JEE Main 2022 · July session

JEE Main 25 July 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 33 easy. Its hard-question count was the joint 19th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 68; 7 questions with a figure

Key findings · 25 Jul 2022, Shift 2

1
11 hard questions (12%): the joint 19th 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 7 of 30 rated hard; Physics had the most easy questions (19 of 30).
3
26 questions tested a new idea, one no earlier year had asked: 33% of the 80 questions tagged to an idea.
4
45 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
50 shared an idea with another 2022 shift (63% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Atoms in Physics (2), Alcohols, Phenols and Ethers in Chemistry (2) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 19Medium 7Hard 4

Top chapters

Atoms2 Q
Current Electricity2 Q
Electrostatic Potential and Capacitance2 Q
Gravitation2 Q
Laws of Motion2 Q
Moving Charges and Magnetism2 Q

Chemistry

30 Q · 10 numerical

Easy 11Medium 19Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 20Hard 7

Top chapters

Question format

Single correct50 Q
Numerical value30 Q
Other3 Q
Match the list3 Q
Diagram based3 Q
Two statements1 Q

What each question asks you to do

Calculation33 Q
Multi-step30 Q
Application10 Q
Recall10 Q
Conceptual6 Q
Data or graph1 Q

Most common: Calculation.

Against the other 2022 shifts

This shift next to the 23 other 2022 shifts Lumi analysed

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

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

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

Drill down

What this shift asked, and its history

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

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

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

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

Every question

All 90 questions of this shift

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

Subject

Difficulty

Idea

Find

90 of 90 questions

Physics30 questions

19 easy7 medium4 hard

Q31
In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V respectively. The modulation index is :
Communication Systems
EasySingle correct
Q32
The electric current in a circular coil of 2 turns produces a magnetic induction $\mathrm{B_1}$ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction $\mathrm{B_2}$ at its centre.…
Moving Charges and Magnetism Biot-Savart Law Field of an N-Turn Flat Coil
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q33
A drop of liquid of density $\boldsymbol{\rho}$ is floating half immersed in a liquid of density $\boldsymbol{\sigma}$ and surface tension $7.5 \times 10^{-4}$ Ncm $^{-1}$ . The radius of drop in cm will be : (g = 10ms $^{-2}$ )
Mechanical Properties of Fluids
HardSingle correct
Q34
Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms $^{-1}$ collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other ?
Laws of Motion Collisions Average Impact Force Calculation
EasySingle correctNew ideaIdea asked in 2 years
Q35
For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero ?
Laws of Motion Newton's Laws of Motion Static Equilibrium
EasySingle correct · figureIdea asked in 4 yearsAsked the year before
Q36
Capacitance of an isolated conducting sphere of radius $\mathbf{R_1}$ becomes n times when it is enclosed by a concentric conducting sphere of radius $\mathbf{R_2}$ connected to earth. The ratio of their radii $\left(\frac{R_2}{R_1}\right)$ is :
Electrostatic Potential and Capacitance
MediumSingle correct
Q37
The ratio of wavelengths of proton and deuteron accelerated by potential $\mathrm{V_p}$ and $\mathrm{V_d}$ is $1:\sqrt{2}$ . Then, the ratio of $\mathrm{V_p}$ to $\mathrm{V_d}$ will be :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q38
For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass…
Ray Optics and Optical Instruments Lens Maker's Formula Thin Lens Formula
HardSingle correctIdea asked in 4 yearsAsked the year before
Q39
Light wave traveling in air along x-direction is given by $\mathrm{E_y} = 540\, \mathrm{Sin}\, \pi \times 10^{4}(x - ct)Vm^{-1}$ . Then, the peak value of magnetic field of wave will be (Given c = $3 \times 10^{8}$ ms $^{-1}$ )
Electromagnetic Waves
EasySingle correct
Q40
When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :
Alternating Current LCR Resonance Resonance Condition
EasySingle correctIdea asked in 2 yearsAsked the year before
Q41
An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of $1 \times 10^{-4}$ Wbm $^{-2}$ . The frequency of revolution of the electron will be (Take mass of electron = $9.0 \times 10^{-31}$ kg)
Moving Charges and Magnetism Lorentz Force Circular Motion in Uniform B-Field
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q42
A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be :
Current Electricity Kirchhoff's Laws Kirchhoff's Voltage Law (KVL)
EasySingle correct · figureIdea asked in 6 years
Q43
The length of a seconds pendulum at a height h = 2R from earth surface will be : (Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = $\pi^{2}$ ms $^{-2}$ )
Gravitation Pendulums Seconds Pendulum
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q44
Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of n will be :
Waves Sound Velocity Speed of Sound in Gas Mixtures
HardSingle correctNew idea
Q45
Let $\eta_1$ is the efficiency of an engine at $\mathrm{T_1}$ = 447°C and $\mathrm{T_2}$ = 147°C while $\eta_2$ is the efficiency at $\mathrm{T_1}$ = 947°C and $\mathrm{T_2}$ = 47°C The ratio $\frac{\eta_1}{\eta_2}$ will be :
Thermodynamics Heat Engines and Refrigerators Carnot Efficiency Limit
EasySingle correctIdea asked in 3 yearsAsked the year before
Q46
An object is taken to a height above the surface of earth at a distance $\frac{5}{4}$ R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :
Gravitation
EasySingle correct
Q47
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms $^{-1}$ gets embedded in it, then loss of kinetic energy will be :
Work, Energy and Power Collisions Inelastic Collisions
EasySingle correctIdea asked in 3 years
Q48
A ball is projected from the ground with a speed 15 ms $^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then 'tan $\theta$ ' will be equal to :
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q49
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be :
Units and Measurements Ohm's Law and Resistance Error Analysis in Ohm's Law
EasySingle correctIdea asked in 5 years
Q50
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$ . The value of principal quantum number 'n' of the excited state will be : (R : Rydberg constant)
Atoms Bohr's Atomic Model Rydberg Formula and Spectra
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q51
A particle is moving in a straight line such that its velocity is increasing at 5 ms $^{-1}$ per meter. The acceleration of the particle is ________ ms $^{-2}$ at a point where its velocity is 20 ms $^{-1}$ .
Motion in a Straight Line Kinematics in 1D Position-Dependent Acceleration (v dv/dx)
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q52
Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of…
System of Particles and Rotational Motion Center of Mass Discrete System COM
EasyNumerical valueNew ideaIdea asked in 3 years
Q53
A block of ice of mass 120 g at temperature 0°C is put in 300 g of water at 25°C. The $x$ g of ice melts as the temperature of the water reaches 0°C. The value of $x$ is ________. [Use specific heat capacity of water = 4200 Jkg $^{-1}$ K $^{-1}$ , Latent heat of…
Thermal Properties of Matter Calorimetry Ice-Water Equilibrium Trap
EasyNumerical valueNew idea
Q54
$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value…
Atoms Bohr's Atomic Model Rydberg Formula and Spectra
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q55
In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ________ cm.
Current Electricity Potentiometer Comparing EMF of Two Cells
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q56
Two ideal diodes are connected in the network as shown is figure. The equivalent resistance between A and B is _______ $\Omega$ .
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Ideal vs. Practical Diode Circuit Analysis
MediumNumerical value · figureIdea asked in 7 yearsAsked the year before
Q57
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two…
Waves SHM Equations Collinear Superposition of SHMs
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q58
Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a…
Electrostatic Potential and Capacitance Dielectrics Dielectric with Battery Disconnected
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q59
A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens.…
Ray Optics and Optical Instruments Spherical Mirrors Virtual Object in Convex Mirror
HardNumerical valueNew idea
Q60
Magnetic flux (in weber) in a closed circuit of resistance 20 $\Omega$ varies with time t(s) as $\phi$ = 8t $^{2}$ - 9t + 5. The magnitude of the induced current at t = 0.25 s will be _______ mA.
Electromagnetic Induction Faraday's Law Faraday's Law Magnitude
EasyNumerical valueIdea asked in 6 yearsAsked the year before

Chemistry30 questions

11 easy19 medium0 hard

Q61
Match List I with List II : List I (molecule) | List II (hybridization ; shape) A. $\mathrm{XeO_3}$ | I. $sp^3d$ ; linear B. $\mathrm{XeF_2}$ | II. $sp^3$ ; pyramidal C. $\mathrm{XeOF_4}$ | III. $sp^3d^3$ ; distorted octahedral D. $\mathrm{XeF_6}$ | IV.…
Chemical Bonding and Molecular Structure Group 17 & 18 Xenon Oxides/Oxyfluorides
MediumMatch the listNew ideaIdea asked in 2 years
Q62
Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y, respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be 1:4. The ratio of molar masses of X and Y is
Solutions Colligative Properties Freezing Point Depression
EasySingle correctIdea asked in 4 yearsAsked the year before
Q63
$\mathrm{K_{a_1}}$ , $\mathrm{K_{a_2}}$ and $\mathrm{K_{a_3}}$ are the respective ionization constants for the following reactions (a), (b), and (c). (a) $\mathrm{H_2C_2O_4 = H^+ + HC_2O_4^-}$ (b) $\mathrm{HC_2O_4^- = H^+ + C_2O_4^{2-}}$ (c)…
Equilibrium Chemical Equilibrium Equilibrium Constant for Modified Equations
MediumSingle correctIdea asked in 4 years
Q64
The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is $\Lambda_{m1}$ and that of 20 moles another identical cell heaving 80 mL NaCl solution is $\Lambda_{m2}$ , The conductivities exhibited by these two cells are same.…
Electrochemistry
MediumSingle correct
Q65
For micelle formation, which of the following statements are correct ? A. Micelle formation is an exothermic process. B. Micelle formation is an endothermic process. C. The entropy change is positive. D. The entropy change is negative.
Surface Chemistry Colloids Micelle Formation and CMC
MediumOtherIdea asked in 3 yearsAsked the year before
Q66
The first ionization enthalpies of Be, B, N and O follow the order
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
EasySingle correctIdea asked in 4 yearsAsked the year before
Q67
Given below are two statements. Statement I: Pig iron is obtained by heating cast iron with scrap iron. Statement II: Pig iron has a relatively lower carbon content than that of cast iron. In the light of the above statements, choose the correct answer from…
General Principles and Processes of Isolation of Elements Metallurgical Extraction Iron Allotropes Carbon Content
EasyTwo statementsNew idea
Q68
High purity (>99.95%) dihydrogen is obtained by
Hydrogen Hydrogen and Hydrides High Purity Dihydrogen Preparation
EasySingle correctIdea asked in 2 years
Q69
The correct order of density is
The s-Block Elements s-Block Elements Density Trends and Anomalies
EasySingle correctNew idea
Q70
The total number of acidic oxides from the following list is $\mathrm{NO, N_2O, B_2O_3, N_2O_5, CO, SO_3, P_4O_{10}}$
The p-Block Elements Periodic Trends Acidic and Basic Character of Oxides
MediumSingle correctIdea asked in 4 years
Q71
The correct order of energy of absorption for the following metal complexes is A : $\mathrm{[Ni(en)_3]^{2+}}$ , B : $\mathrm{[Ni(NH_3)_6]^{2+}}$ , C : $\mathrm{[Ni(H_2O)_6]^{2+}}$
Coordination Compounds Crystal Field Theory Spectrochemical Series
MediumSingle correctIdea asked in 4 years
Q72
Match List I with List II. List I | List II A. Sulphate | I. Pesticide B. Fluoride | II. Bending of bones C. Nicotine | III. Laxative effect D. Sodium arsinite | IV. Herbicide Choose the correct answer from the options given below:
Environmental Chemistry Drinking Water Standards: Fluoride Limits
MediumMatch the listIdea asked in 3 yearsAsked the year before
Q73
Major product of the following reaction is [figure: skeletal drawing, left to right: a C=C double bond at the left end whose inner carbon is bonded directly to the carbonyl carbon (C=O, O drawn below); the carbonyl carbon is also bonded to a chain oxygen;…
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q74
What is the major product of the following reaction ? [figure: skeletal drawing of a carbon chain with a branch point (two bond stubs on a central carbon) joined to a carbonyl carbon (C=O, O drawn below) with an H drawn at the right of that carbon] --(-OH,…
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Self-Aldol Condensation
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q75
Arrange the following in decreasing acidic strength. (A) [figure: benzene ring with OH and NO2 para to each other] (B) [figure: benzene ring with OH and NO2 meta to each other] (C) [figure: benzene ring with OH and OCH3 meta to each other] (D) [figure:…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q76
$\mathrm{CH_3-CH_2-CN}$ --( $\mathrm{CH_3MgBr}$ , Ether)--> A --( $\mathrm{H_3O^+}$ )--> B --(Zn-Hg, HCl)--> C The correct structure of C is
Aldehydes, Ketones and Carboxylic Acids Alkanes and Free Radicals Clemmensen Reduction to Alkanes
MediumOtherNew ideaIdea asked in 3 years
Q77
Match List I with List II : List I Polymer | List II used for items A. Nylon 6,6 | I. Buckets B. Low density polythene | II. Non-stick utensils C. High density polythene | III. Bristles of brushes D. Teflon | IV. Toys Choose the correct answer from the…
Polymers Common Addition Polymers
EasyMatch the listNew idea
Q78
Glycosidic linkage between C1 of $\alpha$ -glucose and C2 of $\beta$ –fructose is found in
Biomolecules Carbohydrates Sucrose Structure and Linkage
EasySingle correctIdea asked in 2 yearsAsked the year before
Q79
Some drugs bind to a site other than the active site of an enzyme. This site is known as
Chemistry in Everyday Life Competitive vs Allosteric Enzyme Inhibition
EasySingle correctIdea asked in 2 yearsAsked the year before
Q80
In base vs. acid titration, at the end point methyl orange is present as
Equilibrium pH and Buffers Predicting Indicator Color
MediumSingle correctNew idea
Q81
56.0 L of nitrogen is mixed with excess of hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be __ L.
Some Basic Concepts of Chemistry Stoichiometry Gaseous Stoichiometry
MediumNumerical valueNew idea
Q82
A sealed flask with a capacity of 2 dm $^3$ contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is _______ $^\circ$ C. [Nearest integer] (Given: R = 8.3 J…
States of Matter Ideal Gas Laws Ideal Gas Equation
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q83
When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are ________.
Structure of Atom Bohr's Atomic Theory Number of Spectral Lines in Transitions
EasyNumerical valueNew ideaIdea asked in 2 years
Q84
While performing a thermodynamics experiment, a student made the following observations. $\mathrm{HCl + NaOH \rightarrow NaCl + H_2O}$ $\Delta H = -57.3$ kJ mol $^{-1}$ $\mathrm{CH_3COOH + NaOH \rightarrow CH_3COONa + H_2O}$ $\Delta H = -55.3$ kJ mol $^{-1}$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy of Ionization of Weak Acids/Bases
MediumNumerical valueNew idea
Q85
For the decomposition of azomethane, $\mathrm{CH_3N_2CH_3(g) \rightarrow CH_3CH_3(g) + N_2(g)}$ , a first order reaction, the variation in partial pressure with time at 600 K is given as [figure: graph of $\ln\left(\frac{p}{p0}\right)$ (y-axis) versus t/s…
Chemical Kinetics Integrated Rate Equations First Order Half-Life
MediumNumerical value · figureNew ideaIdea asked in 3 years
Q86
The sum of number of lone pairs of electrons present on the central atoms of $\mathrm{XeO_3}$ , $\mathrm{XeOF_4}$ and $\mathrm{XeF_6}$ , is ________
Chemical Bonding and Molecular Structure Group 17 & 18 Xenon Fluorides
MediumNumerical valueNew ideaIdea asked in 2 years
Q87
The spin-only magnetic moment value of $\mathrm{M^{3+}}$ ion (in gaseous state) from the pairs $\mathrm{Cr^{3+}/Cr^{2+}}$ , $\mathrm{Mn^{3+}/Mn^{2+}}$ , $\mathrm{Fe^{3+}/Fe^{2+}}$ and $\mathrm{Co^{3+}/Co^{2+}}$ that has negative standard electrode potential,…
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q88
A sample of 4.5 mg of an unknown monohydric alcohol, R-OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is __ g/mol. [Nearest integer]
Alcohols, Phenols and Ethers Mole Concept Molar Mass and Gas Volume
MediumNumerical valueIdea asked in 3 years
Q89
The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and substance B from the base line are 3.25 cm, 2.08 cm and 1.05 cm, respectively. The ratio of $\mathrm{R_f}$ values of A to B…
Organic Chemistry: Some Basic Principles and Techniques Adsorption Adsorption Chromatography Principle
EasyNumerical valueNew ideaIdea asked in 2 years
Q90
The total number of monobromo derivatives formed by the alkanes with molecular formula $\mathrm{C_5H_{12}}$ is (excluding stereo isomers) _______.
Organic Chemistry: Some Basic Principles and Techniques Structural Isomerism Enumeration of Structural Isomers
MediumNumerical valueIdea asked in 4 yearsAsked the year before

Maths30 questions

3 easy20 medium7 hard

Q1
For $z \in \mathbb{C}$ if the minimum value of $\left(\left|z-3\sqrt{2}\right|+\left|z-p\sqrt{2}i\right|\right)$ is $5\sqrt{2}$ , then a value of $p$ is ___________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Triangle Inequality Extrema
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q2
The number of real values of $\lambda$ , such that the system of linear equations $2x-3y+5z=9$ $x+3y-z=-18$ $3x-y+(\lambda^{2}-|\lambda|)z=16$ has no solutions, is
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
The number of bijective functions $f:\{1,3,5,7,\ldots,99\}\rightarrow\{2,4,6,8,\ldots.,100\}$ , such that $f(3)\geq f(9)\geq f(15)\geq f(21)\geq\ldots.\geq f(99)$ , is ________.
Permutations and Combinations Permutations with Fixed Relative Order
HardSingle correctNew idea
Q4
The remainder when $(11)^{1011}+(1011)^{11}$ is divided by 9 is
Binomial Theorem
MediumSingle correct
Q5
The sum $\sum_{n=1}^{21}\frac{3}{(4n-1)(4n+3)}$ is equal to
Sequences and Series AP and GP Method of Differences for Telescoping Series
EasySingle correctIdea asked in 6 yearsAsked the year before
Q6
$\lim_{x\to\frac{\pi}{4}}\frac{8\sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2}\sin 2x}$ is equal to
Limits and Derivatives L'Hopital's Rule Single Application of L'Hopital
MediumSingle correctNew idea
Q7
$\lim_{n\to\infty}\frac{1}{2^{n}}\left(\frac{1}{\sqrt{1-\frac{1}{2^{n}}}}+\frac{1}{\sqrt{1-\frac{2}{2^{n}}}}+\frac{1}{\sqrt{1-\frac{3}{2^{n}}}}+\ldots.+\frac{1}{\sqrt{1-\frac{2^{n}-1}{2^{n}}}}\right)$ is equal to
Integrals Integral as Limit of Sum Summation to Riemann Form
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q8
If $A$ and $B$ are two events such that $P(A)=\frac{1}{3},P(B)=\frac{1}{5}$ and $P(A\cup B)=\frac{1}{2}$ , then $P(A|B')+P(B|A')$ is equal to
Probability Conditional Probability Conditional Probability Definition
EasySingle correctIdea asked in 2 yearsAsked the year before
Q9
Let $[t]$ denote the greatest integer less than or equal to $t$ . Then the value of the integral $\int_{-3}^{101}\left([\sin(\pi x)]+e^{[\cos(2\pi x)]}\right)dx$ is equal to
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q10
Let the point $P(\alpha,\beta)$ be at a unit distance from each of the two lines $L_1:3x-4y+12=0$ , and $L_2:8x+6y+11=0$ . If $P$ lies below $L_1$ and above $L_2$ , then $100(\alpha+\beta)$ is equal to
Straight Lines Straight Line Distance Perpendicular distance from point
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q11
Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x,y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$ . If the curve passes through the points $(1,2)$ and $(8,1)$ , then $\left|y\left(\frac{1}{8}\right)\right|$ is…
Differential Equations Variable Separable Form Geometric Applications
MediumSingle correctNew idea
Q12
If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$ -axis and the line $\frac{x}{7}-\frac{y}{2\sqrt{6}}=1$ on the $y$ -axis, then the eccentricity of the ellipse is
Conic Sections Ellipse Eccentricity Eccentricity calculation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q13
The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2-2x-2y=1$ meet at the point $P$ . Then the area (in unit $^2$ ) of the triangle $PAB$ is:
Conic Sections General Conic Section Tangent to General Conic (T=0)
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q14
Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is :
Conic Sections Ellipse Eccentricity Coordinates of foci
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q15
A plane $E$ is perpendicular to the two planes $2x-2y+z=0$ and $x-y+2z=4$ , and passes through the point $P(1,-1,1)$ . If the distance of the plane $E$ from the point $Q(a,a,2)$ is $3\sqrt{2}$ , then $(PQ)^2$ is equal to
Three Dimensional Geometry Planes in 3D Plane Perpendicular to Two Planes
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 years
Q17
Let $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a}\times\vec{b}=2\hat{i}-\hat{k}$ and $\vec{a}\cdot\vec{b}=3$ . Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :
Vector Algebra Dot Product Scalar and Vector Projection
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q18
If the mean deviation about median for the numbers $3,5,7,2k,12,16,21,24$ , arranged in the ascending order, is 6 then the median is
Statistics
MediumSingle correct
Q19
$2\sin\left(\frac{\pi}{22}\right)\sin\left(\frac{3\pi}{22}\right)\sin\left(\frac{5\pi}{22}\right)\sin\left(\frac{7\pi}{22}\right)\sin\left(\frac{9\pi}{22}\right)$ is equal to :
Trigonometric Functions Trigonometric Identities Product of Cosines with Doubling Angles
HardSingle correctNew ideaIdea asked in 2 years
Q20
Consider the following statements : $P$ : Ramu is intelligent. $Q$ : Ramu is rich. $R$ : Ramu is not honest. The negation of the statement “Ramu is intelligent and honest if and only if Ramu is not rich” can be expressed as :
Mathematical Reasoning
MediumOther
Q21
Let $A=\{1,2,3,4,5,6,7\}$ . Define $B=\{T\subseteq A:\text{either }1\notin T\text{ or }2\in T\}$ and $C=\{T\subseteq A:T\text{ the sum of all the elements of }T\text{ is a prime number}\}$ . Then the number of elements in the set $B\cup C$ is ___________.
Relations and Functions Sets and Relations Subsets and Proper Subsets
HardNumerical valueNew idea
Q22
Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0)=p,p\neq0$ , and $f(1)=\frac{1}{3}$ . If the equations $f(x)=0$ and $fofofof(x)=0$ have a common real root, then $f(-3)$ is equal to ___________.
Complex Numbers and Quadratic Equations Quadratic Roots Common Root Condition
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q23
Let $A=\begin{bmatrix}1&a&a\\0&1&b\\0&0&1\end{bmatrix}$ , $a,b\in\mathbb{R}$ . If for some $n\in\mathbb{N}$ , $A^{n}=\begin{bmatrix}1&48&2160\\0&1&96\\0&0&1\end{bmatrix}$ then $n+a+b$ is equal to ___________.
Matrices Matrix Multiplication Powers of Square Matrices
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q24
The sum of the maximum and minimum values of the function $f(x)=|5x-7|+[x^2+2x]$ in the interval $\left[\frac{5}{4},2\right]$ , where $[t]$ is the greatest integer $\leq t$ , is ___________.
Continuity and Differentiability Maxima and Minima Extrema Involving Greatest Integer Function
MediumNumerical valueNew idea
Q25
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\ y(1)=1$ . If for some $n\in\mathbb{N}$ , $y(2)\in[n-1,n)$ , then $n$ is equal to ___________.
Differential Equations Homogeneous Equations Substitution y = vx
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q26
Let $f$ be a twice differentiable function on $\mathbb{R}$ . If $f'(0)=4$ and $f(x)+\int_0^x(x-t)f'(t)\,dt=\left(e^{2x}+e^{-2x}\right)\cos 2x+\frac{2}{a}x$ , then $(2a+1)^5a^2$ is equal to ___________.
Integrals Leibniz Rule Solving Integral Equations
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q27
Let $a_n=\int_{-1}^{n}\left(1+\frac{x}{2}+\frac{x^2}{3}+\ldots\ldots+\frac{x^{n-1}}{n}\right)dx$ for every $n\in\mathbb{N}$ . Then the sum of all the elements of the set $\{n\in\mathbb{N}:a_n\in(2,30)\}$ is ___________.
Integrals
HardNumerical value
Q28
If the circles $x^2+y^2+6x+8y+16=0$ and $x^2+y^2+2\left(3-\sqrt{3}\right)x+2\left(4-\sqrt{6}\right)y=k+6\sqrt{3}+8\sqrt{6},\ k>0$ , touch internally at the point $P(\alpha,\beta)$ , then $\left(\alpha+\sqrt{3}\right)^2+\left(\beta+\sqrt{6}\right)^2$ is equal…
Conic Sections Circle Tangents Common Tangent of Touching Circles
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q29
Let the area enclosed by the $x$ -axis, and the tangent and normal drawn to the curve $4x^3-3xy^2+6x^2-5xy-8y^2+9x+14=0$ at the point $(-2,3)$ be $A$ . Then $8A$ is equal to ___________.
Application of Derivatives Tangents and Normals Area of Triangle Formed by Tangent and Normal
HardNumerical valueNew idea
Q30
Let $x=\sin\left(2\tan^{-1}\alpha\right)$ and $y=\sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)$ . If $S=\{\alpha\in\mathbb{R}:y^2=1-x\}$ , then $\sum_{\alpha\in S}16\alpha^3$ is equal to ___________.
Inverse Trigonometric Functions Inverse Trig Identities 2tan-1(x) to sin-1 and cos-1 Conversions
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.