JEE Main 2022 · June session

JEE Main 30 June 2022, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 32 easy. Its hard-question count was the joint 14th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Aldehydes, Ketones and Carboxylic Acids, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 12; 13% of the shift
Chapters asked: 63; 14 questions with a figure

Key findings · 30 Jun 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 10 of 30 rated hard; Physics had the most easy questions (15 of 30).
3
20 questions tested a new idea, one no earlier year had asked: 27% of the 74 questions tagged to an idea.
4
51 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: Alternating Current in Physics (2), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 15Hard 0

Top chapters

Alternating Current2 Q
Atoms2 Q
Current Electricity2 Q
Electrostatic Potential and Capacitance2 Q
Mechanical Properties of Fluids2 Q
Motion in a Plane2 Q

Chemistry

30 Q · 10 numerical

Easy 13Medium 15Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 4Medium 16Hard 10

Top chapters

Complex Numbers and Quadratic Equations3 Q
Conic Sections3 Q
Determinants3 Q
Application of Derivatives2 Q
Differential Equations2 Q
Integrals2 Q

Question format

Single correct52 Q
Numerical value30 Q
Diagram based6 Q
Match the list2 Q

What each question asks you to do

Calculation33 Q
Multi-step24 Q
Application17 Q
Recall9 Q
Conceptual4 Q
Data or graph3 Q

Most common: Calculation.

Against the other 2022 shifts

This shift next to the 23 other 2022 shifts Lumi analysed

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

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

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

Drill down

What this shift asked, and its history

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

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

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

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

Every question

All 90 questions of this shift

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

Subject

Difficulty

Idea

Find

90 of 90 questions

Physics30 questions

15 easy15 medium0 hard

Q31
At t=0, truck, starting from rest, moves in the positive $x$ -direction at uniform acceleration of 5 $\mathrm{ms^{-2}}$ . At t=20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball,…
Motion in a Plane Kinematics in 2D Projectile from a Moving Frame
MediumSingle correctNew idea
Q32
If n main scale divisions coincide with (n+1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :
Units and Measurements
EasySingle correct
Q33
The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3ρ and 5ρ respectively. The ratio of their acceleration due to gravity is :
Gravitation
EasySingle correct
Q34
Two projectiles $\mathrm{P_1}$ and $\mathrm{P_2}$ thrown with speed in the ratio $\sqrt{3}:\sqrt{2}$ , attain the same height during their motion. If $\mathrm{P_2}$ is thrown at an angle of $60^\circ$ with the horizontal, the angle of projection of…
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q35
An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed $v$ . The coefficient of viscosity of the solution is given by :
Mechanical Properties of Fluids Viscosity Terminal Velocity of Rising Bubbles
MediumSingle correctNew ideaIdea asked in 3 years
Q36
A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value…
Laws of Motion Friction Block on a Vertical Wall
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q37
Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q38
The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is : (Given $0^\circ$ C=273 K)
Thermal Properties of Matter
EasySingle correct
Q39
A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii $\mathrm{r_1}$ and $\mathrm{r_2}$ respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :
Moving Charges and Magnetism Biot-Savart Law Field at Center of Spiral Coil
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q40
$\mathrm{C_o}$ is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\varepsilon_r$ (as shown in Fig. 2), the new…
Electrostatic Potential and Capacitance Dielectrics Partial and Multiple Slabs
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q41
A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 $\mathrm{cm^3}$ to 150 $\mathrm{cm^3}$ adiabatically. In this process, the value of workdone on the gas will be :
Thermodynamics Thermodynamic Processes Adiabatic Work Evaluation
MediumSingle correctNew idea
Q42
Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ =4.0 cm, frequency $\nu$ =100 Hz and travelling in positive $x$ -axis direction ?
Waves Waves on Strings Direction of Wave Propagation
EasySingle correctNew idea
Q43
A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be : (Take : e= $1.6\times10^{-19}$ C, $\mathrm{m_p}$ = $1.67\times10^{-27}$ kg)
Moving Charges and Magnetism Lorentz Force Cyclotron Frequency and Energy
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q44
An expression for oscillating electric field in a plane electromagnetic wave is given as $\mathrm{E_z}$ =300 sin $(5\pi\times10^3 x-3\pi\times10^{11}\mathrm{t})$ $\mathrm{Vm^{-1}}$ Then, the value of magnetic field amplitude will be : (Given : speed of light…
Electromagnetic Waves
EasySingle correct
Q45
An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $\Omega$ . If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance…
Current Electricity Ohm's Law and Resistance Resistivity and Geometry
EasySingle correctIdea asked in 4 yearsAsked the year before
Q46
In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency ( $f_2$ ) and new quality factor ( $\mathrm{Q_2}$ ) will be : ( $f_1$ =original resonant frequency, $\mathrm{Q_1}$ =original quality factor)
Alternating Current LCR Resonance Q-Factor Formula in LCR
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q47
Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9 : 16. (Assuming intensity of light is directly proportional to the width of slits)
Wave Optics Young's Double Slit Intensity Ratio from Slit Widths
EasySingle correctIdea asked in 4 yearsAsked the year before
Q48
A source of monochromatic light liberates $9\times10^{20}$ photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating at same power will…
Dual Nature of Radiation and Matter Photoelectric Effect Photon Flux and Beam Power
EasySingle correctIdea asked in 4 yearsAsked the year before
Q49
A speech signal given by 11 sin (2200 $\pi$ t)V is used for amplitude modulation with a carrier signal given by 44 sin(6600 $\pi$ t)V. The minimum amplitude of modulated wave will be :
Communication Systems
EasySingle correct
Q50
A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :
Atoms Bohr's Atomic Model Angular Momentum Quantization
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q51
A person starts his journey from centre ‘O’ of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of…
Motion in a Straight Line Kinematics in 1D Average Speed Special Cases
EasyNumerical value · figureNew ideaIdea asked in 4 years
Q52
An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 $\mathrm{kmh^{-1}}$ in the direction of wind which is blowing at 72 $\mathrm{kmh^{-1}}$ speed. Frequency of siren is…
Waves Doppler Effect Effect of Wind Velocity
MediumNumerical valueNew idea
Q53
Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the…
System of Particles and Rotational Motion Moment of Inertia MOI of Discrete Particles
EasyNumerical value · figureIdea asked in 3 years
Q54
The excess pressure inside a liquid drop is 500 $\mathrm{Nm^{-2}}$ . If the radius of the drop is 2 mm, the surface tension of liquid is $x\times10^{-3}\ \mathrm{Nm^{-1}}$ . The value of $x$ is __________.
Mechanical Properties of Fluids Surface Tension Excess Pressure in Drops
EasyNumerical valueNew idea
Q55
Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be __________ E. Where E is the potential energy of a single smaller drop.
Electrostatic Potential and Capacitance Electric Potential Self-Energy of a Spherical Shell
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q56
The circuit diagram of potentiometer used to measure the internal resistance of a cell (E) is shown in figure. The key ‘K’ is kept closed so as to send constant current through potentiometer wire. When key ‘ $\mathrm{K_1}$ ’ is kept open the null point is…
Current Electricity Potentiometer Internal Resistance Measurement
MediumNumerical value · figureNew ideaIdea asked in 2 years
Q57
A series LCR circuit with R = $\frac{250}{11}$ $\Omega$ and $\mathrm{X_L}$ = $\frac{70}{11}$ $\Omega$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be __________ $\mu$ F. (Take :…
Alternating Current LCR Resonance Power Factor at Resonance
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q58
The refractive index of an equilateral prism is $\sqrt{2}$ . The angle of emergence under minimum deviation position of prism, in degree, is __________.
Ray Optics and Optical Instruments Prism Deviation Minimum Deviation Condition
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q59
A hydrogen atom in its first excited state absorbs a photon of energy $x\times10^{-2}$ eV and excited to a higher energy state where the potential energy of electron is $-1.08$ eV. The value of $x$ is __________.
Atoms Bohr's Atomic Model Energy Level Calculations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q60
The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0−15 V) as shown in figure. A zener diode with maximum potential $\mathrm{V_z}$ =10 V and maximum power dissipation of 0.4 W is connected across…
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Power Dissipation Limits
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before

Chemistry30 questions

13 easy15 medium2 hard

Q61
An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm $^{-3}$ . The number of atoms present in 300 g of the element X is ___________. Given : Avogadro constant, $\mathrm{N_A}=6.0\times10^{23}$ …
The Solid State Crystal Lattices Unit Cell Density
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q62
The number of radial nodes and total number of nodes in 4p orbital respectively are :
Structure of Atom Quantum Numbers Calculation of Radial and Angular Nodes
EasySingle correctIdea asked in 5 yearsAsked the year before
Q63
For a solution of the gases A, B, C and D in water at 298 K, the values of Henry's law constant ( $\mathrm{K_H}$ ) are 30.40, 2.34, $1.56\times10^{-5}$ and 0.513 k bar respectively. In the given graph, the lines marked as 'p' and 's' correspond respectively to :
Solutions
MediumDiagram based · figure
Q64
The equilibrium constant for the reversible reaction $2\mathrm{A(g)} \rightleftharpoons 2\mathrm{B(g)}+\mathrm{C(g)}$ is $\mathrm{K_1}$ and for the reaction $\frac{3}{2}\mathrm{A(g)} \rightleftharpoons \frac{3}{2}\mathrm{B(g)}+\frac{3}{4}\mathrm{C(g)}$ is…
Equilibrium Chemical Equilibrium Equilibrium Constant for Modified Equations
EasySingle correctIdea asked in 4 years
Q65
In which of the following half cells, electrochemical reaction is pH dependent ?
Electrochemistry Nernst Equation pH Dependence of Electrode Potential
EasySingle correctIdea asked in 4 yearsAsked the year before
Q66
The correct order of electron gain enthalpy ( $-$ ve value) is :
Classification of Elements and Periodicity in Properties Periodic Trends Electron Gain Enthalpy
EasySingle correctIdea asked in 5 yearsAsked the year before
Q67
$\Delta \mathrm{G}^\circ$ vs T plot for the formation of MgO, involving reaction $2\mathrm{Mg}+\mathrm{O_2}\rightarrow 2\mathrm{MgO}$ , will look like :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Phase Transitions
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q68
Match List - I with List - II : List - I (a) Sodium hydride (b) Silane (c) Vanadium hydride (d) Aluminium hydride List - II (i) Lewis acid (ii) Saline hydride (iii) Molecular hydride (iv) Non-stoichiometric hydride Correct answer is :
Hydrogen Hydrogen and Hydrides Ionic or Saline Hydrides
MediumMatch the listIdea asked in 2 yearsAsked the year before
Q69
Correct statement about alkali metal oxides is
The s-Block Elements s-Block Elements Formation of Oxides, Peroxides, and Superoxides
EasySingle correctIdea asked in 4 yearsAsked the year before
Q70
$\mathrm{A}\xrightarrow{573\ \mathrm{K}}$ Red phosphorus $\xrightarrow[\text{under pressure}]{\text{heat ; 803 K}} \mathrm{B}$ Red phosphorus is obtained by heating "A" at 573 K, and can be converted to "B" by heating at 803 K under pressure. A and B,…
The p-Block Elements Group 15 & 16 Phosphorus Allotropes
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q71
Correct formula of the compound which gives a white precipitate with $\mathrm{BaCl_2}$ solution, but not with $\mathrm{AgNO_3}$ solution, is
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
EasySingle correctIdea asked in 7 yearsAsked the year before
Q72
Which one of the following chemicals has not been used for the dry cleaning of clothes ?
Chemistry in Everyday Life Environmental Chemistry Green Chemistry Alternatives in Daily Applications
EasySingle correctIdea asked in 2 yearsAsked the year before
Q73
TLC analysis of a mixture having 3 components (A, B, C) using silica gel as the stationary phase gave following $\mathrm{R_f}$ values; for A=0.72, B=0.48, C=0.20. Regarding the above observations, which one of the following statements is not correct for…
Organic Chemistry: Some Basic Principles and Techniques
MediumSingle correct
Q74
Consider the given chemical reaction [structure: a six-membered saturated carbon ring bearing a C(=O)OH group (carbonyl O drawn above the carbon, OH to its right)] $\xrightarrow[\text{(ii) } \mathrm{H_2O}]{\text{(i) Red P, } \mathrm{Cl_2}}$ P (Major Product)…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Hell-Volhard-Zelinsky Reaction
EasyDiagram based · figureIdea asked in 4 yearsAsked the year before
Q75
Choose the reaction which is not possible :
Aldehydes, Ketones and Carboxylic Acids
HardDiagram based · figure
Q76
Which among the following will be the major product of the given reaction ? [structure: skeletal chain: a terminal bond to a C=O carbon (O drawn above), two CH2, a second C=O carbon (O drawn below), two CH2, then CO2H]…
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Intramolecular Aldol
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q77
[structure: A + $\mathrm{CH_3CH_2OH}$ $\longrightarrow$ benzene ring] $\xrightarrow[\text{(iii) HCl}]{\text{(i) } \mathrm{H_2SO_4}\text{ (oleum), }\Delta\ \text{(ii) NaOH}}$ B Consider the above reaction sequence. Identify the component A and component B :
Amines Diazonium Salts Reduction to Benzene via Ethanol
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q78
Match List - I with List - II. List - I Polymer (a) Acrilan (b) Neoprene (c) Polystyrene (d) Buna-N List - II Repeat Unit (i) $-(\mathrm{CH_2-C(Cl)=CH-CH_2})_n-$ [drawn with Cl on the C that is double bonded to CH] (ii) $-(\mathrm{CH_2-CH})_n-$ [drawn with…
Polymers Neoprene Synthesis
EasyMatch the list · figureIdea asked in 2 yearsAsked the year before
Q79
The sugar produced after complete hydrolysis of DNA is
Biomolecules
EasySingle correct
Q80
The reagent neutral ferric chloride is used to detect the presence of ___________
Alcohols, Phenols and Ethers Anion Analysis Acetate Neutral FeCl3 Test
EasySingle correctNew ideaIdea asked in 2 years
Q81
Blister copper is produced by reaction of copper oxide with copper sulphide. $2\mathrm{Cu_2O}+\mathrm{Cu_2S}\rightarrow 6\mathrm{Cu}+\mathrm{SO_2}$ When $2.86\times10^3$ g of $\mathrm{Cu_2O}$ and $4.77\times10^3$ g of $\mathrm{Cu_2S}$ are used for reaction,…
Some Basic Concepts of Chemistry Stoichiometry Limiting Reagent Identification
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q82
Amongst the following, the number of molecule/(s) having net resultant dipole moment is ___________. $\mathrm{NF_3}$ , $\mathrm{BF_3}$ , $\mathrm{BeF_2}$ , $\mathrm{CHCl_3}$ , $\mathrm{H_2S}$ , $\mathrm{SiF_4}$ , $\mathrm{CCl_4}$ , $\mathrm{PF_5}$
Chemical Bonding and Molecular Structure VSEPR Theory Net Dipole Moment from VSEPR Symmetry
EasyNumerical valueIdea asked in 4 years
Q83
1.0 mol of monoatomic ideal gas is expanded from state 1 to state 2 as shown in the figure. The magnitude of the work done for the expansion of gas from state 1 to state 2 at 300 K is ___________ J. (Nearest integer) (Given : R=8.3 J K $^{-1}$ mol $^{-1}$ ,…
Thermodynamics (Chemistry)First Law of Thermodynamics Work and Heat in Isothermal Processes
MediumNumerical value · figureNew ideaIdea asked in 3 years
Q84
For the reaction P $\rightarrow$ B, the values of frequency factor A and activation energy $\mathrm{E_A}$ are $4\times10^{13}$ s $^{-1}$ and 8.3 kJ mol $^{-1}$ respectively. If the reaction is of first order, the temperature at which the rate constant is…
Chemical Kinetics Arrhenius Equation Arrhenius Exponential Form
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
100 mL of 0.3 M acetic acid is shaken with 0.8 g of wood charcoal. The final concentration of acetic acid in the solution after adsorption is 0.125 M. The mass of acetic acid adsorbed per gram of carbon is ___________ $\times10^{-4}$ g. (Given : Molar mass…
Surface Chemistry
MediumNumerical value
Q86
In the following brown complex, the oxidation state of iron is +___________. $[\mathrm{Fe(H_2O)_6}]^{2+}+\mathrm{NO}\rightarrow[\mathrm{Fe(H_2O)_5(NO)}]^{2+}+\mathrm{H_2O}$ Brown complex
Coordination Compounds Group 15 & 16 Brown Ring Test for Nitrates
MediumNumerical valueNew idea
Q87
Spin only magnetic moment ( $\mu_s$ ) of $\mathrm{K_3[Fe(CN)_6]}$ is ___________ B.M. (Nearest integer).
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q88
An organic compound with 51.6% sulfur is heated in a Carius tube. The amount of this compound which will form 0.752 g of barium sulphate is ___________ $\times10^{-1}$ g. (Given molar mass of barium sulphate 233 g mol $^{-1}$ ) (Nearest integer).
Organic Chemistry: Some Basic Principles and Techniques
MediumNumerical value
Q89
A hydrocarbon 'X' is found to have molar mass of 80. A 10.0 mg of compound 'X' on hydrogenation consumed 8.40 mL of $\mathrm{H_2}$ gas (measured at STP). Ozonolysis of compound 'X' yields only formaldehyde and dialdehyde. The total number of…
Hydrocarbons Alkenes and Alkynes Reductive Ozonolysis Products
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q90
How many of the following drugs belong to the tranquilizer class ___________ ? Veronal, Luminal, Propanal, Seconal
Chemistry in Everyday Life Classes of Tranquilizers
EasyNumerical valueIdea asked in 2 yearsAsked the year before

Maths30 questions

4 easy16 medium10 hard

Q1
Let $S_1 = \left\{x \in \mathbf{R} - \{1, 2\} : \frac{(x+2)(x^2+3x+5)}{-2+3x-x^2} \geq 0\right\}$ and $S_2 = \{x \in \mathbf{R} : 3^{2x} - 3^{x+1} - 3^{x+2} + 27 \leq 0\}$ . Then, $S_1 \cup S_2$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q2
The real part of the complex number $\frac{(1+2i)^8 \cdot (1-2i)^2}{(3+2i) \cdot \overline{(4-6i)}}$ is equal to :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Form for Binomial Powers
MediumSingle correctNew idea
Q3
Let S be the set of all integral values of $\alpha$ for which the sum of squares of two real roots of the quadratic equation $3x^2 + (\alpha-6)x + (\alpha+3) = 0$ is minimum. Then S :
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q4
Let $A = \begin{bmatrix} 1 & -2 & \alpha \\ \alpha & 2 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & \alpha \\ -1 & 2 \\ 4 & -5 \end{bmatrix}$ , $\alpha \in \mathbf{C}$ . Then the absolute value of the sum of all values of $\alpha$ for which $\det(AB) = 0$ …
Determinants Matrix Multiplication Determinant of Product
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q5
Let A and B be two square matrices of order 2. If $\det(A) = 2$ , $\det(B) = 3$ and $\det\left(\left(\det\left(5\left(\det A\right)B\right)\right)A^2\right) = 2^{a}3^{b}5^{c}$ for some a, b, $c \in \mathbf{N}$ , then $a+b+c$ is equal to :
Determinants Matrix Multiplication Determinant of Product
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q6
For two positive real numbers a and b such that $\frac{1}{a^2} + \frac{1}{b^3} = 4$ , the minimum value of the constant term in the expansion of $\left(ax^{\frac{1}{8}} + bx^{-\frac{1}{12}}\right)^{10}$ is :
Binomial Theorem
HardSingle correct
Q7
The value of $1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3+\ldots+11}$ is equal to :
Sequences and Series AP and GP Method of Differences (Vn Method)
EasySingle correctNew ideaIdea asked in 5 years
Q8
If $xy^4$ attains maximum value at the point $(x, y)$ on the line passing through the points $(50+\alpha, 0)$ and $(0, 50+\alpha)$ , $\alpha > 0$ , then $(x, y)$ also lies on the line :
Application of Derivatives Maxima and Minima Optimization Problems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q9
Let $f(x) = 4x^3 - 11x^2 + 8x - 5$ , $x \in \mathbf{R}$ . Then $f$ :
Application of Derivatives Monotonicity Finding Intervals
EasySingle correctIdea asked in 5 yearsAsked the year before
Q10
Let m and M respectively be the minimum and the maximum values of $f(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x$ , $x \in \left[0, \frac{\pi}{8}\right]$ . Then $m+M$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Complementary Identities
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q11
$\lim_{n\to\infty} \sum_{r=1}^{n} \frac{r}{2r^2 - 7rn + 6n^2}$ is equal to :
Integrals Integral as Limit of Sum Summation to Riemann Form
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q12
Let $\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}$ , a, b, $c \in \mathbf{R}$ , represents a circle with center $(\alpha, \beta)$ . Then, $\alpha + 2\beta$ is equal to :
Differential Equations Variable Separable Form Direct Integration
HardSingle correctIdea asked in 3 yearsAsked the year before
Q13
Let $\alpha_1, \alpha_2$ ( $\alpha_1 < \alpha_2$ ) be the values of $\alpha$ for the points $(\alpha, -3)$ , $(2, 0)$ and $(1, \alpha)$ to be collinear. Then the equation of the line, passing through $(\alpha_1, \alpha_2)$ and making an angle of $\frac{\pi}{3}$ …
Straight Lines
EasySingle correct
Q14
Consider three circles : $C_1 : x^2 + y^2 = r^2$ $C_2 : (x-1)^2 + (y-1)^2 = r^2$ $C_3 : (x-2)^2 + (y-1)^2 = r^2$ If a line L : $y = mx + c$ be a common tangent to $C_1, C_2$ and $C_3$ such that $C_1$ and $C_3$ lie on one side of line L while $C_2$ lies on…
Conic Sections Circle Tangents Condition of tangency
HardSingle correctIdea asked in 4 yearsAsked the year before
Q15
Let the eccentricity of the ellipse $x^2 + a^2y^2 = 25a^2$ be b times the eccentricity of the hyperbola $x^2 - a^2y^2 = 5$ , where a is the minimum distance between the curves $y = e^x$ and $y = \log_e x$ . Then $a^2 + \frac{1}{b^2}$ is equal to :
Conic Sections Ellipse Eccentricity Eccentricity calculation
HardSingle correctIdea asked in 6 yearsAsked the year before
Q16
The distance of the point $(3, 2, -1)$ from the plane $3x - y + 4z + 1 = 0$ along the line $\frac{2-x}{2} = \frac{y-3}{2} = \frac{z+1}{1}$ is equal to :
Three Dimensional Geometry Point-Plane Distance Distance Along a Line
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q17
Let a vector $\vec{c}$ be coplanar with the vectors $\vec{a} = -\hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . If the vector $\vec{c}$ also satisfies the conditions…
Vector Algebra Triple Products Solving for Unknown in Coplanarity
HardSingle correctIdea asked in 4 yearsAsked the year before
Q18
If a random variable X follows the Binomial distribution B(5, p) such that $P(X=0) = P(X=1)$ , then $\frac{P(X=2)}{P(X=3)}$ is equal to :
Probability
EasySingle correct
Q19
Let $\alpha = \tan\left(\frac{5\pi}{16}\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right)$ and $\beta = \cos\left(\sin^{-1}\left(\frac{4}{5}\right) + \sec^{-1}\left(\frac{5}{3}\right)\right)$ where the inverse trigonometric functions take…
Inverse Trigonometric Functions Inverse Trig Identities Trig of Sum of Inverse Trig Functions
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q20
The conditional statement $((p \wedge q) \rightarrow ((\sim p) \vee r)) \vee (((\sim p) \vee r) \rightarrow (p \wedge q))$ is :
Mathematical Reasoning
MediumSingle correct
Q21
The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is __________.
Permutations and Combinations Permutations of Distinct Objects
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q22
Let for $f(x) = a_0x^2 + a_1x + a_2$ , $f'(0) = 1$ and $f'(1) = 0$ . If $a_0, a_1, a_2$ are in an arithmatico-geometric progression, whose corresponding A.P. has common difference 1 and corresponding G.P. has common ratio 2, then $f(4)$ is equal to __________.
Sequences and Series Arithmetico-Geometric Series AGP General Term
MediumNumerical valueNew ideaIdea asked in 2 years
Q23
Suppose $\lim_{x\to 0} \frac{F(x)}{x^3}$ exists and is equal to L, where $F(x) = \begin{vmatrix} a + \sin\frac{x}{2} & -b\cos x & 0 \\ -b\cos x & 0 & a + \sin\frac{x}{2} \\ 0 & a + \sin\frac{x}{2} & -b\cos x \end{vmatrix}$ . Then, $-112$ L is equal to…
Determinants L'Hopital's Rule L'Hopital on Determinant Functions
HardNumerical valueNew idea
Q24
If for some $\alpha > 0$ , the area of the region $\{(x, y) : |x+\alpha| \leq y \leq 2 - |x|\}$ is equal to $\frac{3}{2}$ , then the area of the region $\{(x, y) : 0 \leq y \leq x + 2\alpha, |x| \leq 1\}$ is equal to __________.
Application of Integrals Area Under Curves Finding Unknown Parameters from Area
HardNumerical valueNew ideaIdea asked in 2 years
Q25
Let $f(t) = \int_0^t e^{x^3}\left(\frac{x^8}{(x^6 + 2x^3 + 2)^2}\right) dx$ . If $f(1) + f'(1) = \alpha e - \frac{1}{6}$ , then the value of $150\alpha$ is equal to __________.
Integrals Leibniz Rule Variable Limit Leibniz
HardNumerical valueNew idea
Q26
A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate at which the virus spreads is directly proportional to the product of the number of infected students and the…
Differential Equations Variable Separable Form Proportional Rate Problems
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q27
Let PQ be a focal chord of length 6.25 units of the parabola $y^2 = 4x$ . If O is the vertex of the parabola, then 10 times the area (in sq. units) of $\Delta POQ$ is equal to __________.
Conic Sections Parabola Focal Chords Length of focal chord
MediumNumerical valueNew idea
Q28
Consider a triangle ABC whose vertices are $A(0, \alpha, \alpha)$ , $B(\alpha, 0, \alpha)$ and $C(\alpha, \alpha, 0)$ , $\alpha > 0$ . Let D be a point moving on the line $x + z - 3 = 0 = y$ and G be the centroid of $\Delta ABC$ . If the minimum length of GD is…
Three Dimensional Geometry Lines in 3D Perpendicular Distance from Point to Line
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q29
The probability distribution of X is : X: 0, 1, 2, 3 P(X): $\frac{1-d}{4}$ , $\frac{1+2d}{4}$ , $\frac{1-4d}{4}$ , $\frac{1+3d}{4}$ For the minimum possible value of d, sixty times the mean of X is equal to __________.
Probability
MediumNumerical value
Q30
Let $S_1 = \{x \in [0, 12\pi] : \sin^5 x + \cos^5 x = 1\}$ and $S_2 = \{x \in [0, 8\pi] : \sin^7 x + \cos^7 x = 1\}$ Then $n(S_1) - n(S_2)$ is equal to __________.
Trigonometric Functions General Solutions Periodic Root Scaling in Large Intervals
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.