JEE Main 2025 · April session

JEE Main 7 April 2025, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 9 were rated hard and 24 easy. Its hard-question count was the joint 4th highest of the 8 2025 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 9; 12% of the shift
Chapters asked: 56; 18 questions with a figure

Key findings · 7 Apr 2025, Shift 1

1
9 hard questions (12%): the joint 4th highest count of the 8 2025 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 4 of 25 rated hard; Physics had the most easy questions (10 of 25).
3
12 questions tested a new idea, one no earlier year had asked: 18% of the 66 questions tagged to an idea.
4
35 came back from 2024: the same idea had been asked in the 2024 shifts Lumi analysed.
5
21 shared an idea with another 2025 shift (32% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Ray Optics and Optical Instruments in Physics (3), Biomolecules in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 10Medium 12Hard 3

Top chapters

Chemistry

25 Q · 5 numerical

Easy 10Medium 13Hard 2

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 17Hard 4

Top chapters

Question format

Single correct42 Q
Numerical value15 Q
Diagram based7 Q
Two statements5 Q
Other4 Q
Match the list2 Q

What each question asks you to do

Multi-step32 Q
Calculation25 Q
Application8 Q
Conceptual4 Q
Recall3 Q
Data or graph3 Q

Most common: Multi-step.

Against the other 2025 shifts

This shift next to the 7 other 2025 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
2 Apr, Shift 1	75	21%	12%	20%	21%	44%
2 Apr, Shift 2	75	31%	8%	20%	22%	33%
3 Apr, Shift 1	74	28%	14%	20%	25%	38%
3 Apr, Shift 2	75	29%	8%	20%	31%	36%
4 Apr, Shift 2	75	24%	20%	20%	21%	45%
7 Apr, Shift 1	75	32%	12%	20%	18%	43%
7 Apr, Shift 2	75	24%	12%	20%	25%	45%
8 Apr, Shift 2	75	27%	17%	20%	20%	40%

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

Open25 this shift3092 · 33%33%8/830299720720358540200225
Open25 this shift3084 · 33%33%8/830298716720359538199224
Open25 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 75 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

75 of 75 questions

Physics25 questions

10 easy12 medium3 hard

Q26
If $\epsilon_0$ denotes the permittivity of free space and $\Phi_E$ is the flux of the electric field through the area bounded by the closed surface, then dimensions of $\left(\epsilon_0 \frac{d\phi_E}{dt}\right)$ are that of :
Units and Measurements Parallel Plate Capacitors Displacement Current Between Plates
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q27
Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:
Ray Optics and Optical Instruments Lens Maker's Formula Lenses Separated by a Distance
EasySingle correctIdea asked in 6 yearsAsked the year before
Q28
An object of mass 1000 g experiences a time dependent force $\vec{F} = \left(2t\,\hat{i} + 3t^2\,\hat{j}\right)\mathrm{N}$ . The power generated by the force at time t is:
Work, Energy and Power Power 3D Vector Calculation of Power
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q29
A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the centre of mass of the system: (Consider L = 10 cm)
System of Particles and Rotational Motion Center of Mass COM of Bent Wires
EasySingle correct · figureNew idea
Q30
A cubic block of mass m is sliding down on an inclined plane at $60^\circ$ with an acceleration of $\frac{g}{2}$ , the value of coefficient of kinetic friction is
Laws of Motion Friction Friction on Inclines
EasySingle correctIdea asked in 3 yearsAsked the year before
Q31
Two projectiles are fired from ground with same initial speeds from same point at angles $(45^\circ + \alpha)$ and $(45^\circ - \alpha)$ with horizontal direction. The ratio of their times of flights is
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q32
Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$ . If both the wires are stretched using same force, what would be the ratio of their respective elongations ?
Mechanical Properties of Solids Elasticity Elastic Moduli
EasySingle correctIdea asked in 7 yearsAsked the year before
Q33
Match the LIST-I with LIST-I LIST-I | LIST-II A. Triatomic rigid gas | I. $\frac{C_p}{C_v} = \frac{5}{3}$ B. Diatomic non-rigid gas | II. $\frac{C_p}{C_v} = \frac{7}{5}$ C. Monoatomic gas | III. $\frac{C_p}{C_v} = \frac{4}{3}$ D. Diatomic rigid gas | IV.…
Thermodynamics Kinetic Theory of Gases Gamma and Degrees of Freedom
MediumMatch the listIdea asked in 5 years
Q34
Two harmonic waves moving in the same direction superimpose to form a wave $x = a\cos(1.5t)\cos(50.5t)$ where t is in seconds. Find the period with which they beat. (close to nearest integer)
Waves Beats Resultant Wave Equation in Beats
MediumSingle correctNew idea
Q35
An ac current is represented as $i = 5\sqrt{2} + 10\cos\left(650\pi t + \frac{\pi}{6}\right)$ Amp The r.m.s value of the current is
Alternating Current RMS and Peak Values RMS of DC and AC Superposition
EasySingle correctIdea asked in 2 years
Q36
A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is :
Current Electricity Wheatstone Bridge Hidden Wheatstone Bridges in Complex Networks
MediumDiagram based · figureNew idea
Q37
A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?
Moving Charges and Magnetism Lorentz Force Radius-Kinetic Energy Proportionality
EasyDiagram based · figureIdea asked in 2 years
Q38
Two charges $q_1$ and $q_2$ are separated by a distance of 30 cm. A third charge $q_3$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from…
Electrostatic Potential and Capacitance Electric Potential Work Done in Field
MediumDiagram based · figureIdea asked in 3 years
Q39
The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{Mg} = 1.2 \times 10^{-5}$ ) is :
Magnetism and Matter
MediumSingle correct
Q40
Uniform magnetic fields of different strengths ( $B_1$ and $B_2$ ), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity $v$ and…
Moving Charges and Magnetism Lorentz Force Circular Motion in Uniform B-Field
HardDiagram based · figureIdea asked in 4 years
Q41
Two plane polarized light waves combine at a certain point whose electric field components are $E_1 = E_0 \sin\omega t$ $E_2 = E_0 \sin\left(\omega t + \frac{\pi}{3}\right)$ Find the amplitude of the resultant wave.
Wave Optics Young's Double Slit Resultant Intensity Formula
EasySingle correctIdea asked in 5 yearsAsked the year before
Q42
A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)
Ray Optics and Optical Instruments Lens Maker's Formula Lens Immersed in a Liquid
EasySingle correctIdea asked in 5 yearsAsked the year before
Q43
For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is
Atoms Bohr's Atomic Model Shortest and Longest Wavelengths
EasySingle correctIdea asked in 5 yearsAsked the year before
Q44
In a hydrogen like ion, the energy difference between the $2^{\mathrm{nd}}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is:
Atoms Bohr's Atomic Model Scaling for Hydrogenic Ions
EasySingle correctIdea asked in 2 years
Q45
In the following circuit, the reading of the ammeter will be (Take Zener breakdown voltage = 4 V)
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Regulation
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q46
A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. The moment of inertia of the given system about PQ axis is $\frac{x}{15}$ I, where I is the moment of inertia of the…
System of Particles and Rotational Motion Moment of Inertia MOI of Composite Bodies
HardNumerical value · figureIdea asked in 5 years
Q47
A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^\circ$ C and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x$ = ___________. (Given…
Thermal Properties of Matter Thermal Radiation Stefan-Boltzmann Law
MediumNumerical valueNew idea
Q48
An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is _______ $\times 10^{-1}$ J. (Take $\pi = 3.14$ )
Thermodynamics Thermodynamic Processes Cyclic Process Work
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q49
For ac circuit shown in figure, R = 100 k $\Omega$ and C = 100 pF and the phase difference between $\mathrm{V_{in}}$ and $(\mathrm{V_B} - \mathrm{V_A})$ is $90^\circ$ . The input signal frequency is $10^x$ rad/sec, where 'x' is ______.
Alternating Current Phasor Diagrams Phase Shifting Networks
HardNumerical value · figureNew idea
Q50
A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40…
Ray Optics and Optical Instruments Refraction and Snell's Law Apparent Depth of Immiscible Liquids
MediumNumerical valueIdea asked in 4 yearsAsked the year before

Chemistry25 questions

10 easy13 medium2 hard

Q51
At the sea level, the dry air mass percentage composition is given as nitrogen gas: 70.0, oxygen gas: 27.0 and argon gas: 3.0. If total pressure is 1.15 atm, then calculate the ratio of following respectively: (i) partial pressure of nitrogen gas to partial…
Some Basic Concepts of Chemistry Ideal Gas Laws Dalton's Law
MediumSingle correctIdea asked in 4 years
Q52
Which of the following statements are correct, if the threshold frequency of caesium is $5.16 \times 10^{14}$ Hz? A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs, the ammeter shows the presence…
Structure of Atom Photoelectric Effect Work Function and Threshold
MediumOther · figureIdea asked in 4 yearsAsked the year before
Q53
Total enthalpy change for freezing of 1 mol of water at $10^\circ$ C to ice at $-10^\circ$ C is __________ (Given: $\Delta_{fus}H = x$ kJ/mol $C_p[\mathrm{H_2O(l)}] = y\ \mathrm{J\,mol^{-1}\,K^{-1}}$ $C_p[\mathrm{H_2O(s)}] = z\ \mathrm{J\,mol^{-1}\,K^{-1}}$
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy of Phase Transitions
MediumSingle correctIdea asked in 2 years
Q54
An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water). The pH of HCl solution would (Given log 2 = 0.30)
Equilibrium pH and Buffers pH of Strong Acids and Bases
EasySingle correctIdea asked in 4 years
Q55
Given below are two statements: Statement I: Mohr's salt is composed of only three types of ions-ferrous, ammonium and sulfate. Statement II: If the molar conductance at infinite dilution for ferrous, ammonium and sulfate ions are $x_1$ , $x_2$ and $x_3$ S…
Electrochemistry
MediumTwo statements
Q56
Reaction $\mathrm{A(g) \rightarrow 2B(g) + C(g)}$ is a first order reaction. It was started with pure A t/min | Pressure of system at time t/mm Hg 10 | 160 $\infty$ | 240 Which of the following option is incorrect?
Chemical Kinetics Integrated Rate Equations Gas Kinetics with Complex Stoichiometry
MediumOther · figureIdea asked in 5 yearsAsked the year before
Q57
A person's wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay(r) was found to be proportional with the square of the…
Chemical Kinetics Rate Laws Rate vs Concentration Graphs
MediumDiagram based · figureNew idea
Q58
Match the LIST-I with LIST-I LIST-I (Molecule / ion) | LIST-II (Bond pair : lone pair (on the central atom)) A. $\mathrm{ICl_2^-}$ | I. 4 : 2 B. $\mathrm{H_2O}$ | II. 4 : 1 C. $\mathrm{SO_2}$ | III. 2 : 3 D. $\mathrm{XeF_4}$ | IV. 2 : 2 Choose the correct…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumMatch the listIdea asked in 6 yearsAsked the year before
Q59
The number of valence electrons present in the metal among Cr, Co, Fe and Ni which has the lowest enthalpy of atomisation is
The d- and f-Block Elements d-Block Elements Enthalpy of Atomization
MediumSingle correctNew ideaIdea asked in 2 years
Q60
The group 14 elements A and B have the first ionisation enthalpy values of 708 and 715 kJ $\mathrm{mol^{-1}}$ respectively. The above values are lowest among their group members. The nature of their ions $\mathrm{A^{2+}}$ and $\mathrm{B^{4+}}$ respectively is
The p-Block Elements Group 13 & 14 Inert Pair Effect
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q61
The first transition series metal 'M' has the highest enthalpy of atomisation in its series. One of its aquated ion ( $\mathrm{M^{n+}}$ ) exists in green colour. The nature of the oxide formed by the above $\mathrm{M^{n+}}$ ion is:
The d- and f-Block Elements d-Block Elements Acid-Base Character of Oxides
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q62
An octahedral complex having molecular composition $\mathrm{Co.5NH_3.Cl.SO_4}$ has two isomers A and B. The solution of A gives a white precipitate with $\mathrm{AgNO_3}$ solution and the solution of B gives white precipitate with $\mathrm{BaCl_2}$ solution.…
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
EasySingle correctIdea asked in 7 years
Q63
When a salt is treated with sodium hydroxide solution it gives gas X. On passing gas X through reagent Y a brown coloured precipitate is formed. X and Y respectively, are
Hydrogen Cation Analysis Group 0: Nessler's Reagent Complex Formula
EasySingle correctIdea asked in 2 years
Q64
Given below are two statements: Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent. Statement II: Sodium metal can be used to dry diethyl ether and not ethyl alcohol. In the light of…
Alcohols, Phenols and Ethers
EasyTwo statements
Q65
Which of the following is the correct IUPAC name of given organic compound (X)?
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Functional Group Priority
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q66
The reactions which cannot be applied to prepare an alkene by elimination, are A. [2-bromo-1-methylcyclohexane: cyclohexane ring with a methyl group and an adjacent Br] $\xrightarrow{\mathrm{NaOEt}}$ B.…
Haloalkanes and Haloarenes
MediumOther · figure
Q67
Given below are two statements: Statement I: Ozonolysis followed by treatment with Zn, $\mathrm{H_2O}$ of cis-2-butene gives ethanal. Statement II: The product obtained by ozonolysis followed by treatment with Zn, $\mathrm{H_2O}$ of 3, 6-dimethyloct-4-ene…
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
MediumTwo statementsIdea asked in 7 yearsAsked the year before
Q68
Which of the following compounds is least likely to give effervescence of $\mathrm{CO_2}$ in presence of aq. $\mathrm{NaHCO_3}$ ?
Aldehydes, Ketones and Carboxylic Acids Organic Acidity and Basicity Sodium Bicarbonate Effervescence Test
EasyDiagram based · figureIdea asked in 2 years
Q69
Which of the following amine (s) show (s) positive carbylamine test? A. [aniline: benzene ring bearing $\mathrm{NH_2}$ ] B. $\mathrm{(CH_3)_2NH}$ C. $\mathrm{CH_3NH_2}$ D. $\mathrm{(CH_3)_3N}$ E. [N-methylaniline: benzene ring bearing NH-CH $_3$ ] Choose the…
Amines Carbylamine Reaction
EasyOther · figureIdea asked in 4 years
Q70
Given below are two statements: Statement I: D-(+)-glucose + D-(+) fructose $\xrightarrow{-H_2O}$ Sucrose sucrose $\xrightarrow{\text{hydrolysis}}$ D-(+) glucose + D -(+) fructose Statement II: Invert sugar is formed during sucrose hydrolysis In the light of…
Biomolecules Carbohydrates Inversion of Cane Sugar
MediumTwo statementsIdea asked in 2 years
Q71
1 Faraday electricity was passed through $\mathrm{Cu^{2+}}$ (1.5 M, 1 L) /Cu and 0.1 Faraday was passed through $\mathrm{Ag^+}$ (0.2 M, 1 L)/Ag electrolytic cells. After this the two cells were connected as shown below to make an electrochemical cell. The…
Electrochemistry Nernst Equation Full Cell Nernst Equation
HardNumerical value · figureIdea asked in 6 yearsAsked the year before
Q72
The percentage dissociation of a salt ( $\mathrm{MX_3}$ ) solution at given temperature (van't Hoff factor $i = 2$ ) is ___________ %(Nearest integer)
Solutions Colligative Properties Degree of Dissociation from Van't Hoff Factor
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q73
The number of paramagnetic complexes among $[\mathrm{FeF_6}]^{3-}$ , $[\mathrm{Fe(CN)_6}]^{3-}$ , $[\mathrm{Mn(CN)_6}]^{3-}$ , $[\mathrm{Co(C_2O_4)_3}]^{3-}$ , $[\mathrm{MnCl_6}]^{3-}$ , and $[\mathrm{CoF_6}]^{3-}$ , which involved $\mathrm{d^2sp^3}$ hybridization…
Coordination Compounds Crystal Field Theory High and Low Spin States
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q74
An organic compound weighing 500 mg, produced 220 mg of $\mathrm{CO_2}$ , on complete combustion. The percentage composition of carbon in the compound is ________%. (nearest integer) (Given molar mass in $\mathrm{g\,mol^{-1}}$ of C:12, O:16)
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry POAC in Combustion Analysis
EasyNumerical valueIdea asked in 3 years
Q75
Thyroxine, the hormone has given below structure The percentage of iodine in thyroxine is ______%. (nearest integer) (Given molar mass in $\mathrm{g\,mol^{-1}}$ C:12, H:1, O:16, N:14, I:127)
Biomolecules
EasyNumerical value · figure

Maths25 questions

4 easy17 medium4 hard

Q1
If for $\theta \in \left[-\frac{\pi}{3}, 0\right]$ , the points $(x, y) = \left(3\tan\left(\theta+\frac{\pi}{3}\right), 2\tan\left(\theta+\frac{\pi}{6}\right)\right)$ lie on $xy + \alpha x + \beta y + \gamma = 0$ , then $\alpha^2 + \beta^2 + \gamma^2$ is equal…
Trigonometric Functions Trigonometric Identities Elimination of Trigonometric Parameters
MediumSingle correctNew idea
Q2
Among the statements (S1) : The set $\{z \in \mathbb{C} - \{-i\} : |z| = 1$ and $\frac{z-i}{z+i}$ is purely real $\}$ contains exactly two elements, and (S2) : The set $\{z \in \mathbb{C} - \{-1\} : |z| = 1$ and $\frac{z-1}{z+1}$ is purely imaginary $\}$ …
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Purely Real and Imaginary Euler Conditions
MediumTwo statementsIdea asked in 3 yearsAsked the year before
Q3
Let the set of all values of $p \in \mathbb{R}$ , for which both the roots of the equation $x^2 - (p+2)x + (2p+9) = 0$ are negative real numbers, be the interval $(\alpha, \beta]$ . Then $\beta - 2\alpha$ is equal to
Complex Numbers and Quadratic Equations Location of Roots Both Roots Negative
EasySingle correctNew idea
Q4
Let the system of equations : $2x + 3y + 5z = 9$ , $7x + 3y - 2z = 8$ , $12x + 3y - (4+\lambda)z = 16 - \mu$ , have infinitely many solutions. Then the radius of the circle centred at $(\lambda, \mu)$ and touching the line $4x = 3y$ is
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
Let $A$ be a $3 \times 3$ matrix such that $|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81$ . If $S = \left\{n \in \mathbb{Z} : \left(|\mathrm{adj}(\mathrm{adj}\,A)|\right)^{\frac{(n-1)^2}{2}} = |A|^{(3n^2 - 5n - 4)}\right\}$ , then…
Matrices Matrix Inverse Inverse Relation to Double Adjoint
HardSingle correctIdea asked in 6 yearsAsked the year before
Q6
Let $x_1, x_2, x_3, x_4$ be in a geometric progression. If $2, 7, 9, 5$ are subtracted respectively from $x_1, x_2, x_3, x_4$ , then the resulting numbers are in an arithmetic progression. Then the value of $\frac{1}{24}(x_1 x_2 x_3 x_4)$ is:
Sequences and Series AP and GP Conditions for Three Terms in AP or GP
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q7
The remainder when $\left((64)^{(64)}\right)^{(64)}$ is divided by 7 is equal to
Binomial Theorem
EasySingle correct
Q8
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the…
Permutations and Combinations Combinations of Distinct Objects
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q9
The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $10(\mu + \sigma)$ is…
Statistics Variance and SD Correcting Incorrect Variance
EasySingle correctIdea asked in 6 yearsAsked the year before
Q10
Let P be the parabola, whose focus is $(-2, 1)$ and directrix is $2x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose abscissa is $-2$ , is
Conic Sections General Conic Section Focus-Directrix Form Extraction
MediumSingle correctIdea asked in 3 years
Q11
Let ABC be the triangle such that the equations of lines AB and AC be $3y - x = 2$ and $x + y = 2$ , respectively, and the points B and C lie on $x$ -axis. If P is the orthocentre of the triangle ABC, then the area of the triangle PBC is equal to
Straight Lines
MediumSingle correct
Q12
Let $C_1$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $C_2$ be the circle with centre $(1, 3)$ that touches $C_1$ externally at the point $(\alpha, \beta)$ . If $(\beta - \alpha)^2 = \frac{m}{n}$ , $\gcd(m, n) = 1$ ,…
Conic Sections Circle Tangents Common Tangent of Touching Circles
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q13
Let the line L pass through $(1, 1, 1)$ and intersect the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z}{1}$ . Then, which of the following points lies on the line L?
Three Dimensional Geometry Lines in 3D Condition for Intersection of Two Lines
MediumSingle correctIdea asked in 3 years
Q14
If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $\frac{x}{1} = \frac{y}{\alpha} = \frac{z-5}{1}$ is $\frac{5}{\sqrt{6}}$ , then the sum of all possible values of $\alpha$ is
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q15
Let the angle $\theta$ , $0 < \theta < \frac{\pi}{2}$ between two unit vectors $\hat{a}$ and $\hat{b}$ be $\sin^{-1}\left(\frac{\sqrt{65}}{9}\right)$ . If the vector $\vec{c} = 3\hat{a} + 6\hat{b} + 9(\hat{a} \times \hat{b})$ , then the value of…
Vector Algebra Cross Product Orthogonality Dot Product Trap
MediumSingle correctNew idea
Q16
$\lim_{x \to 0^+} \frac{\tan\left(5(x)^{\frac{1}{3}}\right) \log_e\left(1+3x^2\right)}{\left(\tan^{-1} 3\sqrt{x}\right)^2 \left(e^{5(x)^{\frac{4}{3}}} - 1\right)}$ is equal to
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
Let $x = -1$ and $x = 2$ be the critical points of the function $f(x) = x^3 + ax^2 + b\log_e|x| + 1$ , $x \neq 0$ . Let $m$ and $M$ respectively be the absolute minimum and the absolute maximum values of $f$ in the interval $\left[-2, -\frac{1}{2}\right]$ .…
Application of Derivatives Maxima and Minima Closed Interval Extrema
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q18
The integral $\int_0^{\pi} \frac{(x+3)\sin x}{1+3\cos^2 x}\,dx$ is equal to
Integrals Definite Integral Properties Removing 'x' using King's Property
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q19
If the area of the region bounded by the curves $y = 4 - \frac{x^2}{4}$ and $y = \frac{x-4}{2}$ is equal to $\alpha$ , then $6\alpha$ equals
Application of Integrals Area Under Curves Area Between Curves
EasySingle correctIdea asked in 7 yearsAsked the year before
Q20
Let $y = y(x)$ be the solution curve of the differential equation $x(x^2 + e^x)\,dy + (e^x(x-2)y - x^3)\,dx = 0$ , $x > 0$ , passing through the point $(1, 0)$ . Then $y(2)$ is equal to
Differential Equations Linear Differential Equations LDEs Disguised in Exact Differential Form
HardSingle correctIdea asked in 2 years
Q21
For $n \geq 2$ , let $S_n$ denote the set of all subsets of $\{1, 2, \ldots, n\}$ with no two consecutive numbers. For example $\{1, 3, 5\} \in S_6$ , but $\{1, 2, 4\} \notin S_6$ . Then $n(S_5)$ is equal to ______
Permutations and Combinations Non-Consecutive Selection in a Row
MediumNumerical valueNew idea
Q22
The number of singular matrices of order 2, whose elements are from the set $\{2, 3, 6, 9\}$ , is ___________.
Matrices Matrix Inverse Singular and Non-singular Matrices
MediumNumerical valueNew ideaIdea asked in 2 years
Q23
Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ having one of its focus at $P(-3, 0)$ . If the latus ractum through its other focus subtends a right angle at $P$ and $a^2 b^2 = \alpha\sqrt{2} - \beta$ , $\alpha, \beta \in \mathbb{N}$ , then…
Conic Sections
HardNumerical value
Q24
The number of relations on the set $A = \{1, 2, 3\}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive but not symmetric, is ___________.
Relations and Functions Sets and Relations Counting Relations
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q25
The number of points of discontinuity of the function $f(x) = \left[\frac{x^2}{2}\right] - [\sqrt{x}]$ , $x \in [0, 4]$ , where $[\cdot]$ denotes the greatest integer function, is ___________.
Continuity and Differentiability
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 2025 shifts.