JEE Main 2022 · July session

JEE Main 29 July 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 20 were rated hard and 28 easy. Its hard-question count was the 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: 20; 22% of the shift
Chapters asked: 66; 13 questions with a figure

Key findings · 29 Jul 2022, Shift 1

1
20 hard questions (22%): the 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 14 of 30 rated hard; Physics had the most easy questions (14 of 30).
3
30 questions tested a new idea, one no earlier year had asked: 41% of the 74 questions tagged to an idea.
4
43 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
39 shared an idea with another 2022 shift (53% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Units and Measurements in Physics (3), Amines in Chemistry (3) and Sequences and Series in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 14Medium 13Hard 3

Top chapters

Chemistry

30 Q · 10 numerical

Easy 13Medium 14Hard 3

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 15Hard 14

Top chapters

Question format

Single correct45 Q
Numerical value30 Q
Diagram based9 Q
Other2 Q
Assertion–reason2 Q
Two statements1 Q
Match the list1 Q

What each question asks you to do

Multi-step33 Q
Calculation32 Q
Conceptual18 Q
Recall6 Q
Data or graph1 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

14 easy13 medium3 hard

Q31
Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $\rho$ and radius of the drop is r,…
Units and Measurements Surface Tension Oscillation Frequency of a Liquid Drop
MediumAssertion–reasonNew idea
Q32
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.
Motion in a Straight Line Kinematics in 1D Kinematic Symmetry in Free Fall
MediumSingle correctNew idea
Q33
If $t = \sqrt{x} + 4$ , then $\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)_{t=4}$ is :
Motion in a Straight Line Kinematics in 1D Calculus in Kinematics
EasySingle correctIdea asked in 5 yearsAsked the year before
Q34
A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed $\nu$ . Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and…
Laws of Motion Circular Motion Centripetal Acceleration
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q35
A ball is projected with kinetic energy E, at an angle of $60^\circ$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q36
Two bodies of mass 1 kg and 3 kg have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :
System of Particles and Rotational Motion Center of Mass Discrete System COM
EasySingle correctNew ideaIdea asked in 3 years
Q37
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R) : Because the angle of contact between the…
Mechanical Properties of Fluids Surface Tension Angle of Contact
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q38
If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :
Mechanical Properties of Solids Elasticity Elastic Moduli
EasySingle correctIdea asked in 7 yearsAsked the year before
Q39
The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$ , is given by :
Oscillations Pendulums Pendulum on a Smooth Incline
MediumSingle correctNew idea
Q40
A spherically symmetric charge distribution is considered with charge density varying as $\rho(r) = \begin{cases} \rho_0\left(\frac{3}{4} - \frac{r}{R}\right) & \text{for } r \le R \\ \text{zero} & \text{for } r > R \end{cases}$ Where, r(r < R) is the…
Electric Charges and Fields Gauss's Law Field of Non-uniform Spherical Charge
HardSingle correct · figureNew idea
Q41
Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the…
Electrostatic Potential and Capacitance Conductors in Fields Equipotential Nature of Conductors
EasyTwo statementsNew idea
Q42
Two metallic wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :
Current Electricity Ohm's Law and Resistance Resistivity and Geometry
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q43
An alternating emf $E = 440\sin 100\pi t$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi}$ H. If an a.c. ammeter is connected in the circuit, its reading will be :
Alternating Current RMS and Peak Values AC Measuring Instruments
EasySingle correctIdea asked in 2 yearsAsked the year before
Q44
A coil of inductance 1 H and resistance 100 $\Omega$ is connected to a battery of 6 V. Determine approximately : (a) The time elapsed before the current acquires half of its steady - state value. (b) The energy stored in the magnetic field associated with…
Electromagnetic Induction Lenz's Law Opposing Current Growth and Decay
HardSingle correctNew idea
Q45
Match List - I with List - II : List - I | List - II (a) UV rays | (i) Diagnostic tool in medicine (b) X-rays | (ii) Water purification (c) Microwave | (iii) Communication, Radar (d) Infrared wave | (iv) Improving visibility in foggy days Choose the correct…
Electromagnetic Waves
EasyMatch the list
Q46
The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$ . To double the kinetic energy, the incident light must have wavelength :
Dual Nature of Radiation and Matter Photoelectric Effect Einstein's Photoelectric Equation
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q47
Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.
Atoms Bohr's Atomic Model Energy Level Calculations
EasySingle correctIdea asked in 6 yearsAsked the year before
Q48
Find the modulation index of an AM wave having 8 V variation where maximum amplitude of the AM wave is 9 V.
Communication Systems
EasySingle correct
Q49
A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?
Units and Measurements
EasySingle correct
Q50
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted : (A) Screw moves 0.5 mm on main scale in one complete rotation (B) Total divisions on circular scale = 50 (C) Main scale reading is 2.5 mm (D)…
Units and Measurements
MediumOther · figure
Q51
An object is projected in the air with initial velocity u at an angle $\theta$ . The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The…
Motion in a Plane Projectile Motion Complementary Angles Range and Ratios
MediumNumerical valueNew ideaIdea asked in 2 years
Q52
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha$ h (h << $R_e$ ) from the earth surface. The value of $\alpha$ will be __________.…
Gravitation
MediumNumerical value
Q53
The pressure $P_1$ and density $d_1$ of diatomic gas $\left(\gamma = \frac{7}{5}\right)$ changes suddenly to $P_2$ (> $P_1$ ) and $d_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes __________ times of its initial…
Thermodynamics Thermodynamic Processes Adiabatic T-V and P-T Relations
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q54
One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4}$ R J/mol K; then the value of $\alpha$ will be __________. (Assume that the given diatomic gas has no…
Kinetic Theory Kinetic Theory of Gases Internal Energy of Gas Mixtures
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q55
The current I flowing through the given circuit will be __________ A.
Current Electricity Kirchhoff's Laws Short Circuits and Equipotential Nodes
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q56
A closely wounded circular coil of radius 5 cm produces a magnetic field of $37.68 \times 10^{-4}$ T at its center. The current through the coil is __________ A. [Given, number of turns in the coil is 100 and $\pi$ = 3.14]
Moving Charges and Magnetism Biot-Savart Law Field of an N-Turn Flat Coil
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q57
Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $\pi$ . The difference of resultant intensities, at the point A and B, will be __________ I.
Wave Optics Young's Double Slit Resultant Intensity Formula
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q58
A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is __________ A- $\mathrm{m^2}$ . [Given $\pi$ = 3.14]
Moving Charges and Magnetism Magnetic Dipole Moment Magnetic moment of a current loop
MediumNumerical valueNew idea
Q59
The X-Y plane be taken as the boundary between two transparent media $M_1$ and $M_2$ . $M_1$ in $Z \ge 0$ has a refractive index of $\sqrt{2}$ and $M_2$ with $Z < 0$ has a refractive index of $\sqrt{3}$ . A ray of light travelling in $M_1$ along the direction…
Ray Optics and Optical Instruments Refraction and Snell's Law Vector Form of Snell's Law
HardNumerical valueNew idea
Q60
If the potential barrier across a p-n junction is 0.6 V. Then the electric field intensity, in the depletion region having the width of $6 \times 10^{-6}$ m, will be __________ $\times 10^5$ N/C.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Depletion Region Formation
EasyNumerical valueNew ideaIdea asked in 2 years

Chemistry30 questions

13 easy14 medium3 hard

Q61
Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule ?
Chemical Bonding and Molecular Structure VSEPR Theory VSEPR in Odd-Electron Molecules
EasySingle correctNew idea
Q62
$\mathrm{N_{2(g)}+3H_{2(g)} \rightleftharpoons 2NH_{3(g)}}$ 20 g 5 g Consider the above reaction, the limiting reagent of the reaction and number of moles of $\mathrm{NH_3}$ formed respectivly are :
Some Basic Concepts of Chemistry Stoichiometry Limiting Reagent Identification
EasySingle correctIdea asked in 4 yearsAsked the year before
Q63
100 mL of 5% (w/v) solution of NaCl in water was prepared in 250 mL beaker. Albumin from the egg was poured into NaCl solution and stirred well. This resulted in a/an :
Surface Chemistry Colloids Lyophilic and Lyophobic Sols
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q64
The first ionization enthalpy of Na, Mg and Si, respectively, are : 496, 737 and 786 kJ $\mathrm{mol^{-1}}$ . The first ionization enthalpy (kJ $\mathrm{mol^{-1}}$ ) of Al is :
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q65
In metallurgy the term “gangue” is used for :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Flux and Slag Chemistry
EasySingle correctNew idea
Q66
The reaction of zinc with excess of aqueous alkali, evolves hydrogen gas and gives :
The d- and f-Block Elements
EasySingle correct
Q67
Lithium nitrate and sodium nitrate, when heated separately, respectively, give :
The s-Block Elements s-Block Elements Thermal Stability Trends
EasySingle correctIdea asked in 2 yearsAsked the year before
Q68
Number of lone pairs of electrons in the central atom of $\mathrm{SCl_2}$ , $\mathrm{O_3}$ , $\mathrm{ClF_3}$ and $\mathrm{SF_6}$ , respectively, are :
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q69
In following pairs, the one in which both transition metal ions are colourless is :
The d- and f-Block Elements d-Block Elements Color and Catalysis
EasySingle correctIdea asked in 4 yearsAsked the year before
Q70
In neutral or faintly alkaline medium, $\mathrm{KMnO_4}$ being a powerful oxidant can oxidize, thiosulphate almost quantitatively, to sulphate. In this reaction overall change in oxidation state of manganese will be :
The d- and f-Block Elements d-Block Elements Specific KMnO4 Oxidations in Neutral/Alkaline Medium
MediumSingle correctNew ideaIdea asked in 2 years
Q71
Which among the following pairs has only herbicides ?
Chemistry in Everyday Life
EasySingle correct
Q72
Which among the following is the strongest Bronsted base ?
Amines Aliphatic Amine Basicity
MediumDiagram based · figureIdea asked in 2 yearsAsked the year before
Q73
Which among the following pairs of the structures will give different products on ozonolysis ? (Consider the double bonds in the structures are rigid and not delocalized.)
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
HardDiagram based · figureIdea asked in 7 yearsAsked the year before
Q74
[figure: CH3CH2CH2-Cl, a three-carbon chain bearing Cl; left arrow with AgCN, $\mathrm{C_2H_5OH-H_2O}$ gives 'A' (Major Product); right arrow with NaCN, $\mathrm{C_2H_5OH-H_2O}$ gives 'B' (Major Product)] Considering the above reactions, the compound 'A' and…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Ambident Nucleophiles (Cyanide vs Isocyanide)
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q75
[figure: 4-hydroxybenzaldehyde (OH at top, CHO at bottom of benzene ring) $\xrightarrow{\mathrm{Br_2}}$ A $\xrightarrow{\mathrm{NH_2OH}}$ B $\xrightarrow[\Delta]{\mathrm{P_2O_5}}$ C] Consider the above reaction sequence, the Product 'C' is :
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Geometrical Isomerism in Oximes
MediumDiagram based · figureNew idea
Q76
[figure: 'A' ( $\mathrm{C_8H_6Cl_2O}$ ) $\xrightarrow{\mathrm{NH_3}}$ $\mathrm{C_8H_8ClNO}$ $\xrightarrow[\mathrm{NaOH}]{\mathrm{Br_2}}$ a benzene ring with $\mathrm{CH_3}$ (top), Cl (upper right, adjacent to $\mathrm{CH_3}$ ) and $\mathrm{H_2N}$ (lower left,…
Amines Hofmann Bromamide Degradation
HardDiagram based · figureIdea asked in 5 yearsAsked the year before
Q77
[figure: benzenediazonium chloride (benzene ring bearing $\mathrm{N^{+}\equiv NCl^{-}}$ ) + 'A' $\xrightarrow{\mathrm{NaOH}}$ Product (Orange-red dye)] Which among the following represent reagent 'A' ?
Amines Diazonium Salts Azo Coupling Reactions
EasyDiagram based · figureIdea asked in 5 yearsAsked the year before
Q78
Consider the following reaction sequence : [figure: 4-aminobenzonitrile (benzene ring with $\mathrm{NH_2}$ at top, CN at bottom) $\xrightarrow[\mathrm{(ii)\ H_2O}]{\mathrm{(i)\ AlH\ (i\text{-}Bu)_2}}$ 'A'…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives DIBAL-H Selective Reduction
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q79
Which of the following compounds is an example of hypnotic drug ?
Chemistry in Everyday Life Barbiturates as Hypnotic Tranquilizers
EasySingle correctNew idea
Q80
A compound ‘X’ is acidic and it is soluble in NaOH solution, but insoluble in $\mathrm{NaHCO_3}$ solution. Compound ‘X’ also gives violet colour with neutral $\mathrm{FeCl_3}$ solution. The compound ‘X’ is :
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q81
Resistance of a conductivity cell (cell constant 129 $\mathrm{m^{-1}}$ ) filled with 74.5 ppm solution of KCl is 100 $\Omega$ (labelled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50 $\Omega$ (labelled as…
Electrochemistry
HardNumerical value
Q82
Ionic radii of cation $\mathrm{A^+}$ and anion $\mathrm{B^-}$ are 102 and 181 pm respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for $\mathrm{B^-}$ . $\mathrm{A^+}$ is present in all octahedral…
The Solid State Crystal Lattices Edge-Radius Relationships
MediumNumerical valueNew ideaIdea asked in 2 years
Q83
The minimum uncertainty in the speed of an electron in an one dimensional region of length $2a_0$ (Where $a_0$ = Bohr radius 52.9 pm) is __________ $\mathrm{km\ s^{-1}}$ . (Given : Mass of electron = $9.1\times10^{-31}$ kg, Planck’s constant h =…
Structure of Atom
MediumNumerical value
Q84
When 600 mL of 0.2 M $\mathrm{HNO_3}$ is mixed with 400 mL of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is __________ $\times10^{-2}$ °C. (Enthalpy of neutralisation = 57 kJ $\mathrm{mol^{-1}}$ and Specific heat of water = 4.2…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Constant Enthalpy of Neutralization
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q85
If $\mathrm{O_2}$ gas is bubbled through water at 303 K, the number of millimoles of $\mathrm{O_2}$ gas that dissolve in 1 litre of water is __________. (Nearest Integer) (Given : Henry’s Law constant for $\mathrm{O_2}$ at 303 K is 46.82 k bar and partial…
Solutions
MediumNumerical value
Q86
If the solubility product of PbS is $8\times10^{-28}$ , then the solubility of PbS in pure water at 298 K is $x\times10^{-16}$ $\mathrm{mol\ L^{-1}}$ . The value of $x$ is __________. (Nearest Integer) [Given : $\sqrt{2}$ = 1.41]
Equilibrium Solubility Product Solubility-Ksp Relationship
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q87
The reaction between X and Y is first order with respect to X and zero order with respect to Y. Experiment | [X] $\mathrm{mol\ L^{-1}}$ | [Y] $\mathrm{mol\ L^{-1}}$ | Initial rate $\mathrm{mol\ L^{-1}\ min^{-1}}$ I | 0.1 | 0.1 | $2\times10^{-3}$ II | L | 0.2…
Chemical Kinetics Rate Laws Initial Rates Method
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q88
In a linear tetrapeptide (Constituted with different amino acids), (number of amino acids) $-$ (number of peptide bonds) is __________.
Biomolecules
EasyNumerical value
Q89
In bromination of Propyne, with Bromine 1, 1, 2, 2-tetrabromopropane is obtained in 27% yield. The amount of 1, 1, 2, 2-tetrabromopropane obtained from 1 g of Bromine in this reaction is __________ $\times10^{-1}$ g. (Nearest integer) (Molar Mass : Bromine =…
Hydrocarbons Stoichiometry Theoretical and Percent Yield
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q90
$\mathrm{[Fe(CN)_6]^{3-}}$ should be an inner orbital complex. Ignoring the pairing energy, the value of crystal field stabilization energy for this complex is ( $-$ ) __________ $\Delta_\mathrm{o}$ . (Nearest integer)
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumNumerical valueIdea asked in 6 yearsAsked the year before

Maths30 questions

1 easy15 medium14 hard

Q1
Let R be a relation from the set $\{1, 2, 3, \ldots, 60\}$ to itself such that $R = \{(a, b) : b = pq$ , where $p, q \geq 3$ are prime numbers $\}$ . Then, the number of elements in R is :
Relations and Functions Sets and Relations Counting Relations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q2
If $z = 2 + 3i$ , then $z^5 + (\overline{z})^5$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Simplifying Conjugate Binomial Sums
EasySingle correctNew idea
Q3
Let A and B be two $3 \times 3$ non-zero real matrices such that AB is a zero matrix. Then
Determinants Cramer's Rule Homogeneous System Solutions
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q4
If $\frac{1}{(20 - a)(40 - a)} + \frac{1}{(40 - a)(60 - a)} + \ldots + \frac{1}{(180 - a)(200 - a)} = \frac{1}{256}$ , then the maximum value of a is :
Sequences and Series AP and GP Method of Differences for Telescoping Series
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
If $\lim_{x \to 0} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$ , where $\alpha, \beta, \gamma \in \mathbf{R}$ , then which of the following is NOT correct ?
Limits and Derivatives L'Hopital's Rule Determining Unknown Constants from Finite Limits
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q6
The integral $\int_0^{\pi/2} \frac{1}{3 + 2\sin x + \cos x}\, dx$ is equal to :
Integrals Integration by Substitution Weierstrass Substitution
HardSingle correctIdea asked in 2 years
Q7
Let the solution curve $y = y(x)$ of the differential equation $(1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1$ pass through the point $\left(0, \frac{\pi}{2}\right)$ . Then, $\lim_{x \to \infty} e^x y(x)$ is equal to :
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q8
Let a line L pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$ , $b \in \mathbf{R} - \left\{\frac{4}{3}\right\}$ . If the line L also passes through the point $(1, 1)$ and touches the circle $17(x^2 + y^2) = 16$ , then the…
Straight Lines Circle Tangents Condition of tangency
HardSingle correctIdea asked in 4 yearsAsked the year before
Q9
If the foot of the perpendicular from the point $A(-1, 4, 3)$ on the plane $P : 2x + my + nz = 4$ , is $\left(-2, \frac{7}{2}, \frac{3}{2}\right)$ , then the distance of the point A from the plane P, measured parallel to a line with direction ratios…
Three Dimensional Geometry Point-Plane Distance Distance Along a Line
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q10
Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$ . Let $\vec{c}$ be a vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda\vec{c}$ . If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of…
Vector Algebra Triple Products VTP BAC-CAB Expansion
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q11
The angle of elevation of the top of a tower from a point A due north of it is $\alpha$ and from a point B at a distance of 9 units due west of A is $\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)$ . If the distance of the point B from the tower is 15 units, then…
Trigonometric Functions
MediumSingle correct
Q12
The statement $(p \wedge q) \Rightarrow (p \wedge r)$ is equivalent to :
Mathematical Reasoning
MediumSingle correct
Q13
Let the circumcentre of a triangle with vertices $A(a, 3)$ , $B(b, 5)$ and $C(a, b)$ , $ab > 0$ be $P(1, 1)$ . If the line AP intersects the line BC at the point $Q(k_1, k_2)$ , then $k_1 + k_2$ is equal to :
Straight Lines Properties of Triangles Inradius and Circumradius
HardSingle correctIdea asked in 3 yearsAsked the year before
Q14
Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$ . If $\theta$ is the angle between the vectors $(\hat{a} + \hat{b})$ and $(\hat{a} + 2\hat{b} + 2(\hat{a} \times \hat{b}))$ , then the value of…
Vector Algebra Cross Product Magnitude and Sine Formula
HardSingle correctIdea asked in 7 yearsAsked the year before
Q15
If $f(\alpha) = \int_1^{\alpha} \frac{\log_{10} t}{1 + t}\, dt$ , $\alpha > 0$ , then $f(e^3) + f(e^{-3})$ is equal to :
Integrals Definite Integral Properties Reciprocal Limits Substitution Trick
HardSingle correctNew idea
Q16
The area of the region $\{(x, y) : |x - 1| \leq y \leq \sqrt{5 - x^2}\}$ is equal to :
Application of Integrals Area Under Curves Area with Modulus
MediumSingle correctNew ideaIdea asked in 4 years
Q17
Let the focal chord of the parabola $P : y^2 = 4x$ along the line $L : y = mx + c$ , $m > 0$ meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola $H : x^2 - y^2 = 4$ . If O is the vertex of P and F is the focus of H on the…
Conic Sections Parabola Focal Chords Equation of focal chord
HardSingle correctNew ideaIdea asked in 2 years
Q18
The number of points, where the function $f : \mathbf{R} \to \mathbf{R}$ , $f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|$ , is NOT differentiable, is :
Continuity and Differentiability Differentiability of Modulus Functions
HardSingle correctIdea asked in 5 yearsAsked the year before
Q19
Let $S = \{1, 2, 3, \ldots, 2022\}$ . Then the probability, that a randomly chosen number n from the set S such that HCF $(n, 2022) = 1$ , is :
Probability
MediumSingle correct
Q20
Let $f(x) = 3^{(x^2 - 2)^3 + 4}$ , $x \in \mathbf{R}$ . Then which of the following statements are true ? P : $x = 0$ is a point of local minima of $f$ Q : $x = \sqrt{2}$ is a point of inflection of $f$ R : $f'$ is increasing for $x > \sqrt{2}$
Application of Derivatives Maxima and Minima Points of Inflection
HardOtherNew idea
Q21
Let $S = \{\theta \in (0, 2\pi) : 7\cos^2\theta - 3\sin^2\theta - 2\cos^2 2\theta = 2\}$ . Then, the sum of roots of all the equations $x^2 - 2(\tan^2\theta + \cot^2\theta)x + 6\sin^2\theta = 0$ , $\theta \in S$ , is __________.
Trigonometric Functions General Solutions Higher Power Reduction Identities
HardNumerical valueNew idea
Q22
Let the mean and the variance of 20 observations $x_1, x_2, \ldots, x_{20}$ be 15 and 9, respectively. For $\alpha \in \mathbf{R}$ , if the mean of $(x_1 + \alpha)^2, (x_2 + \alpha)^2, \ldots, (x_{20} + \alpha)^2$ is 178, then the square of the maximum value…
Statistics Variance and SD Relationship Between RMS, Mean, and Variance
MediumNumerical valueNew idea
Q23
Let a line with direction ratios $a, -4a, -7$ be perpendicular to the lines with direction ratios $3, -1, 2b$ and $b, a, -2$ . If the point of intersection of the line $\frac{x + 1}{a^2 + b^2} = \frac{y - 2}{a^2 - b^2} = \frac{z}{1}$ and the plane…
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q24
Let $a_1, a_2, a_3, \ldots$ be an A.P. If $\sum_{r=1}^{\infty} \frac{a_r}{2^r} = 4$ , then $4a_2$ is equal to __________.
Sequences and Series Arithmetico-Geometric Series Sum of Infinite AGP
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q25
Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $\left(\sqrt[4]{2} + \frac{1}{\sqrt[4]{3}}\right)^n$ , in the increasing powers of $\frac{1}{\sqrt[4]{3}}$ be $\sqrt[4]{6} : 1$ . If the sixth term…
Binomial Theorem
HardNumerical value
Q26
The number of matrices of order $3 \times 3$ , whose entries are either 0 or 1 and the sum of all the entries is a prime number, is __________.
Matrices Permutations and Combinations Combinations of Distinct Objects
MediumNumerical valueIdea asked in 8 yearsAsked the year before
Q27
Let $p$ and $p + 2$ be prime numbers and let $\Delta = \begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \end{vmatrix}$ Then the sum of the maximum values of $\alpha$ and $\beta$ , such that $p^{\alpha}$ and…
Determinants Cramer's Rule Quick Identification via Proportionality
HardNumerical valueNew idea
Q28
If $\frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + \frac{1}{4 \times 5 \times 6} + \ldots + \frac{1}{100 \times 101 \times 102} = \frac{k}{101}$ , then $34k$ is equal to __________.
Sequences and Series AP and GP Method of Differences (Vn Method)
MediumNumerical valueNew ideaIdea asked in 5 years
Q29
Let $S = \{4, 6, 9\}$ and $T = \{9, 10, 11, \ldots, 1000\}$ . If $A = \{a_1 + a_2 + \ldots + a_k : k \in \mathbf{N},\ a_1, a_2, a_3, \ldots, a_k \in S\}$ , then the sum of all the elements in the set $T - A$ is equal to __________.
Relations and Functions
HardNumerical value
Q30
Let the mirror image of a circle $c_1 : x^2 + y^2 - 2x - 6y + \alpha = 0$ in line $y = x + 1$ be $c_2 : 5x^2 + 5y^2 + 10gx + 10fy + 38 = 0$ . If r is the radius of circle $c_2$ , then $\alpha + 6r^2$ is equal to __________.
Conic Sections Circle Tangents Reflection of Center Across Tangent
MediumNumerical 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.