JEE Main 2024 · January session

JEE Main 31 January 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 35 easy. Its hard-question count was the joint 6th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Complex Numbers and Quadratic Equations, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 61; 8 questions with a figure

Key findings · 31 Jan 2024, Shift 1

1
11 hard questions (12%): the joint 6th 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; Chemistry had the most easy questions (17 of 30).
3
22 questions tested a new idea, one no earlier year had asked: 31% of the 72 questions tagged to an idea.
4
26 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
37 shared an idea with another 2024 shift (51% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Complex Numbers and Quadratic Equations in Maths (4).

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 17Medium 13Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 19Hard 9

Top chapters

Complex Numbers and Quadratic Equations4 Q
Conic Sections3 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q
Probability2 Q

Question format

Single correct48 Q
Numerical value30 Q
Other5 Q
Two statements3 Q
Match the list2 Q
Assertion–reason2 Q

What each question asks you to do

Multi-step31 Q
Calculation23 Q
Application17 Q
Recall12 Q
Conceptual5 Q
Data or graph2 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
A force is represented by $F=ax^2+bt^{\frac{1}{2}}$ where $x$ = distance and $t$ = time. The dimensions of $b^2/a$ are:
Units and Measurements
EasySingle correct
Q32
The relation between time 't' and distance 'x' is $t=\alpha x^2+\beta x$ , where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is :
Motion in a Straight Line Kinematics in 1D Implicit Time-Position Equations
MediumSingle correctIdea asked in 3 years
Q33
A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$ . If the distance of the coin from the center of the disc is $r$ , the maximum angular velocity which can be given to the disc, so that the coin does not slip away,…
Laws of Motion Circular Motion Coin Slipping on a Rotating Disc
EasySingle correctIdea asked in 2 years
Q34
In the given arrangement of a doubly inclined plane two blocks of masses $M$ and $m$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is…
Laws of Motion Friction Friction on Inclines
MediumSingle correct · figureIdea asked in 3 years
Q35
An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:
System of Particles and Rotational Motion Collisions Momentum in Explosions
EasySingle correctIdea asked in 3 years
Q36
Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $\left(\frac{2\sqrt{2}+1}{32}\right)\frac{Gm^2}{L^2}$ , the length of the sides of the square is
Gravitation
EasySingle correct
Q37
A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?
Mechanical Properties of Fluids Viscosity Velocity-Time Graph of Terminal Velocity
EasySingle correct · figureNew idea
Q38
The given figure represents two isobaric processes for the same mass of an ideal gas, then
Thermal Properties of Matter Thermodynamic Processes Isobaric Process Analysis
EasySingle correct · figureIdea asked in 3 years
Q39
The parameter that remains the same for molecules of all gases at a given temperature is :
Kinetic Theory Kinetic Theory of Gases Kinetic Energy and Temp
EasySingle correctIdea asked in 7 yearsAsked the year before
Q40
Two charges $q$ and $3q$ are separated by a distance 'r ' in air. At a distance $x$ from charge $q$ , the resultant electric field is zero. The value of $x$ is :
Electric Charges and Fields Electric Field Neutral Point Location
EasySingle correctNew ideaIdea asked in 2 years
Q41
Two conductors have the same resistances at $0^\circ$ C but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$ . The respective temperature coefficients for their series and parallel combinations are :
Current Electricity Ohm's Law and Resistance Equivalent Temperature Coefficient in Series
MediumSingle correctNew idea
Q42
A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B=B_0\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is:
Moving Charges and Magnetism
MediumSingle correct · figure
Q43
A coil is places perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2 s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is:
Electromagnetic Induction Faraday's Law N-Turns Multiplier for Coils
EasySingle correctNew ideaIdea asked in 2 years
Q44
In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5\times10^{10}$ Hz and an amplitude of 50 Vm $^{-1}$ . The total average energy density of the electromagnetic field of the wave is : [Use $\varepsilon_0=8.85\times10^{-12}$ …
Electromagnetic Waves
EasySingle correct
Q45
The refractive index of a prism with apex angle $A$ is $\cot A/2$ . The angle of minimum deviation is :
Ray Optics and Optical Instruments Prism Deviation Minimum Deviation Condition
MediumSingle correctIdea asked in 5 years
Q46
When a metal surface is illuminated by light of wavelength $\lambda$ , the stopping potential is 8V. When the same surface is illuminated by light of wavelength $3\lambda$ , stopping potential is 2V. The threshold wavelength for this surface is:
Dual Nature of Radiation and Matter Photoelectric Effect Two-Wavelength System of Equations
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q47
If the wavelength of the first member of Lyman series of hydrogen is $\lambda$ . The wavelength of the second member will be
Atoms Bohr's Atomic Model Rydberg Formula and Spectra
EasySingle correctIdea asked in 6 yearsAsked the year before
Q48
Identify the logic operation performed by the given circuit.
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
EasySingle correct · figureIdea asked in 7 yearsAsked the year before
Q49
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be:
Waves Resonance in Air Columns Open Organ Pipe Harmonics
EasySingle correctIdea asked in 2 yearsAsked the year before
Q50
If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be:
Units and Measurements
EasySingle correct
Q51
A body starts falling freely from height $H$ hits an inclined plane in its path at height $h$ . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which the body will take…
Motion in a Plane Kinematics in 2D Horizontal Strike on an Incline
HardNumerical valueNew idea
Q52
A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m/s. The absolute value of work done on the disc to stop it is ________ J.
System of Particles and Rotational Motion
MediumNumerical value
Q53
The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ________ $m$ . (Take density of sea water = $10^3$ kgm $^{-3}$ , Bulk modulus of rubber = $9\times10^8$ Nm $^{-2}$ , and $g=10$ ms $^{-2}$ )
Mechanical Properties of Solids Elasticity Compression at Liquid Depth
EasyNumerical valueNew idea
Q54
A particle performs simple harmonic motion with amplitude $A$ . Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$ . The new amplitude of motion is $\frac{nA}{3}$ . The value of $n$ is ________.
Oscillations SHM Equations Velocity and Accel vs Position
MediumNumerical valueIdea asked in 4 years
Q55
A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm , while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than…
Electrostatic Potential and Capacitance Dielectrics Dielectric with Battery Connected
MediumNumerical valueIdea asked in 3 years
Q56
Equivalent resistance of the following network is ________ $\Omega$ .
Current Electricity Kirchhoff's Laws Finite Ladder Networks
MediumNumerical value · figureNew idea
Q57
An electron moves through a uniform magnetic field $\vec{B}=B_0\hat{i}+2B_0\hat{j}\ T$ . At a particular instant of time, the velocity of electron is $\vec{u}=3\hat{i}+5\hat{j}\ m/s$ . If the magnetic force acting on electron is $\vec{F}=5e\hat{k}\ N$ , where…
Moving Charges and Magnetism Lorentz Force Determinant Form of Magnetic Force
MediumNumerical valueNew idea
Q58
A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$ ( $L=l^2$ ). The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times10^{-7}\,H$ , where $x=$ _______.
Electromagnetic Induction Inductance Mutual Inductance of Concentric Square Loops
HardNumerical valueIdea asked in 2 years
Q59
Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60^\circ$ . If $\frac{I_1}{I_2}=\frac{10}{x}$ then $x=$ …
Wave Optics Young's Double Slit Resultant Intensity Formula
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q60
The mass defect in a particular reaction is 0.4g. The amount of energy liberated is $n\times10^7$ kWh, where $n=$ _______. (speed of light = $3 imes10^8$ m/s)
Nuclei Nuclear Binding Energy Mass Defect Calculation
EasyNumerical valueIdea asked in 3 years

Chemistry30 questions

17 easy13 medium0 hard

Maths30 questions

2 easy19 medium9 hard

Q1
If $f(x)=\frac{4x+3}{6x-4},\ x\neq\frac{2}{3}$ and $(f\circ f)(x)=g(x)$ , where $g:\mathbb{R}-\left\{\frac{2}{3}\right\}\rightarrow\mathbb{R}-\left\{\frac{2}{3}\right\}$ , then $(g\circ g\circ g)(4)$ is equal to
Relations and Functions
MediumSingle correct
Q2
Let S be the set of postive integral values of $a$ for which $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}<0,\ \forall x\in\mathbb{R}$ . Then, the number of elements in S is :
Complex Numbers and Quadratic Equations Quadratic Roots Always Negative Condition
EasySingle correctNew idea
Q3
If $f(x)=\begin{vmatrix}x^3 & 2x^2+1 & 1+3x\\ 3x^2+2 & 2x & x^3+6\\ x^3-x & 4 & x^2-2\end{vmatrix}$ for all $x\in\mathbb{R}$ , then $2f(0)+f'(0)$ is equal to
Determinants Chain Rule Chain Rule in Determinants
MediumSingle correctNew idea
Q4
If the system of linear equations $x-2y+z=-4$ $2x+\alpha y+3z=5$ $3x-y+\beta z=3$ has infinitely many solutions, then $12\alpha+13\beta$ is equal to
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q5
The sum of the series $\frac{1}{1-3\cdot1^2+1^4}+\frac{2}{1-3\cdot2^2+2^4}+\frac{3}{1-3\cdot3^2+3^4}+\ldots$ up to 10-terms is
Sequences and Series AP and GP Method of Differences for Telescoping Series
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q6
$\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}$
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q7
Let $a$ be the sum of all coefficients in the expansion of $(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024}$ and $b=\lim_{x\to0}\left(\frac{\int_0^x\frac{\log(1+t)}{t^{2024}+1}dt}{x^2}\right)$ . If the equations $cx^2+dx+e=0$ and $2bx^2+ax+4=0$ have a common root,…
Complex Numbers and Quadratic Equations Quadratic Roots Complex Conjugate Roots
HardSingle correctIdea asked in 4 years
Q8
For $0<c<b<a$ , let $(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0$ and $\alpha\neq1$ be one of its root. Then, among the two statements (I) If $\alpha\in(-1,0)$ , then $b$ cannot be the geometric mean of $a$ and $c$ (II) If $\alpha\in(0,1)$ , then $b$ may be the geometric…
Complex Numbers and Quadratic Equations Quadratic Roots Zero Sum of Coefficients Shortcut
MediumTwo statementsNew idea
Q9
Let $g(x)$ be a linear funchion and $f(x)=\begin{cases}g(x), & x\leq0\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}, & x>0\end{cases}$ is continuous at $x=0$ . If $f'(1)=f(-1)$ , then the value $g(3)$ is
Continuity and Differentiability Continuity of f(x)^g(x)
HardSingle correctNew idea
Q10
The area of the region $\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\}$ is
Application of Integrals Area Under Curves Area of Inequalities
HardSingle correctIdea asked in 8 yearsAsked the year before
Q11
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x\tan x)},\ x\in\left(0,\frac{\pi}{2}\right)$ satisfying the condition $y\left(\frac{\pi}{4}\right)=2$ . Then, $y\left(\frac{\pi}{3}\right)$ is
Differential Equations Linear Differential Equations Integrating Factors with Trigonometric Functions
HardSingle correctIdea asked in 4 years
Q12
The solution curve of the differential equation $y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0$ passing through the point $(e,1)$ is
Differential Equations Homogeneous Equations Alternative Substitution x = vy
MediumSingle correctIdea asked in 2 years
Q13
If one of the diameters of the circle $x^2+y^2-10x+4y+13=0$ is a chord of another circle C, whose center is the point of intersection of the lines $2x+3y=12$ and $3x-2y=5$ , then the radius of the circle C is :
Conic Sections
MediumSingle correct
Q14
Let $\alpha,\beta,\gamma,\delta\in\mathbb{Z}$ and let $A(\alpha,\beta)$ , $B(1,0)$ , $C(\gamma,\delta)$ and $D(1,2)$ be the vertices of a parallelogram ABCD. If $AB=\sqrt{10}$ and the points A and C lie on the line $3y=2x+1$ , then…
Straight Lines
MediumSingle correct
Q15
The distance of the point $Q(0,2,-2)$ form the line passing through the point $P(5,-4,3)$ and perpendicular to the lines $\vec{r}=\left(-3\hat{i}+2\hat{k}\right)+\lambda\left(2\hat{i}+3\hat{j}+5\hat{k}\right),\ \lambda\in\mathbb{R}$ and…
Three Dimensional Geometry Lines in 3D Line Perpendicular to Two Given Lines
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q16
If the foci of a hyperbola are same as that of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point…
Conic Sections
HardSingle correct
Q17
Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is
Probability Variance and SD Variance via Relative Frequencies
MediumSingle correctNew idea
Q18
Let $\vec{a}=3\hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=4\hat{i}+\hat{j}+7\hat{k}$ and $\vec{c}=\hat{i}-3\hat{j}+4\hat{k}$ be three vectors. If a vectors $\vec{p}$ satisfies $\vec{p}\times\vec{b}=\vec{c}\times\vec{b}$ and $\vec{p}\cdot\vec{a}=0$ , then…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is
Probability Conditional Probability Independence Criterion
EasySingle correctIdea asked in 3 years
Q20
For $\alpha,\beta,\gamma\neq0$ , if $\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi$ and $(\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3\alpha\beta$ , then $\gamma$ equals
Inverse Trigonometric Functions Inverse Trig Identities Conditional Identity: Sum of sin-1 to pi
HardSingle correctNew idea
Q21
Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on A. Let S be the equivalence relation on A such that $R\subset S$ and the number of elements in S is n. Then, the minimum value of n is ______
Relations and Functions Sets and Relations Equivalence Relations
MediumNumerical valueIdea asked in 4 years
Q22
If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg(z)}\right)$ , where $z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi}i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi}i}\right]$ , $i=\sqrt{-1}$ , then the distance of…
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q23
The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to ______
Permutations and Combinations
MediumNumerical value
Q24
In the expansion of $(1+x)(1-x^2)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5,\ x\neq0$ , the sum of the coefficients of $x^3$ and $x^{-13}$ is equal to ______
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
MediumNumerical valueIdea asked in 2 years
Q25
Let $S=(-1,\infty)$ and $f:S\to\mathbb{R}$ be defined as $f(x)=\int_{-1}^{x}(e^t-1)^{11}(2t-1)^5(t-2)^7(t-3)^{12}(2t-10)^{61}\,dt$ , Let p = Sum of squares of the values of $x$ , where $f(x)$ attains local maxima on $S$ , and q = Sum of the values of x, where…
Application of Derivatives Maxima and Minima Extrema of Integral Functions (Leibniz Rule)
HardNumerical valueNew idea
Q26
Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\frac{4^x}{4^x+2}$ and $M=\int_{f(a)}^{f(1-a)}x\sin^4\left(x(1-x)\right)dx,\ N=\int_{f(a)}^{f(1-a)}\sin^4\left(x(1-x)\right)dx;\ a\neq\frac{1}{2}$ . If…
Integrals Definite Integral Properties King's Property
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q27
If the integral $525\int_0^{\frac{\pi}{2}}\sin2x\cos^{\frac{11}{2}}x\left(1+\cos^{\frac{5}{2}}x\right)^{\frac{1}{2}}dx$ is equal to $\left(n\sqrt{2}-64\right)$ , then $n$ is equal to ______
Integrals Integration by Substitution Fractional Powers LCM Substitution
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q28
Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ be $(\pm5,0)$ and $\sqrt{50}$ , respectively. Then, the square of the eccentricity of the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{a^2b^2}=1$ equals ______
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q29
Let Q and R be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y,\ z=1$ and $x=-y,\ z=-1$ respectively. If $\angle QPR$ is a right angle, then $12a^2$ is equal to ______
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q30
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,\ |\vec{b}|=4$ , and $\vec{a}\cdot\vec{b}=2$ . If $\vec{c}=\left(2\vec{a}\times\vec{b}\right)-3\vec{b}$ and the angle between $\vec{b}$ and $\vec{c}$ is $\alpha$ , then $192\sin^2\alpha$ is equal…
Vector Algebra Cross Product Lagrange's Identity
MediumNumerical valueIdea asked in 5 yearsAsked the year before

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.