JEE Main 2024 · April session

JEE Main 6 April 2024, Shift 1

88 questions (2 more dropped by NTA): 30 numerical-answer and 58 multiple choice. 10 were rated hard and 38 easy. Its hard-question count was the joint 8th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Chemical Bonding and Molecular Structure, with 4 questions.

Questions: 88; 2 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 10; 11% of the shift
Chapters asked: 60; 13 questions with a figure

Key findings · 6 Apr 2024, Shift 1

1
10 hard questions (11%): the joint 8th 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 8 of 28 rated hard; Physics had the most easy questions (20 of 30).
3
13 questions tested a new idea, one no earlier year had asked: 18% of the 72 questions tagged to an idea.
4
30 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
42 shared an idea with another 2024 shift (58% 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), Chemical Bonding and Molecular Structure in Chemistry (4) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 20Medium 9Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Maths

28 Q · 10 numerical

Easy 5Medium 15Hard 8

Top chapters

Conic Sections3 Q
Relations and Functions3 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q

Question format

Single correct43 Q
Numerical value30 Q
Match the list6 Q
Diagram based4 Q
Two statements3 Q
Other2 Q

What each question asks you to do

Calculation40 Q
Multi-step19 Q
Conceptual12 Q
Recall10 Q
Diagram reading4 Q
Application3 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
Open28 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 88 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

88 of 88 questions

Physics30 questions

20 easy9 medium1 hard

Q31
Four particles $A, B, C, D$ of mass $\frac{m}{2}$ , $m$ , $2m$ , $4m$ , have same momentum, respectively. The particle with maximum kinetic energy is :
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q32
A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_1}{m_2}$ is:
Laws of Motion Newton's Laws of Motion Standard Atwood Machine
MediumSingle correctIdea asked in 3 years
Q33
To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E$ , g = acceleration due to gravity on the surface of earth):
Gravitation Gravitational Potential Escape Velocity and Potential Relation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q34
A train starting from rest first accelerates uniformly up to a speed of 80 $km/h$ for time $t$ , then it moves with a constant speed for time $3t$ . The average speed of the train for this duration of journey will be (in $km/h$ ) :
Motion in a Straight Line Kinematics in 1D Acceleration-Deceleration Motion Profiles
EasySingle correctIdea asked in 2 years
Q35
A small ball of mass m and density $\rho$ is dropped in a viscous liquid of density $\rho_0$ . After sometime, the ball falls with constant velocity. The viscous force on the ball is :
Mechanical Properties of Fluids Viscosity Terminal Velocity Calculation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q36
The specific heat at constant pressure of a real gas obeying $PV^2 = RT$ equation is:
Thermodynamics First Law of Thermodynamics Mayer's Relation (Cp and Cv)
HardSingle correctIdea asked in 3 years
Q37
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
Kinetic Theory Kinetic Theory of Gases Molecular Speed Ratios
EasySingle correctIdea asked in 4 yearsAsked the year before
Q38
$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$ . The electric field at any point on the surface of the spherical shell is :
Electric Charges and Fields Gauss's Law Electrostatic Pressure
MediumSingle correctNew idea
Q39
Electromagnetic waves travel in a medium with speed of $1.5\times10^8$ m s $^{-1}$ . The relative permeability of the medium is 2.0. The relative permittivity will be:
Electromagnetic Waves
EasySingle correct
Q40
The value of unknown resistance ( $x$ ) for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is :
Current Electricity Wheatstone Bridge Balanced Bridge Equation
MediumSingle correct · figureIdea asked in 3 years
Q41
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the…
Units and Measurements
EasySingle correct
Q42
Match List I with List II LIST I A. Torque B. Magnetic field C. Magnetic moment D. Permeability of free space LIST II I. $[M^1L^1T^{-2}A^{-2}]$ II. $[L^2A^1]$ III. $[M^1T^{-2}A^{-1}]$ IV. $[M^1L^2T^{-2}]$ Choose the correct answer from the options given below:
Units and Measurements
MediumMatch the list
Q43
An element $\Delta l = \Delta x\hat{i}$ is placed at the origin and carries a large current $I$ = 10A. The magnetic field on the $y$ -axis at a distance of 0.5m from the elements $\Delta x$ of 1cm length is :
Moving Charges and Magnetism Biot-Savart Law Vector form of Biot-Savart Law
EasySingle correct · figureNew idea
Q44
Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the…
Alternating Current LCR Resonance Impedance at Resonance
EasyTwo statementsIdea asked in 3 years
Q45
To find the spring constant ( $k$ ) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is :
Units and Measurements
EasySingle correct
Q46
Which of the following phenomena does not explain by wave nature of light. A. reflection B. diffraction C. photoelectric effect D. interference E. polarization Choose the most appropriate answer from the options given below:
Wave Optics Photoelectric Effect Failure of Classical Wave Theory
EasySingle correctIdea asked in 2 years
Q47
In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo sensitive material is :
Dual Nature of Radiation and Matter Photoelectric Effect Einstein's Photoelectric Equation
EasySingle correctIdea asked in 5 years
Q48
The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
Atoms Bohr's Atomic Model Shortest and Longest Wavelengths
EasySingle correctIdea asked in 5 yearsAsked the year before
Q49
The correct truth table for the following logic circuit is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
EasyDiagram based · figureIdea asked in 7 yearsAsked the year before
Q50
A bullet of mass 50 $g$ is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :
Work, Energy and Power Work and Kinetic Energy Kinetic Energy Calculation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q51
The refractive index of prism is $\mu = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is __________ $^\circ$ .
Ray Optics and Optical Instruments Prism Deviation Minimum Deviation Condition
MediumNumerical valueIdea asked in 5 years
Q52
A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is __________ cm/s.
Oscillations SHM Equations Extrema of Kinematic and Energy Variables
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q53
For three vectors $\vec{A} = (-x\hat{i} - 6\hat{j} - 2\hat{k})$ , $\vec{B} = (-\hat{i} + 4\hat{j} + 3\hat{k})$ and $\vec{C} = (-8\hat{i} - \hat{j} + 3\hat{k})$ , if $\vec{A}\cdot(\vec{B}\times\vec{C}) = 0$ , then value of $x$ is __________.
Motion in a Plane
EasyNumerical value
Q54
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$ . The value of $x$ is __________.
Mechanical Properties of Fluids Surface Tension Splitting and Coalescence
EasyNumerical valueIdea asked in 5 years
Q55
When a $dc$ voltage of 100V is applied to an inductor, a $dc$ current of 5A flows through it. When an $ac$ voltage of 200V peak value is connected to inductor, its inductive reactance is found to be $20\sqrt{3}\Omega$ . The power dissipated in the circuit is…
Alternating Current Phasor Diagrams Real Inductor (Choke Coil) Phasors
MediumNumerical valueIdea asked in 3 years
Q56
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be __________ hours 30 minutes.
System of Particles and Rotational Motion Angular Momentum Conservation of Angular Momentum
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q57
A circular coil having 200 turns, $2.5\times10^{-4}$ m $^2$ area and carrying 100 $\mu$ A current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment ( $\vec{M}$ ) was directed along $\vec{B}$ . Amount of work, required to rotate the…
Moving Charges and Magnetism Magnetic Dipole Moment Work done in rotating a dipole
EasyNumerical valueIdea asked in 3 years
Q58
A wire of resistance $R$ and radius $r$ is stretched till its radius became $r/2$ . If new resistance of the stretched wire is $x\,R$ , then value of $x$ is __________.
Current Electricity Ohm's Law and Resistance Resistance of Stretched Wires
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q59
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x\sigma}{\epsilon_o}$ . The value of $x$ is __________ (all quantities are measured in SI units).
Electric Charges and Fields Electric Field Field of Parallel Charged Sheets
MediumNumerical value · figureIdea asked in 2 years
Q60
Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is $E/x$ , then $x$ = __________. (Given $a_o$ = 0.529 Å, $E$ = energy of electron in ground state).
Atoms Bohr's Atomic Model Energy Level Calculations
EasyNumerical valueIdea asked in 6 yearsAsked the year before

Chemistry30 questions

13 easy16 medium1 hard

Maths28 questions

5 easy15 medium8 hard

Q1
Let the relations $R_1$ and $R_2$ on the set $X = \{1, 2, 3, \ldots., 20\}$ be given by $R_1 = \{(x, y): 2x - 3y = 2\}$ and $R_2 = \{(x, y): -5x + 4y = 0\}$ . If $M$ and $N$ be the minimum number of elements required to be added in $R_1$ and $R_2$ ,…
Relations and Functions Sets and Relations Relation Types
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q2
The function $f(x)=\frac{x^2+2x-15}{x^2-4x+9}$ , $x \in \mathbb{R}$ is
Relations and Functions Functions and Domain Range of Quadratic Rational Functions
MediumSingle correctNew idea
Q3
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Permutations and Combinations Geometrical Combinatorics: Lines and Polygons
MediumSingle correctNew idea
Q4
Let $\alpha, \beta$ be the distinct roots of the equation $x^2-(t^2-5t+6)x+1=0$ , $t \in \mathbb{R}$ and $a_n=\alpha^n+\beta^n$ . Then the minimum value of $\frac{a_{2023}+a_{2025}}{a_{2024}}$ is
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
HardSingle correctIdea asked in 7 yearsAsked the year before
Q5
For $\alpha, \beta \in \mathbb{R}$ and a natural number $n$ , let $A_r=\begin{vmatrix} r & 1 & \frac{n^2}{2}+\alpha \\ 2r & 2 & n^2-\beta \\ 3r-2 & 3 & \frac{n(3n-1)}{2} \end{vmatrix}$ . Then $2A_{10}-A_8$ is
Determinants
MediumSingle correct
Q7
Let $A = \{n \in [100, 700] \cap \mathbb{N}: n$ is neither a multiple of 3 nor a multiple of 4 $\}$ . Then the number of elements in $A$ is
Relations and Functions Sets and Relations Venn Diagrams
EasySingle correctIdea asked in 3 years
Q8
If $f(x)=\begin{cases} x^3\sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}$ , then
Continuity and Differentiability Existence of Higher Order Derivatives
MediumSingle correctIdea asked in 3 years
Q9
The interval in which the function $f(x)=x^x$ , $x>0$ , is strictly increasing is
Application of Derivatives Monotonicity Monotonicity of Variable Exponent Functions
EasySingle correctNew idea
Q10
Let a variable line of slope $m>0$ passing through the point $(4,-9)$ intersect the coordinate axes at the points $A$ and $B$ . The minimum value of the sum of the distances of $A$ and $B$ from the origin is
Straight Lines Straight Line Distance Origin Distance to Intercept Form
HardSingle correctIdea asked in 2 yearsAsked the year before
Q11
$\int_0^{\pi/4}\frac{\cos^2 x\ \sin^2 x}{(\cos^3 x+\sin^3 x)^2}dx$ is equal to
Integrals Integration by Substitution Trigonometric Substitution
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q12
Let the area of the region enclosed by the curves $y=3x$ , $2y=27-3x$ and $y=3x-x\sqrt{x}$ be $A$ . Then $10A$ 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 of the differential equation $(1+x^2)\frac{dy}{dx}+y=e^{\tan^{-1}x}$ , $y(1)=0$ . Then $y(0)$ is
Differential Equations Linear Differential Equations Integrating Factor Calculation
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q14
Let $y=y(x)$ be the solution of the differential equation $(2x\log_e x)\frac{dy}{dx}+2y=\frac{3}{x}\log_e x$ , $x>0$ and $y(e^{-1})=0$ . Then, $y(e)$ is equal to
Differential Equations Linear Differential Equations Coefficient Normalization for Standard Form
MediumSingle correctIdea asked in 3 years
Q15
A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are $m$ and $n$ , respectively, then $m + n^2$ is equal to
Conic Sections
EasySingle correct
Q17
The shortest distance between the lines $\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}$ and $\frac{x+1}{2}=\frac{y-1}{1}=\frac{z-9}{-3}$ is
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
MediumSingle correctIdea asked in 5 years
Q18
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is
Statistics Variance and SD Correcting Incorrect Variance
EasySingle correctIdea asked in 6 yearsAsked the year before
Q19
If $A(3,1,-1)$ , $B\left(\frac{5}{3},\frac{7}{3},\frac{1}{3}\right)$ , $C(2,2,1)$ and $D\left(\frac{10}{3},\frac{2}{3},\frac{-1}{3}\right)$ are the vertices of a quadrilateral $ABCD$ , then its area is
Vector Algebra Cross Product Area of Quadrilateral via Diagonals
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q20
A company has two plants $A$ and $B$ to manufacture motorcycles. $60\%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B$ . $80\%$ of the motorcycles manufactured at plant $A$ are rated of the standard quality, while…
Probability Bayes' Theorem Bayes' Theorem Application
EasySingle correctIdea asked in 6 yearsAsked the year before
Q21
Let $x_1, x_2, x_3, x_4$ be the solution of the equation $4x^4+8x^3-17x^2-12x+9=0$ and $\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16}m$ . Then the value of $m$ is __________
Complex Numbers and Quadratic Equations Quadratic Roots Root-Coefficient Relation
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let $\alpha\beta\gamma=45$ ; $\alpha, \beta, \gamma \in \mathbb{R}$ . If $x(\alpha,1,2)+y(1,\beta,2)+z(2,3,\gamma)=(0,0,0)$ for some $x,y,z \in \mathbb{R}$ , $xyz\neq 0$ , then $6\alpha+4\beta+\gamma$ is equal to __________
Determinants Cramer's Rule Parameter Evaluation in Homogeneous Systems
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q23
If the second, third and fourth terms in the expansion of $(x+y)^n$ are $135$ , $30$ and $\frac{10}{3}$ , respectively, then $6(n^3+x^2+y)$ is equal to __________
Binomial Theorem Binomial Coefficients Ratio of Consecutive Coefficients
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q24
Let the first term of a series be $T_1=6$ and its $r^{\text{th}}$ term $T_r=3T_{r-1}+6^r$ , $r=2,3,\ldots\ldots, n$ . If the sum of the first $n$ terms of this series is $\frac{1}{5}\left(n^2-12n+39\right)\left(4\cdot6^n-5\cdot3^n+1\right)$ , then $n$ is equal…
Sequences and Series Arithmetico-Geometric Series AGP Recurrence Relation
HardNumerical valueIdea asked in 2 years
Q25
Let $r_k=\frac{\int_0^1\left(1-x^7\right)^k dx}{\int_0^1\left(1-x^7\right)^{k+1}dx}$ , $k \in \mathbb{N}$ . Then the value of $\sum_{k=1}^{10}\frac{1}{7\left(r_k-1\right)}$ is equal to __________
Integrals Definite Integral Properties Reduction Formulae in Definite Integrals
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q26
Let $L_1, L_2$ be the lines passing through the point $P(0,1)$ and touching the parabola $9x^2+12x+18y-14=0$ . Let $Q$ and $R$ be the points on the lines $L_1$ and $L_2$ such that the $\Delta PQR$ is an isosceles triangle with base $QR$ . If the slopes of the…
Conic Sections General Conic Section Pair of Tangents (SS1 = T^2)
HardNumerical valueNew idea
Q27
Let a conic $C$ pass through the point $(4,-2)$ and $P(x,y)$ , $x \geq 3$ , be any point on $C$ . Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3,-5)$ . If the focal…
Conic Sections General Conic Section Condition for a Parabola
HardNumerical valueNew idea
Q28
Let $P$ be the point $(10,-2,-1)$ and $Q$ be the foot of the perpendicular drawn from the point $R(1,7,6)$ on the line passing through the points $(2,-5,11)$ and $(-6,7,-5)$ . Then the length of the line segment $PQ$ is equal to __________.
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q29
Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$ , $\vec{b}=3\hat{i}+4\hat{j}-5\hat{k}$ and a vector $\vec{c}$ be such that $\vec{a}\times\left(\vec{b}+\vec{c}\right)+\vec{b}\times\vec{c}=\hat{i}+8\hat{j}+13\hat{k}$ . If $\vec{a}\cdot\vec{c}=13$ , then…
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q30
For $n \in \mathbb{N}$ , if $\cot^{-1}3+\cot^{-1}4+\cot^{-1}5+\cot^{-1}n=\frac{\pi}{4}$ , then $n$ is equal to __________.
Inverse Trigonometric Functions Inverse Trig Identities Piecewise cot-1 to tan-1 Conversion
MediumNumerical valueNew ideaIdea asked in 2 years

Dropped from the final key and left out of every count: Q6, Q16.

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.