JEE Main 2022 · June session

JEE Main 25 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: 62; 10 questions with a figure

Key findings · 25 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 9 of 30 rated hard; Physics had the most easy questions (15 of 30).
3
25 questions tested a new idea, one no earlier year had asked: 34% of the 73 questions tagged to an idea.
4
41 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 (51% 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), Biomolecules 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 15Hard 0

Top chapters

Laws of Motion3 Q
Alternating Current2 Q
Current Electricity2 Q
Electrostatic Potential and Capacitance2 Q
Kinetic Theory2 Q
Motion in a Plane2 Q

Chemistry

30 Q · 10 numerical

Easy 8Medium 19Hard 3

Top chapters

Maths

30 Q · 10 numerical

Easy 4Medium 17Hard 9

Top chapters

Conic Sections4 Q
Application of Derivatives3 Q
Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Integrals2 Q
Three Dimensional Geometry2 Q

Question format

Single correct44 Q
Numerical value30 Q
Diagram based7 Q
Assertion–reason4 Q
Two statements2 Q
Match the list2 Q
Other1 Q

What each question asks you to do

Calculation35 Q
Multi-step20 Q
Application15 Q
Conceptual9 Q
Recall8 Q
Data or graph2 Q
Diagram reading1 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 easy15 medium0 hard

Q31
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls $A$ and $B$ thrown with same velocity ‘ $u$ ’ at two different angles with horizontal attained the same range $R$ . If $A$ and…
Motion in a Plane Projectile Motion Complementary Angles Range and Ratios
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q32
Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_P(t) = \alpha t + \beta t^2$ and $X_Q(t) = ft - t^2$ . At what time, both the buses have same velocity ?
Motion in a Straight Line Kinematics in 1D Calculus in Kinematics
EasySingle correctIdea asked in 5 yearsAsked the year before
Q33
A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$ . The coefficient of static friction between the…
Laws of Motion Circular Motion Coin Slipping on a Rotating Disc
EasySingle correctNew ideaIdea asked in 2 years
Q34
A solid metallic cube having total surface area $24\ \mathrm{m}^2$ is uniformly heated. If its temperature is increased by $10^\circ\mathrm{C}$ , calculate the increase in volume of the cube. (Given $\alpha = 5.0 \times 10^{-4}\ ^\circ\mathrm{C}^{-1}$ ) .
Thermal Properties of Matter Thermal Expansion Volume Expansion
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q35
A copper block of mass 5.0 kg is heated to a temperature of $500^\circ\mathrm{C}$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : $0.39\ \mathrm{J\ g^{-1}\ ^\circ C^{-1}}$ and latent heat of…
Thermal Properties of Matter Calorimetry Latent Heat and Phase Change
EasySingle correctIdea asked in 3 yearsAsked the year before
Q36
The ratio of specific heats $\left(\frac{C_P}{C_V}\right)$ in terms of degree of freedom ( $f$ ) is given by :
Kinetic Theory Kinetic Theory of Gases Gamma and Degrees of Freedom
EasySingle correctIdea asked in 5 yearsAsked the year before
Q37
For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $P(R,\theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$ -axis and $v$ is uniform speed) :
Motion in a Plane Kinematics in 2D Uniform Circular Motion
EasySingle correctNew ideaIdea asked in 2 years
Q38
Two metallic plates form a parallel plate capacitor. The distance between the plates is ‘ $d$ ’. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Inserted Conducting Slab
EasySingle correctNew ideaIdea asked in 2 years
Q39
Two cells of same emf but different internal resistances $r_1$ and $r_2$ are connected in series with a resistance $R$ . The value of resistance $R$ , for which the potential difference across second cell is zero, is :
Current Electricity Kirchhoff's Laws Series Combination of Cells
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q40
Given below are two statements : Statement – I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement – II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments…
Magnetism and Matter
MediumTwo statements
Q41
A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to
Moving Charges and Magnetism Ampere's Circuital Law Ideal Infinite Solenoid
EasySingle correctIdea asked in 4 yearsAsked the year before
Q42
A sinusoidal voltage $V(t)$ = 210 sin 3000 $t$ volt is applied to a series LCR circuit in which $L$ = 10 $mH$ , $C$ =25 µ $F$ and $R$ = 100 $\Omega$ . The phase difference ( $\Phi$ )between the applied voltage and resultant current will be :
Alternating Current Phasor Diagrams Impedance Triangle Construction
MediumSingle correctIdea asked in 4 years
Q43
The electromagnetic waves travel in a medium at a speed of $2.0 \times 10^8$ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :
Electromagnetic Waves
EasySingle correct
Q44
The interference pattern is obtained with two coherent light sources of intensity ratio 4:1. And the ratio $\frac{I_{\mathrm{max}} + I_{\mathrm{min}}}{I_{\mathrm{max}} - I_{\mathrm{min}}}$ is $\frac{5}{x}$ . Then, the value of $x$ will be equal to :
Wave Optics Young's Double Slit Intensity Ratio from Slit Widths
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q45
A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster’s angle. Choose the most suitable option for the phenomenon related to the prism.
Wave Optics Polarization Brewster's Angle
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q46
A proton, a neutron, an electron and an $\alpha$ -particle have same energy. If $\lambda_p, \lambda_n, \lambda_e$ and $\lambda_\alpha$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct…
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q47
Which of the following figure represents the variation of $\ln\left(\frac{R}{R_0}\right)$ with $\mathrm{l}_n A$ (if $R$ = radius of a nucleus and $A$ = its mass number)
Nuclei Nuclear Binding Energy Nuclear Radius and Density
EasyDiagram based · figureIdea asked in 5 years
Q48
Identify the logic operation performed by the given circuit :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q49
Match List I with List II List I | List II A. Facsimile | I. Static Document Image B. Guided media Channel | II. Local Broadcast Radio C. Frequency Modulation | III. Rectangular wave D. Digital Signal | IV. Optical Fiber Choose the correct answer from the…
Communication Systems
EasyMatch the list
Q50
If $n$ represents the actual number of deflections in a converted galvanometer of resistance $G$ and shunt resistance $S$ . Then the total current $I$ when its figure of merit is $K$ will be :
Moving Charges and Magnetism
MediumSingle correct
Q51
For $z =a^2x^3y^{\frac{1}{2}}$ , where ‘ $a$ ’ is a constant. If percentage error in measurement of ‘ $x$ ’ and ‘ $y$ ’ are 4% and 12%, respectively, then the percentage error for ‘ $z$ ’ will be ____________%.
Units and Measurements Ohm's Law and Resistance Error Analysis in Ohm's Law
EasyNumerical valueIdea asked in 5 years
Q52
A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then…
Laws of Motion Circular Motion Friction on Unbanked Flat Curves
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q53
A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F = \sqrt{x}\,N$ as shown in figure. The value of $x$ = ____________.
Laws of Motion Newton's Laws of Motion Force Resolution on Inclined Planes
MediumNumerical value · figureNew idea
Q54
Moment of Inertia (M.I.) of four bodies having same mass ‘ $M$ ’ and radius ‘ $2R$ ’ are as follows : $\mathrm{I}_1$ = M.I. of solid sphere about its diameter $\mathrm{I}_2$ = M.I. of solid cylinder about its axis $\mathrm{I}_3$ = M.I. of solid circular disc…
System of Particles and Rotational Motion Moment of Inertia MOI of Standard Shapes
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q55
Two satellites $S_1$ and $S_2$ are revolving in circular orbits around a planet with radius $R_1$ = 3200 km and $R_2$ = 800 km respectively. The ratio of speed of satellite $S_1$ to the speed of satellite $S_2$ in their respective orbits would be $\frac{1}{x}$ …
Gravitation Orbital Mechanics Orbital Velocity
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q56
When a gas filled in a closed vessel is heated by raising the temperature by $1^\circ\mathrm{C}$ , its pressure increases by 0.4%. The initial temperature of the gas is ____________ $K$ .
Kinetic Theory Ideal Gas Laws Individual Gas Laws
MediumNumerical valueNew ideaIdea asked in 2 years
Q57
27 identical drops are charged at $22V$ each. They combine to form a bigger drop. The potential of the bigger drop will be ____________ $V$ .
Electrostatic Potential and Capacitance
MediumNumerical value
Q58
The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________%.
Current Electricity Ohm's Law and Resistance Resistance of Stretched Wires
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q59
In a series LCR circuit, the inductance, capacitance and resistance are $L$ = 100 mH, C= 100 µ $F$ and $R$ = $10\ \Omega$ respectively. They are connected to an AC source of voltage 220 $V$ and frequency of 50 Hz. The approximate value of current in the circuit…
Alternating Current LCR Resonance Impedance at Resonance
EasyNumerical value · figureIdea asked in 3 yearsAsked the year before
Q60
In an experiment of $CE$ configuration of n-p-n transistor, the transfer characteristics are observed as given in figure. If the input resistance is 200 $\Omega$ and output resistance is 60 $\Omega$ , the voltage gain in this experiment will be ____________.
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors CE Amplifier Voltage Gain
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before

Chemistry30 questions

8 easy19 medium3 hard

Q61
The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is: [Given: The threshold frequency of platinum is $1.3 \times 10^{15}\ \mathrm{s^{-1}}$ and…
Structure of Atom Photoelectric Effect Work Function and Threshold
EasySingle correctNew ideaIdea asked in 4 years
Q62
At 25°C and 1 atm pressure, the enthalpy of combustion of benzene (l) and acetylene (g) are -3268 $\mathrm{kJ\ mol^{-1}}$ and -1300 $\mathrm{kJ\ mol^{-1}}$ , respectively. The change in enthalpy for the reaction 3 $\mathrm{C_2H_2}$ (g)…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Formation and Combustion
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q63
Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by 0.2 °C. The percentage association of solute A in water, is : [Given: Molar mass of A = 93 $\mathrm{g\ mol^{-1}}$ . Molal depression…
Solutions Colligative Properties Degree of Association from Van't Hoff Factor
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q64
The $\mathrm{K_{sp}}$ for bismuth sulphide ( $\mathrm{Bi_2S_3}$ ) is $1.08 \times 10^{-73}$ . The solubility of $\mathrm{Bi_2S_3}$ in $\mathrm{mol\ L^{-1}}$ at 298 K is
Equilibrium Solubility Product Solubility-Ksp Relationship
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q65
Match List I with List II. List I | List II A. Zymase | I. Stomach B. Diastase | II. Yeast C. Urease | III. Malt D. Pepsin | IV. Soyabean Choose the correct answer from the options given below:
Biomolecules
EasyMatch the list
Q66
The correct order of electron gain enthalpies of Cl, F, Te and Po is
Classification of Elements and Periodicity in Properties Periodic Trends Electron Gain Enthalpy
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q67
Given below are two statements. Statement I: During electrolytic refining, blister copper deposits precious metals. Statement II: In the process of obtaining pure copper by electrolysis method, copper blister is used to make the anode. In the light of the…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Metal Refining Techniques
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q68
Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : The amphoteric nature of water is explained by using Lewis acid/base concept. Reason R : Water acts as an acid with $\mathrm{NH_3}$ and as a…
Equilibrium
MediumAssertion–reason
Q69
The correct order of reduction potentials of the following pairs is A. $\mathrm{Cl_2/Cl^{-}}$ B. $\mathrm{I_2/I^{-}}$ C. $\mathrm{Ag^{+}/Ag}$ D. $\mathrm{Na^{+}/Na}$ E. $\mathrm{Li^{+}/Li}$ Choose the correct answer from the options given below.
Electrochemistry Nernst Equation Standard Cell Potential
EasyOtherIdea asked in 7 yearsAsked the year before
Q70
The number of bridged oxygen atoms present in compound B formed from the following reactions is $\mathrm{Pb(NO_3)_2} \xrightarrow{673\ \mathrm{K}} \mathrm{A + PbO + O_2}$ $\mathrm{A} \xrightarrow{\mathrm{Dimerise}} \mathrm{B}$
The p-Block Elements Stoichiometry Thermal Decomposition of Nitrates
MediumSingle correctNew idea
Q71
The metal ion (in gaseous state) with lowest spin-only magnetic moment value is
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q72
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Polluted water may have a value of BOD of the order of 17 ppm. Reason R: BOD is a measure of oxygen required to oxidise both the bio-degradable…
Environmental Chemistry Water Quality BOD and COD
MediumAssertion–reasonIdea asked in 4 yearsAsked the year before
Q73
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A mixture contains benzoic acid and napthalene. The pure benzoic acid can be separated out by the use of benzene. Reason R: Benzoic acid is…
Organic Chemistry: Some Basic Principles and Techniques
MediumAssertion–reason
Q74
During halogen test, sodium fusion extract is boiled with concentrated $\mathrm{HNO_3}$ to
Organic Chemistry: Some Basic Principles and Techniques
MediumSingle correct
Q75
Amongst the following, the major product of the given chemical reaction is [drawn: six-membered ring containing one O, with a double bond drawn on the ring edge on the side next to the O] $\xrightarrow[\mathrm{CH_3OH}]{\mathrm{Br_2}}$ Major Product
Hydrocarbons Alkenes and Alkynes Halohydrin Formation Regiochemistry
HardDiagram based · figureIdea asked in 2 yearsAsked the year before
Q76
In the given reaction $2\mathrm{A}$ $\xrightarrow[\text{(iii) } \mathrm{H_2O\ /\ H^+}]{\text{(i) 2 Mg, THF; (ii) Methyl benzoate}}$ [drawn product: central C bearing OH on top and three benzene rings attached, one at left, one at right, one at bottom] ‘A’…
Alcohols, Phenols and Ethers Nucleophilic Addition Grignard Reagent Addition
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q77
Which of the following conditions or reaction sequence will NOT give acetophenone as the major product ?
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Nucleophilic Acyl Substitution
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q78
The major product formed in the following reaction, is [drawn: zigzag carbon chain with a methyl-type branch at the left end, ending in OH] + [drawn: six-membered ring with one O and a double bond on the ring edge next to the O] $\xrightarrow{\mathrm{H^+}}$
Alcohols, Phenols and Ethers
HardDiagram based · figure
Q79
Which of the following ketone will NOT give enamine on treatment with secondary amines? [where t-Bu is –C(CH $_3$ ) $_3$ ]
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Enamine Formation
MediumDiagram based · figureNew idea
Q80
An antiseptic dettol is a mixture of two compounds ‘A’ and ‘B’ where A has 6 $\pi$ electrons and B has 2 $\pi$ electrons. What is ‘B’?
Chemistry in Everyday Life Chemical Composition of Dettol
MediumSingle correctNew idea
Q81
A protein ‘A’ contains 0.30% of glycine (molecular weight 75). The minimum molar mass of the protein ‘A’ is __________ $\times 10^3\ \mathrm{g\ mol^{-1}}$ [nearest integer]
Biomolecules Mole Concept Minimum Molar Mass Calculation
EasyNumerical valueNew idea
Q82
A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is 27 °C. At 03:00 pm, when the temperature is 45°C, the pressure in the tank will be ________ atm. [nearest integer]
States of Matter Ideal Gas Laws Individual Gas Laws
EasyNumerical valueNew ideaIdea asked in 2 years
Q83
Amongst $\mathrm{BeF_2}$ , $\mathrm{BF_3}$ , $\mathrm{H_2O}$ , $\mathrm{NH_3}$ , $\mathrm{CCl_4}$ and HCl, the number of molecules with non-zero net dipole moment is __________.
Chemical Bonding and Molecular Structure VSEPR Theory Net Dipole Moment from VSEPR Symmetry
MediumNumerical valueIdea asked in 4 years
Q84
At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is __________. [integer answer]
Chemical Kinetics Rate Laws Nth-Order Half-Life Proportionality
EasyNumerical valueNew idea
Q85
A solution of $\mathrm{Fe_2(SO_4)_3}$ is electrolyzed for ‘x’ min with a current of 1.5 A to deposit 0.3482 g of Fe. The value of x is ________. [nearest integer] Given : 1 F = 96500 $\mathrm{C\ mol^{-1}}$ Atomic mass of Fe = 56 $\mathrm{g\ mol^{-1}}$
Electrochemistry Faraday's Laws of Electrolysis Faraday's First Law
EasyNumerical valueNew ideaIdea asked in 2 years
Q86
Consider the following reactions : $\mathrm{PCl_3 + H_2O \rightarrow A + HCl}$ $\mathrm{A + H_2O \rightarrow B + HCl}$ The number of ionisable protons present in the product B is ________.
The p-Block Elements Group 15 & 16 Hydrolysis of Phosphorus Halides
MediumNumerical valueNew idea
Q87
Amongst $\mathrm{FeCl_3.3H_2O}$ , $\mathrm{K_3[Fe(CN)_6]}$ and $\mathrm{[Co(NH_3)_6]Cl_3}$ , the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ________ B.M. [nearest integer]
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q88
The Novolac polymer has mass of 963 g. The number of monomer units present in it are ________
Polymers Novolac Structure and Role
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q89
How many of the given compounds will give a positive Biuret test __________ ? Glycine, Glycylalanine, Tripeptide, Biuret
Biomolecules
MediumNumerical value
Q90
The neutralization occurs when 10 mL of 0.1M acid ‘A’ is allowed to react with 30 mL of 0.05 M base $\mathrm{M(OH)_2}$ . The basicity of the acid ‘A’ is __________. [M is a metal]
Some Basic Concepts of Chemistry Mole Concept Normality and n-factor Calculation
EasyNumerical valueIdea asked in 4 yearsAsked the year before

Maths30 questions

4 easy17 medium9 hard

Q1
Let $A = \{x \in \mathbb{R} : |x+1| < 2\}$ and $B = \{x \in \mathbb{R} : |x-1| \geq 2\}$ . Then which one of the following statements is NOT true ?
Relations and Functions Sets and Relations Intervals as Subsets of R
EasySingle correctIdea asked in 3 yearsAsked the year before
Q2
Let $a, b \in \mathbb{R}$ be such that the equation $ax^2 - 2bx + 15 = 0$ has a repeated root $\alpha$ . If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2bx + 21 = 0$ , then $\alpha^2 + \beta^2$ is equal to:
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q3
Let $z_1$ and $z_2$ be two complex numbers such that $\overline{z_1} = i\overline{z_2}$ and $\arg\left(\frac{z_1}{\overline{z_2}}\right) = \pi$ . Then
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Principal Argument Arithmetic
MediumSingle correctIdea asked in 2 years
Q4
The system of equations $-kx + 3y - 14z = 25$ $-15x + 4y - kz = 3$ $-4x + y + 3z = 4$ is consistent for all $k$ in the set
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
$\lim_{x \to \frac{\pi}{2}} \left( \tan^2 x \left( \left(2\sin^2 x + 3\sin x + 4\right)^{\frac{1}{2}} - \left(\sin^2 x + 6\sin x + 2\right)^{\frac{1}{2}} \right) \right)$ is equal to
Limits and Derivatives L'Hopital's Rule Conjugation vs L'Hopital for Radicals
HardSingle correctIdea asked in 3 yearsAsked the year before
Q6
The area of the region enclosed between the parabolas $y^2 = 2x - 1$ and $y^2 = 4x - 3$ is
Application of Integrals Area Under Curves Area Between Two Standard Parabolas
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q7
The coefficient of $x^{101}$ in the expression $(5+x)^{500} + x(5+x)^{499} + x^2(5+x)^{498} + ....... + x^{500}$ , $x > 0$ , is
Binomial Theorem Binomial Coefficients Geometric Progression of Expansions
MediumSingle correctNew ideaIdea asked in 2 years
Q8
The sum $1 + 2 \cdot 3 + 3 \cdot 3^2 + ....... + 10 \cdot 3^9$ is equal to :
Sequences and Series Arithmetico-Geometric Series Sum of Finite AGP
EasySingle correctNew ideaIdea asked in 2 years
Q9
Let $P$ be the plane passing through the intersection of the planes $\vec{r} \cdot \left(\hat{i} + 3\hat{j} - \hat{k}\right) = 5$ and $\vec{r} \cdot \left(2\hat{i} - \hat{j} + \hat{k}\right) = 3$ , and the point $(2, 1, -2)$ . Let the position vectors of the…
Three Dimensional Geometry Planes in 3D Relative Position of Two Points
MediumSingle correctNew idea
Q10
A circle touches both the $y$ -axis and the line $x + y = 0$ . Then the locus of its center is:
Conic Sections
MediumSingle correct
Q11
Water is being filled at the rate of $1\ \mathrm{cm}^3 / \mathrm{sec}$ in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in $\mathrm{cm}^2 / \mathrm{sec}$ ) at…
Application of Derivatives Chain Rule Chain Rule in Related Rates
MediumSingle correctIdea asked in 2 years
Q12
If $b_n = \int_0^{\frac{\pi}{2}} \frac{\cos^2 nx}{\sin x}\,dx$ , $n \in \mathbb{N}$ , then
Integrals Definite Integral Properties Reduction Formulae in Definite Integrals
HardSingle correctIdea asked in 4 yearsAsked the year before
Q13
If $y = y(x)$ is the solution of the differential equation $2x^2 \frac{dy}{dx} - 2xy + 3y^2 = 0$ such that $y(e) = \frac{e}{3}$ , then $y(1)$ is equal to
Differential Equations Homogeneous Equations Finding Particular Solutions
MediumSingle correctNew idea
Q14
If the angle made by the tangent at the point $(x_0, y_0)$ on the curve $x = 12\,(t + \sin t \cos t)$ , $y = 12\,(1 + \sin t)^2$ , $0 < t < \frac{\pi}{2}$ , with the positive $x$ -axis is $\frac{\pi}{3}$ , then $y_0$ is equal to:
Application of Derivatives Tangents and Normals Tangents to Parametric Curves
MediumSingle correctNew idea
Q15
The value of $2\sin(12^\circ) - \sin(72^\circ)$ is :
Trigonometric Functions Trigonometric Identities Values of Non-Standard Specific Angles
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark $n$ is $\frac{1}{n}$ . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :
Probability
HardSingle correct
Q17
The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow ((\sim p) \vee q)$ is logically equivalent to :
Mathematical Reasoning
EasySingle correct
Q18
If the line $y = 4 + kx$ , $k > 0$ , is the tangent to the parabola $y = x - x^2$ at the point $P$ and $V$ is the vertex of the parabola, then the slope of the line through $P$ and $V$ is:
Conic Sections Tangents and Normals Condition for a Line to Touch a Curve
MediumSingle correctNew idea
Q19
The value of $\tan^{-1}\left(\frac{\cos\left(\frac{15\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right)$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Periodic Reduction of sin-1(sin x) and cos-1(cos x)
EasySingle correctNew ideaIdea asked in 2 years
Q20
The line $y = x + 1$ meets the ellipse $\frac{x^2}{4} + \frac{y^2}{2} = 1$ at two points $P$ and $Q$ . If $r$ is the radius of the circle with $PQ$ as diameter then $(3r)^2$ is equal to :
Conic Sections
MediumSingle correct
Q21
Let $A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix}$ and $B = \begin{pmatrix} -1 & 2 \\ -1 & 2 \end{pmatrix}$ . Then the number of elements in the set $\{(n, m) : n, m \in \{1, 2, ........, 10\}$ and $nA^n + mB^m = I\ \}$ is ____________.
Matrices Matrix Multiplication Idempotent and Nilpotent Matrices
MediumNumerical valueNew ideaIdea asked in 2 years
Q22
Let $f(x) = \left[2x^2 + 1\right]$ and $g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}$ , where $[t]$ is the greatest integer $\leq t$ . Then, in the open interval $(-1, 1)$ , the number of points where $fog$ is discontinuous is equal to…
Continuity and Differentiability Continuity and Differentiability of Composite Functions
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q23
The value of $b > 3$ for which $12\int_3^b \frac{1}{(x^2 - 1)(x^2 - 4)}\,dx = \log_e\left(\frac{49}{40}\right)$ , is equal to ____________.
Integrals
MediumNumerical value
Q24
If the sum of the co-efficients of all the positive even powers of $x$ in the binomial expansion of $\left(2x^3 + \frac{3}{x}\right)^{10}$ is $5^{10} - \beta \cdot 3^9$ , then $\beta$ is equal to ______________.
Binomial Theorem Binomial Coefficients Sum of Even and Odd Coefficients
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q25
If the mean deviation about the mean of the numbers 1, 2, 3, ....., $n$ , where $n$ is odd, is $\frac{5(n+1)}{n}$ , then $n$ is equal to ______________.
Statistics
MediumNumerical value
Q26
Let $\vec{b} = \hat{i} + \hat{j} + \lambda\hat{k}$ , $\lambda \in \mathbb{R}$ . If $\vec{a}$ is a vector such that $\vec{a} \times \vec{b} = 13\hat{i} - \hat{j} - 4\hat{k}$ and $\vec{a} \cdot \vec{b} + 21 = 0$ , then…
Vector Algebra Cross Product Simultaneous Cross and Dot Equations
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q27
The total number of three-digit numbers, with one digit repeated exactly two times, is ____________.
Permutations and Combinations Permutations of Distinct Objects
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q28
Let $f(x) = |(x-1)(x^2 - 2x - 3)| + x - 3$ , $x \in \mathbb{R}$ . If $m$ and $M$ are respectively the number of points of local minimum and local maximum of $f$ in the interval $(0, 4)$ , then $m + M$ is equal to ____________.
Application of Derivatives Maxima and Minima Extrema of Modulus Functions
HardNumerical valueNew idea
Q29
Let the eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $\frac{5}{4}$ . If the equation of the normal at the point $\left(\frac{8}{\sqrt{5}}, \frac{12}{5}\right)$ on the hyperbola is $8\sqrt{5}x + \beta y = \lambda$ , then…
Conic Sections Normals to Conics Hyperbola Normal Point Form
HardNumerical valueIdea asked in 3 years
Q30
Let $l_1$ be the line in $xy$ -plane with $x$ and $y$ intercepts $\frac{1}{8}$ and $\frac{1}{4\sqrt{2}}$ respectively, and $l_2$ be the line in $zx$ -plane with $x$ and $z$ intercepts $-\frac{1}{8}$ and $-\frac{1}{6\sqrt{3}}$ respectively. If $d$ is the…
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
HardNumerical valueIdea asked in 5 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.