JEE Main 2022 · June session

JEE Main 28 June 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 29 easy. Its hard-question count was the joint 19th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Application of Derivatives, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 62; 13 questions with a figure

Key findings · 28 Jun 2022, Shift 1

1
11 hard questions (12%): the joint 19th 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 10 of 30 rated hard; Chemistry had the most easy questions (17 of 30).
3
29 questions tested a new idea, one no earlier year had asked: 38% of the 77 questions tagged to an idea.
4
40 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
37 shared an idea with another 2022 shift (48% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Semiconductor Electronics: Materials, Devices and Simple Circuits in Physics (3), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 11Medium 19Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 17Medium 12Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 19Hard 10

Top chapters

Question format

Single correct44 Q
Numerical value30 Q
Diagram based7 Q
Two statements4 Q
Assertion–reason3 Q
Match the list2 Q

What each question asks you to do

Multi-step24 Q
Calculation21 Q
Conceptual18 Q
Application12 Q
Recall12 Q
Diagram reading2 Q
Data or graph1 Q

Most common: Multi-step.

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

11 easy19 medium0 hard

Q31
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coeffcient of viscosity. Reason R : Coefficient of viscosity =…
Units and Measurements Viscosity Units and Dimensions of Viscosity
MediumAssertion–reasonIdea asked in 2 yearsAsked the year before
Q32
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration ( $a$ ) is varying with time $t$ as $a = k^2rt^2$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is given…
Work, Energy and Power Power Power in Non-Uniform Circular Motion
MediumSingle correctNew idea
Q33
Motion of a particle in $x$ - $y$ plane is described by a set of following equations $x = 4\sin\left(\frac{\pi}{2}-\omega t\right)$ m and $y = 4\sin(\omega t)$ m. The path of the particle will be :
Oscillations SHM Equations Perpendicular Superposition (Lissajous)
EasySingle correctNew idea
Q34
Match List-I with List-II List - I | List - II A. Moment of inertia of solid sphere of radius R about any tangent. | I. $\frac{5}{3}MR^2$ B. Moment of inertia of hollow sphere (R) about any tangent. | II. $\frac{7}{5}MR^2$ C. Moment of inertia of circular…
System of Particles and Rotational Motion Moment of Inertia MOI of a Disk About Tangents
MediumMatch the listNew idea
Q35
Two planets A and B of equal mass are having their period of revolutions $\mathrm{T_A}$ and $\mathrm{T_B}$ such that $\mathrm{T_A} = 2\mathrm{T_B}$ . These planets are revolving in the circular orbits of radii $\mathrm{r_A}$ and $\mathrm{r_B}$ respectively.…
Gravitation Orbital Mechanics Kepler's Laws
EasySingle correctIdea asked in 4 yearsAsked the year before
Q36
A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :
Mechanical Properties of Fluids Surface Tension Splitting and Coalescence
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q37
Given below are two statements : Statement – I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state $(\mathrm{P_1, V_1, T_1})$ to state $(\mathrm{P_2, V_2, T_2})$ , then work done is…
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
MediumTwo statementsIdea asked in 7 yearsAsked the year before
Q38
Given below are two statements : Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement-II : An electric dipole is placed in a non-uniform…
Electric Charges and Fields Electric Field Superposition Principle for Electric Fields
MediumTwo statementsIdea asked in 4 years
Q39
The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :
Electric Charges and Fields Electric Field Superposition Principle for Electric Fields
MediumSingle correct · figureIdea asked in 4 years
Q40
An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.
Moving Charges and Magnetism Ampere's Circuital Law Magnetic Field of a Hollow Cylindrical Pipe
MediumDiagram based · figureNew idea
Q41
A radar sends an electromagnetic signal of electric field ( $\mathrm{E_o}$ ) = 2.25 V/m and magnetic field ( $\mathrm{B_o}$ ) = $1.5\times10^{-8}$ T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo)…
Electromagnetic Waves
MediumSingle correct
Q42
The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -
Ray Optics and Optical Instruments Prism Deviation Prism Refractive Index
MediumSingle correctNew ideaIdea asked in 3 years
Q43
The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $\mathrm{\AA}$ is used to see the object will be :
Ray Optics and Optical Instruments Single Slit Diffraction Resolving Power of a Telescope
EasySingle correctNew ideaIdea asked in 2 years
Q44
The de Broglie wavelengths for an electron and a photon are $\lambda_e$ and $\lambda_p$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?
Dual Nature of Radiation and Matter Matter Waves Electron vs Photon (Same Energy)
MediumSingle correctNew idea
Q45
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, $\mathrm{K_p}$ are related as :
Nuclei Nuclear Binding Energy Q-Value and Reaction Spontaneity
MediumSingle correctIdea asked in 2 years
Q46
In the following circuit, the correct relation between output (Y) and inputs A and B will be :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q47
For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Forward and Reverse Biasing
EasySingle correctNew ideaIdea asked in 4 years
Q48
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : n-p-n transistor permits more current than a p-n-p transistor. Reason R : Electrons have greater mobility as a charge carrier. Choose the…
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors NPN vs PNP Preference and Carrier Mobility
EasyAssertion–reasonNew idea
Q49
Match List-I with List-II List - I | List - II A. Television signal | I. 03 KHz B. Radio signal | II. 20 KHz C. High Quality Music | III. 02 MHz D. Human speech | IV. 06 MHz Choose the correct answer from the options given below :
Communication Systems
EasyMatch the list
Q50
The velocity of sound in a gas, in which two wavelengths 4.08m and 4.16m produce 40 beats in 12s, will be :
Waves Beats Beat Frequency Calculation
MediumSingle correctNew idea
Q51
A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at $60°$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob…
Work, Energy and Power Work and Kinetic Energy Conservation of Mechanical Energy
EasyNumerical value · figureIdea asked in 4 yearsAsked the year before
Q52
A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 $\Omega$ . The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2…
Current Electricity Wheatstone Bridge Meter Bridge End Corrections
MediumNumerical value · figureNew idea
Q53
Current measured by the ammeter (A) in the reported circuit when no current flows through 10 $\Omega$ resistance, will be __________ A.
Current Electricity Wheatstone Bridge Balanced Bridge Equation
MediumNumerical value · figureIdea asked in 3 years
Q54
An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$ F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is ___________ s.
Alternating Current Phasor Diagrams Impedance Triangle Construction
MediumNumerical value · figureIdea asked in 4 years
Q55
The position vector of 1 kg object is $\vec{r} = \left(3\hat{i} - \hat{j}\right)$ m and its velocity $\vec{v} = \left(3\hat{j} + \hat{k}\right)\ \mathrm{ms^{-1}}$ . The magnitude of its angular momentum is $\sqrt{x}$ Nm where x is ____________.
System of Particles and Rotational Motion Angular Momentum Angular Momentum of Particle
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q56
A man of 60 kg is running on the road and suddenly jumps into a stationary trolley car of mass 120 kg. Then, the trolley car starts moving with velocity 2 $\mathrm{ms^{-1}}$ . The velocity of the running man was ____________ $\mathrm{ms^{-1}}$ , when he jumps…
System of Particles and Rotational Motion Center of Mass COM Velocity Conservation
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q57
A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is…
Laws of Motion Newton's Laws of Motion Ideal String Tension
MediumNumerical value · figureNew ideaIdea asked in 2 years
Q58
The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be ___________ J. (Given R = 8.31 J/mol.K)
Kinetic Theory Kinetic Theory of Gases Degrees of Freedom
EasyNumerical valueNew ideaIdea asked in 3 years
Q59
A singly ionized magnesium atom (A=24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ________ cm.
Moving Charges and Magnetism Lorentz Force Circular Motion in Uniform B-Field
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q60
A telegraph line of length 100 km has a capacity of 0.01 $\mu$ F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ____________…
Alternating Current LCR Resonance Resonant Frequency Calculation
EasyNumerical valueIdea asked in 4 yearsAsked the year before

Chemistry30 questions

17 easy12 medium1 hard

Q61
The incorrect statement about the imperfections in solids is :
The Solid State Solid State Defects Schottky Defect
EasySingle correctNew idea
Q62
The Zeta potential is related to which property of colloids ?
Surface Chemistry Colloids Zeta Potential and Helmholtz Double Layer
EasySingle correctIdea asked in 2 yearsAsked the year before
Q63
Element “E” belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above “E” in the group is
Classification of Elements and Periodicity in Properties Quantum Numbers Predicting Periodic Table Position
EasySingle correctNew idea
Q64
Given are two statements one is labelled as Assertion A and other is labelled as Reason R. Assertion A :Magnesium can reduce $\mathrm{Al_2O_3}$ at a temperature below 1350°C, while above 1350°C aluminium can reduce MgO. Reason R : The melting and boiling…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Intersections
MediumAssertion–reasonIdea asked in 2 years
Q65
Dihydrogen reacts with CuO to give
Hydrogen Hydrogen and Hydrides Reducing Action on Metal Oxides
EasySingle correctNew idea
Q66
Nitrogen gas is obtained by thermal decomposition of
The p-Block Elements Group 15 & 16 Preparation of Dinitrogen
EasySingle correctIdea asked in 2 years
Q67
Given below are two statements : Statement I :The pentavalent oxide of group-15 element, $\mathrm{E_2O_5}$ , is less acidic than trivalent oxide, $\mathrm{E_2O_3}$ , of the same element. Statement II :The acidic character of trivalent oxide of group 15…
The p-Block Elements Periodic Trends Acidic and Basic Character of Oxides
MediumTwo statementsIdea asked in 4 years
Q68
Which one of the lanthanoids given below is the most stable in divalent form?
The d- and f-Block Elements f-Block Elements Lanthanide Oxidation States
EasySingle correctIdea asked in 3 yearsAsked the year before
Q69
Given below are two statements : Statement I : $\mathrm{[Ni(CN)_4]^{2-}}$ is square planar and diamagnetic complex, with $dsp^2$ hybridization for Ni but $\mathrm{[Ni(CO)_4]}$ is tetrahedral, paramagnetic and with $sp^3$ - hybridization for Ni. Statement II :…
Coordination Compounds Crystal Field Theory d8 Square Planar Preference
MediumTwo statementsIdea asked in 2 yearsAsked the year before
Q70
Which amongst the following is not a pesticide ?
Environmental Chemistry Pesticides and Herbicides Toxicity
EasySingle correctNew ideaIdea asked in 2 years
Q71
Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate ?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q72
Which of the following structures are aromatic in nature ?
Hydrocarbons Aromatic Hydrocarbons Huckel's Rule (4n+2)
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q73
The major product (P) in the reaction [reaction drawn: Ph at left, zigzag chain of three carbons with a C=C double bond between the first and second carbons, Br at the right end of the chain] $\xrightarrow{\mathrm{HBr}}$ ?(P) [Ph is - $\mathrm{C_6H_5}$ ] is
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q74
The correct structure of product ‘A’ formed in the following reaction, $\mathrm{PhCHO + Ph \cdot CHO} \xrightarrow[\text{in } \mathrm{D_2O}]{\mathrm{NaOD}} A + \mathrm{Ph-C(=O)-O^-}$ (Ph is - $\mathrm{C_6H_5}$ ) is
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Cannizzaro Reaction
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q75
Which one of the following compounds is inactive towards $\mathrm{S_N1}$ reaction ?
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Bredt's Rule and Bridgehead Halides
MediumDiagram based · figureNew idea
Q76
Identify the major product formed in the following sequence of reactions : [benzene ring with NH2 substituent] $\xrightarrow[\substack{(2)\ \mathrm{NaNO_2/HCl}\\(3)\ \mathrm{H_3PO_2}}]{(1)\ \mathrm{Br_2\,/\,H_2O}}$
Amines Diazonium Salts Deamination Byproducts: Hypophosphorous Acid
MediumDiagram based · figureIdea asked in 2 yearsAsked the year before
Q77
A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives a/an
Amines Reaction of Primary Aliphatic Amines with HNO2
EasySingle correctNew ideaIdea asked in 2 years
Q78
Which one of the following is NOT a copolymer ?
Polymers Homopolymers vs Copolymers
EasySingle correctNew idea
Q79
Stability of $\alpha$ - Helix structure of proteins depends upon
Biomolecules
EasySingle correct
Q80
The formula of the purple colour formed in Laissaigne’s test for sulphur using sodium nitroprusside is
Organic Chemistry: Some Basic Principles and Techniques Anion Analysis Sulfide Sodium Nitroprusside Test
EasySingle correctIdea asked in 3 yearsAsked the year before
Q81
A 2.0 g sample containing $\mathrm{MnO_2}$ is treated with HCl liberating $\mathrm{Cl_2}$ . The $\mathrm{Cl_2}$ gas is passed into a solution of KI and 60.0 mL of 0.1 M $\mathrm{Na_2S_2O_3}$ is required to titrate the liberated iodine. The percentage of…
Some Basic Concepts of Chemistry Redox Reactions Thiosulfate-Iodine Reaction Stoichiometry
MediumNumerical valueNew ideaIdea asked in 2 years
Q82
If the work function of a metal is $6.63 \times 10^{-19}$ J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ________ nm. (Nearest integer) [Given : h = $6.63 \times 10^{-34}$ J s, and c = $3 \times 10^8$ m…
Structure of Atom Photoelectric Effect Work Function and Threshold
EasyNumerical valueNew ideaIdea asked in 4 years
Q83
The hybridization of P exhibited in $\mathrm{PF_5}$ is $sp^xd^y$ . The value of y is ________
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q84
4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. The amount of heat absorbed in this expansion is ________ L atm.
Thermodynamics (Chemistry)Thermodynamic Processes Free Expansion of Ideal Gas
EasyNumerical valueNew ideaIdea asked in 2 years
Q85
The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is $\frac{x}{17}$ . The value of x is ________.
Solutions Colligative Properties Relative Lowering of VP
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q86
The solubility product of a sparingly soluble salt $\mathrm{A_2X_3}$ is $1.1 \times 10^{-23}$ . If specific conductance of the solution is $3 \times 10^{-5}$ S $\mathrm{m^{-1}}$ , the limiting molar conductivity of the solution is $x \times 10^{-3}$ S…
Electrochemistry
HardNumerical value
Q87
The quantity of electricity in Faraday needed to reduce 1 mol of $\mathrm{Cr_2O_7^{2-}}$ to $\mathrm{Cr^{3+}}$ is ________
Electrochemistry Faraday's Laws of Electrolysis Charge-Mole Relationship
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q88
For a first order reaction A $\rightarrow$ B, the rate constant, k = $5.5 \times 10^{-14}$ $\mathrm{s^{-1}}$ . The time required for 67% completion of reaction is $x \times 10^{-1}$ times the half life of reaction. The value of x is ________ (Nearest integer)…
Chemical Kinetics Integrated Rate Equations First Order Fractional Completion Shortcuts
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q89
Number of complexes which will exhibit synergic bonding amongst, $\mathrm{[Cr(CO)_6]}$ , $\mathrm{[Mn(CO)_5]}$ and $\mathrm{[Mn_2(CO)_{10}]}$ is ________.
Coordination Compounds Molecular Orbital Theory LUMO as Pi-Acceptor
MediumNumerical valueNew idea
Q90
In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is ________% (nearest integer) (Relative atomic masses of Ag and Br are 108u and 80u, respectively).
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Gravimetric Precipitation Analysis
EasyNumerical valueIdea asked in 5 yearsAsked the year before

Maths30 questions

1 easy19 medium10 hard

Q1
If $\sum_{k=1}^{31}\left({}^{31}C_k\right)\left({}^{31}C_{k-1}\right)-\sum_{k=1}^{30}\left({}^{30}C_k\right)\left({}^{30}C_{k-1}\right)=\frac{\alpha(60!)}{(30!)(31!)}$ , where $\alpha\in\mathbb{R}$ , then the value of $16\alpha$ is equal to
Binomial Theorem Binomial Coefficients Product Sums with Constant Index Difference
HardSingle correctNew idea
Q2
Let a function $f:\mathbb{N}\to\mathbb{N}$ be defined by $f(n)=\begin{cases}2n, & n=2,4,6,8,....\\ n-1, & n=3,7,11,15,....\\ \frac{n+1}{2}, & n=1,5,9,13,....\end{cases}$ then, $f$ is
Relations and Functions
MediumSingle correct
Q3
If the system of linear equations $2x+3y-z=-2$ $x+y+z=4$ $x-y+|\lambda|z=4\lambda-4$ where $\lambda\in\mathbb{R}$ , has no solution, then
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q4
Let $A$ be a matrix of order $3\times3$ and $\det(A)=2$ . Then $\det(\det(A)\,\mathrm{adj}(5\,\mathrm{adj}(A^3)))$ is equal to __________.
Determinants Matrix Inverse Determinant of Adjoint of Inverse
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q5
The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is
Permutations and Combinations Fundamental Counting Principle
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q6
Let $A_1, A_2, A_3, ....$ be an increasing geometric progression of positive real numbers. If $A_1A_3A_5A_7=\frac{1}{1296}$ and $A_2+A_4=\frac{7}{36}$ , then the value of $A_6+A_8+A_{10}$ is equal to
Sequences and Series AP and GP GP General Term
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q7
Let $[t]$ denote the greatest integer less than or equal to $t$ . Then, the value of the integral $\int_0^1[-8x^2+6x-1]\,dx$ is equal to
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardSingle correctIdea asked in 7 yearsAsked the year before
Q8
Let $f:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=\begin{cases}[e^x], & x<0\\ ae^x+[x-1], & 0\le x<1\\ b+[\sin(\pi x)], & 1\le x<2\\ [e^{-x}]-c, & x\ge2\end{cases}$ where $a, b, c\in\mathbb{R}$ and $[t]$ denotes greatest integer less than or equal to $t$ .…
Continuity and Differentiability Continuity involving GIF and Fractional Part
HardSingle correctIdea asked in 6 yearsAsked the year before
Q9
The area of the region $S=\{(x, y): y^2\le8x,\ y\ge\sqrt{2}x,\ x\ge1\}$ is
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q10
Let the solution curve $y=y(x)$ of the differential equation $\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right]x\frac{dy}{dx}=x+\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right]y$ pass through the points $(1, 0)$ and $(2\alpha, \alpha)$ , $\alpha>0$ .…
Differential Equations Homogeneous Equations Substitution y = vx
HardSingle correctIdea asked in 6 yearsAsked the year before
Q11
Let $y=y(x)$ be the solution of the differential equation $x(1-x^2)\frac{dy}{dx}+(3x^2y-y-4x^3)=0,\ x>1$ , with $y(2)=-2$ . Then $y(3)$ is equal to
Differential Equations Linear Differential Equations Coefficient Normalization for Standard Form
HardSingle correctNew ideaIdea asked in 3 years
Q12
The number of real solutions of $x^7+5x^3+3x+1=0$ is equal to ________.
Application of Derivatives Monotonicity Counting Roots using Monotonicity
MediumSingle correctNew ideaIdea asked in 2 years
Q13
Let the eccentricity of the hyperbola $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\sqrt{\frac{5}{2}}$ and length of its latus rectum be $6\sqrt{2}$ , If $y=2x+c$ is a tangent to the hyperbola $H$ , then the value of $c^2$ is equal to
Conic Sections
MediumSingle correct
Q14
If the tangents drawn at the points O(0, 0) and P $\left(1+\sqrt{5}, 2\right)$ on the circle $x^2+y^2-2x-4y=0$ intersect at the point Q, then the area of the triangle OPQ is equal to
Conic Sections Circle Tangents Area of Tangent-Chord Triangle
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q15
If two distinct points Q, R lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the point P is $(1, -2, 3)$ , then the area of the triangle PQR is equal to
Three Dimensional Geometry Planes in 3D Direction of Line of Intersection
HardSingle correctNew idea
Q16
The acute angle between the planes P $_1$ and P $_2$ , when P $_1$ and P $_2$ are the planes passing through the intersection of the planes $5x+8y+13z-29=0$ and $8x-7y+z-20=0$ and the points $(2, 1, 3)$ and $(0, 1, 2)$ , respectively, is
Three Dimensional Geometry Planes in 3D Family of Planes
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q17
Let the plane $P:\vec{r}\cdot\vec{a}=d$ contain the line of intersection of two planes $\vec{r}\cdot\left(\hat{i}+3\hat{j}-\hat{k}\right)=6$ and $\vec{r}\cdot\left(-6\hat{i}+5\hat{j}-\hat{k}\right)=7$ . If the plane $P$ passes through the point…
Three Dimensional Geometry Planes in 3D Family of Planes
HardSingle correctIdea asked in 4 yearsAsked the year before
Q18
The probability, that in a randomly selected 3-digit number at least two digits are odd, is
Probability
MediumSingle correct
Q19
Let AB and PQ be two vertical poles, 160 $m$ apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let $\frac{\pi}{8}$ and $\theta$ be the angles of elevation from C to P and A, respectively. If the height of pole PQ…
Trigonometric Functions
MediumSingle correct
Q20
Let $p, q, r$ be three logical statements. Consider the compound statements $S_1:((\sim p)\vee q)\vee((\sim p)\vee r)$ and $S_2: p\to(q\vee r)$ Then, which of the following is NOT true ?
Mathematical Reasoning
MediumSingle correct
Q21
Let $R_1$ and $R_2$ be relations on the set $\{1, 2, ...., 50\}$ such that $R_1=\{(p, p^n): p$ is a prime and $n\ge0$ is an integer $\}$ and $R_2=\{(p, p^n): p$ is a prime and $n=0$ or $1\}$ . Then, the number of elements in $R_1-R_2$ is__________.
Relations and Functions Sets and Relations Counting Relations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
The number of real solutions of the equation $e^{4x}+4e^{3x}-58e^{2x}+4e^x+1=0$ is __________.
Application of Derivatives Quadratic Roots Exponential Reducible to Quadratic
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q23
The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to __________.
Statistics Variance and SD Correcting Incorrect Variance
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q24
If $\vec{a}=2\hat{i}+\hat{j}+3\hat{k}$ , $\vec{b}=3\hat{i}+3\hat{j}+\hat{k}$ and $\vec{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k}$ are coplanar vectors and $\vec{a}\cdot\vec{c}=5$ , $\vec{b}\perp\vec{c}$ , then $122(c_1+c_2+c_3)$ is equal to __________.
Vector Algebra Triple Products Solving for Unknown in Coplanarity
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q25
A ray of light passing through the point P(2, 3) reflects on the $x$ -axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot…
Straight Lines Straight Line Distance Image of a point in a line
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q26
Let $l$ be a line which is normal to the curve $y=2x^2+x+2$ at a point P on the curve. If the point Q(6, 4) lies on the line $l$ and O is origin, then the area of the triangle OPQ is equal to __________.
Application of Derivatives Tangents and Normals Normals Passing Through a Given Point
MediumNumerical valueNew idea
Q27
Let $A=\{1, a_1, a_2 ..... a_{18}, 77\}$ be a set of integers with $1<a_1<a_2<.....<a_{18}<77$ . Let the set $A+A=\{x+y: x, y\in A\}$ contain exactly 39 elements. Then, the value of $a_1+a_2+....+a_{18}$ is equal to __________.
Sequences and Series
HardNumerical value
Q28
The number of positive integers $k$ such that the constant term in the binomial expansion of $\left(2x^3+\frac{3}{x^k}\right)^{12}$ , $x\neq0$ is $2^8\cdot\ell$ , where $\ell$ is an odd integer, is ________.
Binomial Theorem
MediumNumerical value
Q29
The number of elements in the set $\{z=a+ib\in\mathbb{C}: a, b\in\mathbb{Z}$ and $1<|z-3+2i|<4\}$ is __________.
Complex Numbers and Quadratic Equations
MediumNumerical value
Q30
Let the lines $y+2x=\sqrt{11}+7\sqrt{7}$ and $2y+x=2\sqrt{11}+6\sqrt{7}$ be normal to a circle $C:(x-h)^2+(y-k)^2=r^2$ . If the line $\sqrt{11}y-3x=\frac{5\sqrt{77}}{3}+11$ is tangent to the circle $C$ , then the value of $(5h-8k)^2+5r^2$ is equal to __________.
Conic Sections Circle Tangents Normal Passes Through Center
HardNumerical valueIdea asked in 3 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 2022 shifts.