JEE Main 2024 · April session

JEE Main 8 April 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 8 were rated hard and 28 easy. Its hard-question count was the joint 15th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 8; 9% of the shift
Chapters asked: 59; 19 questions with a figure

Key findings · 8 Apr 2024, Shift 1

1
8 hard questions (9%): the joint 15th 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 30 rated hard; Physics had the most easy questions (16 of 30).
3
14 questions tested a new idea, one no earlier year had asked: 19% of the 75 questions tagged to an idea.
4
27 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
38 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: Units and Measurements in Physics (3), Coordination Compounds in Chemistry (3) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 16Medium 13Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 10Medium 19Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 22Hard 6

Top chapters

Application of Derivatives3 Q
Complex Numbers and Quadratic Equations3 Q
Conic Sections2 Q
Differential Equations2 Q
Integrals2 Q
Matrices2 Q

Question format

Single correct44 Q
Numerical value30 Q
Diagram based5 Q
Match the list4 Q
Two statements3 Q
Other3 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step33 Q
Calculation24 Q
Application13 Q
Conceptual9 Q
Recall8 Q
Data or graph2 Q
Diagram reading1 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 easy13 medium1 hard

Q31
In an expression $a\times10^b$ :
Units and Measurements
EasySingle correct
Q32
A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :
Motion in a Plane Circular Motion Angular and Linear Kinematics
EasySingle correctNew ideaIdea asked in 2 years
Q33
A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies ( $K_B:K_A$ ) is :
System of Particles and Rotational Motion Collisions Momentum in Explosions
EasySingle correctIdea asked in 3 years
Q34
A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:
Laws of Motion Collisions Average Impact Force Calculation
EasySingle correctIdea asked in 2 years
Q35
Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q36
Correct Bernoulli's equation is (symbols have their usual meaning) :
Mechanical Properties of Fluids Fluid Dynamics Bernoulli's Equation
EasySingle correctIdea asked in 5 yearsAsked the year before
Q37
Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:
Thermodynamics First Law of Thermodynamics Adiabatic P-V Relation
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q38
Two planets A and B having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of A is $L$ and that of B is $3L$ , the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:
Gravitation Orbital Mechanics Kepler's Laws
HardSingle correctIdea asked in 4 yearsAsked the year before
Q39
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature ( $27^\circ$ C). The ratio of specific heat of gases at constant volume respectively is:
Kinetic Theory Kinetic Theory of Gases Law of Equipartition
EasySingle correctIdea asked in 4 years
Q40
In the given circuit, the terminal potential difference of the cell is :
Current Electricity Kirchhoff's Laws Cell EMF and Internal Resistance
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q41
Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic…
Magnetism and Matter
MediumOther
Q42
Average force exerted on a non-reflecting surface at normal incidence is $2.4\times10^{-4}$ N. If 360 W/cm $^2$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:
Electromagnetic Waves Thermal Radiation Thermal Radiation Pressure
MediumSingle correctIdea asked in 3 years
Q43
Critical angle of incidence for a pair of optical media is $45^\circ$ . The refractive indices of first and second media are in the ratio:
Ray Optics and Optical Instruments Refraction and Snell's Law Total Internal Reflection
EasySingle correctIdea asked in 6 yearsAsked the year before
Q44
A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume $h=6.63\times10^{-34}$ J s, $m_e=9.0\times10^{-31}$ kg and $m_p=1836$ times $m_e$ )
Dual Nature of Radiation and Matter Matter Waves Wavelength from Kinetic Energy
EasySingle correctIdea asked in 4 yearsAsked the year before
Q45
Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
Electrostatic Potential and Capacitance Conductors in Fields Charge Ratio of Connected Distant Spheres
EasySingle correctIdea asked in 2 years
Q46
Binding energy of a certain nucleus is $18\times10^8$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:
Nuclei Nuclear Binding Energy Mass Defect Calculation
EasySingle correctIdea asked in 3 years
Q47
The output Y of following circuit for given inputs is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q48
Young's modulus is determined by the equation given by $Y=49000\frac{m}{l}\frac{\mathrm{dyne}}{\mathrm{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules( $Y$ ) is estimated by taking data from…
Units and Measurements Elasticity Error Analysis in Searle's Experiment
MediumSingle correctIdea asked in 4 years
Q49
The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier…
Units and Measurements
MediumSingle correct
Q50
A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:
Alternating Current LCR Resonance Resistance Effect on Resonance Curve
EasySingle correctIdea asked in 2 years
Q51
Three vectors $\overrightarrow{OP}$ , $\overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A\sqrt{x}$ . The value of $x$ is ________.
Motion in a Plane Kinematics in 2D Vector Component Resolution
EasyNumerical value · figureIdea asked in 4 yearsAsked the year before
Q52
A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of $x$ and $y$ coordinates of center of mass of plate in $\frac{n}{9}$ . The value of $n$ is ________.
System of Particles and Rotational Motion Center of Mass COM of Composite Bodies
MediumNumerical value · figureIdea asked in 3 years
Q53
A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8\times10^3\ \mathrm{kg\,m^{-3}}$ and surface tension of soap solution is $0.28\ \mathrm{N\,m^{-1}}$ , then diameter of the soap bubble is…
Mechanical Properties of Fluids Surface Tension Excess Pressure in Soap Bubbles
MediumNumerical valueIdea asked in 4 years
Q54
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is ________.
Waves Resonance in Air Columns Overtone to Harmonic Translation
MediumNumerical valueNew idea
Q55
An electric field, $\vec{E}=\frac{2\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{6}}$ passes through the surface of 4 m $^2$ area having unit vector $\hat{n}=\left(\frac{2\hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$ . The electric flux for that surface is ________ V m.
Electric Charges and Fields Gauss's Law Electric Flux Calculation
EasyNumerical valueIdea asked in 4 years
Q56
Resistance of a wire at $0\,^\circ$ C, $100\,^\circ$ C and $t\,^\circ$ C is found to be $10\ \Omega$ , $10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature $t$ in Kelvin scale is ________.
Current Electricity Ohm's Law and Resistance Temperature Coefficient of Resistance
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q57
An electron with kinetic energy 5 eV enters a region of uniform magnetic field of 3 $\mu$ T perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves…
Moving Charges and Magnetism Lorentz Force Velocity Selector and Crossed Fields
MediumNumerical valueIdea asked in 3 years
Q58
In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5\times10^{-14}$ m. If target nucleus has atomic number 80, then maximum velocity of $\alpha$ - particle is ____________ $\times10^5$ m/s approximately.…
Atoms Coulomb's Law Distance of Closest Approach
MediumNumerical valueNew idea
Q59
A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be ________ $\times10^{-3}$ rad.
Wave Optics Single Slit Diffraction Single Slit Minima Condition
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q60
A square loop PQRS having 10 turns, area $3.6\times10^{-3}\ \mathrm{m^2}$ and resistance $100\ \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B=0.5$ T as shown. Work done in pulling the loop out of the field in 1.0…
Electromagnetic Induction Faraday's Law Total Heat Dissipation in Transient EMI
MediumNumerical value · figureNew idea

Chemistry30 questions

10 easy19 medium1 hard

Maths30 questions

2 easy22 medium6 hard

Q1
Let $[t]$ be the greatest integer less than or equal to $t$ . Let $A$ be the set of all prime factors of 2310 and $f: A \to \mathbb{Z}$ be the function $f(x)=\left[\log_2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]$ . The number of one-to-one functions…
Relations and Functions Permutations and Combinations Number of Injective Functions
MediumSingle correctIdea asked in 4 years
Q2
Let $z$ be a complex number such that $|z+2|=1$ and $\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$ . Then the value of $\left|\mathrm{Re}\left(\overline{z+2}\right)\right|$ is
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Conjugate and Inverse
MediumSingle correctIdea asked in 3 years
Q3
The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is :
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
EasySingle correctIdea asked in 4 years
Q4
Let $A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}$ . If $A^3=4A^2-A-21I$ , where $I$ is the identity matrix of order $3\times3$ , then $2a+3b$ is equal to
Matrices Matrix Multiplication Cayley-Hamilton Theorem Application
MediumSingle correctIdea asked in 5 years
Q5
The equations of two sides AB and AC of a triangle ABC are $4x+y=14$ and $3x-2y=5$ , respectively. The point $\left(2,-\frac{4}{3}\right)$ divides the third side BC internally in the ratio $2:1$ . the equation of the side BC is
Straight Lines
MediumSingle correct
Q6
If the set $R=\{(a,b): a+5b=42, a,b\in\mathbb{N}\}$ has $m$ elements and $\sum_{n=1}^{m}\left(1-i^{n!}\right)=x+iy$ , where $i=\sqrt{-1}$ , then the value of $m+x+y$ is
Complex Numbers and Quadratic Equations
MediumSingle correct
Q7
For the function $f(x)=(\cos x)-x+1$ , $x\in\mathbb{R}$ , between the following two statements (S1) $f(x)=0$ for only one value of $x$ in $[0,\pi]$ . (S2) $f(x)$ is decreasing in $\left[0,\frac{\pi}{2}\right]$ and increasing in $\left[\frac{\pi}{2},\pi\right]$ .
Application of Derivatives Monotonicity Counting Roots using Monotonicity
MediumTwo statementsIdea asked in 2 years
Q8
The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is
Application of Derivatives Maxima and Minima Cusp Extrema in Fractional Power Functions
MediumSingle correctNew idea
Q9
Let $f(x)=4\cos^3x+3\sqrt{3}\cos^2x-10$ . The number of points of local maxima of $f$ in interval $(0,2\pi)$ is
Application of Derivatives Maxima and Minima Counting Extrema in Periodic Functions
HardSingle correctNew idea
Q10
Let $I(x)=\int\frac{6}{\sin^2x(1-\cot x)^2}dx$ . If $I(0)=3$ , then $I\left(\frac{\pi}{12}\right)$ is equal to
Integrals Integration by Substitution Even Secant/Cosecant Power Substitution
MediumSingle correctNew idea
Q11
The value of $k\in\mathbb{N}$ for which the integral $I_n=\int_0^1(1-x^k)^n dx$ , $n\in\mathbb{N}$ , satisfies $147I_{20}=148I_{21}$ is
Integrals Definite Integral Properties Reduction Formulae in Definite Integrals
HardSingle correctIdea asked in 4 yearsAsked the year before
Q12
Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$ , $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$ . Then the differential equation, whose general solution is $y=c_1f(x)+c_2$ , where $c_1$ and $c_2$ are arbitrary constants, is
Differential Equations Area Under Curves Curves from Area Properties
HardSingle correctIdea asked in 2 years
Q13
Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . Then $y\left(\frac{\pi}{4}\right)$ is equal to
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q14
If the shortest distance between the lines $L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k}$ , $\lambda\in\mathbb{R}$ $L_2:\vec{r}=2(1+\mu)\hat{i}+3(1+\mu)\hat{j}+(5+\mu)\hat{k}$ , $\mu\in\mathbb{R}$ is $\frac{m}{\sqrt{n}}$ , where…
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
MediumSingle correctIdea asked in 5 years
Q15
Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at the point $(6,6)$ . If the point $(6,6)$ divides the line segment joining the centres of the circles $C_1$ and $C_2$ …
Conic Sections Circle Tangents Common Tangent of Touching Circles
MediumSingle correctIdea asked in 4 years
Q16
Let $H:\frac{-x^2}{a^2}+\frac{y^2}{b^2}=1$ be the hyperbola, whose eccentricity is $\sqrt{3}$ and the length of the latus rectum is $4\sqrt{3}$ . Suppose the point $(\alpha,6)$ , $\alpha>0$ lies on $H$ . If $\beta$ is the product of the focal distances of the…
Conic Sections
MediumSingle correct
Q17
Let $P(x,y,z)$ be a point in the first octant, whose projection in the $xy$ -plane is the point $Q$ . Let $OP=\gamma$ ; the angle between $OQ$ and the positive $x$ -axis be $\theta$ ; and the angle between $OP$ and the positive $z$ -axis be $\phi$ , where $O$ is…
Three Dimensional Geometry
MediumSingle correct
Q18
The set of all $\alpha$ , for which the vectors $\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k}$ and $\vec{b}=t\hat{i}-2\hat{j}-2\alpha t\hat{k}$ are inclined at an obtuse angle for all $t\in\mathbb{R}$ , is
Vector Algebra Dot Product Acute and Obtuse Angle Conditions
MediumSingle correctIdea asked in 2 years
Q19
Let the sum of two positive integers be 24. If the probability, that their product is not less than $\frac{3}{4}$ times their greatest possible product, is $\frac{m}{n}$ , where $\gcd(m,n)=1$ , then $n-m$ equals
Probability
MediumSingle correct
Q20
If $\sin x=-\frac{3}{5}$ , where $\pi<x<\frac{3\pi}{2}$ , then $80(\tan^2x-\cos x)$ is equal to
Trigonometric Functions
EasySingle correct
Q21
If the range of $f(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}$ , $\theta\in\mathbb{R}$ is $[\alpha,\beta]$ , then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{\alpha}{\beta}$ , is equal to…
Trigonometric Functions Functions and Domain Range of Quadratic Rational Functions
MediumNumerical valueNew idea
Q22
Let $A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}$ . If the sum of the diagonal elements of $A^{13}$ is $3^n$ , then $n$ is equal to ____________.
Matrices Matrix Multiplication Powers of Square Matrices
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q23
The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to ____________.
Permutations and Combinations Fundamental Counting Principle
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q24
Let $\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r$ and $\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}$ . If $140<\frac{2\alpha}{\beta}<281$ , then the value of $n$ is ____________.
Binomial Theorem Binomial Coefficients Second Derivative Method for Sums
HardNumerical valueIdea asked in 3 years
Q25
Let the positive integers be written in the form : 1 2 3 4 5 6 7 8 9 10 ... If the $k^{\mathrm{th}}$ row contains exactly $k$ numbers for every natural number $k$ , then the row in which the number 5310 will be, is ____________.
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical value · figureIdea asked in 7 yearsAsked the year before
Q26
The value of $\lim_{x\to0}2\left(\frac{1-\cos x\sqrt{\cos2x}\sqrt[3]{\cos3x}\cdots\sqrt[10]{\cos10x}}{x^2}\right)$ is ____________.
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q27
Let the area of the region enclosed by the curve $y=\min\{\sin x,\cos x\}$ and the $x$ -axis between $x=-\pi$ to $x=\pi$ be $A$ . Then $A^2$ is equal to ____________.
Application of Integrals Area Under Curves Area Involving Max/Min Functions
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q28
Let $\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}$ , $\vec{b}=3\hat{i}+7\hat{j}-13\hat{k}$ and $\vec{c}=17\hat{i}-2\hat{j}+\hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r}\times\vec{a}=(\vec{b}+\vec{c})\times\vec{a}$ and…
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q29
If the orthocentre of the triangle formed by the lines $2x+3y-1=0$ , $x+2y-1=0$ and $ax+by-1=0$ , is the centroid of another triangle, whose circumcentre and orthocentre respectively are $(3,4)$ and $(-6,-8)$ , then the value of $|a-b|$ is ____________.
Straight Lines Properties of Triangles Euler Line Collinearity and Ratios
HardNumerical valueNew idea
Q30
Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively, then…
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.