JEE Main 2022 · June session

JEE Main 27 June 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 7 were rated hard and 31 easy. Its hard-question count was the 24th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 7; 8% of the shift
Chapters asked: 70; 8 questions with a figure

Key findings · 27 Jun 2022, Shift 1

1
7 hard questions (8%): the 24th 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 5 of 30 rated hard; Physics had the most easy questions (14 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
43 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
45 shared an idea with another 2022 shift (58% 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), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 14Medium 16Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 14Medium 14Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 22Hard 5

Top chapters

Conic Sections3 Q
Application of Derivatives2 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q

Question format

Single correct42 Q
Numerical value30 Q
Match the list8 Q
Diagram based4 Q
Two statements3 Q
Assertion–reason2 Q
Other1 Q

What each question asks you to do

Calculation34 Q
Multi-step28 Q
Recall11 Q
Application8 Q
Conceptual8 Q
Data or graph1 Q

Most common: Calculation.

Against the other 2022 shifts

This shift next to the 23 other 2022 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
24 Jun, Shift 1	89	29%	17%	34%	31%	37%
24 Jun, Shift 2	90	40%	14%	33%	39%	36%
25 Jun, Shift 1	90	44%	13%	33%	33%	30%
25 Jun, Shift 2	90	30%	13%	33%	34%	22%
26 Jun, Shift 1	89	34%	16%	34%	37%	32%
26 Jun, Shift 2	90	30%	13%	33%	36%	27%
27 Jun, Shift 1	90	34%	8%	33%	38%	31%
27 Jun, Shift 2	90	32%	17%	33%	34%	46%
28 Jun, Shift 1	90	32%	12%	33%	38%	27%
28 Jun, Shift 2	90	30%	17%	33%	33%	31%
29 Jun, Shift 1	90	41%	11%	33%	36%	30%
29 Jun, Shift 2	88	35%	9%	33%	41%	30%
30 Jun, Shift 1	90	36%	13%	33%	27%	27%
25 Jul, Shift 1	88	28%	15%	33%	38%	38%
25 Jul, Shift 2	90	37%	12%	33%	33%	33%
26 Jul, Shift 1	90	27%	13%	33%	34%	31%
26 Jul, Shift 2	89	37%	16%	34%	41%	38%
27 Jul, Shift 1	89	29%	15%	34%	30%	32%
27 Jul, Shift 2	88	19%	15%	33%	40%	35%
28 Jul, Shift 1	90	36%	17%	33%	36%	30%
28 Jul, Shift 2	90	28%	14%	33%	40%	28%
29 Jul, Shift 1	90	31%	22%	33%	41%	37%
29 Jul, Shift 2	90	39%	12%	33%	48%	32%
30 Jul, Shift 2	90	30%	17%	33%	36%	33%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open30 this shift3084 · 33%33%8/830298716720359538199224
Open30 this shift3065 · 33%33%8/829299715710354533200225

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Every question

All 90 questions of this shift

The opening words of each question, with its chapter, topic, idea and how hard it was. Open one for the full text, options and the official answer. “New idea” means no earlier year had tested it.

Subject

Difficulty

Idea

Find

90 of 90 questions

Physics30 questions

14 easy16 medium0 hard

Q31
A projectile is launched at an angle ‘ $\alpha$ ’ with the horizontal with a velocity $20\ \mathrm{ms^{-1}}$ . After $10\ \mathrm{s}$ , its inclination with horizontal is ‘ $\beta$ ’. The value of $\tan\beta$ will be : ( $g=10\ \mathrm{ms^{-2}}$ ).
Motion in a Plane Projectile Motion Instantaneous Projectile Velocity
MediumSingle correctNew ideaIdea asked in 3 years
Q32
A girl standing on road holds her umbrella at $45^\circ$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}\ \mathrm{kmh^{-1}}$ , the rain drops hit her head vertically. The speed of rain drops with…
Motion in a Plane Relative Velocity Rain-Man Problems
MediumSingle correctNew idea
Q33
A silver wire has a mass $(0.6\pm0.006)$ g, radius $(0.5\pm0.005)$ mm and length $(4\pm0.04)$ cm. The maximum percentage error in the measurement of its density will be :
Units and Measurements Ohm's Law and Resistance Error Analysis in Ohm's Law
EasySingle correctIdea asked in 5 years
Q34
A system of two blocks of masses $m=2$ kg and $M=8$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks…
Laws of Motion Friction Two-Block Friction Systems
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q35
Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates $(0, 0)$ cm and $(x, 0)$ cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which…
System of Particles and Rotational Motion Center of Mass Discrete System COM
EasySingle correctNew ideaIdea asked in 3 years
Q36
A $72\ \Omega$ galvanometer is shunted by a resistance of $8\ \Omega$ . The percentage of the total current which passes through the galvanometer is :
Moving Charges and Magnetism Kirchhoff's Laws Current Division Rule
EasySingle correctIdea asked in 3 yearsAsked the year before
Q37
Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements,…
Gravitation
EasyTwo statements
Q38
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass ? (Assume the collision to be head-on elastic collision)
Work, Energy and Power Collisions Fractional Kinetic Energy Transfer
EasySingle correctIdea asked in 2 yearsAsked the year before
Q39
The velocity of a small ball of mass ‘m’ and density $d_1$ , when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_2$ , then the viscous force acting on the ball, will be :
Mechanical Properties of Fluids Viscosity Terminal Velocity Calculation
MediumSingle correctNew ideaIdea asked in 3 years
Q40
The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is : [Permeability of free space $\mu_0=4\pi\times10^{-7}$ Wb/A-m]
Magnetism and Matter
EasySingle correct
Q41
The current flowing through an ac circuit is given by $I=5\sin(120\pi t)$ A How long will the current take to reach the peak value starting from zero ?
Alternating Current RMS and Peak Values Time from Zero to Peak
EasySingle correctNew ideaIdea asked in 2 years
Q42
Match List - I with List - II : List - I List - II (a) Ultravoilet rays (i) Study crystal structure (b) Microwaves (ii) Greenhouse effect (c) Infrared waves (iii) Sterilizing surgical instrument (d) X-rays (iv) Radar system Choose the correct answer from the…
Electromagnetic Waves
EasyMatch the list
Q43
An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $(\lambda_\alpha:\lambda_{C12})$ is :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q44
A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.
Electric Charges and Fields Electric Field Field of Parallel Charged Sheets
MediumSingle correctNew ideaIdea asked in 2 years
Q45
The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :
Oscillations SHM Equations Phase and Initial Conditions
EasySingle correctIdea asked in 3 yearsAsked the year before
Q46
An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :
Waves Doppler Effect Moving Observer Cases
EasySingle correctNew idea
Q47
Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$ . The incident angle is twice that of refracting angle. Then, the angle of incidence will be :
Ray Optics and Optical Instruments Refraction and Snell's Law Snell's Law Application
MediumSingle correctIdea asked in 4 years
Q48
A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (Given, Planck’s constant $=6.6\times10^{-34}$ Js).
Atoms Bohr's Atomic Model Angular Momentum Quantization
EasySingle correctIdea asked in 5 yearsAsked the year before
Q49
Identify the correct Logic Gate for the following output (Y) of two inputs A and B.
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Timing Diagrams and Waveform Analysis
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q50
A mixture of hydrogen and oxygen has volume $2000\ \mathrm{cm^3}$ , temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be : [Take gas constant…
Kinetic Theory Ideal Gas Laws Ideal Gas Equation
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q51
In a carnot engine, the temperature of reservoir is $527^\circ$ C and that of sink is 200 K. If the workdone by the engine when it transfers heat from reservior to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is __________…
Thermodynamics Second Law and Entropy Carnot Engine Efficiency
EasyNumerical valueNew idea
Q52
A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be __________.
Alternating Current Phasor Diagrams Purely Resistive Phasor Diagram
MediumNumerical value · figureNew idea
Q53
In Young’s double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength…
Wave Optics Young's Double Slit Position of nth Maximum and Minimum
MediumNumerical valueNew idea
Q54
A beam of monochromatic light is used to excite the electron in $\mathrm{Li^{++}}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x\times10^{-10}$ m. The value of $x$ is __________. [Given hc $=1242$ eV nm]
Atoms Bohr's Atomic Model Energy Level Calculations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q55
A cell, shunted by a $8\ \Omega$ resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by $4\ \Omega$ resistance. The value of internal resistance of the cell will be __________ $\Omega$ .
Current Electricity Potentiometer Internal Resistance Measurement
MediumNumerical valueNew ideaIdea asked in 2 years
Q56
The current density in a cylindrical wire of radius 4 mm is $4\times10^6\ \mathrm{Am^{-2}}$ . The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and R is __________ $\pi$ A.
Current Electricity Ohm's Law and Resistance Integrating Non-Uniform Current Density
MediumNumerical valueNew idea
Q57
A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is __________ nJ.
Electrostatic Potential and Capacitance Parallel Plate Capacitors Charge Sharing and Heat Loss
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q58
The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $K\sqrt{5}\times10^2$ m. The value of K is __________.…
Communication Systems
MediumNumerical value
Q59
The area of cross-section of a large tank is $0.5\ \mathrm{m^2}$ . It has a narrow opening near the bottom having area of cross-section $1\ \mathrm{cm^2}$ . A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the…
Mechanical Properties of Fluids Fluid Dynamics Torricelli's Law of Efflux
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q60
A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed $v$ . The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value…
Work, Energy and Power Collisions Ballistic Pendulum
MediumNumerical valueIdea asked in 3 yearsAsked the year before

Chemistry30 questions

14 easy14 medium2 hard

Q61
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g mol $^{-1}$ respectively], is ‘x’ g ml $^{-1}$ .…
Solutions Mole Concept Molality Calculation
EasyAssertion–reasonIdea asked in 2 yearsAsked the year before
Q62
Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List - II and select the most appropriate option. List - I (Shape) (A) T-shaped (B) Trigonal planar (C) Square planar (D) See-saw List - II (Molecules) (I)…
Chemical Bonding and Molecular Structure VSEPR Theory T-Shaped Geometry (SN=5, 2 LP)
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q63
Match List - I with List - II. List - I (A) Spontaneous process (B) Process with $\Delta$ P = 0, $\Delta$ T = 0 (C) $\Delta\mathrm{H_{reaction}}$ (D) Exothermic Process List - II (I) $\Delta$ H < 0 (II) $\Delta\mathrm{G_{T,P}}$ < 0 (III) Isothermal and isobaric…
Thermodynamics (Chemistry)Gibbs Free Energy Spontaneity Criteria
EasyMatch the listNew ideaIdea asked in 2 years
Q64
Match List - I with List - II. List - I (A) Lyophilic colloid (B) Emulsion (C) Positively charged colloid (D) Negatively charged colloid List - II (I) Liquid-liquid colloid (II) Protective colloid (III) $\mathrm{FeCl_3}$ + NaOH (IV) $\mathrm{FeCl_3}$ + hot…
Surface Chemistry Colloids Colloid Classification by State
EasyMatch the listIdea asked in 4 yearsAsked the year before
Q65
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The ionic radii of $\mathrm{O^{2-}}$ and $\mathrm{Mg^{2+}}$ are same. Reason (R) : Both $\mathrm{O^{2-}}$ and $\mathrm{Mg^{2+}}$ are…
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasyAssertion–reasonIdea asked in 5 yearsAsked the year before
Q66
Match List - I with List - II. List - I (A) Concentration of gold ore (B) Leaching of alumina (C) Froth stabiliser (D) Blister copper List - II (I) Aniline (II) NaOH (III) $\mathrm{SO_2}$ (IV) NaCN Choose the correct answer from the options given below.
General Principles and Processes of Isolation of Elements Metallurgical Extraction MacArthur-Forrest Cyanide Process
MediumMatch the listIdea asked in 2 yearsAsked the year before
Q67
Addition of $\mathrm{H_2SO_4}$ to $\mathrm{BaO_2}$ produces :
Hydrogen Hydrogen and Hydrides H2O2 Preparation from Barium Peroxide
EasySingle correctIdea asked in 2 yearsAsked the year before
Q68
$\mathrm{BeCl_2}$ reacts with $\mathrm{LiAlH_4}$ to give :
The s-Block Elements s-Block Elements Nature of s-Block Hydrides
MediumSingle correctNew idea
Q69
Match List - I with List - II. List - I (Si-Compounds) (A) $\mathrm{(CH_3)_4Si}$ (B) $\mathrm{(CH_3)Si(OH)_3}$ (C) $\mathrm{(CH_3)_2Si(OH)_2}$ (D) $\mathrm{(CH_3)_3Si(OH)}$ List - II (Si-Polymeric/Other Products) (I) Chain Silicone (II) Dimeric Silicone…
The p-Block Elements Group 13 & 14 Silicones and Zeolites
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q70
Heating white phosphorus with conc. NaOH solution gives mainly :
The p-Block Elements Group 15 & 16 Preparation of Phosphine
EasySingle correctIdea asked in 2 years
Q71
Which of the following will have maximum stabilization due to crystal field ?
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q72
Given below are two Statements : Statement I : Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide. Statement II : Photochemical smog has components, ozone, nitric oxide, acrolein, formaldehyde, PAN etc. In…
Environmental Chemistry Classical vs Photochemical Smog
EasyTwo statementsIdea asked in 3 yearsAsked the year before
Q73
Which of the following is structure of a separating funnel ?
Organic Chemistry: Some Basic Principles and Techniques
EasyDiagram based · figure
Q74
‘A’ and ‘B’ respectively are : A $\xrightarrow[\text{(2) Zn - H}_2\text{O}]{\text{(1) O}_3}$ Ethane-1,2-dicarbaldehyde + Glyoxal/Oxaldehyde B $\xrightarrow[\text{(2) Zn - H}_2\text{O}]{\text{(1) O}_3}$ 5-oxohexanal
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q75
The major product of the following reaction is : [figure: reactant drawn as a benzene ring with a substituent F ortho to a side chain and $\mathrm{NO_2}$ para to it; the side chain is a zigzag carbon chain whose carbon attached to the ring bears I on a bold…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms SN2 Transition State
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q76
Which of the following reactions will yield benzaldehyde as a product ? (A) [figure: benzene ring bearing COOH] $\xrightarrow[\text{(ii) H}_2/\text{Pd/BaSO}_4]{\text{(i) SOCl}_2\text{, Quinoline}}$ (B) [figure: benzene ring bearing $\mathrm{CH_2OH}$ ]…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Rosenmund Reduction
MediumOther · figureIdea asked in 4 yearsAsked the year before
Q77
Given below are two statements : Statement - I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom. Statement - II : The group is migrated in Hofmann degradation reaction…
Amines Hofmann Bromamide Degradation
MediumTwo statementsIdea asked in 5 yearsAsked the year before
Q78
Match List - I with List - II. List - I (Polymer) (A) Bakelite (B) Glyptal (C) PVC (D) Polystyrene List - II (Used in) (I) Radio and television cabinets (II) Electrical switches (III) Paints and Lacquers (IV) Water pipes Choose the correct answer from the…
Polymers Common Addition Polymers
EasyMatch the listNew idea
Q79
L-isomer of a compound ‘A’ ( $\mathrm{C_4H_8O_4}$ ) gives a positive test with $\mathrm{[Ag(NH_3)_2]^+}$ . Treatment of ‘A’ with acetic anhydride yields triacetate derivative. Compound ‘A’ produces an optically active compound (B) and an optically inactive…
Biomolecules Carbohydrates Selective Oxidation of Monosaccharides
HardDiagram based · figureNew ideaIdea asked in 3 years
Q80
Match List - I with List - II. List - I (A) [figure: a bracketed cation drawn with a central N bonded to three $\mathrm{CH_3}$ groups and to $\mathrm{CH_3(CH_2)_{15}}$ , positive charge outside the bracket] $\mathrm{Br^-}$ (B) $\mathrm{CH_3-(CH_2)_{11}}$ …
Chemistry in Everyday Life Cationic Detergents and Hair Conditioners
EasyMatch the list · figureNew idea
Q81
Metal deficiency defect is shown by $\mathrm{Fe_{0.93}O}$ . In the crystal, some $\mathrm{Fe^{2+}}$ cations are missing and loss of positive charge is compensated by the presence of $\mathrm{Fe^{3+}}$ ions. The percentage of $\mathrm{Fe^{2+}}$ ions in the…
The Solid State Solid State Defects Non-Stoichiometric Composition Calculations
MediumNumerical valueNew idea
Q82
If the uncertainty in velocity and position of a minute particle in space are, $2.4\times10^{-26}$ (m s $^{-1}$ ) and $10^{-7}$ (m) respectively. The mass of the particle in g is __________. (Nearest integer) (Given : h = $6.626\times10^{-34}$ Js)
Structure of Atom
MediumNumerical value
Q83
2 g of a non-volatile non-electrolyte solute is disolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 8. The elevation in boiling points of A and B are in the ratio $\frac{x}{y}$ ( $x : y$ ). The value of $y$ …
Solutions Colligative Properties Boiling Point Elevation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q84
$\mathrm{2NOCl(g) \rightleftharpoons 2NO(g) + Cl_2(g)}$ In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be 0.4 mol/L. The equilibrium constant at 30°C is __________…
Equilibrium Chemical Equilibrium ICE Table Construction
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q85
The limiting molar conductivities of NaI, $\mathrm{NaNO_3}$ and $\mathrm{AgNO_3}$ are 12.7, 12.0 and 13.3 mS m $^2$ mol $^{-1}$ , respectively (all at 25°C). The limiting molar conductivity of AgI at this temperature is __________ mS m $^2$ mol $^{-1}$ .
Electrochemistry
MediumNumerical value
Q86
The rate constant for a first order reaction is given by the following equation : $\ln k = 33.24 - \frac{2.0\times10^4\ \mathrm{K}}{T}$ The Activation energy for the reaction is given by __________ kJ mol $^{-1}$ . (In Nearest integer) (Given : R = 8.3 J…
Chemical Kinetics Arrhenius Equation Activation Energy Calculation
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q87
The number of statement(s) correct from the following for Copper (at. no. 29) is/are __________. (A) Cu(II) complexes are always paramagnetic (B) Cu(I) complexes are generally colourless (C) Cu(I) is easily oxidized (D) In Fehling solution, the active…
The d- and f-Block Elements d-Block Elements Aqueous Stability of Cu+ vs Cu2+
MediumNumerical valueNew ideaIdea asked in 2 years
Q88
Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the mangenese product formed from the above reaction is __________ B.M. (Nearest Integer)
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q89
Two elements A and B which form 0.15 moles of $\mathrm{A_2B}$ and $\mathrm{AB_3}$ type compounds. If both $\mathrm{A_2B}$ and $\mathrm{AB_3}$ weigh equally, then the atomic weight of A is __________ times of atomic weight of B.
Some Basic Concepts of Chemistry Mole Concept Molar Mass and Gas Volume
MediumNumerical valueIdea asked in 3 years
Q90
Total number of possible stereoisomers of dimethyl cyclopentane is __________.
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Chirality in Substituted Cycloalkanes
HardNumerical valueNew idea

Maths30 questions

3 easy22 medium5 hard

Q1
The area of the polygon, whose vertices are the non-real roots of the equation $\bar{z} = iz^2$ is :
Complex Numbers and Quadratic Equations Roots of Unity Roots of z^n = z_0
MediumSingle correctNew idea
Q2
Let the system of linear equations $x+2y+z=2$ , $\alpha x+3y-z=\alpha$ , $-\alpha x+y+2z=-\alpha$ be inconsistent. Then $\alpha$ is equal to :
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
If $x=\sum_{n=0}^{\infty} a^n$ , $y=\sum_{n=0}^{\infty} b^n$ , $z=\sum_{n=0}^{\infty} c^n$ , where a, b, c are in A.P. and $|a|<1$ , $|b|<1$ , $|c|<1$ , $abc \neq 0$ , then :
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q4
Let $\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}$ , where a, b, c are constants, represent a circle passing through the point $(2, 5)$ . Then the shortest distance of the point $(11, 6)$ from this circle is :
Differential Equations Homogeneous Equations Recognizing Exact Differentials in Homogeneous Forms
HardSingle correctNew ideaIdea asked in 2 years
Q5
Let a be an integer such that $\lim_{x \to 7} \frac{18-[1-x]}{[x-3a]}$ exists, where $[t]$ is greatest integer $\leqslant t$ . Then a is equal to :
Limits and Derivatives Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q6
The number of distinct real roots of $x^4-4x+1=0$ is :
Application of Derivatives Maxima and Minima Analyzing Polynomial Roots via Extrema
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q7
The lengths of the sides of a triangle are $10+x^2$ , $10+x^2$ and $20-2x^2$ . If for $x=k$ , the area of the triangle is maximum, then $3k^2$ is equal to :
Application of Derivatives Maxima and Minima Optimization Problems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q8
If $\cos^{-1}\left(\frac{y}{2}\right) = \log_e\left(\frac{x}{5}\right)^5$ , $|y|<2$ , then :
Continuity and Differentiability Chain Rule Second Order Implicit Chain Rule
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q9
If $\int \frac{(x^2+1)e^x}{(x+1)^2}\,dx = f(x)e^x+C$ , where C is a constant, then $\frac{d^3f}{dx^3}$ at $x=1$ is equal to :
Integrals Integration by Parts Exponential Form with Improper Rational Functions
MediumSingle correctNew idea
Q10
The value of the integral $\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)}\,dx$ is equal to :
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q11
If $\frac{dy}{dx}+\frac{2^{x-y}(2^y-1)}{2^x-1}=0$ , $x, y>0$ , $y(1)=1$ , then $y(2)$ is equal to :
Differential Equations Variable Separable Form Exponential Sum/Difference Separation
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q12
In an isosceles triangle ABC, the vertex A is $(6, 1)$ and the equation of the base BC is $2x+y=4$ . Let the point B lie on the line $x+3y=7$ . If $(\alpha, \beta)$ is the centroid of $\Delta$ ABC, then $15(\alpha+\beta)$ is equal to :
Straight Lines Straight Line Distance Foot of the perpendicular
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q13
Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ , be $\frac{1}{4}$ . If this ellipse passes through the point $\left(-4\sqrt{\frac{2}{5}}, 3\right)$ , then $a^2+b^2$ is equal to :
Conic Sections Ellipse Eccentricity Eccentricity calculation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q14
If two straight lines whose direction cosines are given by the relations $l+m-n=0$ , $3l^2+m^2+cnl=0$ are parallel, then the positive value of c is :
Three Dimensional Geometry Angle Between Lines Parallelism Condition
MediumSingle correctNew idea
Q15
Let $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}-3\hat{j}+2\hat{k}$ . Then the number of vectors $\vec{b}$ such that $\vec{b}\times\vec{c}=\vec{a}$ and $|\vec{b}| \in \{1, 2, \ldots\ldots, 10\}$ is :
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q16
Five numbers $x_1, x_2, x_3, x_4, x_5$ are randomly selected from the numbers $1, 2, 3, \ldots\ldots, 18$ and are arranged in the increasing order $(x_1 < x_2 < x_3 < x_4 < x_5)$ . The probability that $x_2=7$ and $x_4=11$ is :
Probability Permutations and Combinations Combinations of Distinct Objects
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q17
Let X be a random variable having binomial distribution $B(7, p)$ . If $P(X=3)=5P(X=4)$ , then the sum of the mean and the variance of X is :
Probability
MediumSingle correct
Q18
The value of $\cos\left(\frac{2\pi}{7}\right)+\cos\left(\frac{4\pi}{7}\right)+\cos\left(\frac{6\pi}{7}\right)$ is equal to :
Trigonometric Functions Trigonometric Identities Trigonometric Sums via Roots of Unity
MediumSingle correctNew idea
Q19
$\sin^{-1}\left(\sin\frac{2\pi}{3}\right)+\cos^{-1}\left(\cos\frac{7\pi}{6}\right)+\tan^{-1}\left(\tan\frac{3\pi}{4}\right)$ is equal to :
Inverse Trigonometric Functions Inverse Trig Domains Evaluating arcsin(sin x) Outside Principal Branch
EasySingle correctNew idea
Q20
The boolean expression $(\sim(p\wedge q))\vee q$ is equivalent to :
Mathematical Reasoning
EasySingle correct
Q21
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function defined by $f(x)=\frac{2e^{2x}}{e^{2x}+e}$ . Then $f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\ldots+f\left(\frac{99}{100}\right)$ is equal to ____________.
Relations and Functions
MediumNumerical value
Q22
If the sum of all the roots of the equation $e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0$ is $\log_e p$ , then p is equal to ____________.
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q23
The positive value of the determinant of the matrix A, whose $\mathrm{Adj}(\mathrm{Adj}(A)) = \begin{pmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{pmatrix}$ , is ____________.
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumNumerical valueIdea asked in 6 years
Q24
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is ____________.
Permutations and Combinations The Gap Method
MediumNumerical valueNew idea
Q25
If the coefficient of $x^{10}$ in the binomial expansion of $\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$ is $5^k \cdot l$ , where $l, k \in \mathbf{N}$ and $l$ is co-prime to 5, then k is equal to ____________.
Binomial Theorem
HardNumerical value
Q26
Let $A_1 = \{(x, y) : |x| \leqslant y^2, |x|+2y \leqslant 8\}$ and $A_2 = \{(x, y) : |x|+|y| \leqslant k\}$ . If $27\,(\text{Area } A_1) = 5\,(\text{Area } A_2)$ , then k is equal to :
Application of Integrals Area Under Curves Area of Inequalities
HardNumerical valueIdea asked in 8 yearsAsked the year before
Q27
If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots$ is $\frac{m}{n}$ , where m and n are co-prime numbers, then $m+n$ is equal to ____________.
Sequences and Series AP and GP Method of Differences (Vn Method)
HardNumerical valueNew ideaIdea asked in 5 years
Q28
A rectangle R with end points of one of its sides as $(1, 2)$ and $(3, 6)$ is inscribed in a circle. If the equation of a diameter of the circle is $2x-y+4=0$ , then the area of R is ____________.
Conic Sections
MediumNumerical value
Q29
A circle of radius 2 unit passes through the vertex and the focus of the parabola $y^2=2x$ and touches the parabola $y=\left(x-\frac{1}{4}\right)^2+\alpha$ , where $\alpha>0$ . Then $(4\alpha-8)^2$ is equal to ____________.
Conic Sections
HardNumerical value
Q30
Let the mirror image of the point $(a, b, c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6, \beta, \gamma)$ . If $a+b+c=5$ , then $7\beta-9\gamma$ is equal to ____________.
Three Dimensional Geometry Point-Plane Distance Image of a Point
MediumNumerical valueIdea asked in 4 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.