JEE Main 2024 · April session

JEE Main 8 April 2024, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 30 easy. Its hard-question count was the joint 6th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 59; 12 questions with a figure

Key findings · 8 Apr 2024, Shift 2

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 10 of 30 rated hard; Chemistry had the most easy questions (17 of 30).
3
14 questions tested a new idea, one no earlier year had asked: 19% of the 74 questions tagged to an idea.
4
36 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
44 shared an idea with another 2024 shift (59% 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), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Straight Lines in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 11Medium 18Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 17Medium 13Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 18Hard 10

Top chapters

Straight Lines3 Q
Application of Derivatives2 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q

Question format

Single correct46 Q
Numerical value30 Q
Two statements6 Q
Diagram based3 Q
Match the list3 Q
Other2 Q

What each question asks you to do

Calculation35 Q
Multi-step25 Q
Conceptual16 Q
Recall8 Q
Application4 Q
Diagram reading2 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
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

11 easy18 medium1 hard

Q31
If $\epsilon_0$ is the permittivity of free space and E is the electric field, then $\epsilon_0 E^2$ has the dimensions :
Units and Measurements Coulomb's Law Dimensional Analysis of Permittivity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q32
The angle of projection for a projectile to have same horizontal range and maximum height is :
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q33
A given object takes n times the time to slide down $45^\circ$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $45^\circ$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined…
Laws of Motion Friction Motion Down a Rough Incline
MediumSingle correctIdea asked in 3 years
Q34
A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :
Work, Energy and Power Work and Kinetic Energy Maximum Compression of a Spring
MediumDiagram based · figureIdea asked in 3 years
Q35
A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$ . If another disc of same dimensions but of mass $\frac{M}{2}$ is placed…
System of Particles and Rotational Motion Angular Momentum Conservation of Angular Momentum
EasySingle correctIdea asked in 5 yearsAsked the year before
Q36
Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is $3v$ , the speed of B will be :
Gravitation Orbital Mechanics Orbital Velocity
EasySingle correctIdea asked in 5 yearsAsked the year before
Q37
A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9) :
Mechanical Properties of Fluids Fluid Statics Floating at a Two-Liquid Interface
MediumDiagram based · figureNew idea
Q38
A diatomic gas ( $\gamma=1.4$ ) does 100 J of work in an isobaric expansion. The heat given to the gas is :
Thermodynamics First Law of Thermodynamics Fraction of Heat Converted to Work (Isobaric)
EasySingle correctNew idea
Q39
Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.…
Kinetic Theory Kinetic Theory of Gases Mean Free Path
EasyTwo statementsIdea asked in 4 years
Q40
A capacitor has air as dielectric medium and two conducting plates of area $12\ \mathrm{cm}^2$ and they are $0.6$ cm apart. When a slab of dielectric having area $12\ \mathrm{cm}^2$ and $0.6$ cm thickness is inserted between the plates, one of the conducting…
Electrostatic Potential and Capacitance Dielectrics Partial and Multiple Slabs
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q41
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be ________ to ________ times of its initial length if the water is to be boiled in 15 minutes.
Current Electricity Ohm's Law and Resistance Joule Heating and Power
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q42
A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from axis of the wire is :
Moving Charges and Magnetism Ampere's Circuital Law Field Inside Thick Wire
MediumSingle correctIdea asked in 4 years
Q43
A coil of negligible resistance is connected in series with $90\ \Omega$ resistor across $120$ V, $60$ Hz supply. A voltmeter reads $36$ V across resistance. Inductance of the coil is :
Alternating Current Phasor Diagrams RL Series Phasor Construction
MediumSingle correctNew ideaIdea asked in 2 years
Q44
A plane progressive wave is given by $y = 2\cos 2\pi(330t - x)$ m. The frequency of the wave is :
Waves
EasySingle correct
Q45
The position of the image formed by the combination of lenses is :
Ray Optics and Optical Instruments Lens Maker's Formula Lenses Separated by a Distance
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q46
A proton and an electron have the same de Broglie wavelength. If $K_p$ and $K_e$ be the kinetic energies of proton and electron respectively, then choose the correct relation :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q47
If $M_o$ is the mass of isotope ${}^{12}_{5}\mathrm{B}$ , $M_P$ and $M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is :
Nuclei Nuclear Binding Energy Total Binding Energy
EasySingle correctIdea asked in 2 years
Q48
In a hypothetical fission reaction ${}_{92}X^{236} \rightarrow {}_{56}Y^{141} + {}_{36}Z^{92} + 3\mathbf{R}$ The identity of emitted particles (R) is :
Nuclei Fission and Fusion Nuclear Fission Mechanics
EasySingle correctNew idea
Q49
There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw…
Units and Measurements
MediumSingle correct
Q50
Least count of a vernier caliper is $\frac{1}{20N}$ cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :
Units and Measurements
MediumSingle correct
Q51
A body of mass M thrown horizontally with velocity $v$ from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity $\frac{v}{2}$ from the top of the tower of height 4H…
Motion in a Plane Projectile Motion Horizontal Projection from Height
MediumNumerical valueIdea asked in 4 years
Q52
A circular table is rotating with an angular velocity of $\omega$ rad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are…
System of Particles and Rotational Motion Circular Motion Centrifugal Pseudo-Force
HardNumerical value · figureIdea asked in 3 yearsAsked the year before
Q53
Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ cm/s.
Mechanical Properties of Fluids Viscosity Terminal Velocity of Coalescing Drops
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q54
An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $\left(\frac{25}{\pi}\right)$ Hz. At the position $x = 0.04$ m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is __________…
Oscillations Energy in SHM Kinetic Energy in SHM
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q55
If the net electric field at point P along Y axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5\sqrt{x}}$ , where $x =$ ____________.
Electric Charges and Fields Electric Field Superposition Principle for Electric Fields
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q56
A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of $10\ \Omega$ and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be…
Current Electricity Ohm's Law and Resistance Joule Heating and Power
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q57
The coercivity of a magnet is $5\times10^3$ A/m. The amount of current required to be passed in a solenoid of length 30 cm and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is __________ A.
Magnetism and Matter
MediumNumerical value
Q58
An alternating emf $E = 110\sqrt{2}\ \sin 100t$ volt is applied to a capacitor of $2\,\mu\mathrm{F}$ , the rms value of current in the circuit is __________ mA.
Alternating Current Phasor Diagrams RC Series Phasor Construction
EasyNumerical valueIdea asked in 2 years
Q59
Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ________…
Wave Optics Single Slit Diffraction Diffraction Envelope in YDSE
MediumNumerical valueNew ideaIdea asked in 2 years
Q60
A potential divider circuit is connected with a dc source of 20 V, a light emitting diode of glow in voltage 1.8 V and a zener diode of breakdown voltage of 3.2 V. The length (PR) of the resistive wire is 20 cm. The minimum length of PQ to just glow the LED…
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Regulation
MediumNumerical value · figureIdea asked in 5 years

Chemistry30 questions

17 easy13 medium0 hard

Maths30 questions

2 easy18 medium10 hard

Q1
Let $A = \{2, 3, 6, 8, 9, 11\}$ and $B = \{1, 4, 5, 10, 15\}$ . Let R be a relation on $A \times B$ defined by $(a, b)R(c, d)$ if and only if $3ad - 7bc$ is an even integer. Then the relation R is
Relations and Functions Sets and Relations Relation Types
HardSingle correctIdea asked in 5 yearsAsked the year before
Q2
Let $f(x) = \begin{cases} -a & \text{if } -a \le x \le 0 \\ x + a & \text{if } 0 < x \le a \end{cases}$ where $a > 0$ and $g(x) = (f(|x|) - |f(x)|)/2$ . Then the function $g : [-a, a] \to [-a, a]$ is
Relations and Functions Functions and Domain Domain and Range of Piecewise Functions
MediumSingle correctNew idea
Q3
If the system of equations $x + 4y - z = \lambda$ , $7x + 9y + \mu z = -3$ , $5x + y + 2z = -1$ has infinitely many solutions, then $(2\mu + 3\lambda)$ is equal to :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
If $\alpha \neq a$ , $\beta \neq b$ , $\gamma \neq c$ and $\begin{vmatrix} \alpha & b & c \\ a & \beta & c \\ a & b & \gamma \end{vmatrix} = 0$ , then $\frac{a}{\alpha - a} + \frac{b}{\beta - b} + \frac{\gamma}{\gamma - c}$ is equal to :
Determinants
HardSingle correct
Q5
The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to :
Permutations and Combinations Selection of One or More Objects
HardSingle correctIdea asked in 3 yearsAsked the year before
Q6
If the term independent of $x$ in the expansion of $\left(\sqrt{a}x^2 + \frac{1}{2x^3}\right)^{10}$ is 105, then $a^2$ is equal to :
Binomial Theorem
MediumSingle correct
Q7
The sum of all possible values of $\theta \in [-\pi, 2\pi]$ , for which $\frac{1 + i\cos\theta}{1 - 2i\cos\theta}$ is purely imaginary, is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Purely Real and Imaginary Euler Conditions
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q8
In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is 49. Then the sum of the $4^{th}$ , $6^{th}$ and $8^{th}$ terms is equal to :
Sequences and Series AP and GP GP General Term
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q9
For $a, b > 0$ , let $f(x) = \begin{cases} \frac{\tan((a+1)x) + b\tan x}{x}, & x < 0 \\ 3, & x = 0 \\ \frac{\sqrt{ax + b^2x^2} - \sqrt{ax}}{b\sqrt{a}\,x\sqrt{x}}, & x > 0 \end{cases}$ be a continous function at $x = 0$ . Then $\frac{b}{a}$ is equal to :
Continuity and Differentiability Finding Unknown Constants for Continuity
HardSingle correctIdea asked in 3 years
Q10
If the function $f(x) = 2x^3 - 9ax^2 + 12a^2x + 1$ , $a > 0$ has a local maximum at $x = \alpha$ and a local minimum at $x = \alpha^2$ , then $\alpha$ and $\alpha^2$ are the roots of the equation :
Application of Derivatives Maxima and Minima Finding Parameters from Given Extrema
MediumSingle correctIdea asked in 3 years
Q11
Let $\int_{\alpha}^{\log_e 4} \frac{dx}{\sqrt{e^x - 1}} = \frac{\pi}{6}$ . Then $e^{\alpha}$ and $e^{-\alpha}$ are the roots of the equation :
Integrals Integration by Substitution Exponential Factor Manipulation
HardSingle correctIdea asked in 4 yearsAsked the year before
Q12
The area of the region in the first quadrant inside the circle $x^2 + y^2 = 8$ and outside the parabola $y^2 = 2x$ is equal to :
Application of Integrals Area Under Curves Area Between Curves
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q13
Let $y = y(x)$ be the solution curve of the differential equation $\sec y \frac{dy}{dx} + 2x\sin y = x^3\cos y$ , $y(1) = 0$ . Then $y(\sqrt{3})$ is equal to :
Differential Equations Linear Differential Equations Generalized Substitution for LDEs
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q14
If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin, then the absolute value of the product of all possible values of a is :
Straight Lines Pair of Straight Lines Angle between pair of lines
MediumSingle correctNew idea
Q15
If the image of the point $(-4, 5)$ in the line $x + 2y = 2$ lies on the circle $(x+4)^2 + (y-3)^2 = r^2$ , then r is equal to :
Straight Lines Straight Line Distance Image of a point in a line
EasySingle correctIdea asked in 4 years
Q16
If the shortest distance between the lines $\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4}$ and $\frac{x-2}{4} = \frac{y-4}{6} = \frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$ , then a value of $\lambda$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
Let $\vec{a} = 4\hat{i} - \hat{j} + \hat{k}$ , $\vec{b} = 11\hat{i} - \hat{j} + \hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a} + \vec{b}) \times \vec{c} = \vec{c} \times (-2\vec{a} + 3\vec{b})$ . If $(2\vec{a} + 3\vec{b}) \cdot \vec{c} = 1670$ , then…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
HardSingle correctIdea asked in 6 yearsAsked the year before
Q18
Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ , $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$ and $\vec{c} = 3\hat{i} - \hat{j} + \lambda\hat{k}$ be three vectors. Let $\vec{r}$ be a unit vector along $\vec{b} + \vec{c}$ . If $\vec{r} \cdot \vec{a} = 3$ , then…
Vector Algebra Dot Product Scalar and Vector Projection
MediumSingle correctIdea asked in 5 years
Q19
There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from…
Probability Bayes' Theorem Bayes' Theorem Application
EasySingle correctIdea asked in 6 yearsAsked the year before
Q20
If the value of $\frac{3\cos 36^\circ + 5\sin 18^\circ}{5\cos 36^\circ - 3\sin 18^\circ}$ is $\frac{a\sqrt{5} - b}{c}$ , where a, b, c are natural numbers and $\gcd(a, c) = 1$ , then $a + b + c$ is equal to :
Trigonometric Functions Trigonometric Identities Values of Non-Standard Specific Angles
MediumSingle correctIdea asked in 3 years
Q21
The number of distinct real roots of the equation $|x+1|\,|x+3| - 4|x+2| + 5 = 0$ , is ________
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let a ray of light passing through the point $(3, 10)$ reflects on the line $2x + y = 6$ and the reflected ray passes through the point $(7, 2)$ . If the equation of the incident ray is $ax + by + 1 = 0$ , then $a^2 + b^2 + 3ab$ is equal to ________.
Straight Lines Straight Line Distance Image of a point in a line
MediumNumerical valueIdea asked in 4 years
Q23
An arithmetic progression is written in the following way 2 5 8 11 14 17 20 23 26 29 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The sum of all the terms of the $10^{th}$ row is ________.
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical value · figureIdea asked in 7 yearsAsked the year before
Q24
Let A be the region enclosed by the parabola $y^2 = 2x$ and the line $x = 24$ . Then the maximum area of the rectangle inscribed in the region A is ________.
Application of Derivatives Maxima and Minima Max/Min of Inscribed Geometric Figures
MediumNumerical valueNew idea
Q25
If $\alpha = \lim_{x \to 0^+} \left(\frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}}\right)$ and $\beta = \lim_{x \to 0} (1 + \sin x)^{\frac{1}{2}\cot x}$ are the roots of the quadratic equation $ax^2 + bx - \sqrt{e} = 0$ , then…
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q26
If $\int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}}\,dx = A\left(\frac{\alpha x - 1}{\beta x + 3}\right)^B + C$ , where C is the constant of integration, then the value of $\alpha + \beta + 20AB$ is ________.
Integrals Integration by Substitution Fractional Powers LCM Substitution
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q27
Let $\alpha|x| = |y|e^{xy-\beta}$ , $\alpha, \beta \in \mathbb{N}$ be the solution of the differential equation $x\,dy - y\,dx + xy(x\,dy + y\,dx) = 0$ , $y(1) = 2$ . Then $\alpha + \beta$ is equal to ________
Differential Equations Homogeneous Equations Recognizing Exact Differentials in Homogeneous Forms
HardNumerical valueIdea asked in 2 years
Q28
Let S be the focus of the hyperbola $\frac{x^2}{3} - \frac{y^2}{5} = 1$ , on the positive x-axis. Let C be the circle with its centre at $A(\sqrt{6}, \sqrt{5})$ and passing through the point S. If O is the origin and SAB is a diameter of C, then the square of…
Conic Sections
MediumNumerical value
Q29
Let $P(\alpha, \beta, \gamma)$ be the image of the point $Q(1, 6, 4)$ in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ . Then $2\alpha + \beta + \gamma$ is equal to ________
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumNumerical valueIdea asked in 6 years
Q30
Let $a, b, c \in \mathbb{N}$ and $a < b < c$ . Let the mean, the mean deviation about the mean and the variance of the 5 observations $9, 25, a, b, c$ be $18$ , $4$ and $\frac{136}{5}$ , respectively. Then $2a + b - c$ is equal to ________
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
HardNumerical valueIdea asked in 7 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.