JEE Main 2022 · July session

JEE Main 26 July 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 24 easy. Its hard-question count was the joint 14th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Amines, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 12; 13% of the shift
Chapters asked: 65; 14 questions with a figure

Key findings · 26 Jul 2022, Shift 1

1
12 hard questions (13%): the joint 14th highest count of the 24 2022 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 22%.
2
Maths was the hardest section, with 8 of 30 rated hard; Chemistry had the most easy questions (13 of 30).
3
27 questions tested a new idea, one no earlier year had asked: 34% of the 79 questions tagged to an idea.
4
44 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
46 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), Amines in Chemistry (3) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 11Medium 16Hard 3

Top chapters

Alternating Current2 Q
Current Electricity2 Q
Electromagnetic Waves2 Q
Electrostatic Potential and Capacitance2 Q
Laws of Motion2 Q
Motion in a Plane2 Q

Chemistry

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 0Medium 22Hard 8

Top chapters

Question format

Single correct48 Q
Numerical value30 Q
Diagram based6 Q
Match the list2 Q
Other2 Q
Two statements1 Q
Assertion–reason1 Q

What each question asks you to do

Calculation34 Q
Multi-step28 Q
Application12 Q
Recall7 Q
Conceptual5 Q
Data or graph2 Q
Diagram reading2 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

11 easy16 medium3 hard

Q31
Three masses $M = 100$ kg, $m_1 = 10$ kg and $m_2 = 20$ kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on…
Laws of Motion Newton's Laws of Motion Constrained Motion
HardSingle correct · figureIdea asked in 2 yearsAsked the year before
Q32
A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be :
Electromagnetic Waves
EasySingle correct
Q33
The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is : (Take $\log_{10}1.88 = 0.274$ )
Nuclei Radioactive Decay Activity and Rate of Decay
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q34
A parallel beam of light of wavelength 900 nm and intensity $100\ \mathrm{Wm^{-2}}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1\ \mathrm{cm^2}$ area perpendicular to the beam in one second is :
Dual Nature of Radiation and Matter Photoelectric Effect Photon Flux and Beam Power
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q35
In Young's double slit experiment, the fringe width is 12 mm. If the entire arrangement is placed in water of refractive index $\frac{4}{3}$ , then the fringe width becomes (in mm) :
Wave Optics Young's Double Slit Effect of Medium on Fringes
EasySingle correctNew ideaIdea asked in 2 years
Q36
The magnetic field of a plane electromagnetic wave is given by : $\vec{B} = 2\times10^{-8}\sin(0.5\times10^{3}x + 1.5\times10^{11}t)\,\hat{j}$ T. The amplitude of the electric field would be :
Electromagnetic Waves
MediumSingle correct
Q37
In a series LR circuit $X_L = R$ and power factor of the circuit is $P_1$ . When capacitor with capacitance C such that $X_L = X_C$ is put in series, the power factor becomes $P_2$ . The ratio $\frac{P_1}{P_2}$ is :
Alternating Current Phasor Diagrams Power Factor from Phasors
EasySingle correctIdea asked in 5 yearsAsked the year before
Q38
A charge particle is moving in a uniform magnetic field $\left(2\hat{i} + 3\hat{j}\right)$ T. If it has an acceleration of $\left(\alpha\hat{i} - 4\hat{j}\right)\ \mathrm{m/s^2}$ , then the value of $\alpha$ will be :
Moving Charges and Magnetism Lorentz Force Magnetic Force Vector Calculation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q39
$B_X$ and $B_Y$ are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of $B_X$ and $B_Y$ is :
Moving Charges and Magnetism Biot-Savart Law Field at center of circular arc
EasySingle correctIdea asked in 6 yearsAsked the year before
Q40
The current I in the given circuit will be :
Current Electricity Kirchhoff's Laws Balanced Wheatstone Bridge
MediumDiagram based · figureNew idea
Q41
The total charge on the system of capacitors $C_1 = 1\ \mu$ F, $C_2 = 2\ \mu$ F, $C_3 = 4\ \mu$ F and $C_4 = 3\ \mu$ F connected in parallel is : (Assume a battery of 20 V is connected to the combination)
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
EasySingle correctIdea asked in 6 yearsAsked the year before
Q42
When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :
Oscillations SHM Equations Velocity vs Position Graph
EasySingle correctIdea asked in 2 yearsAsked the year before
Q43
7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40K at constant pressure. The increase in the internal energy of the gas in this process is : (Given $R = 8.3\ \mathrm{JK^{-1}\,mol^{-1}}$ )
Thermodynamics First Law of Thermodynamics Internal Energy Calculation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q44
A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
EasySingle correctIdea asked in 7 yearsAsked the year before
Q45
A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be : (Given $\pi = 3.14$ )
Mechanical Properties of Fluids Surface Tension Splitting and Coalescence
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q46
The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be : (Radius of earth = 6400 km)
Gravitation
EasySingle correct
Q47
As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant $2\ \mathrm{Nm^{-1}}$ . If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is :
Work, Energy and Power Center of Mass COM of Two-Block Spring System
MediumSingle correct · figureNew idea
Q48
A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of $4\ \mathrm{m/s^2}$ and then climbs up with an acceleration of $5\ \mathrm{m/s^2}$ . Choose the correct option (…
Laws of Motion Newton's Laws of Motion Monkey Climbing Rope Problems
MediumSingle correctNew idea
Q49
Two projectiles thrown at $30°$ and $45°$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q50
A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is : [Screw gauge…
Units and Measurements
MediumSingle correct
Q51
If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y = 5x(1-x)$ . The $y$ component vector of the initial velocity is __________ $\hat{j}$ . (Take $g = 10\ \mathrm{m/s^2}$ )
Motion in a Plane Projectile Motion Trajectory Equation Application
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q52
A disc of mass 1 kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the…
System of Particles and Rotational Motion Moment of Inertia MOI of Discrete Particles
HardNumerical valueIdea asked in 3 years
Q53
In an experiment to determine the Young's modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0.4 mm with an uncertainty of $\pm$ 0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4…
Mechanical Properties of Solids Elasticity Error Analysis in Searle's Experiment
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q54
When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be $\frac{x}{3}$ Hz where $x =$ __________.
Waves Doppler Effect Moving Source Cases
MediumNumerical valueNew ideaIdea asked in 2 years
Q55
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ( $t_1$ and $t_2$ ) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Multiple Dielectric Configurations
MediumNumerical value · figureNew idea
Q56
Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $l_1$ is 40 cm. Now an unknown resistance $x$ is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the…
Current Electricity Wheatstone Bridge Meter Bridge Principles
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q57
The effective current I in the given circuit at very high frequencies will be __________ A.
Alternating Current LCR Resonance High-Frequency Blocking in Series LCR
HardNumerical value · figureNew idea
Q58
The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5 and its both the surfaces have same radius of curvature R. The value of R…
Ray Optics and Optical Instruments Lens Maker's Formula 1/v versus 1/u Graph
MediumNumerical value · figureNew idea
Q59
In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be “a $\lambda$ ” between the wavelength of $3^{\mathrm{rd}}$ transition line of Paschen series and that of $2^{\mathrm{nd}}$ …
Atoms Bohr's Atomic Model Rydberg Formula and Spectra
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q60
In the circuit shown below, maximum zener diode current will be __________ mA.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Regulation
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before

Chemistry30 questions

13 easy16 medium1 hard

Q61
Match List - I with List - II. List - I (Compound) (A) $\mathrm{BrF_5}$ (B) $[\mathrm{CrF_6}]^{3-}$ (C) $\mathrm{O_3}$ (D) $\mathrm{PCl_5}$ List - II (Shape) (I) bent (II) square pyramidal (III) trigonal bipyramidal (IV) octahedral Choose the correct answer…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 5 Derivative Shapes
EasyMatch the listIdea asked in 3 years
Q62
Match List - I with List - II. List - I (Processes/Reactions) (A) $2\mathrm{SO_2(g)} + \mathrm{O_2(g)} \rightarrow 2\mathrm{SO_3(g)}$ (B) $4\mathrm{NH_3(g)} + 5\mathrm{O_2(g)} \rightarrow 4\mathrm{NO(g)} + 6\mathrm{H_2O(g)}$ (C)…
Surface Chemistry Adsorption Adsorption Theory of Heterogeneous Catalysis
EasyMatch the listNew ideaIdea asked in 2 years
Q63
Given two statements below : Statement I : In $\mathrm{Cl_2}$ molecule the covalent radius is double of the atomic radius of chlorine. Statement II : Radius of anionic species is always greater than their parent atomic radius. Choose the most appropriate…
Classification of Elements and Periodicity in Properties Periodic Trends Van der Waals vs Covalent vs Metallic Radii
MediumTwo statementsNew ideaIdea asked in 2 years
Q64
Refining using liquation method is the most suitable for metals with :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Liquation Refining Principle
EasySingle correctIdea asked in 2 yearsAsked the year before
Q65
Which of the following can be used to prevent the decomposition of $\mathrm{H_2O_2}$ ?
Hydrogen Hydrogen and Hydrides Storage and Stabilization of H2O2
EasySingle correctNew ideaIdea asked in 2 years
Q66
Reaction of $\mathrm{BeCl_2}$ with $\mathrm{LiAlH_4}$ gives : (A) $\mathrm{AlCl_3}$ (B) $\mathrm{BeH_2}$ (C) LiH (D) LiCl (E) $\mathrm{BeAlH_4}$ Choose the correct answer from options given below :
The s-Block Elements s-Block Elements Nature of s-Block Hydrides
MediumOtherNew idea
Q67
Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of “X” with 6-equivalents of “Y”. “X” and “Y”, respectively are :
The p-Block Elements Group 13 & 14 Borazine Structure and Reactivity
EasySingle correctIdea asked in 3 years
Q68
Which of the given reactions is not an example of disproportionation reaction ?
Redox Reactions Disproportionation Balancing
EasySingle correctIdea asked in 3 yearsAsked the year before
Q69
The dark purple colour of $\mathrm{KMnO_4}$ disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :
Redox Reactions Permanganate n-Factor Across Media
EasySingle correctIdea asked in 3 yearsAsked the year before
Q70
$\dot{\mathrm{C}}\mathrm{l} + \mathrm{CH_4} \rightarrow \mathrm{A} + \mathrm{B}$ A and B in the above atmospheric reaction step are :
Environmental Chemistry Ozone Layer Depletion
EasySingle correctIdea asked in 4 yearsAsked the year before
Q71
Which technique among the following, is most appropriate in separation of a mixture of 100 mg of $p$ -nitrophenol and picric acid ?
Organic Chemistry: Some Basic Principles and Techniques
MediumSingle correct
Q72
The difference in the reaction of phenol with bromine in chloroform and bromine in water medium is due to :
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Bromination Solvent Effect
EasySingle correctIdea asked in 3 yearsAsked the year before
Q73
Which of the following compounds is not aromatic ?
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Annulene Planarity and Aromaticity
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q74
The products formed in the following reaction, A and B are [figure: six-membered ring with a C=O at the top vertex; the bottom ring carbon bears H and CHO] $\xrightarrow{[\mathrm{Ag(NH_3)_2}]^+\ \mathrm{OH^-}}$ A $\xrightarrow{\mathrm{NaBH_4}}$ B
Aldehydes, Ketones and Carboxylic Acids
MediumDiagram based · figure
Q75
Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide (PhMgBr) followed by acidic hydrolysis ? [figure: central carbon bonded to Ph (above), Ph (left), OH (right) and $\mathrm{CH_3}$ (below)]
Alcohols, Phenols and Ethers Alcohols and Phenols Grignard Synthesis of Alcohols
MediumOther · figureIdea asked in 3 years
Q76
The major product of the following reaction is [figure: benzene ring with $\mathrm{OCH_3}$ on the top vertex and $\mathrm{O_2N}$ on the adjacent upper-left vertex] $\xrightarrow[\text{(ii) } \mathrm{CH_3CH_2OH}]{\text{(i) Na/liq.}\mathrm{NH_3}}$
Amines Aromatic Hydrocarbons Birch Reduction Regioselectivity
HardDiagram based · figureNew idea
Q77
The correct stability order of the following diazonium salt is (A) [figure: benzene ring with $^{+}\mathrm{N_2Cl^-}$ at the top and $\mathrm{OCH_3}$ at the bottom (para)] (B) [figure: benzene ring with $\mathrm{N_2^+Cl^-}$ at the top and $\mathrm{NO_2}$ at…
Amines Diazonium Salts Resonance Stability of Aryl Diazonium Salts
MediumDiagram based · figureNew idea
Q78
Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents ?
Chemistry in Everyday Life Soaps and Detergents
EasySingle correctNew idea
Q79
Which one of the following is a reducing sugar ?
Biomolecules Carbohydrates Reducing vs Non-reducing Sugars
MediumDiagram based · figureIdea asked in 4 years
Q80
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Experimental reaction of $\mathrm{CH_3Cl}$ with aniline and anhydrous $\mathrm{AlCl_3}$ does not give $o$ and $p$ -methylaniline. Reason…
Amines Aromatic Hydrocarbons Friedel-Crafts Failure with Aniline
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q81
Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 L solution of Mg of concentration 48 ppm. The number of atoms of Mg in this solution is $x \times 10^{20}$ atoms. The value of $x$ is __________. (Nearest Integer) (Given :…
Some Basic Concepts of Chemistry Mole Concept PPM and Mass Percentage
MediumNumerical valueIdea asked in 5 years
Q82
A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is __________ bar. (Nearest Integer)
States of Matter Ideal Gas Laws Dalton's Law
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
The wavelength of an electron and a neutron will become equal when the velocity of the electron is $x$ times the velocity of neutron. The value of $x$ is __________. (Nearest Integer) (Mass of electron is $9.1 \times 10^{-31}$ kg and mass of neutron is…
Structure of Atom Matter Waves Basic Wavelength-Momentum Relation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q84
2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure. The temperature of the calorimeter rises from 298 K to 300 K. The enthalpy change during the combustion of coal is $-x$ kJ mol $^{-1}$ . The value of $x$ is __________.…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bomb Calorimetry Calculations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q85
When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of nitric acid is evaporated. The molarity of the remaining nitric acid solution is $x \times 10^{-2}$ M. (Nearest Integer) (Molar mass of nitric acid is 63 g…
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q86
At 298 K, the equilibrium constant is $2 \times 10^{15}$ for the reaction : $\mathrm{Cu(s)} + 2\mathrm{Ag^+(aq)} \rightleftharpoons \mathrm{Cu^{2+}(aq)} + 2\mathrm{Ag(s)}$ The equilibrium constant for the reaction…
Equilibrium Chemical Equilibrium Equilibrium Constant for Modified Equations
MediumNumerical valueIdea asked in 4 years
Q87
The amount of charge in F (Faraday) required to obtain one mole of iron from $\mathrm{Fe_3O_4}$ is ____________. (Nearest Integer)
Electrochemistry Faraday's Laws of Electrolysis Charge-Mole Relationship
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q88
For a reaction $\mathrm{A} \rightarrow 2\mathrm{B} + \mathrm{C}$ the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L $^{-1}$ respectively. The order of the reaction is __________. (Nearest Integer)
Chemical Kinetics Integrated Rate Equations Nth-Order Half-Life Proportionality
MediumNumerical valueNew idea
Q89
The difference between spin only magnetic moment values of $[\mathrm{Co(H_2O)_6}]\mathrm{Cl_2}$ and $[\mathrm{Cr(H_2O)_6}]\mathrm{Cl_3}$ is __________.
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q90
In the presence of sunlight, benzene reacts with $\mathrm{Cl_2}$ to give product, X. The number of hydrogens in X is __________.
Haloalkanes and Haloarenes Aromatic Hydrocarbons Radical Chlorination of Benzene (BHC Formation)
EasyNumerical valueNew idea

Maths30 questions

0 easy22 medium8 hard

Q1
Let $f : \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $f\,(3x) - f\,(x) = x$ . If $f\,(8) = 7$ , then $f\,(14)$ is equal to :
Continuity and Differentiability Differentiability via Functional Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q2
Let O be the origin and A be the point $z_1 = 1 + 2i$ . If B is the point $z_2$ , $\mathrm{Re}(z_2) < 0$ , such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true ?
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Coni Method (Rotation Theorem)
MediumSingle correctNew idea
Q3
If the system of linear equations. $8x + y + 4z = -2$ $x + y + z = 0$ $\lambda x - 3y = \mu$ has infinitely many solutions, then the distance of the point $\left(\lambda,\ \mu,\ -\frac{1}{2}\right)$ from the plane $8x + y + 4z + 2 = 0$ is :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
Let A be a $2 \times 2$ matrix with $\det\,(\mathrm{A}) = -1$ and $\det\,((\mathrm{A} + \mathrm{I})\,(\mathrm{Adj}\,(\mathrm{A}) + \mathrm{I})) = 4$ . Then the sum of the diagonal elements of A can be :
Matrices Matrix Inverse Cofactor Matrix and Adjoint
HardSingle correctIdea asked in 5 yearsAsked the year before
Q5
The odd natural number a, such that the area of the region bounded by $y = 1$ , $y = 3$ , $x = 0$ , $x = y^{a}$ is $\frac{364}{3}$ , is equal to :
Application of Integrals Area Under Curves Area with Y-Axis
MediumSingle correctNew idea
Q6
Consider two G.Ps. $2,\ 2^2,\ 2^3,\ \ldots$ and $4,\ 4^2,\ 4^3,\ \ldots$ of 60 and n terms respectively. If the geometric mean of all the $60 + n$ terms is $(2)^{\frac{225}{8}}$ , then $\sum_{k=1}^{n} k(n - k)$ is equal to :
Sequences and Series AP and GP Product of n Geometric Means
MediumSingle correctNew idea
Q7
If the function $f(x) = \begin{cases} \dfrac{\log_e (1 - x + x^2) + \log_e (1 + x + x^2)}{\sec x - \cos x}, & x \in \left(\dfrac{-\pi}{2}, \dfrac{\pi}{2}\right) - \{0\} \\ \mathrm{k}, & x = 0 \end{cases}$ is continuous at $x = 0$ , then k is equal to :
Continuity and Differentiability Finding Unknown Constants for Continuity
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q8
If $f(x) = \begin{cases} x + \mathrm{a}, & x \leq 0 \\ |x - 4|, & x > 0 \end{cases}$ and $g(x) = \begin{cases} x + 1, & x < 0 \\ (x - 4)^2 + \mathrm{b}, & x \geq 0 \end{cases}$ are continuous on $\mathbf{R}$ , then $(g o f)\,(2) + (f o g)\,(-2)$ is equal to :
Continuity and Differentiability Finding Unknown Constants for Continuity
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q9
Let $f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2 (\mathrm{b}^2 - 4), & x > 1 \end{cases}$ . Then the set of all values of b, for which $f(x)$ has maximum value at $x = 1$ , is :
Application of Derivatives Maxima and Minima Extrema at Piecewise Junctions
MediumSingle correctNew idea
Q10
If $\mathrm{a} = \lim_{n \to \infty} \sum_{k=1}^{n} \dfrac{2n}{n^2 + k^2}$ and $f(x) = \sqrt{\dfrac{1 - \cos x}{1 + \cos x}}$ , $x \in (0, 1)$ , then :
Integrals Integral as Limit of Sum Summation to Riemann Form
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q11
If $\frac{dy}{dx} + 2y \tan x = \sin x$ , $0 < x < \frac{\pi}{2}$ and $y\left(\frac{\pi}{3}\right) = 0$ , then the maximum value of $y(x)$ is :
Differential Equations Linear Differential Equations Particular Solution Solving
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q12
A point P moves so that the sum of squares of its distances from the points $(1,\ 2)$ and $(-2,\ 1)$ is 14. Let $f\,(x,\ y) = 0$ be the locus of P, which intersects the $x$ -axis at the points A, B and the $y$ -axis at the points C, D. Then the area of the…
Conic Sections General Conic Section Condition for a Circle
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q13
Let the tangent drawn to the parabola $y^2 = 24x$ at the point $(\alpha,\ \beta)$ is perpendicular to the line $2x + 2y = 5$ . Then the normal to the hyperbola $\frac{x^2}{\alpha^2} - \frac{y^2}{\beta^2} = 1$ at the point $(\alpha + 4,\ \beta + 4)$ does NOT…
Conic Sections Normals to Conics Hyperbola Normal Point Form
MediumSingle correctIdea asked in 3 years
Q14
The length of the perpendicular from the point $(1,\ -2,\ 5)$ on the line passing through $(1,\ 2,\ 4)$ and parallel to the line $x + y - z = 0 = x - 2y + 3z - 5$ is :
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q15
Let $\overrightarrow{\mathrm{a}} = \alpha \hat{i} + \hat{j} - \hat{k}$ and $\overrightarrow{\mathrm{b}} = 2\hat{i} + \hat{j} - \alpha \hat{k}$ , $\alpha > 0$ . If the projection of $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ on the vector…
Vector Algebra Cross Product Magnitude and Sine Formula
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q16
The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $\mathrm{P}(\mathrm{X} = 1) = \frac{4}{243}$ , then $\mathrm{P}(\mathrm{X} = 4 \text{ or } 5)$ is equal to :
Probability
MediumSingle correct
Q17
Let $\mathrm{E}_1$ , $\mathrm{E}_2$ , $\mathrm{E}_3$ be three mutually exclusive events such that $\mathrm{P}(\mathrm{E}_1) = \frac{2 + 3\mathrm{p}}{6}$ , $\mathrm{P}(\mathrm{E}_2) = \frac{2 - \mathrm{p}}{8}$ and…
Probability
MediumSingle correct
Q18
Let $\mathrm{S} = \{\theta \in [0,\ 2\pi] : 8^{2\sin^2\theta} + 8^{2\cos^2\theta} = 16\}$ . Then $\mathrm{n}(\mathrm{S}) + \sum_{\theta \in \mathrm{S}} \left(\sec\left(\frac{\pi}{4} + 2\theta\right) \mathrm{cosec}\left(\frac{\pi}{4} + 2\theta\right)\right)$ …
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
HardSingle correctIdea asked in 5 yearsAsked the year before
Q19
$\tan\left(2\tan^{-1}\frac{1}{5} + \sec^{-1}\frac{\sqrt{5}}{2} + 2\tan^{-1}\frac{1}{8}\right)$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Sum of Three Inverse Tangents
MediumSingle correctNew idea
Q20
The statement $(\sim(\mathrm{p} \Leftrightarrow \sim\mathrm{q})) \wedge \mathrm{q}$ is :
Relations and Functions
MediumSingle correct
Q21
If for some $\mathrm{p},\ \mathrm{q},\ \mathrm{r} \in \mathbf{R}$ , not all have same sign, one of the roots of the equation $(\mathrm{p}^2 + \mathrm{q}^2)x^2 - 2\mathrm{q}(\mathrm{p} + \mathrm{r})x + \mathrm{q}^2 + \mathrm{r}^2 = 0$ is also a root of the…
Complex Numbers and Quadratic Equations Quadratic Roots Common Root Condition
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q22
The number of 5-digit natural numbers, such that the product of their digits is 36, is __________.
Permutations and Combinations Permutations with Repetition
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q23
The series of positive multiples of 3 is divided into sets : $\{3\}$ , $\{6,\ 9,\ 12\}$ , $\{15,\ 18,\ 21,\ 24,\ 27\}$ , $\ldots$ Then the sum of the elements in the $11^{\text{th}}$ set is equal to __________.
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q24
The number of distinct real roots of the equation $x^5(x^3 - x^2 - x + 1) + x\ (3x^3 - 4x^2 - 2x + 4) - 1 = 0$ is ___________.
Application of Derivatives Maxima and Minima Analyzing Polynomial Roots via Extrema
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q25
If the coefficients of $x$ and $x^2$ in the expansion of $(1 + x)^{\mathrm{p}}\ (1 - x)^{\mathrm{q}}$ , $\mathrm{p},\ \mathrm{q} \leq 15$ , are $-3$ and $-5$ respectively, then the coefficient of $x^3$ is equal to __________.
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
MediumNumerical valueNew ideaIdea asked in 2 years
Q26
If $\mathrm{n}(2\mathrm{n} + 1) \int_0^1 (1 - x^{\mathrm{n}})^{2\mathrm{n}}\ \mathrm{d}x = 1177 \int_0^1 (1 - x^{\mathrm{n}})^{2\mathrm{n}+1}\ \mathrm{d}x$ , then $\mathrm{n} \in \mathbf{N}$ is equal to __________.
Integrals
HardNumerical value
Q27
Let a curve $y = y(x)$ pass through the point $(3,\ 3)$ and the area of the region under this curve, above the $x$ -axis and between the abscissae 3 and $x(>3)$ be $\left(\frac{y}{x}\right)^3$ . If this curve also passes through the point…
Differential Equations Area Under Curves Curves from Area Properties
HardNumerical valueNew ideaIdea asked in 2 years
Q28
The equations of the sides AB, BC and CA of a triangle ABC are $2x + y = 0$ , $x + \mathrm{p}y = 15\mathrm{a}$ and $x - y = 3$ respectively. If its orthocentre is $(2,\ \mathrm{a})$ , $-\frac{1}{2} < \mathrm{a} < 2$ , then p is equal to __________.
Straight Lines
MediumNumerical value
Q29
Let the function $f(x) = 2x^2 - \log_e x$ , $x > 0$ , be decreasing in $(0,\ \mathrm{a})$ and increasing in $(\mathrm{a},\ 4)$ . A tangent to the parabola $y^2 = 4\mathrm{a}x$ at a point P on it passes through the point $(8\mathrm{a},\ 8\mathrm{a} - 1)$ but…
Application of Derivatives Normals to Conics Parabola Normal Point Form
HardNumerical valueIdea asked in 2 yearsAsked the year before
Q30
Let Q and R be two points on the line $\frac{x + 1}{2} = \frac{y + 2}{3} = \frac{z - 1}{2}$ at a distance $\sqrt{26}$ from the point P(4, 2, 7). Then the square of the area of the triangle PQR is __________.
Three Dimensional Geometry Lines in 3D General Point Parameterization
HardNumerical valueNew ideaIdea asked in 2 years

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2022 shifts.