JEE Main 2021 · February session

JEE Main 24 February 2021, Shift 2

88 questions (2 more dropped by NTA): 28 numerical-answer and 60 multiple choice. 4 were rated hard and 38 easy. Its hard-question count was the 22nd highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Amines, with 4 questions.

Questions: 88; 2 dropped by NTA
Numerical answer: 28; 32% of the shift
Hard: 4; 5% of the shift
Chapters asked: 59; 14 questions with a figure

Key findings · 24 Feb 2021, Shift 2

1
4 hard questions (5%): the 22nd highest count of the 24 2021 shifts Lumi analysed. Across those shifts the hard share ran from 3% to 17%.
2
Maths was the hardest section, with 3 of 28 rated hard; Physics had the most easy questions (18 of 30).
3
47 questions tested a new idea, one no earlier year had asked: 63% of the 75 questions tagged to an idea.
4
27 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
44 shared an idea with another 2021 shift (59% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Electromagnetic Waves in Physics (3), Amines in Chemistry (4) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 18Medium 11Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 14Medium 16Hard 0

Top chapters

Maths

28 Q · 8 numerical

Easy 6Medium 19Hard 3

Top chapters

Application of Derivatives3 Q
Three Dimensional Geometry3 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Determinants2 Q
Integrals2 Q

Question format

Single correct42 Q
Numerical value28 Q
Diagram based8 Q
Match the list5 Q
Two statements2 Q
Other2 Q
Assertion–reason1 Q

What each question asks you to do

Calculation31 Q
Multi-step18 Q
Recall14 Q
Application14 Q
Conceptual9 Q
Data or graph1 Q
Diagram reading1 Q

Most common: Calculation.

Against the other 2021 shifts

This shift next to the 23 other 2021 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 Feb, Shift 1	90	36%	7%	33%	68%	24%
24 Feb, Shift 2	88	43%	5%	32%	63%	21%
25 Feb, Shift 1	90	23%	11%	33%	65%	30%
25 Feb, Shift 2	89	35%	10%	34%	67%	24%
26 Feb, Shift 1	88	50%	3%	33%	78%	17%
26 Feb, Shift 2	90	27%	12%	33%	80%	29%
16 Mar, Shift 2	90	31%	7%	33%	69%	33%
17 Mar, Shift 1	89	39%	8%	34%	61%	26%
17 Mar, Shift 2	89	36%	17%	34%	66%	32%
18 Mar, Shift 1	90	40%	9%	33%	74%	24%
18 Mar, Shift 2	90	34%	9%	33%	63%	28%
22 Jul, Shift 2	90	40%	12%	33%	67%	28%
25 Jul, Shift 1	90	31%	13%	33%	56%	34%
25 Jul, Shift 2	90	48%	3%	33%	63%	27%
3 Aug, Shift 1	90	32%	11%	33%	68%	21%
3 Aug, Shift 2	90	32%	7%	33%	61%	24%
4 Aug, Shift 1	90	40%	8%	33%	62%	29%
4 Aug, Shift 2	90	32%	7%	33%	65%	41%
26 Aug, Shift 1	89	27%	15%	34%	66%	30%
26 Aug, Shift 2	89	21%	9%	34%	60%	28%
27 Aug, Shift 1	90	27%	13%	33%	63%	34%
27 Aug, Shift 2	90	29%	9%	33%	72%	29%
31 Aug, Shift 1	90	27%	11%	33%	70%	24%
31 Aug, Shift 2	90	30%	13%	33%	72%	31%

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
Open28 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 88 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

88 of 88 questions

Physics30 questions

18 easy11 medium1 hard

Q1
The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$ . Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The…
Units and Measurements
MediumSingle correct
Q2
A particle is projected with velocity $v_0$ along $x$ -axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. $ma = -\alpha x^2$ . The distance at which the particle stops :
Motion in a Straight Line Kinematics in 1D Position-Dependent Acceleration (v dv/dx)
MediumSingle correctNew ideaIdea asked in 4 years
Q3
A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :
System of Particles and Rotational Motion Center of Mass COM of Composite Bodies
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q4
A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator ? [Use $g = \frac{GM}{R^2} = 9.8\ \mathrm{ms^{-2}}$ and radius of earth, R = 6400 km.]
Gravitation Circular Motion Centrifugal Pseudo-Force
MediumSingle correctNew ideaIdea asked in 3 years
Q5
If one mole of an ideal gas at $(P_1, V_1)$ is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to…
Thermodynamics Thermodynamic Processes Cyclic Process Work
HardDiagram based · figureNew ideaIdea asked in 4 years
Q6
On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :
Kinetic Theory Kinetic Theory of Gases Gas Pressure Derivation
EasySingle correctNew idea
Q7
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k$ , the frequency of oscillation of given body is :
Oscillations SHM Equations Springs in Parallel
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q8
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :
Oscillations SHM Equations Velocity vs Position Graph
EasySingle correctNew ideaIdea asked in 2 years
Q9
Which of the following equations represents a travelling wave ?
Waves Waves on Strings Linear Wave Differential Equation
EasySingle correctNew idea
Q10
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance $x$ ( $x \ll d$ ) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having…
Electric Charges and Fields Coulomb's Law Small Oscillations of a Displaced Charge
MediumSingle correctNew ideaIdea asked in 2 years
Q11
Figure shows a circuit that contains four identical resistors with resistance $R = 2.0\ \Omega$ , two identical inductors with inductance $L = 2.0\ \mathrm{mH}$ and an ideal battery with emf $E = 9\ \mathrm{V}$ . The current 'i' just after the switch 'S' is…
Alternating Current Inductance Self-Inductance and Back EMF
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q12
A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :
Magnetism and Matter
EasySingle correct
Q13
Match List - I with List - II. List - I List - II (a) Source of microwave frequency (i) Radioactive decay of nucleus (b) Source of infrared frequency (ii) Magnetron (c) Source of Gamma Rays (iii) Inner shell electrons (d) Source of X-rays (iv) Vibration of…
Electromagnetic Waves
EasyMatch the list
Q14
If the source of light used in a Young's double slit experiment is changed from red to violet :
Wave Optics Young's Double Slit YDSE Fringe Width
EasySingle correctIdea asked in 5 yearsAsked the year before
Q15
An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :
Dual Nature of Radiation and Matter X-Ray Production Cutoff Wavelength Calculation
EasySingle correctNew idea
Q16
The de Broglie wavelength of a proton and $\alpha$ -particle are equal. The ratio of their velocities is :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q17
According to Bohr atom model, in which of the following transitions will the frequency be maximum ?
Atoms Bohr's Atomic Model Energy Level Calculations
EasySingle correctNew ideaIdea asked in 6 years
Q18
Zener breakdown occurs in a $p - n$ junction having $p$ and $n$ both :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Avalanche vs. Zener Breakdown Mechanisms
EasySingle correctNew idea
Q19
Given below are two statements : Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement II : In the study of transistor, the amplification factor…
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors Transistor Biasing and Structure
EasyTwo statementsNew idea
Q20
The logic circuit shown above is equivalent to :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q21
Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies $(\mathrm{K.E.})_A : (\mathrm{K.E.})_B$ will be $\frac{A}{1}$ , so the value of A will be __________.
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasyNumerical valueNew ideaIdea asked in 4 years
Q22
A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be __________ cm.
Mechanical Properties of Solids Elasticity Elastic Moduli
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q23
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is __________ $\times 10^{-1}\ \mathrm{kg\ m^2}$ .
System of Particles and Rotational Motion Moment of Inertia MOI of a Polygonal Wire Loop
MediumNumerical valueNew idea
Q24
The root mean square speed of molecules of a given mass of a gas at $27^\circ\mathrm{C}$ and 1 atmosphere pressure is $200\ \mathrm{ms^{-1}}$ . The root mean square speed of molecules of the gas at $127^\circ\mathrm{C}$ and 2 atmosphere pressure is…
Kinetic Theory Kinetic Theory of Gases Molecular Speed Types
EasyNumerical valueNew ideaIdea asked in 3 years
Q25
Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be __________ Hz. [Velocity of sound in air is 340 m/s.]
Waves Doppler Effect Doppler Beat Frequency Calculation
MediumNumerical valueNew ideaIdea asked in 2 years
Q26
A point charge of $+12\ \mu\mathrm{C}$ is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ $\times 10^3\ \mathrm{Nm^2/C}$ .
Electric Charges and Fields Gauss's Law Flux via Cube Symmetry
MediumNumerical value · figureNew ideaIdea asked in 2 years
Q27
A cylindrical wire of radius 0.5 mm and conductivity $5 \times 10^7\ \mathrm{S/m}$ is subjected to an electric field of $10\ \mathrm{mV/m}$ . The expected value of current in the wire will be $x^3\pi$ mA. The value of $x$ is __________.
Current Electricity Ohm's Law and Resistance Current Density Vector and Flux
EasyNumerical valueNew idea
Q28
A series LCR circuit is designed to resonate at an angular frequency $\omega_0 = 10^5\ \mathrm{rad/s}$ . The circuit draws 16 W power from 120 V source at resonance. The value of resistance 'R' in the circuit is __________ $\Omega$ .
Alternating Current LCR Resonance Power Factor at Resonance
EasyNumerical valueNew ideaIdea asked in 3 years
Q29
An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be __________ $\times 10^{-2}$ cm.
Electromagnetic Waves
EasyNumerical value
Q30
A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is $-5$ dB per km and cable length is 20 km. The power received at receiver is $10^{-x}$ W. The value of $x$ is __________. [Gain in dB $= 10\log_{10}\left(\frac{P_o}{P_i}\right)$ ]
Electromagnetic Waves
EasyNumerical value

Chemistry30 questions

14 easy16 medium0 hard

Q31
According to Bohr's atomic theory : (A) Kinetic energy of electron is $\propto \frac{Z^2}{n^2}$ . (B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\propto Z^2$ . (C) Frequency of revolution of electron in an orbit is…
Structure of Atom Bohr's Atomic Theory Total, Kinetic, and Potential Energy
MediumSingle correctNew ideaIdea asked in 4 years
Q32
The correct shape and I $-$ I $-$ I bond angles respectively in $\mathrm{I_3^-}$ ion are :
Chemical Bonding and Molecular Structure VSEPR Theory Linear Geometry of Trihalide Ions
EasySingle correctNew idea
Q33
Most suitable salt which can be used for efficient clotting of blood will be :
Surface Chemistry Colloids Hardy-Schulze Rule
EasySingle correctIdea asked in 3 yearsAsked the year before
Q34
The correct set from the following in which both pairs are in correct order of melting point is :
Chemical Bonding and Molecular Structure
MediumSingle correct
Q35
Match List - I with List - II. List - I (Metal) | List - II (Ores) (a) Aluminium | (i) Siderite (b) Iron | (ii) Calamine (c) Copper | (iii) Kaolinite (d) Zinc | (iv) Malachite Choose the correct answer from the options given below :
General Principles and Processes of Isolation of Elements
EasyMatch the list
Q36
Given below are two statements : one is labelled as $\textbf{Assertion A}$ and the other is labelled as $\textbf{Reason R}$ . $\textbf{Assertion A :}$ Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the…
Hydrogen
EasyAssertion–reason
Q37
Match List - I with List - II. List - I (Salt) | List - II (Flame colour wavelength) (a) LiCl | (i) 455.5 nm (b) NaCl | (ii) 670.8 nm (c) RbCl | (iii) 780.0 nm (d) CsCl | (iv) 589.2 nm Choose the correct answer from the options given below :
The s-Block Elements s-Block Elements Flame Coloration
MediumMatch the listNew ideaIdea asked in 4 years
Q38
The $\textbf{incorrect}$ statement among the following is :
The d- and f-Block Elements d-Block Elements Acid-Base Character of Oxides
MediumSingle correctIdea asked in 4 years
Q39
What is the correct order of the following elements with respect to their density ?
The d- and f-Block Elements d-Block Elements Density Trends and Maxima
EasySingle correctNew idea
Q40
The calculated magnetic moments (spin only value) for species $\mathrm{[FeCl_4]^{2-}}$ , $\mathrm{[Co(C_2O_4)_3]^{3-}}$ and $\mathrm{MnO_4^{2-}}$ respectively are :
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q41
Given below are two statements : $\textbf{Statement I :}$ The value of the parameter “Biochemical Oxygen Demand (BOD)” is important for survival of aquatic life. $\textbf{Statement II :}$ The optimum value of BOD is 6.5 ppm. In the light of the above…
Environmental Chemistry Water Quality BOD and COD
EasyTwo statementsIdea asked in 4 yearsAsked the year before
Q42
The diazonium salt of which of the following compounds will form a coloured dye on reaction with $\beta$ -Naphthol in NaOH ?
Amines Diazonium Salts Azo Coupling Reactions
EasySingle correct · figureNew ideaIdea asked in 5 years
Q43
Which one of the following compounds is non-aromatic ?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
EasySingle correct · figureIdea asked in 5 yearsAsked the year before
Q44
Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of $\mathrm{HgSO_4}$ and $\mathrm{H_2SO_4}$ ?
Aldehydes, Ketones and Carboxylic Acids Alkenes and Alkynes Kucherov Alkyne Hydration
EasySingle correct · figureIdea asked in 4 yearsAsked the year before
Q45
The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is : (i) [figure: benzene ring with Cl] (ii) [figure: benzene ring with Cl and, opposite it, $\mathrm{NO_2}$ ] (iii) [figure: benzene ring with…
Haloalkanes and Haloarenes Aromatic Hydrocarbons SNAr and Meisenheimer Complex
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q46
[Reaction scheme: reactant $\xrightarrow{?}$ product] Which of the following reagent is suitable for the preparation of the product in the above reaction ?
Aldehydes, Ketones and Carboxylic Acids Alkanes and Free Radicals Wolff-Kishner Reduction to Alkanes
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q47
What is the correct sequence of reagents used for converting nitrobenzene into $m$ -dibromobenzene ? [Scheme: nitrobenzene $\rightarrow$ $\rightarrow$ $\rightarrow$ $\rightarrow$ $m$ -dibromobenzene]
Amines Diazonium Salts Sandmeyer Reaction
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q48
In polymer Buna-S : ‘S’ stands for :
Polymers Buna-S (SBR) Monomers
EasySingle correctNew ideaIdea asked in 2 years
Q49
Match List - I and List - II. List - I | List - II (a) Valium | (i) Antifertility drug (b) Morphine | (ii) Pernicious anaemia (c) Norethindrone | (iii) Analgesic (d) Vitamin $\mathrm{B_{12}}$ | (iv) Tranquilizer
Chemistry in Everyday Life Antifertility Drugs
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q50
Match List - I and List - II. List - I | List - II (a) $\mathrm{R-C(=O)-Cl \rightarrow R-CHO}$ | (i) $\mathrm{Br_2}$ /NaOH (b) $\mathrm{R-CH_2-COOH \rightarrow R-CH(Cl)-COOH}$ | (ii) $\mathrm{H_2}$ /Pd $-\mathrm{BaSO_4}$ (c)…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Rosenmund Reduction
MediumMatch the list · figureIdea asked in 4 yearsAsked the year before
Q51
The formula of a gaseous hydrocarbon which requires 6 times of its own volume of $\mathrm{O_2}$ for complete oxidation and produces 4 times its own volume of $\mathrm{CO_2}$ is $\mathrm{C_xH_y}$ . The value of $y$ is __________.
Some Basic Concepts of Chemistry Stoichiometry Eudiometry and Gas Mixture Analysis
MediumNumerical valueNew ideaIdea asked in 2 years
Q52
The volume occupied by 4.75 g of acetylene gas at $50^\circ$ C and 740 mmHg pressure is __________ L. (Rounded off to the nearest integer) [Given R $= 0.0826$ L atm $\mathrm{K^{-1}\,mol^{-1}}$ ]
States of Matter Ideal Gas Laws Ideal Gas Equation
EasyNumerical valueNew ideaIdea asked in 2 years
Q53
Assuming ideal behaviour, the magnitude of log K for the following reaction at $25^\circ$ C is $x \times 10^{-1}$ . The value of $x$ is __________. (Integer answer) $\mathrm{3HC{\equiv}CH_{(g)} \rightleftharpoons C_6H_{6(l)}}$ [Given :…
Equilibrium Gibbs Free Energy Gibbs Energy and Equil
MediumNumerical valueNew ideaIdea asked in 5 years
Q54
$\mathrm{C_6H_6}$ freezes at $5.5^\circ$ C. The temperature at which a solution of 10 g of $\mathrm{C_4H_{10}}$ in 200 g of $\mathrm{C_6H_6}$ freeze is __________ $^\circ$ C. (The molal freezing point depression constant of $\mathrm{C_6H_6}$ is $5.12^\circ$ C/m.)
Solutions Colligative Properties Freezing Point Depression
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q55
The solubility product of $\mathrm{PbI_2}$ is $8.0 \times 10^{-9}$ . The solubility of lead iodide in 0.1 molar solution of lead nitrate is $x \times 10^{-6}$ mol/L. The value of $x$ is __________. (Rounded off to the nearest integer) [Given $\sqrt{2} = 1.41$ ]
Equilibrium Solubility Product Common Ion Effect
MediumNumerical valueNew ideaIdea asked in 4 years
Q56
The magnitude of the change in oxidising power of the $\mathrm{MnO_4^-/Mn^{2+}}$ couple is $x \times 10^{-4}$ V, if the $\mathrm{H^+}$ concentration is decreased from 1 M to $10^{-4}$ M at $25^\circ$ C. (Assume concentration of $\mathrm{MnO_4^-}$ and…
Electrochemistry Nernst Equation pH Dependence of Electrode Potential
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q57
Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at $25^\circ$ C. After 9 h, the fraction of sucrose remaining is $f$ . The value of $\log_{10}\left(\frac{1}{f}\right)$ is __________…
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q58
Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is __________. (A) $\alpha$ -sulphur (B) $\beta$ -sulphur (C) $\mathrm{S_2}$ -form
The p-Block Elements Group 15 & 16 Sulfur Allotropes
MediumNumerical valueNew idea
Q59
The total number of amines among the following which can be synthesized by Gabriel synthesis is __________. (A) [figure: $\mathrm{CH_3}$ and $\mathrm{CH_3}$ both bonded to a CH, which is bonded to $\mathrm{CH_2-NH_2}$ ] (B) $\mathrm{CH_3CH_2NH_2}$ (C)…
Amines Gabriel Phthalimide Synthesis
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q60
1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is __________ $\times 10^{-2}$ .
Amines Stoichiometry Theoretical and Percent Yield
EasyNumerical valueNew ideaIdea asked in 2 years

Maths28 questions

6 easy19 medium3 hard

Q61
Let a, b $\in$ R. If the mirror image of the point P(a, 6, 9) with respect to the line $\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is (20, b, $-$ a $-$ 9), then $|a+b|$ is equal to :
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q62
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be $\left(\frac{10}{3},\frac{7}{3}\right)$ . If $\alpha$ , $\beta$ are the roots of the equation $ax^2+bx+1=0$ , then the value of…
Straight Lines Quadratic Roots Symmetric Functions
MediumSingle correctNew ideaIdea asked in 5 years
Q63
If P is a point on the parabola $y=x^2+4$ which is closest to the straight line $y=4x-1$ , then the co-ordinates of P are :
Application of Derivatives Maxima and Minima Shortest Distance Between Curves
MediumSingle correctNew ideaIdea asked in 3 years
Q64
For which of the following curves, the line $x+\sqrt{3}y=2\sqrt{3}$ is the tangent at the point $\left(\frac{3\sqrt{3}}{2},\frac{1}{2}\right)$ ?
Conic Sections General Conic Section Tangent to General Conic (T=0)
EasySingle correctIdea asked in 3 yearsAsked the year before
Q65
The value of the integral, $\int_{1}^{3}[x^2-2x-2]\mathrm{d}x$ , where $[x]$ denotes the greatest integer less than or equal to $x$ , is :
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q66
The negation of the statement $\sim p\wedge(p\vee q)$ is :
Mathematical Reasoning
EasySingle correct
Q67
Let A and B be $3\times3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $(\mathrm{A^2B^2}-\mathrm{B^2A^2})\mathrm{X}=\mathrm{O}$ , where X is a $3\times1$ column matrix of unknown variables…
Matrices Cramer's Rule Skew-Symmetric Coefficient Matrices
HardSingle correctNew idea
Q68
Let $f(x)$ be a differentiable function defined on [0, 2] such that $f'(x)=f'(2-x)$ for all $x\in(0, 2)$ , $f(0)=1$ and $f(2)=e^2$ . Then the value of $\int_{0}^{2}f(x)\,dx$ is :
Integrals Definite Integral Properties King's Property
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q69
Let $f$ be a twice differentiable function defined on R such that $f(0)=1$ , $f'(0)=2$ and $f'(x)\neq0$ for all $x\in$ R. If $\begin{vmatrix}f(x)&f'(x)\\f'(x)&f''(x)\end{vmatrix}=0$ , for all $x\in$ R, then the value of $f(1)$ lies in the interval :
Determinants Variable Separable Form Determinant Form Differential Equations
MediumSingle correctNew idea
Q70
If the curve $y=ax^2+bx+c$ , $x\in$ R, passes through the point (1, 2) and the tangent line to this curve at origin is $y=x$ , then the possible values of a, b, c are :
Application of Derivatives Tangents and Normals Equation of Tangent
EasySingle correctNew ideaIdea asked in 2 years
Q71
If $n\geq2$ is a positive integer, then the sum of the series ${}^{n+1}C_2+2\left({}^{2}C_2+{}^{3}C_2+{}^{4}C_2+\ldots.+{}^{n}C_2\right)$ is :
Permutations and Combinations Binomial Coefficients Hockey Stick Identity
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q72
For the system of linear equations : $x-2y=1$ , $x-y+kz=-2$ , $ky+4z=6$ , $k\in$ R, consider the following statements : (A) The system has unique solution if $k\neq2$ , $k\neq-2$ . (B) The system has unique solution if $k=-2$ . (C) The system has unique solution…
Determinants Cramer's Rule Condition for Unique Solution
MediumOtherNew ideaIdea asked in 3 years
Q73
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=\begin{cases}-55x, & \text{if } x<-5\\ 2x^3-3x^2-120x, & \text{if } -5\leq x\leq4\\ 2x^3-3x^2-36x-336, & \text{if } x>4,\end{cases}$ Let A = $\{x\in\mathbf{R}: f \text{ is increasing}\}$ . Then A is equal to :
Application of Derivatives Monotonicity Monotonicity in Piecewise Functions
MediumSingle correctNew idea
Q74
A possible value of $\tan\left(\frac{1}{4}\sin^{-1}\frac{\sqrt{63}}{8}\right)$ is :
Inverse Trigonometric Functions Inverse Trig Identities Half-Angle Inverse Trig Evaluations
MediumSingle correctNew idea
Q75
The angle of elevation of a jet plane from a point A on the ground is $60^\circ$ . After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to $30^\circ$ . If the jet plane is flying at a constant height, then its height is :
Trigonometric Functions
EasySingle correct
Q76
The vector equation of the plane passing through the intersection of the planes $\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k})=1$ and $\vec{r}\cdot(\hat{i}-2\hat{j})=-2$ , and the point (1, 0, 2) is :
Three Dimensional Geometry Planes in 3D Family of Planes
EasySingle correctIdea asked in 4 yearsAsked the year before
Q77
For the statements p and q, consider the following compound statements : (a) $(\sim q\wedge(p\to q))\to\sim p$ (b) $((p\vee q)\wedge\sim p)\to q$ Then which of the following statements is correct ?
Mathematical Reasoning
MediumOther
Q78
If a curve $y=f(x)$ passes through the point (1, 2) and satisfies $x\frac{dy}{dx}+y=bx^4$ , then for what value of b, $\int_{1}^{2}f(x)\mathrm{d}x=\frac{62}{5}$ ?
Differential Equations Linear Differential Equations Standard Linear Form Identification
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q79
The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :
Probability
HardSingle correct
Q80
The area of the region : R = {(x, y) : $5x^2\leq y\leq2x^2+9$ } is :
Application of Integrals Area Under Curves Area Between Two Standard Parabolas
EasySingle correctNew ideaIdea asked in 4 years
Q81
If the variance of 10 natural numbers 1, 1, 1, ..., 1, $k$ is less than 10, then the maximum possible value of $k$ is __________.
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q82
Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ( $-$ 5, 0). If the locus of the point P is a circle of radius r, then $4r^2$ is equal to __________.
Conic Sections Power of a Point Locus of Constant Tangent Ratio
MediumNumerical valueNew idea
Q84
Let $i=\sqrt{-1}$ . If $\frac{(-1+i\sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i\sqrt{3})^{21}}{(1+i)^{24}}=k$ , and $\mathrm{n}=[|k|]$ be the greatest integral part of $|k|$ . Then $\sum_{j=0}^{n+5}(j+5)^2-\sum_{j=0}^{n+5}(j+5)$ is equal to __________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form De Moivre's Theorem for Integer Powers
MediumNumerical valueNew idea
Q85
The students $\mathrm{S_1, S_2, \ldots., S_{10}}$ are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is __________.
Permutations and Combinations Division of Objects into Groups
HardNumerical valueNew ideaIdea asked in 3 years
Q87
If $a+\alpha=1$ , $b+\beta=2$ and $af(x)+\alpha f\left(\frac{1}{x}\right)=bx+\frac{\beta}{x}$ , $x\neq0$ , then the value of the expression $\frac{f(x)+f\left(\frac{1}{x}\right)}{x+\frac{1}{x}}$ is __________.
Relations and Functions
MediumNumerical value
Q88
Let $\lambda$ be an integer. If the shortest distance between the lines $x-\lambda=2y-1=-2z$ and $x=y+2\lambda=z-\lambda$ is $\frac{\sqrt{7}}{2\sqrt{2}}$ , then the value of $|\lambda|$ is __________.
Three Dimensional Geometry Skew Lines Vector Shortest Distance Formula
MediumNumerical valueNew ideaIdea asked in 5 years
Q89
The sum of first four terms of a geometric progression (G.P.) is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}$ . If the product of first three terms of the G.P. is 1, and the third term is $\alpha$ , then $2\alpha$ is __________.
Sequences and Series AP and GP GP Reciprocal Transformation
MediumNumerical valueNew idea
Q90
The number of the real roots of the equation $(x+1)^2+|x-5|=\frac{27}{4}$ is ________.
Complex Numbers and Quadratic Equations Quadratic Roots Roots of Modulus Quadratics
MediumNumerical valueIdea asked in 6 yearsAsked the year before

Dropped from the final key and left out of every count: Q83, Q86.

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 2021 shifts.