JEE Main 2022 · June session

JEE Main 25 June 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 40 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: 63; 8 questions with a figure

Key findings · 25 Jun 2022, Shift 1

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 12 of 30 rated hard; Chemistry had the most easy questions (21 of 30).
3
27 questions tested a new idea, one no earlier year had asked: 33% of the 81 questions tagged to an idea.
4
47 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 (46% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Alternating Current in Physics (2), Alcohols, Phenols and Ethers in Chemistry (2) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 18Medium 12Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 21Medium 9Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 17Hard 12

Top chapters

Question format

Single correct52 Q
Numerical value30 Q
Diagram based5 Q
Match the list1 Q
Two statements1 Q
Other1 Q

What each question asks you to do

Multi-step27 Q
Conceptual27 Q
Calculation26 Q
Recall5 Q
Application4 Q
Diagram reading1 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

18 easy12 medium0 hard

Q31
If Z = $\frac{A^2B^3}{C^4}$ , then the relative error in Z will be :
Units and Measurements
EasySingle correct
Q32
$\vec{A}$ is a vector quantity such that $|\vec{A}|$ =non - zero constant. Which of the following expression is true for $\vec{A}$ ?
Motion in a Plane
EasySingle correct
Q33
Which of the following relations is true for two unit vector $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each other ?
Motion in a Plane
MediumSingle correct
Q34
If force $\vec{F}=3\hat{i}+4\hat{j}-2\hat{k}$ acts on a particle having position vector $2\hat{i}+\hat{j}+2\hat{k}$ then, the torque about the origin will be :
System of Particles and Rotational Motion Torque and Equilibrium 3D Torque Components
EasySingle correctIdea asked in 2 yearsAsked the year before
Q35
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).
Gravitation
EasySingle correct
Q36
The terminal velocity ( $v_t$ ) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :
Mechanical Properties of Fluids Viscosity Radius Dependence of Terminal Velocity
EasySingle correctNew ideaIdea asked in 2 years
Q37
The relation between root mean square speed ( $v_{rms}$ ) and most probable speed ( $v_p$ ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :
Kinetic Theory Kinetic Theory of Gases Molecular Speed Ratios
EasySingle correctIdea asked in 4 yearsAsked the year before
Q38
In the figure, a very large plane sheet of positive charge is shown. $P_1$ and $P_2$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields $E_1$ and $E_2$ at…
Electric Charges and Fields Electric Field Field of an Infinite Non-Conducting Sheet
EasyDiagram based · figureIdea asked in 4 years
Q39
Match List - I with List - II. List - I List - II (A) AC generator (I) Detects the presence of current in the circuit (B) Galvanometer (II) Converts mechanical energy into electrical energy (C) Transformer (III) Works on the principle of resonance in AC…
Alternating Current
EasyMatch the list
Q40
A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its…
Moving Charges and Magnetism Ampere's Circuital Law Field Inside Thick Wire
EasySingle correctIdea asked in 4 yearsAsked the year before
Q41
If wattless current flows in the AC circuit, then the circuit is :
Alternating Current Phasor Diagrams Wattless (Reactive) Current Component
EasySingle correctNew idea
Q42
The electric field in an electromagnetic wave is given by $E=56.5\sin\omega(t-x/c)\ \mathrm{NC^{-1}}$ . Find the intensity of the wave if it is propagating along $x$ -axis in the free space. (Given $\epsilon_0=8.85\times10^{-12}\mathrm{C^2N^{-1}m^{-2}}$ )
Electromagnetic Waves
EasySingle correct
Q43
The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\pi/2$ at point P and $\pi$ at point Q. Then the difference between the resultant intensities at P and Q will be :
Wave Optics Young's Double Slit Resultant Intensity Formula
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q44
A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be…
Ray Optics and Optical Instruments Refraction and Snell's Law Total Internal Reflection
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q45
Given below are two statements : Statement I : Davisson-Germer experiment establishes the wave nature of electrons. Statement II : If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct…
Dual Nature of Radiation and Matter Matter Waves Davisson-Germer Experiment Analysis
EasyTwo statementsNew idea
Q46
The ratio for the speed of the electron in the $3^{rd}$ orbit of $\mathrm{He^+}$ to the speed of the electron in the $3^{rd}$ orbit of hydrogen atom will be :
Atoms Bohr's Atomic Model Electron Velocity in Orbit
EasySingle correctIdea asked in 2 yearsAsked the year before
Q47
The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Photodiode Reverse Bias Rationale
EasySingle correctIdea asked in 2 yearsAsked the year before
Q48
A signal of 100 THz frequency can be transmitted with maximum efficiency by :
Communication Systems
EasySingle correct
Q49
The difference of speed of light in the two media A and B ( $v_A-v_B$ ) is $2.6\times10^7$ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum…
Ray Optics and Optical Instruments Refraction and Snell's Law Refractive Index and Speed
MediumSingle correctNew ideaIdea asked in 2 years
Q50
A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for $\frac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of G ?
Moving Charges and Magnetism Wheatstone Bridge Kelvin's Method for Galvanometer Resistance
MediumSingle correctNew idea
Q51
A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of…
Laws of Motion Friction Hanging Chain Problem
MediumNumerical valueNew idea
Q52
A 0.5 kg block moving at a speed of 12 $\mathrm{ms^{-1}}$ compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be __________ $\mathrm{Nm^{-1}}$ .
Work, Energy and Power Work and Kinetic Energy Work Done by a Spring Force
MediumNumerical valueNew idea
Q53
The velocity of upper layer of water in a river is 36 $\mathrm{kmh^{-1}}$ . Shearing stress between horizontal layers of water is $10^{-3}\ \mathrm{Nm^{-2}}$ . Depth of the river is __________ m. (Co-efficient of viscosity of water is $10^{-2}$ Pa.s)
Mechanical Properties of Fluids Viscosity Newton's Law of Viscosity
MediumNumerical valueNew idea
Q54
A steam engine intakes 50 g of steam at $100^\circ$ C per minute and cools it down to $20^\circ$ C. If latent heat of vaporization of steam is 540 cal $\mathrm{g^{-1}}$ , then the heat rejected by the steam engine per minute is __________ $\times10^3$ cal.…
Thermal Properties of Matter Calorimetry Latent Heat and Phase Change
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q55
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is __________ cm.
Waves Resonance in Air Columns Overlapping Resonances in Open and Closed Pipes
MediumNumerical valueNew idea
Q56
The equivalent capacitance between points A and B in below shown figure will be __________ $\mu$ F.
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q57
A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is __________ J.
Current Electricity Ohm's Law and Resistance Joule Heating and Power
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q58
The total current supplied to the circuit as shown in figure by the 5 V battery is __________ A.
Current Electricity Kirchhoff's Laws Circuit Symmetry Analysis
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q59
The current in a coil of self inductance 2.0 H is increasing according to I=2 sin( $t^2$ ) A. The amount of energy spent during the period when current changes from 0 to 2 A is __________ J.
Electromagnetic Induction Inductance Energy Stored in Inductors
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q60
A force on an object of mass 100 g is $(10\,\hat{i}+5\hat{j})$ N. The position of that object at t = 2 s is $(a\hat{i}+b\hat{j})$ m after starting from rest. The value of $\frac{a}{b}$ will be __________.
Laws of Motion Newton's Laws of Motion F=ma for Single Body
EasyNumerical valueIdea asked in 6 yearsAsked the year before

Chemistry30 questions

21 easy9 medium0 hard

Q61
Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron ? (A) $\mathrm{NO}$ (B) $\mathrm{N_2}$ (C) $\mathrm{O_2}$ (D) $\mathrm{C_2}$ (E) $\mathrm{B_2}$ Choose the **most appropriate**…
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
MediumOtherIdea asked in 3 yearsAsked the year before
Q62
**Incorrect** statement for Tyndall effect is :
Surface Chemistry Colloids Optical and Kinetic Properties
EasySingle correctIdea asked in 5 yearsAsked the year before
Q63
The pair, in which ions are isoelectronic with $\mathrm{Al^{3+}}$ is :
Classification of Elements and Periodicity in Properties Quantum Numbers Isoelectronic Species Configurations
EasySingle correctNew idea
Q64
Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :
General Principles and Processes of Isolation of Elements Metallurgical Extraction MacArthur-Forrest Cyanide Process
EasySingle correctIdea asked in 2 yearsAsked the year before
Q65
Number of electron deficient molecules among the following $\mathrm{PH_3}$ , $\mathrm{B_2H_6}$ , $\mathrm{CCl_4}$ , $\mathrm{NH_3}$ , $\mathrm{LiH}$ and $\mathrm{BCl_3}$ is
The p-Block Elements Group 13 & 14 Diborane Structure
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q66
Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution ?
The s-Block Elements s-Block Elements Hydration Enthalpy Trends
EasySingle correctIdea asked in 3 yearsAsked the year before
Q67
White precipitate of AgCl dissolves in aqueous ammonia solution due to formation of :
Coordination Compounds Cation Analysis AgCl Dissolution in Ammonia
EasySingle correctNew idea
Q68
Cerium (IV) has a noble gas configuration. Which of the following is **correct** statement about it ?
The d- and f-Block Elements f-Block Elements Cerium(IV) as an Oxidizing Agent
EasySingle correctIdea asked in 3 yearsAsked the year before
Q69
Among the following, which is the strongest oxidizing agent ?
The d- and f-Block Elements d-Block Elements Standard Electrode Potential Trends
EasySingle correctIdea asked in 3 yearsAsked the year before
Q70
The eutrophication of water body results in :
Environmental Chemistry Eutrophication and Dissolved Oxygen Limits
EasySingle correctIdea asked in 3 yearsAsked the year before
Q71
Phenol on reaction with dilute nitric acid, gives two products. Which method will be most efficient for large scale separation ?
Organic Chemistry: Some Basic Principles and Techniques Alcohols and Phenols Phenol Nitration Reagent Effects
MediumSingle correctNew ideaIdea asked in 2 years
Q72
In the following structures, which one is having staggered conformation with maximum dihedral angle ?
Organic Chemistry: Some Basic Principles and Techniques Alkanes and Free Radicals Ethane and Butane Conformers
EasyDiagram based · figureIdea asked in 2 yearsAsked the year before
Q73
The product formed in the following reaction. [figure: $\mathrm{(CH_3)_2C{=}CH_2}$ drawn with two $\mathrm{CH_3}$ on the left carbon and $\mathrm{{=}CH_2}$ , plus H attached to a carbon bearing three $\mathrm{CH_3}$ groups, arrow labelled…
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q74
The IUPAC name of ethylidene chloride is :
Haloalkanes and Haloarenes IUPAC Nomenclature IUPAC-Retained Common Names
EasySingle correctNew idea
Q75
The major product in the reaction [figure: $\mathrm{CH_3-C(CH_3)(CH_3)-Cl}$ (central C with $\mathrm{CH_3}$ above, $\mathrm{CH_3}$ below, $\mathrm{CH_3}$ left, Cl right) + $\mathrm{K^+\ ^-O-C(CH_3)(CH_3)-CH_3}$ (central C with $\mathrm{CH_3}$ above,…
Haloalkanes and Haloarenes Alkenes and Alkynes Saytzeff vs. Hofmann Elimination
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q76
The intermediate X, in the reaction : [figure: $\mathrm{CHCl_3}$ + Aq. NaOH + benzene ring with OH substituent, arrow to [X]; below [X] an arrow labelled (1) NaOH (2) $\mathrm{H^+}$ to a benzene ring with OH and CHO on adjacent ring carbons] is:
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
EasyDiagram based · figureIdea asked in 4 yearsAsked the year before
Q77
In the following reaction : [figure: benzene ring bearing a CH carbon with $\mathrm{H_3C}$ and $\mathrm{CH_3}$ on it, $+\ \mathrm{O_2}\rightarrow$ benzene ring bearing a C carbon with $\mathrm{H_3C}$ , $\mathrm{CH_3}$ and $\mathrm{-O-O-H}$ , then arrow…
Alcohols, Phenols and Ethers Alcohols and Phenols Cumene Hydroperoxide Synthesis
EasyDiagram based · figureNew idea
Q78
The reaction of $\mathrm{R-C(=O)-NH_2}$ with bromine and KOH gives $\mathrm{RNH_2}$ as the end product. Which one of the following is the intermediate product formed in this reaction ?
Amines Hofmann Bromamide Degradation
EasySingle correctIdea asked in 5 yearsAsked the year before
Q79
Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes, because :
Chemistry in Everyday Life Colloids Micelle Formation and CMC
EasySingle correctIdea asked in 3 yearsAsked the year before
Q80
Which one of the following is an example of artificial sweetner ?
Chemistry in Everyday Life Artificial Sweetener Structural Properties and Stability
EasySingle correctIdea asked in 3 years
Q81
The number of N atoms in 681 g of $\mathrm{C_7H_5N_3O_6}$ is $x \times 10^{21}$ . The value of $x$ is __________. ( $\mathrm{N_A} = 6.02 \times 10^{23}\ \mathrm{mol^{-1}}$ ) (Nearest Integer)
Some Basic Concepts of Chemistry Mole Concept Mole and Avogadro Calculations
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q82
The distance between $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions in solid NaCl of density $43.1\ \mathrm{g\ cm^{-3}}$ is __________ $\times 10^{-10}$ m. (Nearest Integer) (Given : $\mathrm{N_A} = 6.02 \times 10^{23}\ \mathrm{mol^{-1}}$ )
The Solid State Crystal Lattices Unit Cell Density
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is $x \times 10^{-8}$ m. The value of $x$ is __________. (Nearest Integer) (Given : Energy of the electron in the first shell of the hydrogen atom is…
Structure of Atom Bohr's Atomic Theory Ionization and Excitation Energy
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q84
The standard entropy change for the reaction $4\mathrm{Fe(s)} + 3\mathrm{O_2(g)} \rightarrow 2\mathrm{Fe_2O_3(s)}$ is $-550\ \mathrm{J\ K^{-1}}$ at 298 K. [Given : The standard enthalpy change for the reaction is $-165\ \mathrm{kJ\ mol^{-1}}$ ]. The…
Thermodynamics (Chemistry)Gibbs Free Energy Gibbs Energy and Equil
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q85
1 L aqueous solution of $\mathrm{H_2SO_4}$ contains 0.02 m mol $\mathrm{H_2SO_4}$ . 50% of this solution is diluted with deionized water to give 1 L solution (A). In solution (A), 0.01 m mol of $\mathrm{H_2SO_4}$ are added. Total m mols of $\mathrm{H_2SO_4}$ …
Some Basic Concepts of Chemistry Mole Concept Molarity of Diluted and Mixed Solutions
MediumNumerical valueNew ideaIdea asked in 2 years
Q86
The standard free energy change ( $\Delta \mathrm{G^\circ}$ ) for 50% dissociation of $\mathrm{N_2O_4}$ into $\mathrm{NO_2}$ at 27°C and 1 atm pressure is $-x\ \mathrm{J\ mol^{-1}}$ . The value of $x$ is __________. (Nearest Integer) [Given :…
Equilibrium Chemical Equilibrium Standard Gibbs Free Energy and Equilibrium Constant
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q87
In a cell, the following reactions take place $\mathrm{Fe^{2+}} \rightarrow \mathrm{Fe^{3+}} + \mathrm{e^-}$ $\mathrm{E^\circ_{Fe^{3+}/Fe^{2+}}} = 0.77\ \mathrm{V}$ $2\mathrm{I^-} \rightarrow \mathrm{I_2} + 2\mathrm{e^-}$ …
Electrochemistry Nernst Equation Standard Cell Potential
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q88
For a given chemical reaction $\gamma_1 \mathrm{A} + \gamma_2 \mathrm{B} \rightarrow \gamma_3 \mathrm{C} + \gamma_4 \mathrm{D}$ Concentration of C changes from 10 mmol $\mathrm{dm^{-3}}$ to 20 mmol $\mathrm{dm^{-3}}$ in 10 seconds. Rate of appearance of D is…
Chemical Kinetics Rate Laws Rate and Stoichiometry
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q89
If $[\mathrm{Cu(H_2O)_4}]^{2+}$ absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for $[\mathrm{Cu(H_2O)_6}]^{2+}$ will be __________ $\times 10^{-21}$ J. [Nearest integer] (Given :…
Coordination Compounds Crystal Field Theory Octahedral Field Splitting
MediumNumerical valueNew ideaIdea asked in 3 years
Q90
Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is __________ $\times 10^{-2}$ g. (Atomic mass of Br = 80 g/mol) [Nearest integer]
Hydrocarbons Mole Concept Mole and Avogadro Calculations
EasyNumerical valueIdea asked in 5 yearsAsked the year before

Maths30 questions

1 easy17 medium12 hard

Q1
Let a circle C touch the lines $\mathrm{L_1}$ : $4x-3y+K_1=0$ and $\mathrm{L_2}$ : $4x-3y+K_2=0$ , $K_1, K_2 \in \mathbf{R}$ . If a line passing through the centre of the circle C intersects $\mathrm{L_1}$ at $(-1, 2)$ and $\mathrm{L_2}$ at $(3, -6)$ , then the…
Conic Sections Circle Tangents Family of Circles Touching a Line
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q2
The value of $\int_0^{\pi} \frac{e^{\cos x}\sin x}{(1+\cos^2 x)(e^{\cos x}+e^{-\cos x})}\,dx$ is equal to :
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q3
Let a, b and c be the length of sides of a triangle ABC such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$ If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $\frac{R}{r}$ is equal to :
Trigonometric Functions Properties of Triangles Inradius and Circumradius
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q4
Let $f:\mathbf{N}\to\mathbf{R}$ be a function such that $f(x+y)=2f(x)\,f(y)$ for natural numbers $x$ and $y$ . If $f(1)=2$ , then the value of $\alpha$ for which $\sum_{k=1}^{10} f(\alpha+k)=\frac{512}{3}(2^{20}-1)$ holds, is :
Sequences and Series AP and GP GP Sum of n terms
MediumSingle correctIdea asked in 5 years
Q5
Let A be a $3\times3$ real matrix such that $A\begin{pmatrix}1\\1\\0\end{pmatrix}=\begin{pmatrix}1\\1\\0\end{pmatrix}$ ; $A\begin{pmatrix}1\\0\\1\end{pmatrix}=\begin{pmatrix}-1\\0\\1\end{pmatrix}$ and…
Determinants Cramer's Rule Parametrizing Infinite Solutions
HardSingle correctNew idea
Q6
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=x^3+x-5$ If $g(x)$ is a function such that $f(g(x))=x$ , $\forall$ 'x' $\in \mathbf{R}$ , then $g'(63)$ is equal to __________.
Continuity and Differentiability Chain Rule Derivative of Inverse Functions via Chain Rule
EasySingle correctIdea asked in 3 years
Q7
Consider the following two propositions : P1 : $\sim(p\to\sim q)$ P2 : $(p\wedge\sim q)\wedge((\sim p)\vee q)$ If the proposition $p\to((\sim p)\vee q)$ is evaluated as FALSE, then :
Mathematical Reasoning
MediumSingle correct
Q8
If $\frac{1}{2\cdot3^{10}}+\frac{1}{2^2\cdot3^9}+\ldots+\frac{1}{2^{10}\cdot3}=\frac{K}{2^{10}\cdot3^{10}}$ , then the remainder when K is divided by 6 is :
Sequences and Series AP and GP GP Sum of n terms
MediumSingle correctIdea asked in 5 years
Q9
Let $f(x)$ be a polynomial function such that $f(x)+f'(x)+f''(x)=x^5+64$ . Then, the value of $\lim_{x\to1}\frac{f(x)}{x-1}$ is equal to :
Limits and Derivatives L'Hopital's Rule Derivative Limit Existence Condition
HardSingle correctNew idea
Q10
Let $E_1$ and $E_2$ be two events such that the conditional probabilities $P(E_1|E_2)=\frac{1}{2}$ , $P(E_2|E_1)=\frac{3}{4}$ and $P(E_1\cap E_2)=\frac{1}{8}$ . Then :
Probability Conditional Probability Independence Criterion
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q11
Let $A=\begin{bmatrix}0&-2\\2&0\end{bmatrix}$ . If M and N are two matrices given by $M=\sum_{k=1}^{10}A^{2k}$ and $N=\sum_{k=1}^{10}A^{2k-1}$ then $MN^2$ is :
Matrices Matrix Multiplication Powers of Skew-Symmetric Matrices
MediumSingle correctNew idea
Q12
Let $g:(0,\infty)\to\mathbf{R}$ be a differentiable function such that $\int\left(\frac{x(\cos x-\sin x)}{e^x+1}+\frac{g(x)\left(e^x+1-xe^x\right)}{(e^x+1)^2}\right)\mathrm{d}x=\frac{x\,g(x)}{e^x+1}+c$ , for all $x>0$ , where c is an arbitrary constant. Then :
Application of Derivatives Monotonicity Trigonometric Monotonicity by Quadrant
HardSingle correctNew idea
Q13
Let $f:\mathbf{R}\to\mathbf{R}$ and $g:\mathbf{R}\to\mathbf{R}$ be two functions defined by $f(x)=\log_e(x^2+1)-e^{-x}+1$ and $g(x)=\frac{1-2e^{2x}}{e^x}$ . Then, for which of the following range of $\alpha$ , the inequality…
Application of Derivatives Monotonicity Monotonicity of Composite Functions
HardSingle correctNew idea
Q14
Let $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$ $a_i>0$ , $i=1,2,3$ be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of $\vec{a}$ on the vector $3\hat{i}+4\hat{j}$ be 7. Let $\vec{b}$ be a vector obtained by…
Vector Algebra Dot Product Vectors with Equal Inclination
HardSingle correctNew idea
Q15
Let $y=y(x)$ be the solution of the differential equation $(x+1)y'-y=e^{3x}(x+1)^2$ , with $y(0)=\frac{1}{3}$ . Then, the point $x=-\frac{4}{3}$ for the curve $y=y(x)$ is :
Differential Equations Linear Differential Equations Finding Extrema directly from LDE
MediumSingle correctNew idea
Q16
If $y=m_1x+c_1$ and $y=m_2x+c_2$ , $m_1\neq m_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$ , then the value of $8|m_1m_2|$ is equal to :
Conic Sections Circle Tangents Common Tangent to Circle and Conic
HardSingle correctIdea asked in 3 yearsAsked the year before
Q17
Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : $x+y+z=5$ . If a line L passing through $(1,-1,-1)$ , parallel to the line PQ meets the plane S at R, then $\mathrm{QR}^2$ is equal to :
Three Dimensional Geometry Point-Plane Distance Image of a Point
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q18
If the solution curve $y=y(x)$ of the differential equation $y^2\mathrm{d}x+(x^2-xy+y^2)\mathrm{d}y=0$ , which passes through the point $(1,1)$ and intersects the line $y=\sqrt{3}x$ at the point $(\alpha,\sqrt{3}\alpha)$ , then value of…
Differential Equations Homogeneous Equations Alternative Substitution x = vy
HardSingle correctNew ideaIdea asked in 2 years
Q19
Let $x=2t$ , $y=\frac{t^2}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $SA\perp BA$ , where A is any point on the conic. If k is the ordinate of the centroid of the $\Delta SAB$ , then $\lim_{t\to1}k$ is equal to :
Conic Sections General Conic Section Focus-Directrix Form Extraction
HardSingle correctIdea asked in 3 yearsAsked the year before
Q20
Let a circle C in complex plane pass through the points $z_1=3+4i$ , $z_2=4+3i$ and $z_3=5i$ . If $z(\neq z_1)$ is a point on C such that the line through $z$ and $z_1$ is perpendicular to the line through $z_2$ and $z_3$ , then $\arg(z)$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Geometric Rotation
HardSingle correctIdea asked in 2 years
Q21
Let $C_r$ denote the binomial coefficient of $x^r$ in the expansion of $(1+x)^{10}$ . If for $\alpha,\beta\in\mathbf{R}$ , $C_1+3\cdot2\,C_2+5\cdot3\,C_3+\ldots$ upto 10 terms…
Binomial Theorem Binomial Coefficients AP-Weighted Coefficient Sums
HardNumerical valueIdea asked in 2 yearsAsked the year before
Q22
The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is __________.
Permutations and Combinations Fundamental Counting Principle
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q23
Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$ , where $|\vec{a}|=4$ , $|\vec{b}|=3$ and $\theta\in\left(\frac{\pi}{4},\frac{\pi}{3}\right)$ . Then…
Vector Algebra Cross Product Lagrange's Identity
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q24
Let the abscissae of the two points P and Q be the roots of $2x^2-rx+p=0$ and the ordinates of P and Q be the roots of $x^2-sx-q=0$ . If the equation of the circle described on PQ as diameter is $2(x^2+y^2)-11x-14y-22=0$ , then $2r+s-2q+p$ is equal to…
Conic Sections General Conic Section Condition for a Circle
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q25
The number of values of $x$ in the interval $\left(\frac{\pi}{4},\frac{7\pi}{4}\right)$ for which $14\mathrm{cosec}^2x-2\sin^2x=21-4\cos^2x$ holds, is __________.
Trigonometric Functions General Solutions Reciprocal Function Conversion
MediumNumerical valueNew idea
Q26
For a natural number n, let $\alpha_n=19^n-12^n$ . Then, the value of $\frac{31\alpha_9-\alpha_{10}}{57\alpha_8}$ is __________.
Sequences and Series Quadratic Roots Higher Degree Evaluation via Root Substitution
MediumNumerical valueNew ideaIdea asked in 2 years
Q27
Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)(2+x^{25})\right)^{\frac{1}{50}}$ . If the function $g(x)=f(f(f(x)))+f(f(x))$ , then the greatest integer less than or equal to $g(1)$ is __________.
Relations and Functions
MediumNumerical value
Q28
Let the lines $\mathrm{L_1}$ : $\vec{r}=\lambda\left(\hat{i}+2\hat{j}+3\hat{k}\right)$ , $\lambda\in\mathbf{R}$ $\mathrm{L_2}$ : $\vec{r}=\left(\hat{i}+3\hat{j}+\hat{k}\right)+\mu\left(\hat{i}+\hat{j}+5\hat{k}\right)$ ; $\mu\in\mathbf{R}$ , intersect at the…
Three Dimensional Geometry Planes in 3D Plane Through Point Parallel to Two Vectors
MediumNumerical valueNew idea
Q29
Let A be a $3\times3$ matrix having entries from the set $\{-1,0,1\}$ . The number of all such matrices A having sum of all the entries equal to 5, is __________.
Permutations and Combinations Fundamental Counting Principle
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q30
The greatest integer less than or equal to the sum of first 100 terms of the sequence $\frac{1}{3},\frac{5}{9},\frac{19}{27},\frac{65}{81},\ldots$ is equal to __________.
Sequences and Series AP and GP GP Sum of n terms
MediumNumerical valueIdea asked in 5 years

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.