JEE Main 2022 · July session

JEE Main 26 July 2022, Shift 2

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 14 were rated hard and 33 easy. Its hard-question count was the joint 7th highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 14; 16% of the shift
Chapters asked: 65; 11 questions with a figure

Key findings · 26 Jul 2022, Shift 2

1
14 hard questions (16%): the joint 7th 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 29 rated hard; Chemistry had the most easy questions (16 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
39 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
41 shared an idea with another 2022 shift (55% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 15Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 16Medium 12Hard 2

Top chapters

Maths

29 Q · 10 numerical

Easy 4Medium 15Hard 10

Top chapters

Conic Sections4 Q
Three Dimensional Geometry3 Q
Complex Numbers and Quadratic Equations2 Q
Differential Equations2 Q
Integrals2 Q
Matrices2 Q

Question format

Single correct48 Q
Numerical value30 Q
Diagram based5 Q
Assertion–reason4 Q
Match the list1 Q
Other1 Q

What each question asks you to do

Multi-step34 Q
Calculation32 Q
Recall9 Q
Conceptual8 Q
Application4 Q
Data or graph1 Q
Diagram reading1 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
Open29 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 89 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

89 of 89 questions

Physics30 questions

13 easy15 medium2 hard

Q31
Two projectiles are thrown with same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal respectively. The ratio of their respective ranges will be :
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q32
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $4^{\text{th}}$ Vernier…
Units and Measurements
MediumSingle correct
Q33
A ball of mass 0.15 kg hits the wall with its initial speed of $12\ \text{ms}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of…
Laws of Motion Newton's Laws of Motion Momentum Formulation (F = dp/dt)
EasySingle correctIdea asked in 4 yearsAsked the year before
Q34
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be :
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q35
Two uniformly charged spherical conductors $A$ and $B$ of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the…
Electrostatic Potential and Capacitance Conductors in Fields Surface Charge Density Ratio of Connected Spheres
MediumSingle correctNew ideaIdea asked in 2 years
Q36
The oscillating magnetic field in a plane electromagnetic wave is given by $B_y = 5 \times 10^{-6}\ \sin 1000\pi(5x - 4 \times 10^{8}t)T.$ The amplitude of electric field will be :
Electromagnetic Waves
MediumSingle correct
Q37
Light travels in two media $M_1$ and $M_2$ with speeds $1.5 \times 10^{8}\ ms^{-1}$ and $2.0 \times 10^{8}\ ms^{-1}$ respectively. The critical angle between them is :
Ray Optics and Optical Instruments Refraction and Snell's Law Critical Angle Between Two Dense Media
EasySingle correctNew idea
Q38
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be : (Take radius of earth = 6400 km and $g=10\ ms^{-2}$ )
Gravitation Gravitational Potential Maximum Height Using Exact Potential
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q39
The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation index will be :
Communication Systems
EasySingle correct
Q40
A nucleus of mass M at rest splits into two parts having masses $\frac{M'}{3}$ and $\frac{2M'}{3}$ $(M' < M)$ . The ratio of de Broglie wavelength of two parts will be :
Dual Nature of Radiation and Matter Matter Waves Wavelengths in Radioactive Decay
EasySingle correctIdea asked in 2 yearsAsked the year before
Q41
An ice cube of dimensions 60 cm $\times$ 50 cm $\times$ 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at $0^\circ$ C of temperature is brought to a room of temperature $40^\circ$ C. The rate of melting of ice is…
Thermal Properties of Matter Heat Conduction Fourier's Law of Conduction
MediumSingle correctNew idea
Q42
A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :
Kinetic Theory Kinetic Theory of Gases Gamma and Degrees of Freedom
EasySingle correctIdea asked in 5 yearsAsked the year before
Q43
A transverse wave is represented by $y = 2\sin(\omega t - kx)$ cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be :
Waves Waves on Strings Particle Velocity vs Wave Velocity
MediumSingle correctNew ideaIdea asked in 3 years
Q44
A battery of $6V$ is connected to the circuit as shown below. The current $I$ drawn from the battery is :
Current Electricity Wheatstone Bridge Equivalent Resistance of Balanced Bridge
EasyDiagram based · figureNew idea
Q45
A source of potential difference $V$ is connected to the combination of two identical capacitors as shown in the figure. When key ‘ $K$ ’ is closed, the total energy stored across the combination is $E_1$ . Now key ‘ $K$ ’ is opened and dielectric of dielectric…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Dielectric Insertion (Battery Connected)
HardDiagram based · figureNew idea
Q46
Two concentric circular loops of radii $r_1$ =30 cm and $r_2$ =50 cm are placed in X-Y plane as shown in the figure. A current $I = 7A$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is…
Moving Charges and Magnetism Magnetic Dipole Moment Magnetic moment of a current loop
MediumDiagram based · figureNew idea
Q47
A velocity selector consists of electric field $\vec{E} = E\hat{k}$ and magnetic field $\vec{B} = B\hat{j}$ with $B = 12\ mT$ . The value of $E$ required for an electron of energy $728\ eV$ moving along the positive $x$ -axis to pass undeflected is : (Given,…
Moving Charges and Magnetism Lorentz Force Velocity Selector and Crossed Fields
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q48
Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$ , the acceleration of the system is $a_1$ . When the mass $M_2$ is thrice that of…
Laws of Motion Newton's Laws of Motion Standard Atwood Machine
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q49
Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of
Nuclei Nuclear Binding Energy Nuclear Radius and Density
EasySingle correctIdea asked in 5 years
Q50
The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}m^2$ . The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section…
Mechanical Properties of Solids Elasticity Breaking Stress and Breaking Force
EasySingle correctIdea asked in 4 yearsAsked the year before
Q51
If $\vec{A} = \left(2\hat{i}+3\hat{j}-\hat{k}\right)$ m and $\vec{B} = \left(\hat{i}+2\hat{j}+2\hat{k}\right)$ m. The magnitude of component of vector $\vec{A}$ along vector $\vec{B}$ will be ____________ m.
Motion in a Plane Dot Product Scalar vs Vector Projection Distinction
EasyNumerical valueNew idea
Q52
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ___________ $m$ . Given, the length of the rod is $10\sqrt{3}\ m$ .
System of Particles and Rotational Motion Moment of Inertia Radius of Gyration
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q53
In the given figure, the face $AC$ of the equilateral prism is immersed in a liquid of refractive index ‘ $n$ ’. For incident angle $60^\circ$ at the side $AC$ , the refracteel light beam just grazes along face $AC$ . The refractive index of the liquid…
Ray Optics and Optical Instruments Prism Deviation Grazing Emergence Condition
HardNumerical value · figureNew idea
Q54
Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below : ${}^{2}_{1}X + {}^{2}_{1}X = {}^{4}_{2}Y$ The binding energies per nucleon for ${}^{2}_{1}X$ and ${}^{4}_{2}Y$ are 1.1 MeV and 7.6 MeV respectively. The energy…
Nuclei Nuclear Binding Energy Binding Energy per Nucleon
MediumNumerical valueIdea asked in 6 years
Q55
A uniform heavy rod of mass 20 kg, cross sectional area $0.4\ m^2$ and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x \times 10^{-9}$ m. The value of $x$ is ___________.…
Mechanical Properties of Solids Elasticity Elongation Due to Self-Weight
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q56
The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of 2 $k\Omega$ is connected in the collector branch of the circuit used. The input resistance of the transistor is 0.50 $k\Omega$ . The voltage gain…
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors CE Amplifier Voltage Gain
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q57
Three point charges of magnitude $5\mu C$ , $0.16\mu C$ and $0.3\mu C$ are located at the vertices $A$ , $B$ , $C$ of a right angled triangle whose sides are $AB$ = 3 cm, $BC$ = $3\sqrt{2}$ cm and $CA$ = 3 cm and point $A$ is the right angle corner. Charge at…
Electric Charges and Fields Coulomb's Law Superposition of Forces
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q58
In a coil of resistance 8 $\Omega$ ,the magnetic flux due to an external magnetic field varies with time as $\phi = \frac{2}{3}\left(9 - t^{2}\right)$ . The value of total heat produced in the coil, till the flux becomes zero, will be ___________ $J$ .
Electromagnetic Induction Faraday's Law Faraday's Law Magnitude
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q59
A potentiometer wire of length 300 cm is connected in series with a resistance 780 $\Omega$ and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf 20 mV is found to be 60 cm. The…
Current Electricity Potentiometer Potential Gradient Calculation
MediumNumerical valueIdea asked in 2 years
Q60
As per given figures, two springs of spring constants $k$ and $2k$ are connected to mass $m$ . If the period of oscillation in figure (a) is 3s, then the period of oscillation in figure (b) will be $\sqrt{x}\ s$ . The value of $x$ is ___________.
Oscillations SHM Equations Springs in Series
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before

Chemistry30 questions

16 easy12 medium2 hard

Q61
Hemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is (Given: Atomic mass of Fe is 56 u, $\mathrm{N_A}$ = $6.022 \times 10^{23}$ $\mathrm{mol^{-1}}$ .)
Some Basic Concepts of Chemistry Mole Concept Mole and Avogadro Calculations
EasySingle correctIdea asked in 5 yearsAsked the year before
Q62
Arrange the following in increasing order of their covalent character. A. $\mathrm{CaF_2}$ B. $\mathrm{CaCl_2}$ C. $\mathrm{CaBr_2}$ D. $\mathrm{CaI_2}$ Choose the correct answer from the options given below.
Chemical Bonding and Molecular Structure s-Block Elements Covalent Character in Halides
EasySingle correctNew idea
Q63
Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is (Given: $\mathrm{pK_b}$ …
Equilibrium pH and Buffers Basic Buffer pH Calculation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q64
At 30°C, the half life for the decomposition of $\mathrm{AB_2}$ is 200 s and is independent of the initial concentration of $\mathrm{AB_2}$ . The time required for 80% of the $\mathrm{AB_2}$ to decompose is Given: log 2 = 0.30 log 3 = 0.48
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
Given below are two statements: one is labelled as **Assertion A** and the other is labelled as **Reason R**. **Assertion A:** Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold. **Reason R:**…
Surface Chemistry Colloids Colour Dependence on Particle Size
MediumAssertion–reasonNew idea
Q66
The metal that has very low melting point and its periodic position is closer to a metalloid is
The p-Block Elements
EasySingle correct
Q67
The metal that is not extracted from its sulfide ore is
General Principles and Processes of Isolation of Elements Metallurgical Extraction Bayer Process Chemistry
EasySingle correctIdea asked in 2 yearsAsked the year before
Q68
The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are
Hydrogen Hydrogen and Hydrides Reducing Action of H2O2
EasySingle correctIdea asked in 2 yearsAsked the year before
Q69
Given below are two statements: one is labelled as **Assertion A** and the other is labelled as **Reason R**. **Assertion A:** LiF is sparingly soluble in water. **Reason R:** The ionic radius of $\mathrm{Li^+}$ ion is smallest among its group members, hence…
The s-Block Elements s-Block Elements Anomalous Solubility of Specific Alkali Halides
MediumAssertion–reasonIdea asked in 2 yearsAsked the year before
Q70
Given below are two statements: one is labelled as **Assertion A** and the other is labelled as **Reason R**. **Assertion A:** Boric acid is a weak acid. **Reason R:** Boric acid is not able to release $\mathrm{H^+}$ ion on its own. It receives…
The p-Block Elements Group 13 & 14 Borax and Boric Acid
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q71
The metal complex that is diamagnetic is (Atomic number: Fe,26; Cu,29)
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q72
Match **List I** with **List II**. List I (Pollutant) | List II (Source) A. Microorganisms | I. Strip mining B. Plant nutrients | II. Domestic sewage C. Toxic heavy metals | III. Chemical fertilizer D. Sediment | IV. Chemical factory Choose the correct…
Environmental Chemistry
EasyMatch the list
Q73
The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Functional Group Priority
EasySingle correct · figureIdea asked in 6 years
Q74
Which of the following is not an example of benzenoid compound?
Organic Chemistry: Some Basic Principles and Techniques
MediumDiagram based · figure
Q75
Hydrolysis of which compound will give carbolic acid?
Alcohols, Phenols and Ethers Diazonium Salts High-Temperature Decomposition to Phenol
EasySingle correctNew idea
Q76
[figure: $\mathrm{EtO-C(=O)-H_2C-}$ attached to a five-membered ring having one double bond, with $\mathrm{-CH_2CH_2CN}$ attached to another ring carbon] $\xrightarrow{\text{(i) DiBAL-H, (ii) } \mathrm{H_2O}}$ ? [Et is $\mathrm{-C_2H_5}$ ] Consider the above…
Aldehydes, Ketones and Carboxylic Acids
MediumOther · figure
Q77
The correct sequential order of the reagents for the given reaction is [figure: benzene ring with $\mathrm{NO_2}$ at the top and $\mathrm{NH_2}$ at the bottom, arrow, benzene ring with OH at the top and I at the bottom]
Amines Diazonium Salts Synthesis of Iodobenzene
HardSingle correct · figureNew ideaIdea asked in 2 years
Q78
Vulcanization of rubber is carried out by heating a mixture of
Polymers Natural and Synthetic Rubber
EasySingle correctNew idea
Q79
Animal starch is the other name of
Biomolecules Carbohydrates Structure of Glycogen
EasySingle correctNew idea
Q80
Given below are two statements: one is labelled as **Assertion A** and the other is labelled as **Reason R**. **Assertion A:**Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium. **Reason…
Equilibrium pH and Buffers Predicting Indicator Color
MediumAssertion–reasonNew idea
Q81
A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 $\mathrm{m^3}$ at 6 bar and 27°C. The mass of helium in the mixture is __________ g. (nearest integer) Given: R = 8.3 J $\mathrm{K^{-1}}$ $\mathrm{mol^{-1}}$ (Atomic masses of…
States of Matter Ideal Gas Laws Ideal Gas Equation
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q82
Consider an imaginary ion $^{48}_{22}\mathrm{X}^{3-}$ . The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of ‘a’ is ________. [nearest integer]
Structure of Atom
EasyNumerical value
Q83
For the reaction $\mathrm{H_2F_2(g) \rightarrow H_2(g) + F_2(g)}$ $\Delta U$ = −59.6 kJ $\mathrm{mol^{-1}}$ at 27°C. The enthalpy change for the above reaction is (−) ________ kJ $\mathrm{mol^{-1}}$ [nearest integer] Given: R = 8.314 J…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q84
The elevation in boiling point for 1 molal solution of non-volatile solute A is 3 K. The depression in freezing point for 2 molal solution of A in the same solvent is 6 K. The ratio of $\mathrm{K_b}$ and $\mathrm{K_f}$ i.e., $\mathrm{K_b/K_f}$ is 1: X. The…
Solutions Colligative Properties Boiling Point Elevation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q85
20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of $\mathrm{Cu^{2+}}$ is found to be ________ $\times 10^{-2}$ M. [nearest integer] Given…
Redox Reactions Iodometric Titration Reactions
MediumNumerical valueNew ideaIdea asked in 2 years
Q86
The number of non-ionisable protons present in the product B obtained from the following reactions is ________. $\mathrm{C_2H_5OH + PCl_3 \rightarrow C_2H_5Cl + A}$ $\mathrm{A + PCl_3 \rightarrow B}$
The p-Block Elements Group 15 & 16 Phosphorus Oxoacids
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q87
The spin-only magnetic moment value of the compound with strongest oxidizing ability among $\mathrm{MnF_4}$ , $\mathrm{MnF_3}$ and $\mathrm{MnF_2}$ is ________ B.M. [nearest integer]
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q88
Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is ________.
Organic Chemistry: Some Basic Principles and Techniques
HardNumerical value
Q89
A 100 mL solution of $\mathrm{CH_3CH_2MgBr}$ on treatment with methanol produces 2.24 mL of a gas at STP. The weight of gas produced is ________ mg. [nearest integer]
Alcohols, Phenols and Ethers Alkanes and Free Radicals Alkane Synthesis via Grignard Protonation
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q90
How many of the following drugs is/are example(s) of broad spectrum antibiotics ? Ofloxacin, Penicillin G, Terpineol, Salvarsan.
Chemistry in Everyday Life Broad vs Narrow Spectrum Antibiotics
EasyNumerical valueNew idea

Maths29 questions

4 easy15 medium10 hard

Q1
The minimum value of the sum of the squares of the roots of $x^2+(3-a)x+1=2a$ is:
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
EasySingle correctIdea asked in 5 yearsAsked the year before
Q2
If $z=x+iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5i|=0$ , then
Complex Numbers and Quadratic Equations
MediumSingle correct
Q3
Let $A=\begin{bmatrix}1\\1\\1\end{bmatrix}$ and $B=\begin{bmatrix}9^2&-10^2&11^2\\12^2&13^2&-14^2\\-15^2&16^2&17^2\end{bmatrix}$ , then the value of $A'BA$ is:
Matrices Matrix Multiplication Row-by-Column Multiplication
EasySingle correctIdea asked in 2 yearsAsked the year before
Q4
$\sum_{\substack{i,j=0\\ i\neq j}}^{n}{}^nC_i\,{}^nC_j$ is equal to
Binomial Theorem Binomial Coefficients Double Summation of Coefficients
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q5
Let P and Q be any points on the curves $(x-1)^2+(y+1)^2=1$ and $y=x^2$ , respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval
Application of Derivatives Maxima and Minima Shortest Distance Between Curves
HardSingle correctIdea asked in 3 yearsAsked the year before
Q7
Let $\beta=\lim_{x\to 0}\frac{\alpha x-(e^{3x}-1)}{\alpha x(e^{3x}-1)}$ for some $\alpha\in\mathbb{R}$ . Then the value of $\alpha+\beta$ is :
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q8
The value of $\log_e 2\,\frac{d}{dx}\left(\log_{\cos x}\mathrm{cosec}\,x\right)$ at $x=\frac{\pi}{4}$ is
Continuity and Differentiability Chain Rule Derivative of Variable Base Logarithms
MediumSingle correctNew idea
Q9
$\int_0^{20\pi}\left(|\sin x|+|\cos x|\right)^2dx$ is equal to
Integrals Definite Integral Properties Periodic Function Property
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q10
Let the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ , $x\in(-1,1)$ pass through the origin. Then $\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}f(x)\,dx$ is equal to
Differential Equations Linear Differential Equations Particular Solution Solving
HardSingle correctIdea asked in 4 yearsAsked the year before
Q11
The acute angle between the pair of tangents drawn to the ellipse $2x^2+3y^2=5$ from the point $(1,3)$ is
Conic Sections Pair of Straight Lines Combined Equation of Tangents (SS1=T^2)
HardSingle correctNew idea
Q12
The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2)^2$ is
Conic Sections Tangents and Normals Common Tangents to Two Curves
MediumSingle correctNew idea
Q13
Let the abscissae of the two points P and Q on a circle be the roots of $x^2-4x-6=0$ and the ordinates of P and Q be the roots of $y^2+2y-7=0$ . If PQ is a diameter of the circle $x^2+y^2+2ax+2by+c=0$ , then the value of $(a+b-c)$ is __________.
Conic Sections
MediumSingle correct
Q14
If the line $x-1=0$ is a directrix of the hyperbola $kx^2-y^2=6$ , then the hyperbola passes through the point
Conic Sections
MediumSingle correct
Q15
A vector $\vec{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i},\ \hat{i}+\hat{j}$ and the plane determined by the vectors $\hat{i}-\hat{j},\ \hat{i}+\hat{k}$ . The obtuse angle between $\vec{a}$ and the vector…
Three Dimensional Geometry Planes in 3D Direction of Line of Intersection
MediumSingle correctNew idea
Q16
If $0<x<\frac{1}{\sqrt{2}}$ and $\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}$ , then a value of $\sin\left(\frac{2\pi\alpha}{\alpha+\beta}\right)$ is
Inverse Trigonometric Functions Inverse Trig Identities Complementary Identities
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q17
Negation of the Boolean expression $p\Leftrightarrow(q\Rightarrow p)$ is
Mathematical Reasoning
EasySingle correct
Q18
Let $X$ be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$ . Then, $54\,P(X\leq 2)$ is equal to
Probability
MediumSingle correct
Q19
The integral $\int\frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}}\sin 2x\right)}dx$ is equal to
Integrals Integration by Substitution Twin Trigonometric Integrals Substitution
HardSingle correctIdea asked in 2 yearsAsked the year before
Q20
The area bounded by the curves $y=|x^2-1|$ and $y=1$ is
Application of Integrals Area Under Curves Area with Modulus
MediumSingle correctNew ideaIdea asked in 4 years
Q21
Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$ . Then the number of elements in the set $\{C\subseteq A: C\cap B\neq\phi\}$ is ________
Relations and Functions Sets and Relations Subsets and Proper Subsets
EasyNumerical valueNew idea
Q22
The largest value of $a$ , for which the perpendicular distance of the plane containing the lines $\vec{r}=(\hat{i}+\hat{j})+\lambda(\hat{i}+a\hat{j}-\hat{k})$ and $\vec{r}=(\hat{i}+\hat{j})+\mu(-\hat{i}+\hat{j}-a\hat{k})$ from the point $(2,1,4)$ is…
Three Dimensional Geometry Planes in 3D Plane Containing Two Lines
HardNumerical valueIdea asked in 2 years
Q23
Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ___________.
Permutations and Combinations Fundamental Counting Principle
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q24
If $\sum_{k=1}^{10}\frac{k}{k^4+k^2+1}=\frac{m}{n}$ , where $m$ and $n$ are co-prime, then $m+n$ is equal to __________
Sequences and Series AP and GP Method of Differences for Telescoping Series
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q25
If the sum of solutions of the system of equations $2\sin^2\theta-\cos 2\theta=0$ and $2\cos^2\theta+3\sin\theta=0$ in the interval $[0,2\pi]$ is $k\pi$ , then $k$ is equal to ________.
Trigonometric Functions General Solutions Simultaneous Trigonometric Equations
MediumNumerical valueNew idea
Q26
The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the…
Statistics Variance and SD Updating Variance After Removing an Observation
MediumNumerical valueNew idea
Q27
The plane passing through the line $L: lx-y+3(1-l)z=1,\ x+2y-z=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$ . If $\theta$ is the acute angle between the line $L$ and the $y$ -axis, then $415\cos^2\theta$ is equal to _________.
Three Dimensional Geometry Planes in 3D Family of Planes
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q28
Suppose $y=y(x)$ be the solution curve to the differential equation $\frac{dy}{dx}-y=2-e^{-x}$ such that $\lim_{x\to\infty}y(x)$ is finite. If $a$ and $b$ are respectively the $x$ - and $y$ - intercepts of the tangent to the curve at $x=0$ , then the value of…
Differential Equations Linear Differential Equations Asymptotic Behavior of LDE Solutions
HardNumerical valueNew ideaIdea asked in 2 years
Q29
Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ________.
Sequences and Series
HardNumerical value
Q30
The number of matrices $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ , where $a,b,c,d\in\{-1,0,1,2,3,\ldots..,10\}$ , such that $A=A^{-1}$ , is _______.
Matrices Matrix Inverse Inverse of Involutory Matrices
HardNumerical valueNew idea

Dropped from the final key and left out of every count: Q6.

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.