Trigonometric Forms
MediumSingle correctIdea asked in 2 years
Q2
Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then, the maximum value of $|z-(6+8i)|$ is equal to
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Triangle Inequality Extrema
MediumSingle correctIdea asked in 5 years
Q3
Let $\alpha, \beta;\ \alpha>\beta$ , be the roots of the equation $x^2-\sqrt{2}x-\sqrt{3}=0$ . Let $P_n=\alpha^n-\beta^n,\ n\in\mathbb{N}$ . Then $\left(11\sqrt{3}-10\sqrt{2}\right)P_{10}+\left(11\sqrt{2}+10\right)P_{11}-11P_{12}$ is equal to
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
Let $B=\begin{bmatrix}1&3\\1&5\end{bmatrix}$ and $A$ be a $2\times2$ matrix such that $AB^{-1}=A^{-1}$ . If $BCB^{-1}=A$ and $C^4+\alpha C^2+\beta I=O$ , then $2\beta-\alpha$ is equal to
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
HardSingle correctIdea asked in 5 years
Q5
$\lim_{x\to0}\frac{e-(1+2x)^{\frac{1}{2x}}}{x}$ is equal to
Limits and Derivatives L'Hopital's Rule Indeterminate Power Forms
HardSingle correctIdea asked in 3 years
Q6
The sum of the coefficient of $x^{2/3}$ and $x^{-2/5}$ in the binomial expansion of $\left(x^{2/3}+\frac{1}{2}x^{-2/5}\right)^9$ is
Binomial Theorem
MediumSingle correct
Q7
Let $a, ar, ar^2, \ldots$ be an infinite G.P. If $\sum_{n=0}^{\infty}ar^n=57$ and $\sum_{n=0}^{\infty}a^3r^{3n}=9747$ , then $a+18r$ is equal to
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q8
If $\log_e y=3\sin^{-1}x$ , then $(1-x^2)y''-xy'$ at $x=\frac{1}{2}$ is equal to
Continuity and Differentiability Chain Rule Second Order Implicit Chain Rule
MediumSingle correctIdea asked in 4 years
Q9
$\lim_{x\to\frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi/2)^3}\left(\sin\left(2t^{1/3}\right)+\cos\left(t^{1/3}\right)\right)dt}{\left(x-\frac{\pi}{2}\right)^2}\right)$ is equal to
Integrals Leibniz Rule Limit Evaluation
HardSingle correctIdea asked in 2 years
Q10
The area (in square units) of the region enclosed by the ellipse $x^2+3y^2=18$ in the first quadrant below the line $y=x$ is
Application of Integrals Area Under Curves Ellipse Segment Area via Eccentric Angle
MediumSingle correctNew idea
Q11
The integral $\int_{1/4}^{3/4}\cos\left(2\cot^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx$ is equal to
Integrals Inverse Trig Identities Multiple Angle Inverse ID
MediumSingle correctIdea asked in 2 years
Q12
The value of the integral $\int_{-1}^{2}\log_e\left(x+\sqrt{x^2+1}\right)dx$ is
Integrals Integration by Parts Logarithm of Quadratic Roots
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q13
Let $\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0$ . Then at $x=2$ , $y''+y+1$ is equal to
Differential Equations Leibniz Rule Solving Integral Equations
HardSingle correctIdea asked in 6 yearsAsked the year before
Q14
Two vertices of a triangle ABC are A $(3,-1)$ and B $(-2,3)$ , and its orthocentre is P $(1,1)$ . If the coordinates of the point C are $(\alpha,\beta)$ and the centre of the circle circumscribing the triangle PAB is $(h,k)$ , then the value of…
Straight Lines
MediumSingle correct
Q15
Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E:\frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$ . If the length of the transverse axis of $H$ …
Conic Sections Ellipse Eccentricity Coordinates of foci
MediumSingle correctIdea asked in 4 years
Q16
Consider the line L passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point $\left(\frac{11}{3},\frac{11}{3},\frac{19}{3}\right)$ from the line L along the line $\frac{3x-11}{2}=\frac{3y-11}{1}=\frac{3z-19}{2}$ is equal to
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
HardSingle correctIdea asked in 6 yearsAsked the year before
Q17
Between the following two statements: Statement I : Let $\vec{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-\hat{k}$ . Then the vector $\vec{r}$ satisfying $\vec{a}\times\vec{r}=\vec{a}\times\vec{b}$ and $\vec{a}\cdot\vec{r}=0$ is of magnitude…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
HardTwo statementsIdea asked in 6 yearsAsked the year before
Q18
Let $\vec{a}=2\hat{i}+\alpha\hat{j}+\hat{k},\ \vec{b}=-\hat{i}+\hat{k},\ \vec{c}=\beta\hat{j}-\hat{k}$ , where $\alpha$ and $\beta$ are integers and $\alpha\beta=-6$ . Let the values of the ordered pair $(\alpha, \beta)$ , for which the area of the…
Vector Algebra Cross Product Area of Quadrilateral via Diagonals
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q19
If the variance of the frequency distribution | $x$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ | |---|---|---|---|---|---|---| | $f$ | 2 | 1 | 1 | 1 | 1 | 1 | is 160, then the value of $c\in\mathbb{N}$ is
Statistics Variance and SD Variance of Discrete Frequency Distribution
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q20
If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text{th}}$ roll than the number obtained in the $(i-1)^{\text{th}}$ roll, $i=2, 3$ , is equal to
Probability
MediumSingle correct
Q21
Let $A=\{(x, y): 2x+3y=23,\ x, y\in\mathbb{N}\}$ and $B=\{x: (x, y)\in A\}$ . Then the number of one-one functions from $A$ to $B$ is equal to ____________.
Permutations and Combinations
MediumNumerical value
Q22
Consider the matrices : $A=\begin{bmatrix}2&-5\\3&m\end{bmatrix},\ B=\begin{bmatrix}20\\m\end{bmatrix}$ and $X=\begin{bmatrix}x\\y\end{bmatrix}$ . Let the set of all $m$ , for which the system of equations $AX=B$ has a negative solution (i.e., $x<0$ and…
Determinants Cramer's Rule Solving Column Vector Matrix Equations
MediumNumerical valueNew idea
Q23
The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ______________.
Permutations and Combinations Distribution of Identical Objects
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q24
If $\left(\frac{1}{\alpha+1}+\frac{1}{\alpha+2}+\cdots+\frac{1}{\alpha+1012}\right)-\left(\frac{1}{2\cdot1}+\frac{1}{4\cdot3}+\frac{1}{6\cdot5}+\cdots+\frac{1}{2024\cdot2023}\right)=\frac{1}{2024}$ , then $\alpha$ is equal to ____________.
Sequences and Series AP and GP Method of Differences for Telescoping Series
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Let the set of all values of $p$ , for which $f(x)=(p^2-6p+8)\left(\sin^2 2x-\cos^2 2x\right)+2(2-p)x+7$ does not have any critical point, be the interval $(a, b)$ . Then $16ab$ is equal to __________.
Application of Derivatives Maxima and Minima Critical vs Stationary Points
MediumNumerical valueIdea asked in 3 years
Q26
For a differentiable function $f:\mathbb{R}\to\mathbb{R}$ , suppose $f'(x)=3f(x)+\alpha$ , where $\alpha\in\mathbb{R}$ , $f(0)=1$ and $\lim_{x\to-\infty}f(x)=7$ . Then $9f(-\log_e 3)$ is equal to __________.
Differential Equations Linear Differential Equations Asymptotic Behavior of LDE Solutions
MediumNumerical valueIdea asked in 2 years
Q27
Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$ . If the set of all values of $\alpha$ , for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha, 0)$ are bisected by the parabola $P$ is the interval…
Conic Sections General Conic Section Chord Bisected at a Given Point (T=S1)
HardNumerical valueIdea asked in 3 years
Q28
Let $A$ , $B$ and $C$ be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through $C$ parallel to the $x$ -axis at the point $D$ . Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$ . Then…
Conic Sections
HardNumerical value
Q29
The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$ , from the origin is __________.
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumNumerical valueIdea asked in 6 years
Q30
Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2\sin^{-1}x+3\cos^{-1}x=\frac{2\pi}{5}$ , is __________.
Inverse Trigonometric Functions Inverse Trig Identities Complementary Identities
MediumNumerical valueIdea asked in 3 years

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.