JEE Main 2022 · June session

JEE Main 26 June 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 27 easy. Its hard-question count was the joint 14th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 12; 13% of the shift
Chapters asked: 69; 13 questions with a figure

Key findings · 26 Jun 2022, Shift 2

1
12 hard questions (13%): the joint 14th highest count of the 24 2022 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 22%.
2
Maths was the hardest section, with 11 of 30 rated hard; Physics had the most easy questions (15 of 30).
3
28 questions tested a new idea, one no earlier year had asked: 36% of the 77 questions tagged to an idea.
4
41 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
43 shared an idea with another 2022 shift (56% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Laws of Motion in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 10Medium 20Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 17Hard 11

Top chapters

Question format

Single correct55 Q
Numerical value30 Q
Diagram based3 Q
Assertion–reason1 Q
Match the list1 Q

What each question asks you to do

Calculation30 Q
Multi-step24 Q
Application12 Q
Recall11 Q
Conceptual10 Q
Diagram reading2 Q
Data or graph1 Q

Most common: Calculation.

Against the other 2022 shifts

This shift next to the 23 other 2022 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
24 Jun, Shift 1	89	29%	17%	34%	31%	37%
24 Jun, Shift 2	90	40%	14%	33%	39%	36%
25 Jun, Shift 1	90	44%	13%	33%	33%	30%
25 Jun, Shift 2	90	30%	13%	33%	34%	22%
26 Jun, Shift 1	89	34%	16%	34%	37%	32%
26 Jun, Shift 2	90	30%	13%	33%	36%	27%
27 Jun, Shift 1	90	34%	8%	33%	38%	31%
27 Jun, Shift 2	90	32%	17%	33%	34%	46%
28 Jun, Shift 1	90	32%	12%	33%	38%	27%
28 Jun, Shift 2	90	30%	17%	33%	33%	31%
29 Jun, Shift 1	90	41%	11%	33%	36%	30%
29 Jun, Shift 2	88	35%	9%	33%	41%	30%
30 Jun, Shift 1	90	36%	13%	33%	27%	27%
25 Jul, Shift 1	88	28%	15%	33%	38%	38%
25 Jul, Shift 2	90	37%	12%	33%	33%	33%
26 Jul, Shift 1	90	27%	13%	33%	34%	31%
26 Jul, Shift 2	89	37%	16%	34%	41%	38%
27 Jul, Shift 1	89	29%	15%	34%	30%	32%
27 Jul, Shift 2	88	19%	15%	33%	40%	35%
28 Jul, Shift 1	90	36%	17%	33%	36%	30%
28 Jul, Shift 2	90	28%	14%	33%	40%	28%
29 Jul, Shift 1	90	31%	22%	33%	41%	37%
29 Jul, Shift 2	90	39%	12%	33%	48%	32%
30 Jul, Shift 2	90	30%	17%	33%	36%	33%

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

15 easy14 medium1 hard

Q31
The dimension of mutual inductance is :
Units and Measurements Inductance Dimensional Analysis of Inductance
EasySingle correctNew idea
Q32
In the arrangement shown in figure $a_1,a_2,a_3$ and $a_4$ are the accelerations of masses $m_1,m_2,m_3$ and $m_4$ respectively. Which of the following relation is true for this arrangement ?
Laws of Motion Newton's Laws of Motion Constrained Motion
HardDiagram based · figureIdea asked in 2 yearsAsked the year before
Q33
Arrange the four graphs in descending order of total work done; where $W_1,W_2,W_3$ and $W_4$ are the work done corresponding to figure a, b, c and d respectively.
Work, Energy and Power Work and Kinetic Energy Work from Force-Displacement Graph
MediumDiagram based · figureNew idea
Q34
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is -
System of Particles and Rotational Motion
EasySingle correct
Q35
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any…
Gravitation
MediumAssertion–reason
Q36
If $p$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in the pipe of diameter d, the correct formula for Reynolds number $R_e$ is :
Mechanical Properties of Fluids Viscosity Reynolds Number
EasySingle correctNew idea
Q37
A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at $27^\circ$ C. The ratio of their average kinetic energy per molecule respectively will be :
Kinetic Theory Kinetic Theory of Gases Law of Equipartition
EasySingle correctIdea asked in 4 yearsAsked the year before
Q38
The charge on capacitor of capacitance $15\mu F$ in the figure given below is :
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q39
A parallel plate capacitor with plate area A and plate separation d=2 m has a capacitance of $4\ \mu F$ . The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K=3 (as shown in figure)…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Partially Filled Dielectric Slab
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q40
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $\mu$ C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :
Electric Charges and Fields Conductors in Fields Surface Charge Distribution
MediumSingle correctNew ideaIdea asked in 2 years
Q41
The equivalent resistance between points A and B in the given network is :
Current Electricity Kirchhoff's Laws Circuit Symmetry Analysis
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q42
A bar magnet having a magnetic moment of $2.0 \times 10^{5}\ JT^{-1}$ , is placed along the direction of uniform magnetic field of magnitude B= $14 \times 10^{-5}\ T$ . The work done in rotating the magnet slowly through $60^\circ$ from the direction of field…
Magnetism and Matter Magnetic Dipole Moment Work done in rotating a dipole
EasySingle correctIdea asked in 3 years
Q43
Two coils of self inductance $L_1$ and $L_2$ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :
Electromagnetic Induction Inductance Inductor Combinations
MediumSingle correct · figureNew idea
Q44
A metallic conductor of length 1m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 $rad\ s^{-1}$ . If the horizontal component of earth's magnetic field is $0.2 \times 10^{-4}\ T$ , then emf induced…
Electromagnetic Induction Faraday's Law Rotational Motional EMF
EasySingle correctNew ideaIdea asked in 4 years
Q45
Which is the correct ascending order of wavelengths ?
Electromagnetic Waves
EasySingle correct
Q46
For a specific wavelength 670 nm of light coming from a galaxy moving with velocity $v$ , the observed wavelength is 670.7 nm. The value of $v$ is :
Wave Optics Doppler Effect Light Doppler Approximation
EasySingle correctIdea asked in 2 yearsAsked the year before
Q47
A metal surface is illuminated by a radiation of wavelength 4500 Å. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90°with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function…
Dual Nature of Radiation and Matter Photoelectric Effect Work Function and Threshold
MediumSingle correctNew ideaIdea asked in 4 years
Q48
A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be :
Nuclei Radioactive Decay Parallel Decay Branching
EasySingle correctIdea asked in 2 yearsAsked the year before
Q49
The positive feedback is required by an amplifier to act an oscillator. The feedback here means :
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors Transistor as an Oscillator
EasySingle correctNew idea
Q50
A sinusoidal wave $y(t) = 40\sin(10 \times 10^{6}\ \pi t)$ is amplitude modulated by another sinusoidal wave $x(t) = 20\sin(1000\pi t)$ . The amplitude of minimum frequency component of modulated signal is :
Communication Systems
MediumSingle correct
Q51
A ball is projected vertically upward with an initial velocity of 50 $ms^{-1}$ at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = ________s, second ball will meet the first ball ( $g = 10\ ms^{-2}$ ).
Motion in a Straight Line Kinematics in 1D Meeting Point Condition
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q52
A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 $ms^{-1}$ . The impulse imparted to the ball is ________ Ns.
Laws of Motion Collisions Vector Impulse in Direction Changes
EasyNumerical valueNew idea
Q53
A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7^{th}$ and $8^{th}$ ball is ________ N when…
Laws of Motion Newton's Laws of Motion Slipping Chain on a Smooth Table
MediumNumerical value · figureNew idea
Q54
A geyser heats water flowing at a rate of 2.0 kg per minute from $30^\circ$ C to $70^\circ$ C. If geyser operates on a gas burner, the rate of combustion of fuel will be ________ $g\ min^{-1}$ [Heat of combustion = $8 \times 10^{3}\ Jg^{-1}$ , Specific heat of…
Thermal Properties of Matter Calorimetry Specific Heat Capacity
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q55
A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ________ K.
Thermodynamics Second Law and Entropy Carnot Engine Efficiency
MediumNumerical valueNew idea
Q56
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ________ Hz.
Waves Beats Frequency Calculation in a Tuning Fork Series
MediumNumerical valueNew idea
Q57
Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of $10^{-5}\ N$ , then separation between the wires is ________ cm.
Moving Charges and Magnetism
EasyNumerical value
Q58
A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}\ m$ . The refractive index of water is $\frac{4}{3}$ . The area of the surface of water through which light from the bulb can emerge out is $x\pi\ m^2$ . The value of $x$ is…
Ray Optics and Optical Instruments Refraction and Snell's Law Circle of Illuminance (Fish-Eye View)
MediumNumerical valueNew idea
Q59
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ________…
Units and Measurements
EasyNumerical value
Q60
The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 Å is 0.42 V. If the threshold frequency is $x \times 10^{13}$ /s , where $x$ is ________ (nearest integer). (Given, speed light = $3 \times 10^{8}$ m/s…
Dual Nature of Radiation and Matter Photoelectric Effect Work Function and Threshold
MediumNumerical valueNew ideaIdea asked in 4 years

Chemistry30 questions

10 easy20 medium0 hard

Q61
The number of radial and angular nodes in 4d orbital are, respectively
Structure of Atom Quantum Numbers Calculation of Radial and Angular Nodes
EasySingle correctIdea asked in 5 yearsAsked the year before
Q62
Match List I with List II. List I (Enzyme): A. Invertase; B. Zymase; C. Diastase; D. Maltase List II (Conversion of): I. Starch into maltose; II. Maltose into glucose; III. Glucose into ethanol; IV. Cane sugar into glucose Choose the most appropriate answer…
Biomolecules
MediumMatch the list
Q63
Which of the following elements is considered as a metalloid?
Classification of Elements and Periodicity in Properties
EasySingle correct
Q64
The role of depressants in 'Froth Floation method' is to
General Principles and Processes of Isolation of Elements Adsorption Adsorption in Froth Flotation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q65
Boiling of hard water is helpful in removing the temporary hardness by converting calcium hydrogen carbonate and magnesium hydrogen carbonate to
Hydrogen Hydrogen and Hydrides Temporary Hardness and Clark's Method
EasySingle correctIdea asked in 2 yearsAsked the year before
Q66
s-block element which **cannot** be qualitatively confirmed by the flame test is
The s-Block Elements s-Block Elements Flame Coloration
EasySingle correctIdea asked in 4 yearsAsked the year before
Q67
The oxide which contains an odd electron at the nitrogen atom is
The p-Block Elements Group 15 & 16 Nitrogen Oxides Structure
EasySingle correctIdea asked in 3 yearsAsked the year before
Q68
Which one of the following is an example of disproportionation reaction ?
Redox Reactions Disproportionation Balancing
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q69
The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from +3 oxidation state?
The d- and f-Block Elements f-Block Elements Lanthanide Oxidation States
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q70
The measured BOD values for four different water samples (A-D) are as follows: A = 3 ppm; B=18 ppm; C=21 ppm; D=4 ppm. The water samples which can be called as highly polluted with organic wastes, are
Environmental Chemistry Water Quality BOD and COD
EasySingle correctIdea asked in 4 yearsAsked the year before
Q71
The correct order of nucleophilicity is
Organic Chemistry: Some Basic Principles and Techniques SN1 and SN2 Mechanisms Nucleophilicity vs Basicity
MediumSingle correctNew idea
Q72
Oxidation of toluene to benzaldehyde can be easily carried out with which of the following reagents?
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Side-chain Oxidation
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q73
The major product in the following reaction [drawn skeletal structure with a double bond at the end of the chain] --(i) $\mathrm{Hg(OAc)_2}$ , $\mathrm{H_2O}$ ; (ii) $\mathrm{NaBH_4}$ --> ? is
Hydrocarbons Alkenes and Alkynes Oxymercuration-Demercuration
MediumSingle correct · figureNew idea
Q74
Halogenation of which one of the following will yield m-substituted product with respect to methyl group as a major product?
Haloalkanes and Haloarenes Aromatic Hydrocarbons Ortho-Para vs Meta Directing
MediumSingle correct · figureIdea asked in 5 yearsAsked the year before
Q75
The reagent, from the following, which converts benzoic acid to benzaldehyde in one step is [drawn benzene ring with COOH, arrow, drawn benzene ring with CHO]
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Reduction of Acids
MediumSingle correct · figureIdea asked in 5 yearsAsked the year before
Q76
The final product 'A' in the following reaction sequence [drawn structure labelled CH3 CH2 - C - CH3 with O drawn below the carbon] --HCN--> ? --95% $\mathrm{H_2SO_4}$ , Heat--> A is
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Hydrolysis of Cyanohydrins
MediumSingle correct · figureNew idea
Q77
Which statement is NOT correct for p-toluenesulphonyl chloride?
Amines Hinsberg Test
EasySingle correctIdea asked in 5 yearsAsked the year before
Q78
The final product 'C' in the following series of reactions [drawn benzene ring with NO2] --Sn/HCl--> A -- $\mathrm{NaNO_2}$ , HCl--> B -- $\beta$ -Naphthol, NaOH--> C is
Amines Diazonium Salts Coupling with Beta-Naphthol
MediumSingle correct · figureIdea asked in 2 years
Q79
Which of the following is NOT an example of synthetic detergent?
Chemistry in Everyday Life Soaps and Detergents
EasySingle correct · figureNew idea
Q80
Which one of the following is a water soluble vitamin, that is not excreted easily?
Biomolecules
EasySingle correct
Q81
CNG is an important transportation fuel. When 100 g CNG is mixed with 208 g oxygen in vehicles, it leads to the formation of $\mathrm{CO_2}$ and $\mathrm{H_2O}$ and produces large quantity of heat during this combustion ,then the amount of carbon dioxide,…
Some Basic Concepts of Chemistry Mole Concept Limiting Reagent and Reaction Yield
MediumNumerical valueIdea asked in 4 years
Q82
In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is $\mathrm{A_xB_y}$ . The value of $x$ is ____. [nearest integer]
The Solid State Crystal Lattices Empirical Formula from Void Occupancy
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q83
Amongst $\mathrm{SF_4}$ , $\mathrm{XeF_4}$ , $\mathrm{CF_4}$ and $\mathrm{H_2O}$ , the number of species with two lone pairs of electrons is ____.
Chemical Bonding and Molecular Structure VSEPR Theory Geometry vs Shape Distinction
MediumNumerical valueNew ideaIdea asked in 2 years
Q84
A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ $\mathrm{mol^{-1}}$ is __________. [nearest integer]…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg $\mathrm{mol^{-1}}$ in 200 mL of water at 27°C is __________ Pa.[integer value] (use R = 0.083 L bar $\mathrm{mol^{-1}\,K^{-1}}$ )
Solutions Colligative Properties Osmotic Pressure
MediumNumerical valueNew ideaIdea asked in 4 years
Q86
40% of HI undergoes decompostion to $\mathrm{H_2}$ and $\mathrm{I_2}$ at 300 K. $\Delta G^\ominus$ for this decompostion reaction at one atmopsphere pressure is ____ J $\mathrm{mol^{-1}}$ .[nearest integer] (Use R = 8.31 J $\mathrm{K^{-1}\,mol^{-1}}$ ; log 2 =…
Equilibrium Gibbs Free Energy Gibbs Energy and Equil
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q87
$\mathrm{Cu(s)} + \mathrm{Sn^{2+}}$ (0.001M) $\rightarrow \mathrm{Cu^{2+}}$ (0.01M) + $\mathrm{Sn(s)}$ The Gibbs free energy change for the above reaction at 298 K is $x \times 10^{-1}$ kJ $\mathrm{mol^{-1}}$ . The value of $x$ is ____. [nearest integer]…
Electrochemistry Gibbs Free Energy Standard Gibbs Energy and Standard Cell Potential
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q88
Catalyst A reduces the activation energy for a reaction by 10 kJ $\mathrm{mol^{-1}}$ at 300 K. The ratio of rate constants, $\frac{k_{T,\,\mathrm{Catalysed}}}{k_{T,\,\mathrm{Uncatalysed}}}$ is $e^x$ . The value of $x$ is ___. [nearest integer] [Assume that…
Chemical Kinetics Arrhenius Equation Catalyst Effect on Arrhenius Parameters
MediumNumerical valueIdea asked in 3 years
Q89
Reaction of $[\mathrm{Co(H_2O)_6}]^{2+}$ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in $t_{2g}$ -orbitals of the product is ________.
Coordination Compounds Crystal Field Theory Octahedral Field Splitting
MediumNumerical valueNew ideaIdea asked in 3 years
Q90
The moles of methane required to produce 81 g of water after complete combustion is ________ $\times\,10^{-2}$ mol. [nearest integer]
Some Basic Concepts of Chemistry Mole Concept Limiting Reagent and Reaction Yield
EasyNumerical valueIdea asked in 4 years

Maths30 questions

2 easy17 medium11 hard

Q1
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = x - 1$ and $g : \mathbb{R} - \{1, -1\} \rightarrow \mathbb{R}$ be defined as $g(x) = \frac{x^2}{x^2 - 1}$ . Then the function $fog$ is :
Relations and Functions Functions and Domain Range of Composite Functions
MediumSingle correctNew ideaIdea asked in 3 years
Q2
If the system of equations $\alpha x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = \beta$ has infinitely many solutions, then the ordered pair $(\alpha, \beta)$ is equal to :
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
If $A = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n}$ and $B = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}$ , then $\frac{A}{B}$ is equal to :
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q4
$\lim_{x \to 0} \frac{\cos(\sin x) - \cos x}{x^4}$ is equal to :
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q5
Let $f(x) = \min\{1, 1 + x \sin x\}, 0 \leq x \leq 2\pi$ . If $m$ is the number of points, where $f$ is not differentiable and $n$ is the number of points, where $f$ is not continuous, then the ordered pair $(m, n)$ is equal to
Continuity and Differentiability Differentiability of Max/Min Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q6
Cosider a cuboid of sides $2x$ , $4x$ and $5x$ and a closed hemisphere of radius $r$ . If the sum of their surface areas is a constant $k$ , then the ratio $x : r$ , for which the sum of their volumes is maximum, is :
Application of Derivatives Maxima and Minima Optimization Problems
HardSingle correctIdea asked in 5 yearsAsked the year before
Q7
The area of the region bounded by $y^2 = 8x$ and $y^2 = 16(3 - x)$ is equal to:
Application of Integrals Area Under Curves Area Between Two Standard Parabolas
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q8
If $\int \frac{1}{x}\sqrt{\frac{1 - x}{1 + x}}\, dx = g(x) + c$ , $g(1) = 0$ , then $g\left(\frac{1}{2}\right)$ is equal to :
Integrals Integration by Substitution Cosine Double Angle Radical Substitution
HardSingle correctNew idea
Q9
If $y = y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y = x e^x$ , $y(1) = 0$ then the local maximum value of the function $z(x) = x^2 y(x) - e^x$ , $x \in \mathbb{R}$ is :
Differential Equations Linear Differential Equations Exact Differential Recognition in LDEs
HardSingle correctIdea asked in 3 yearsAsked the year before
Q10
If the solution of the differential equation $\frac{dy}{dx} + e^x(x^2 - 2)y = (x^2 - 2x)(x^2 - 2)e^{2x}$ satisfies $y(0) = 0$ , then the value of $y(2)$ is ______
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q11
If $m$ is the slope of a common tangent to the curves $\frac{x^2}{16} + \frac{y^2}{9} = 1$ and $x^2 + y^2 = 12$ , then $12\, m^2$ is equal to :
Conic Sections Tangents and Normals Common Tangents to Two Curves
MediumSingle correctNew idea
Q12
The locus of the mid point of the line segment joining the point $(4, 3)$ and the points on the ellipse $x^2 + 2y^2 = 4$ is an ellipse with eccentricity :
Conic Sections
MediumSingle correct
Q13
The normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$ at the point $(8, 3\sqrt{3})$ on it passes through the point :
Conic Sections Normals to Conics Hyperbola Normal Point Form
MediumSingle correctIdea asked in 3 years
Q14
If the plane $2x + y - 5z = 0$ is rotated about its line of intersection with the plane $3x - y + 4z - 7 = 0$ by an angle of $\frac{\pi}{2}$ , then the plane after the rotation passes through the point :
Three Dimensional Geometry Planes in 3D Family of Planes Perpendicular to a Third Plane
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q15
If the lines $\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})$ and $\vec{r} = (\alpha\hat{i} - \hat{j}) + \mu(2\hat{i} - 3\hat{k})$ are co-planar, then the distance of the plane containing these two lines from the point $(\alpha, 0, 0)$ …
Three Dimensional Geometry Planes in 3D Plane Containing Two Lines
MediumSingle correctIdea asked in 2 years
Q16
Let $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$ , $\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$ be three given vectors. Let $\vec{v}$ be a vector in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\vec{c}$ is…
Vector Algebra Dot Product Scalar and Vector Projection
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q17
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal…
Statistics Variance and SD Correcting Incorrect Variance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q18
$16 \sin(20^\circ) \sin(40^\circ) \sin(80^\circ)$ is equal to :
Trigonometric Functions Trigonometric Identities Sine Product Identity with 60 Degrees
EasySingle correctNew ideaIdea asked in 2 years
Q19
If the inverse trigonometric functions take principal values, then $\cos^{-1}\left(\frac{3}{10}\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right) + \frac{2}{5}\sin\left(\tan^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Evaluating Trig of Inverse Trig
EasySingle correctNew ideaIdea asked in 2 years
Q20
Let $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to :
Semiconductor Electronics: Materials, Devices and Simple Circuits
MediumSingle correct
Q21
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ satisfy $f(x + y) = 2^x f(y) + 4^y f(x)$ , $\forall x, y \in \mathbb{R}$ . If $f(2) = 3$ , then $14 \cdot \frac{f'(4)}{f'(2)}$ is equal to ______.
Continuity and Differentiability Differentiability via Functional Equations
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let $p$ and $q$ be two real numbers such that $p + q = 3$ and $p^4 + q^4 = 369$ . Then $\left(\frac{1}{p} + \frac{1}{q}\right)^{-2}$ is equal to ______.
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q23
If $z^2 + z + 1 = 0$ , $z \in \mathbb{C}$ , then $\left|\sum_{n=1}^{15}\left(z^n + (-1)^n \frac{1}{z^n}\right)^2\right|$ is equal to ______.
Complex Numbers and Quadratic Equations Roots of Unity Roots of z^2 + z + 1 = 0
HardNumerical valueNew ideaIdea asked in 2 years
Q24
Let $X = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}$ , $Y = \alpha I + \beta X + \gamma X^2$ and $Z = \alpha^2 I - \alpha\beta X + (\beta^2 - \alpha\gamma)X^2$ , $\alpha, \beta, \gamma \in \mathbb{R}$ . If…
Matrices Matrix Multiplication Inverse of (I+A) for Nilpotent Matrices
HardNumerical valueNew idea
Q25
The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ______.
Permutations and Combinations Principle of Inclusion-Exclusion in Counting
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q26
If $\left({}^{40}C_0\right) + \left({}^{41}C_1\right) + \left({}^{42}C_2\right) + \ldots + \left({}^{60}C_{20}\right) = \frac{m}{n}\,{}^{60}C_{20}$ $m$ and $n$ are coprime, then $m + n$ is equal to ______.
Binomial Theorem Binomial Coefficients Hockey Stick Identity
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q27
If $a_1\ (> 0), a_2, a_3, a_4, a_5$ are in a G.P., $a_2 + a_4 = 2a_3 + 1$ and $3a_2 + a_3 = 2a_4$ , then $a_2 + a_4 + 2a_5$ is equal to ______.
Sequences and Series AP and GP GP General Term
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q28
The integral $\frac{24}{\pi}\int_0^{\sqrt{2}} \frac{(2 - x^2)\,dx}{(2 + x^2)\sqrt{4 + x^4}}$ is equal to ______.
Integrals Integration by Substitution Factoring Highest Power for Substitution
HardNumerical valueIdea asked in 3 years
Q29
Let a line $L_1$ be tangent to the hyperbola $\frac{x^2}{16} - \frac{y^2}{4} = 1$ and let $L_2$ be the line passing through the origin and perpendicular to $L_1$ . If the locus of the point of intersection of $L_1$ and $L_2$ is…
Conic Sections
HardNumerical value
Q30
If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is $p$ , then $96\,p$ is equal to ______.
Probability
HardNumerical 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 2022 shifts.