JEE Main 2022 · July session

JEE Main 30 July 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 15 were rated hard and 27 easy. Its hard-question count was the joint 2nd highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Chemical Bonding and Molecular Structure, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 15; 17% of the shift
Chapters asked: 65; 13 questions with a figure

Key findings · 30 Jul 2022, Shift 2

1
15 hard questions (17%): the joint 2nd 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 (14 of 30).
3
27 questions tested a new idea, one no earlier year had asked: 36% of the 75 questions tagged to an idea.
4
45 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
50 shared an idea with another 2022 shift (67% 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), Chemical Bonding and Molecular Structure in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 17Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 14Medium 13Hard 3

Top chapters

Maths

30 Q · 10 numerical

Easy 0Medium 18Hard 12

Top chapters

Question format

Single correct46 Q
Numerical value30 Q
Diagram based6 Q
Other4 Q
Two statements3 Q
Match the list1 Q

What each question asks you to do

Multi-step30 Q
Calculation25 Q
Application18 Q
Conceptual10 Q
Recall5 Q
Data or graph2 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

13 easy17 medium0 hard

Q1
If current (I) , kinetic energy (K) and charge (Q) are taken as the fundamental quantities, The dimensional representation of power will be :
Mechanical Properties of Fluids
MediumSingle correct
Q2
Two trucks A and B are approaching each other on a straight path with the velocities of 16 m/s and 20 m/s respectively. When 200 m apart their drivers see each other and applies the breaks simultaneously. If the truck A decelerates with 2 m/s $^2$ and truck B…
Motion in a Straight Line Kinematics in 1D Stopping Distance and Reaction Time
MediumSingle correctNew idea
Q3
A bullet of mass 10 gram is fired with velocity of 100 m/s from the gun of mass 1 kg . Recoil speed of the gun is :
System of Particles and Rotational Motion Center of Mass COM Velocity Conservation
EasySingle correctIdea asked in 2 yearsAsked the year before
Q4
A mass of 0.5 kg is attached to one end of a massless spring whose natural length is 1 m and spring constant is 800 N/m The other end of the spring is fixed while the mass moves in a circular path in a horizontal plane with an angular speed of 20 rad/s. The…
Laws of Motion Circular Motion Spring-Mass in Circular Motion
MediumSingle correctIdea asked in 3 years
Q5
The time period of X planet of our solar system is 8 years. The distance of earth from the sun is $1.5 \times 10^{11}$ m. The distance of the X planet from the sun will be :
Gravitation Orbital Mechanics Kepler's Laws
EasySingle correctIdea asked in 4 yearsAsked the year before
Q6
A block of mass M is attached to a wire. The upper part of wire is made of steel and lower part of wire of copper ( as shown in figure ). Both parts have the same area of cross section . Neglecting the mass of wires, the ratio of longitudinal strain…
Mechanical Properties of Solids Elasticity Series and Parallel Composite Wires
EasySingle correct · figureIdea asked in 4 yearsAsked the year before
Q7
A Carnot engine is operating between the two reservoirs of temperature 227 $^\circ$ C and 127 $^\circ$ C respectively. If the engine performs $1.04 \times 10^5$ J work per cycle. Then, the heat absorbed from hot reservoir per cycle will be :
Thermodynamics Heat Engines and Refrigerators Carnot Efficiency Limit
EasySingle correctIdea asked in 3 yearsAsked the year before
Q8
If the r.m.s speed of oxygen at room temperature is $\sqrt{56}\ \mathrm{m/s}$ . The r.m.s speed of nitrogen at the same temperature is ________.
Kinetic Theory Kinetic Theory of Gases Molecular Speed Types
EasySingle correctIdea asked in 3 yearsAsked the year before
Q9
An oscillating simple pendulum of time period $\mathrm{T_o}$ is placed in a lift which is accelerating upwards with $2.5\ \mathrm{m/s^2}$ . The time period of pendulum in the lift will be (if g = $10\ \mathrm{m/s^2}$ )
Oscillations Pendulums Effective Gravity Effects
EasySingle correctNew idea
Q10
A charge q is uniformly distributed along the length L of a rod. It is then bent in the shape of a semicircle. The magnitude of electric field at the centre of semicircle will be :
Electric Charges and Fields Electric Field Charged Arc Field
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q11
The current I drawn out of the battery connected in the given circuit is:
Current Electricity
MediumSingle correct · figure
Q12
In an A.C circuit , V & I are given by V = 250 sin (100 t) volt and I = 10 sin (100 t + $\frac{\pi}{3}$ ) A respectively The power dissipated in the circuit is:
Alternating Current Phasor Diagrams Power Factor from Phasors
EasySingle correctIdea asked in 5 yearsAsked the year before
Q13
A plane electromagnetic wave propagating in free space has amplitude of electric field of 900 $\frac{\mathrm{N}}{\mathrm{C}}$ . The amplitude of magnetic field will be :__________
Electromagnetic Waves
EasySingle correct
Q14
Two poloroids P $_1$ and P $_2$ are placed parallel to each other with common axis.The light of intensity I $_0$ passes through a polaroid sheet P $_1$ and then passes through polaroid P $_2$ . If P $_2$ is now rotated by 60°, then the intensity of the output…
Wave Optics Polarization Malus's Law Calculation
EasySingle correctIdea asked in 5 yearsAsked the year before
Q15
A wire of length 8 m is bent to form a circular loop in y-z plane. A current of 0.5 A is flowing in anticlockwise direction in it , the magnetic dipole moment of the loop is:
Moving Charges and Magnetism Magnetic Dipole Moment Magnetic moment of a current loop
MediumSingle correctNew idea
Q16
In the following loop, magnitude of the magnetic field produced at the centre (O) of the loop is : (Assume AB and CD are infinitely extended):
Moving Charges and Magnetism Biot-Savart Law Field at center of circular arc
MediumSingle correct · figureIdea asked in 6 yearsAsked the year before
Q17
Using Boh'r model of quantization of angular momentum the relation between the radius 'r' of the n $^{\mathrm{th}}$ allowed orbit of quantum number 'n' for an electron in hydrogen atom is:
Atoms Bohr's Atomic Model Bohr Orbit Radius
EasySingle correctNew ideaIdea asked in 4 years
Q18
[figure: I-V graph] The I-V characteristics given in above figure is related to:
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Solar Cell V-I Characteristics
MediumDiagram based · figureNew idea
Q19
The de Broglie wavelength associated with an electron, accelerated through a potential difference of 15056 V, is:
Dual Nature of Radiation and Matter Matter Waves Wavelength from Accelerating Potential
EasySingle correctIdea asked in 4 yearsAsked the year before
Q20
An amplitude modulate wave consists of following components : Carrier component = 5 V peak value Lower side band component = 2.5 V peak value Upper side band component = 2.5 V peak value The amplitude of modulating signal is:
Communication Systems
EasySingle correct
Q21
A nuclear physicist performed an experiment on the scattering of alpha particles by thin metal foil of gold. The alpha particles were accelerated up to kinetic energy 3.2 Mev. The estimation of the radius of the nucleus of gold element (Z = 79) by him is…
Atoms Electric Potential Distance of Closest Approach
MediumNumerical valueNew idea
Q22
A ring is placed at the bottom of a trough containing four immiscible liquids of refractive indices 1.0, 2.0, 3.0 and 4.0 poured one above the other of heights 10 cm, 20 cm, 30 cm, and 40 cm respectively. The apparent depth at which the ring appears, when…
Ray Optics and Optical Instruments Refraction and Snell's Law Apparent Depth and Shift
MediumNumerical valueNew ideaIdea asked in 3 years
Q23
A sinusoidal voltage V(t) = 200 sin2000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 µF and R =100 Ω. The impedance of the circuit is _______Ω
Alternating Current LCR Resonance Impedance at Resonance
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q24
A cell sends a current through a resistance 4 Ω for time t and sends current through another resistance 16 Ω for the same time t.If the same amount of heat is developed in both the resistances , then the internal resistance of the cell is _____Ω
Current Electricity Kirchhoff's Laws Cell EMF and Internal Resistance
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Combination of four parallel plate air capacitors is shown in figure. Separation between the plate P $_1$ & P $_2$ is $\frac{d}{3}$ and separation between the plates P $_2$ and P $_3$ is d. The equivalent capacitance of the configuration is _______ µF. (Given…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q26
A particle executing SHM has its velocity 20 cm s $^{-1}$ at mean position and acceleration of 25 cm s $^{-2}$ at one of its extreme position. The amplitude of the particle will be ____ cm.
Oscillations SHM Equations Velocity and Accel vs Position
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q27
A water drop of radius 1 cm is broken into eight equal droplets. Surface tension of water is 0.075 N m $^{-1}$ . The gain in surface energy is __________ $\times10^{-7}$ J. (Take $\pi$ = 3.14)
Mechanical Properties of Fluids Surface Tension Splitting and Coalescence
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q28
A fly wheel of mass 10 kg and radius 50 cm is rotating at a rate of 360 rpm. Assuming mass to be concentrated at the rim, the constant retarding torque required to stop the rotation of wheel in 6 rotations will be $x\pi$ Nm. The value of $x$ is ________
System of Particles and Rotational Motion Torque and Equilibrium Work Done by Constant Torque
MediumNumerical valueNew ideaIdea asked in 2 years
Q29
A body moving horizontally on a smooth surface with a speed of 20 ms $^{-1}$ splits into two parts and continue to move in the same direction . The masses of two parts are in the ratio of 1:2. The smaller part moves with a speed of 30 ms $^{-1}$ . The…
Work, Energy and Power Collisions Momentum in Explosions
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q30
Two projectiles are thrown towards each other at 15° and 45° angles respectively with the horizontal at the same speed. The difference between the horizontal distances traveled by the two projectiles is 80 m. The initial speed of the projectiles is…
Motion in a Plane Projectile Motion Complementary Angles Range and Ratios
MediumNumerical valueNew ideaIdea asked in 2 years

Chemistry30 questions

14 easy13 medium3 hard

Q31
Combination of temperature and pressure causing the greatest deviation from ideal gas behaviour is;
States of Matter Real Gases Gas Liquefaction
EasySingle correctNew idea
Q32
When the kinetic energy of an electron is increased nine times, the wavelength of the de-Broglie wave associated with it would become :
Structure of Atom
EasySingle correct
Q33
Which of the following is the plot of Gibb's free energy (G) vs temperature (T), at constant pressure, for a pure substance?
Thermodynamics (Chemistry)Gibbs Free Energy Gibbs Energy vs Temperature Graph
MediumOther · figureNew ideaIdea asked in 2 years
Q34
Freundlich's adsorption isotherm (in terms of concentration) is given by the expression; $\frac{x}{m}=\mathrm{K}\cdot\mathrm{C}^{1/n}$ . The possible conclusions that can be drawn from the expression are : (A) When $\frac{1}{n}=1$ , the adsorption is directly…
Surface Chemistry Adsorption Limits of Freundlich Exponent (1/n)
MediumOtherIdea asked in 2 yearsAsked the year before
Q35
For Periodic Table which of the following statements are TRUE A. Shielding increases as we go down in the group. B. Shielding increases sharply across the period. C. Ionization enthalpy increases down the group. D. Metallic character increases down the…
Classification of Elements and Periodicity in Properties Periodic Trends Ionization Enthalpy Trends
EasyOtherIdea asked in 6 yearsAsked the year before
Q36
Match List I with List II List I | List II A. Cyanide Process | I. Vapour phase refining B. Froth flotation process | II. Aluminium C. Hall-Heroult process | III. Dressing of ZnS D. Mond process | IV. Extraction of Au Choose the correct answer from the…
General Principles and Processes of Isolation of Elements Metallurgical Extraction MacArthur-Forrest Cyanide Process
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q37
The hardness of water is generally expressed in terms of $\mathrm{CaCO_3}$ equivalent. The possible reasons are as follows: (A) Its molar mass is 100, so the calculations become easier. (B) It decomposes at a temperature, 1200 K. (C) It is insoluble in…
Hydrogen Hydrogen and Hydrides Causes of Temporary and Permanent Hardness
MediumOtherIdea asked in 2 years
Q38
The correct option for relative covalent nature of compounds is
Chemical Bonding and Molecular Structure s-Block Elements Covalent Character in Halides
MediumSingle correctNew ideaIdea asked in 2 years
Q39
The $\mathrm{E^o}$ (volt) values are : $\mathrm{Al^{3+}/Al}$ , $-1.66$ , $\mathrm{Sc^{3+}/Sc}$ , $-2.08$ , $\mathrm{Fe^{3+}/Fe^{2+}}$ , $+0.77$ , $\mathrm{Hg_2^{2+}/Hg}$ , $+0.79$ . Arrangement of cations, $\mathrm{Al^{3+}}$ , $\mathrm{Sc^{3+}}$ , $\mathrm{Fe^{3+}}$ …
Electrochemistry Nernst Equation Standard Cell Potential
EasySingle correctIdea asked in 7 yearsAsked the year before
Q40
In low and high spin octahedral $\mathrm{Co^{3+}}$ complexes the number of electrons in $\mathrm{t_{2g}}$ level respectively will be . (given At. no. of Co, 27)
Coordination Compounds Crystal Field Theory High and Low Spin States
EasySingle correctIdea asked in 7 yearsAsked the year before
Q41
Which of the following is not a component of photochemical smog?
Environmental Chemistry Secondary Pollutants in Photochemical Smog
EasySingle correctIdea asked in 2 yearsAsked the year before
Q42
Glycerol can be separated from spent-lye on industrial scale by using
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q43
Which of the following is unstable?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q44
Major product of the following reaction is [figure: skeletal line drawing of a chain with a terminal C=C double bond at the left end, a carbon bearing two short line substituents, a CH2, then a carbon with =O and OH (printed O and OH); arrow with…
Aldehydes, Ketones and Carboxylic Acids
HardDiagram based · figure
Q45
[figure: six-membered ring with three alternating double bonds bearing Br (printed Br); long arrow; six-membered ring with three alternating double bonds bearing COOH (printed COOH)] For the above conversion, the correct sequential addition of reagents is-
Haloalkanes and Haloarenes Carboxylic Acids and Derivatives Carboxylic Acid Synthesis via Grignard and CO2
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q46
Which one of the following compounds can be prepared in good yield by Hoffmann bromamide degradation reaction?
Amines Hofmann Bromamide Degradation
EasyDiagram based · figureIdea asked in 5 yearsAsked the year before
Q47
[figure: six-membered ring with three alternating double bonds bearing $\mathrm{N_2^+Cl^-}$ , then '+ x' (lowercase x as printed) over a long arrow, to a six-membered ring with three alternating double bonds bearing $\mathrm{N_2^+BF_4^-}$ ; then an arrow with…
Amines Diazonium Salts Balz-Schiemann Reaction
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q48
Given below are two statements: Statement I: In Nylon 6, the monomer unit is caprolactam. Statement II: The monomer unit in Nylon 6 is synthesized from cyclohexanone. In the light of the above statements, choose the most appropriate answer from the options…
Polymers Nylon 6 and Caprolactam
EasyTwo statementsNew idea
Q49
Given below are two statements: Statement I: Glycogen is highly branched polysaccharide and commonly known as animal starch due to its similarity with amylopectin. Statement II: Amylose is water insoluble and constitutes about 15-20% of starch. In the light…
Biomolecules Carbohydrates Structure of Glycogen
EasyTwo statementsNew idea
Q50
In the ring test of $\mathrm{NO_3^-}$ ion what is the oxidation number of iron in the complex (brown ring) $[\mathrm{Fe(H_2O)_5NO}]\mathrm{SO_4}$ ?
Coordination Compounds Coordination Nomenclature Oxidation State Calculation
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q51
The density of 4 molal solution of NaOH is 1.160 g $\mathrm{mL^{-1}}$ . The molarity of the solution is ________ M. (Given : Molar mass of NaOH = 40g $\mathrm{mol^{-1)}}$ (nearest integer)
Solutions Mole Concept Molarity and Molality Interconversion
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q52
On the basis of MO. theory, the number of molecules from the following which have bond order two, is ________. $\mathrm{O_2}$ , $\mathrm{O_2^+}$ , $\mathrm{N_2^{2-}}$ , $\mathrm{C_2}$ , $\mathrm{B_2}$
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q53
31 g of ethylene glycol is mixed with 500 g of water. The freezing point of the aqueous solution is ________ K. (in nearest integer) ( $\mathrm{K_f}$ of water = 1.86 K kg $\mathrm{mol^{-1}}$ ) [Molar mass of C, H, O are 12, 1, 16 g $\mathrm{mol^{-1}}$ ]
Solutions Colligative Properties Freezing Point Depression
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q54
50 mL of 0.1 M $\mathrm{CH_3COOH}$ is titrated against 0.1 M NaOH solution. When 10 mL of NaOH is added, the pH of the solution becomes ________ $\times 10^{-1}$ . (nearest integer) Given: pKa ( $\mathrm{CH_3COOH}$ ) = 4.8, log 2 = 0.3
Equilibrium pH and Buffers Acidic Buffer pH Calculation
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q55
For the given cell $\mathrm{Zn(s)} \mid \mathrm{Zn^{2+}}$ ( $\mathrm{C_1}$ , M) $\parallel$ $\mathrm{Zn}$ $^{2+}$ ( $\mathrm{C_2}$ M) $\mid \mathrm{Zn(s)}$ the change in Gibbs energy ( $\Delta G$ ) will be zero when $\frac{\mathrm{C_1}}{\mathrm{C_2}}$ is equal to…
Electrochemistry Nernst Equation Concentration Cells
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q56
$\mathrm{X} \rightarrow \mathrm{Y} + \mathrm{Z}$ X decomposes at 700 K to give Y and Z. The results of two measurements are : Initial concentration of X / (mol/L) | 6.0 | 12.0 Half life / s | 1.0 | 2.0 The rate constant for the reaction is ________ (in…
Chemical Kinetics Integrated Rate Equations Nth-Order Half-Life Proportionality
MediumNumerical valueNew idea
Q57
Consider the molecules / ions given below $\mathrm{XeO_3}$ , $\mathrm{BF_4^-}$ , $\mathrm{I_3^-}$ , $\mathrm{SF_6}$ , $\mathrm{PCl_5}$ The ratio of number of molecules having $\mathrm{sp^3d}$ hybridisation to those having $\mathrm{sp^3}$ hybridisation is ________
Chemical Bonding and Molecular Structure VSEPR Theory Geometry vs Shape Distinction
MediumNumerical valueNew ideaIdea asked in 2 years
Q58
The number of coloured and paramagnetic ions from the following in aqueous solution are ________. $\mathrm{Ti^{3+}}$ , $\mathrm{Co^{2+}}$ , $\mathrm{Ni^{2+}}$ , $\mathrm{Cu^{2+}}$ , $\mathrm{Cu^{+}}$ , $\mathrm{Ti^{4+}}$ , $\mathrm{Zn^{2+}}$ , $\mathrm{Sc^{3+}}$ …
The d- and f-Block Elements d-Block Elements Color and Catalysis
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q59
The number of isomeric compounds (structural isomers only) possible with the molecular formula $\mathrm{C_5H_{10}O_2}$ , which do not react with metallic sodium is ________.
Aldehydes, Ketones and Carboxylic Acids Structural Isomerism Enumeration of Structural Isomers
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q60
Among the following, how many hydrocarbon (s) with formula $\mathrm{C_{10}\,H_{16}}$ which on reaction with acidic potassium permagenate yield(s) same product ? ________ [figure: five skeletal drawings separated by commas: (1) six-membered ring with a short…
Hydrocarbons Alkenes and Alkynes Oxidative Cleavage with Hot KMnO4
HardNumerical value · figureNew idea

Maths30 questions

0 easy18 medium12 hard

Q61
Let $f: \mathbb{R}-\{5\} \to \mathbb{R}$ be defined as $f(x) = \frac{2x^2+3x-2}{x-5}$ . Then $f$ is
Relations and Functions
MediumSingle correct
Q62
Let $z_1 = 1 + 2i$ , $z_2 = 2 + i$ , $\frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}$ , and $z = \frac{iw}{2-\overline{w}}$ . Consider the statements ( $\mathrm{S}_1$ ) $|z| = \frac{5}{\sqrt{17}}$ ( $\mathrm{S}_2$ ) $\arg(z) + \arg(w) = \tan^{-1}\left(\frac{5}{3}\right)$ .…
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
MediumTwo statementsIdea asked in 5 yearsAsked the year before
Q63
If the system of linear equations $\lambda x + y - z = -1$ $x - y - 3z = 2$ $-x + y + z = \mu$ has infinitely many solutions, then the equation of the line passing through the points $(\lambda+2\mu, 2\lambda+\mu)$ and $(1, \lambda\mu)$ is
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q64
Let $A$ be a matrix and $\begin{bmatrix}1&2\\0&1\end{bmatrix} A \begin{bmatrix}2&0\\-1&1\end{bmatrix} = \begin{bmatrix}1&0\\0&1\end{bmatrix}$ . If $|A|$ and $|A^2|$ are the roots of the quadratic equation $ax^2 + bx + 3 = 0$ , then $a + b - ab$ is equal to
Matrices Matrix Inverse Solving Matrix Equations
MediumSingle correctNew ideaIdea asked in 2 years
Q65
The sum of all values of $n$ , for which ${}^{n-1}C_4 - {}^{n-1}C_3 - \frac{5}{4}\,{}^{n-2}P_2 < 0$ , is
Permutations and Combinations Pascal's Rule Identity
MediumSingle correctNew idea
Q66
The coefficient of $x^{1011}$ in the expression $(1+2x)^{2022} + 2x\,(1+2x)^{2021} + (2x)^2\,(1+2x)^{2020} + ... + (2x)^{2022}$ is
Binomial Theorem Binomial Coefficients Geometric Progression of Expansions
MediumSingle correctNew ideaIdea asked in 2 years
Q67
For $|\alpha| \geq 1$ , let $5^{4-2\alpha}$ , 63, $5^{2\alpha-1}$ be in A.P. with the common difference d. Let $\mathrm{S_n}$ denote the sum of the first n terms of an A.P., whose first term is $\alpha^2$ and the common difference is d. If…
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q68
$2\sum_{n=2}^{\infty} \frac{n(2n^2+3)}{(n+1)!}$ is equal to
Sequences and Series
HardSingle correct
Q69
Let $f(x) = \begin{cases} \dfrac{\sin(\alpha x + 3x) + \sin x}{x}, & x < 0 \\ 2, & x = 0 \\ \dfrac{(x + 6bx^2)^{1/3} - x^{1/3}}{3x^{4/3}}, & x > 0 \end{cases}$ be continuous at $x = 0$ . If $(1-k)\, f\left(\frac{7}{18}\right) = \alpha b$ , then $k$ is equal to
Continuity and Differentiability Continuity at a Point
HardSingle correctIdea asked in 4 yearsAsked the year before
Q70
If $y(x) = \tan x - \int_0^{2x} (x^2 - xt + 1) \sin t\, dt$ , then at $x = \frac{\pi}{3}$ , the value of $2y''' - y''$ is equal to
Continuity and Differentiability Leibniz Rule Higher Order Derivatives
HardSingle correctNew idea
Q71
Let $A_k = \int_{k\pi}^{(k+1)\pi} e^{-x} \sin x\, dx$ , $k = 0, 1, 2, ..., 20$ . Then $\sum_{k=0}^{20} |A_k|$ is equal to
Integrals Definite Integral Properties Periodic Function Property
HardSingle correctIdea asked in 3 yearsAsked the year before
Q72
$\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n(n^2+k^2)}{(n^4+n^2k^2+k^4)}$ is equal to
Integrals Integral as Limit of Sum Algebraic Manipulation to Extract 1/n
HardSingle correctNew idea
Q73
If $y = y(x)$ satisfies the differential equation $x\,dy + \left(x \tan\left(\frac{y}{x}\right) - y\right) dx = 0$ , $x > 0$ , and $y(1) = \frac{\pi}{2}$ , then a value of $y(\sqrt{2}\,)$ is
Differential Equations Homogeneous Equations Homogeneous Equations with Transcendental Functions
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q74
Let the area enclosed by the solution curve $y = y(x)$ of the differential equation $\frac{dy}{dx} + \frac{x-2}{y-b} = 2$ , b > 0, y(5) = 0 is $13\pi$ . Let $y = y(x)$ intersect the $y$ -axis at the points $P$ and $Q$ . If the tangents to $y = y(x)$ at $P$ and…
Application of Integrals Variable Separable Form Implicit Solution Curve Analysis
HardSingle correctNew idea
Q75
If foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{12} = 1$ and the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ coincide, then the eccentricity of the hyperbola, with foci $\left(0, \pm\sqrt{10}\right)$ passing through the point $(a, a+1)$ , is
Conic Sections
MediumSingle correct
Q76
Let the curves $y^2 = kx$ and $xy = -1$ have a common tangent, whose slope is $\frac{1}{2}$ . Then $k$ can NOT lie in the interval
Conic Sections
HardSingle correct
Q77
Let $ax + by + cz + 3 = 0$ be the plane which bisects the acute angle between the planes $2x - y - 2z + 3 = 0$ and $3x - 2y + 6z + 8 = 0$ . Then $a + b + c$ is equal to
Three Dimensional Geometry Planes in 3D Angle Bisector Planes
MediumSingle correctNew idea
Q78
If the mean and median of the data | $x$ | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | | | $f$ | 3 | 6 | 2 | $x$ | $y$ | $\sum f = 20$ | are equal, then $xy^2$ is equal to
Statistics
MediumSingle correct
Q79
The angle of elevation of the top P of a vertical tower for a person standing at a point A on the horizontal ground due north of the tower is $45^{\mathrm{o}}$ . Another person B is standing 50 m west of A on the ground. If the angle of elevation of P at B is…
Trigonometric Functions
MediumSingle correct
Q80
Which of the following is a contradiction?
Mathematical Reasoning
MediumSingle correct
Q81
The number of solutions of the equation $|x^2 + 3x + 2| + |x + 5| - 2 = 0$ , $x \in \mathbb{R}$ , is ________.
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q82
If $p_1$ and $p_2$ , respectively, are the second largest and the fourth largest prime numbers in the factorization of the coefficient of $x^{30}$ in the expansion of $\left(x^2 + 2 + \frac{1}{x^2}\right)^{-5}\left(1 + x^2\right)^{40}$ , then $p_1 + p_2$ is…
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
HardNumerical valueNew ideaIdea asked in 2 years
Q83
The number of integral values of $b$ for which $2x^3 - 3x^2 - 12x + b = 0$ has three distinct real roots is ________.
Application of Derivatives Maxima and Minima Analyzing Polynomial Roots via Extrema
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q84
An air duct is made of a thick metallic sheet. The duct is open from front and back. Its cross-section is a trapezium of base angles $60^{\mathrm{o}}$ and area 1.5 $\mathrm{m^2}$ . Its length is 1 m. (see the figure). If its height $x = x_0$ (in metres) so…
Application of Derivatives Maxima and Minima Optimization Problems
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q85
If the area enclosed by the curves $y = x^2$ , $y^3 = x$ , $x = -1$ and $y = x^2$ , $y^3 = x$ , $x = 1$ , above the line $x = 2y$ is $\frac{n}{n+1}$ , then $n$ is equal to ______.
Application of Integrals Area Under Curves Area Between Curves
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q86
Let $A\,(0, a+2)$ , $B\,(0, a)$ , $C\,(-2, 0)$ and $D\,(2, 0)$ be four points and the lines $AD$ and $BC$ intersect at $P\,(x, y)$ . If the locus of $P$ is the curve $f\,(x, y) = 0$ and the tangent at the point $(4, \gamma)$ on this curve is…
Conic Sections General Conic Section Tangent to General Conic (T=0)
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q87
Let $L_1$ be a line in the $yz$ - plane with $y$ and $z$ intercepts $\frac{1}{4}$ and $\frac{1}{C}$ $(C > 0)$ respectively. Let $L_2$ be the line in the $xz$ - plane with $x$ and $z$ intercepts $\frac{1}{3}$ and $-\frac{1}{C}$ respectively. If the shortest…
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
HardNumerical valueIdea asked in 6 years
Q88
Let $OABC$ be a parallelogram, $O$ be the origin, $A\,(2, 4, -5)$ and $C\,(b, 2, 3)$ . If $P\,(a, a, a)$ and $Q\,(9-a^2, 3, a-1)$ , $a \in \mathbb{N}$ , are two points such that the projection of $\overrightarrow{OP}$ on $\overrightarrow{OB}$ is 2 and…
Vector Algebra Dot Product Scalar and Vector Projection
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q89
The probability distribution of a random variable $X$ is $P(X = i) = \frac{1}{2^i}$ , $i = 1, 2, 3, ........$ The variance of $X$ is equal to ________.
Probability
MediumNumerical value
Q90
Let $S = \left\{\theta \in [0, 2\pi] - \left\{\frac{\pi}{2}, \frac{3\pi}{2}\right\} : \sin^{-1}(\sin\theta) + \cos^{-1}(\cos\theta) + \tan^{-1}(\tan\theta) = \frac{4\pi}{5}\right\}$ . Then $\frac{30}{\pi}\sum_{\theta \in S} \theta$ is equal to ________.
Inverse Trigonometric Functions Inverse Trig Identities Extreme Value Principle in Equations
HardNumerical valueNew idea

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.