JEE Main 2021 · March session

JEE Main 17 March 2021, Shift 2

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 15 were rated hard and 32 easy. Its hard-question count was the highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Amines, with 3 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 15; 17% of the shift
Chapters asked: 64; 14 questions with a figure

Key findings · 17 Mar 2021, Shift 2

1
15 hard questions (17%): the 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 10 of 30 rated hard; Chemistry had the most easy questions (19 of 30).
3
49 questions tested a new idea, one no earlier year had asked: 66% of the 74 questions tagged to an idea.
4
25 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
41 shared an idea with another 2021 shift (55% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Alternating Current in Physics (2), Amines in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

29 Q · 10 numerical

Easy 10Medium 14Hard 5

Top chapters

Chemistry

30 Q · 10 numerical

Easy 19Medium 11Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 17Hard 10

Top chapters

Question format

Single correct42 Q
Numerical value30 Q
Diagram based9 Q
Match the list4 Q
Other3 Q
Two statements1 Q

What each question asks you to do

Multi-step28 Q
Calculation24 Q
Conceptual14 Q
Recall12 Q
Application8 Q
Data or graph2 Q
Diagram reading1 Q

Most common: Multi-step.

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 shift3065 · 33%33%8/829299715710354533200225
Open29 this shift3084 · 33%33%8/830298716720359538199224

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

Physics29 questions

10 easy14 medium5 hard

Q1
A carrier signal C(t) $=25\sin(2.512\times10^{10}t)$ is amplitude modulated by a message signal m(t) $=5\sin(1.57\times10^{8}t)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal ?
Communication Systems
EasySingle correct
Q2
Two cells of emf 2E and E with internal resistance $\mathrm{r_1}$ and $\mathrm{r_2}$ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes…
Current Electricity Kirchhoff's Laws Cell EMF and Internal Resistance
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q3
A sound wave of frequency 245 Hz travels with the speed of 300 $\mathrm{ms^{-1}}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave ?
Waves
MediumSingle correct
Q4
A geostationary satellite is orbiting around an arbitary planet 'P' at a height of 11R above the surface of 'P', R being the radius of 'P'. The time period of another satellite in hours at a height of 2R from the surface of 'P' is ________. 'P' has the time…
Gravitation Orbital Mechanics Orbital Time Period
EasySingle correctIdea asked in 6 yearsAsked the year before
Q5
Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed $v$ along the line joining A and B collides with A.…
Work, Energy and Power Collisions Spring-Mass Impact
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q6
Two particles A and B of equal masses are suspended from two massless springs of spring constants $\mathrm{K_1}$ and $\mathrm{K_2}$ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is
Oscillations SHM Equations Springs in Parallel
EasySingle correctNew ideaIdea asked in 3 years
Q7
Match List - I with List - II List - I List - II (a) Phase difference between current and voltage in a purely resistive AC circuit (i) $\frac{\pi}{2}$ ; current leads voltage (b) Phase difference between current and voltage in a pure inductive AC circuit…
Alternating Current Phasor Diagrams Phase Relations in RLC
EasyMatch the listIdea asked in 5 yearsAsked the year before
Q8
What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?
Alternating Current
EasySingle correct
Q9
A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 $\mathrm{ms^{-1}}$ goes up an inclined plane which makes an angle of $30^\circ$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting…
System of Particles and Rotational Motion
HardDiagram based · figure
Q10
A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g=10\ \mathrm{ms^{-2}}$ )
Motion in a Straight Line Collisions Total Distance for Bouncing Ball
MediumSingle correctNew idea
Q11
The velocity of a particle is $v=v_0+gt+Ft^2$ . Its position is $x=0$ at $t=0$ ; then its displacement after time (t=1) is :
Motion in a Straight Line Kinematics in 1D Calculus in Kinematics
EasySingle correctNew ideaIdea asked in 5 years
Q12
A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle ?
Moving Charges and Magnetism Biot-Savart Law Field of a Hairpin Loop
MediumDiagram based · figureNew idea
Q13
The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region ?
Atoms Bohr's Atomic Model Spectral Series EM Regions
EasySingle correctNew idea
Q14
Two identical photocathodes receive the light of frequencies $f_1$ and $f_2$ respectively. If the velocities of the photo-electrons coming out are $v_1$ and $v_2$ respectively, then
Dual Nature of Radiation and Matter Photoelectric Effect Einstein's Photoelectric Equation
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q15
Which one of the following will be the output of the given circuit ?
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q16
The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15 $\Omega$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC.
Current Electricity Wheatstone Bridge Unbalanced Bridge Analysis
HardDiagram based · figureIdea asked in 3 yearsAsked the year before
Q18
If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta=\frac{\mathrm{C_P}}{\mathrm{C_V}}\right)$ then the value of $\beta$ is :
Kinetic Theory Kinetic Theory of Gases Gamma and Degrees of Freedom
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q19
Which one is the correct option for the two different thermodynamic processes ?
Thermodynamics Thermodynamic Processes Indicator Diagram Conversions
MediumDiagram based · figureIdea asked in 2 yearsAsked the year before
Q20
An object is located at 2 km beneath the surface of the water. If the fractional compression $\frac{\Delta V}{V}$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [ Given : density of water is 1000…
Mechanical Properties of Solids Elasticity Elastic Moduli
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q21
A 2 $\mu$ F capacitor $\mathrm{C_1}$ is first charged to a potential difference of 10 V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor $\mathrm{C_2}$ of 8 $\mu$ F. The charge in $\mathrm{C_2}$ on…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Charge Sharing and Heat Loss
EasyNumerical value · figureIdea asked in 6 yearsAsked the year before
Q22
A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is…
Laws of Motion Friction Impending Motion Analysis
HardNumerical value · figureNew idea
Q23
The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $\frac{2^{\mathrm{rd}}}{3}$ of the distance of the object from the surface. The wavelength of light inside the…
Ray Optics and Optical Instruments
HardNumerical value
Q24
The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by the radiation coming from 60 W at the same distance is $\sqrt{\frac{x}{5}}$ E. Where the value of…
Electromagnetic Waves
EasyNumerical value
Q25
Seawater at a frequency $f=9\times10^{2}$ Hz, has permittivity $\varepsilon=80\varepsilon_0$ and resistivity $\rho=0.25\ \Omega$ m. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source…
Electromagnetic Waves Parallel Plate Capacitors Displacement Current Between Plates
HardNumerical valueNew ideaIdea asked in 5 years
Q26
The electric field in a region is given by $\vec{\mathrm{E}}=\frac{2}{5}\mathrm{E_0}\hat{i}+\frac{3}{5}\mathrm{E_0}\hat{j}$ with $\mathrm{E_0}=4.0\times10^{3}\frac{\mathrm{N}}{\mathrm{C}}$ . The flux of this field through a rectangular surface area 0.4…
Electric Charges and Fields Gauss's Law Electric Flux Calculation
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q27
The disc of mass M with uniform surface mass density $\sigma$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{x}{3}\frac{a}{\pi},\ \frac{x}{3}\frac{a}{\pi}$ where $x$ is ____________. (Round off to…
System of Particles and Rotational Motion Center of Mass COM of Circular Sector
MediumNumerical value · figureNew idea
Q28
A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$ . It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________. (Round off to the…
Laws of Motion Friction Angle of Friction
MediumNumerical valueNew ideaIdea asked in 2 years
Q29
A particle of mass m moves in a circular orbit in a central potential field $\mathrm{U(r)=U_0r^4}$ . If Bohr's quantization conditions are applied, radii of possible orbitals $\mathrm{r_n}$ vary with $\mathrm{n}^{\frac{1}{\alpha}}$ , where $\alpha$ is…
Atoms Bohr's Atomic Model Angular Momentum Quantization
MediumNumerical valueNew ideaIdea asked in 5 years
Q30
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 $\mathrm{cm^3}$ of oleic acid per $\mathrm{cm^3}$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4…
Units and Measurements
MediumNumerical value

Chemistry30 questions

19 easy11 medium0 hard

Q31
Amongst the following, the linear species is :
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 2 Geometry
MediumSingle correctNew idea
Q32
During which of the following processes, does entropy decrease ? (A) Freezing of water to ice at $0^\circ\mathrm{C}$ (B) Freezing of water to ice at $-10^\circ\mathrm{C}$ (C) $\mathrm{N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)}$ (D) Adsorption of $\mathrm{CO(g)}$ …
Thermodynamics (Chemistry)Entropy Predicting Entropy Sign
MediumOtherNew idea
Q33
For the coagulation of a negative sol, the species below, that has the highest flocculating power is :
Surface Chemistry Colloids Hardy-Schulze Rule
EasySingle correctIdea asked in 3 yearsAsked the year before
Q34
The set of elements that differ in mutual relationship from those of the other sets is :
Classification of Elements and Periodicity in Properties Periodic Trends Diagonal Relationship
EasySingle correctNew idea
Q35
Match List - I with List - II : List - I List - II (a) Haematite (i) $\mathrm{Al_2O_3{\cdot}}x\mathrm{H_2O}$ (b) Bauxite (ii) $\mathrm{Fe_2O_3}$ (c) Magnetite (iii) $\mathrm{CuCO_3{\cdot}Cu(OH)_2}$ (d) Malachite (iv) $\mathrm{Fe_3O_4}$ Choose the correct…
General Principles and Processes of Isolation of Elements
EasyMatch the list
Q36
The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are :
Hydrogen Hydrogen and Hydrides Ion-Exchange Resins for Water Softening
EasySingle correctNew ideaIdea asked in 2 years
Q37
One of the by-products formed during the recovery of $\mathrm{NH_3}$ from Solvay process is :
The s-Block Elements s-Block Elements Limitations of the Solvay Process
EasySingle correctNew idea
Q38
The set that represents the pair of neutral oxides of nitrogen is :
The p-Block Elements Group 15 & 16 Nitrogen Oxides Structure
EasySingle correctNew ideaIdea asked in 3 years
Q39
The common positive oxidation states for an element with atomic number 24, are :
The d- and f-Block Elements d-Block Elements Oxidation State Trends
EasySingle correctNew ideaIdea asked in 4 years
Q40
Match List - I with List - II : List - I List - II (a) $[\mathrm{Co(NH_3)_6}]\ [\mathrm{Cr(CN)_6}]$ (i) Linkage isomerism (b) $[\mathrm{Co(NH_3)_3}\ \mathrm{(NO_2)_3}]$ (ii) Solvate isomerism (c) $[\mathrm{Cr(H_2O)_6}]\mathrm{Cl_3}$ (iii) Co-ordination…
Coordination Compounds Coordination Isomerism Structural Isomerism Types
MediumMatch the listNew idea
Q41
Which of the following statement(s) is (are) incorrect reason for eutrophication ? (A) excess usage of fertilisers (B) excess usage of detergents (C) dense plant population in water bodies (D) lack of nutrients in water bodies that prevent plant growth…
Environmental Chemistry Eutrophication and Dissolved Oxygen Limits
EasyOtherIdea asked in 3 yearsAsked the year before
Q42
Nitrogen can be estimated by Kjeldahl's method for which of the following compound ?
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q43
The correct pair(s) of the ambident nucleophiles is (are) : (A) $\mathrm{AgCN/KCN}$ (B) $\mathrm{RCOOAg/RCOOK}$ (C) $\mathrm{AgNO_2/KNO_2}$ (D) $\mathrm{AgI/KI}$
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Ambident Nucleophiles (Cyanide/Nitrite)
MediumOtherNew ideaIdea asked in 3 years
Q44
Given below are two statements : Statement I : 2-methylbutane on oxidation with $\mathrm{KMnO_4}$ gives 2-methylbutan-2-ol. Statement II : n-alkanes can be easily oxidised to corresponding alcohols with $\mathrm{KMnO_4}$ . Choose the correct option :
Hydrocarbons Alkanes and Free Radicals KMnO4 Oxidation of Tertiary Alkanes
MediumTwo statementsNew idea
Q45
Choose the correct statement regarding the formation of carbocations A and B given. $\mathrm{CH_3-CH_2-CH=CH_2 + HBr}$ gives two branches: $\mathrm{CH_3-CH_2-CH_2-\overset{+}{C}H_2 + Br^-}$ "A" $\mathrm{CH_3-CH_2-\overset{+}{C}H-CH_3 + Br^-}$ "B"
Hydrocarbons Alkenes and Alkynes Markovnikov's Rule Application
EasySingle correct · figureIdea asked in 6 yearsAsked the year before
Q46
$\mathrm{C_{12}H_{22}O_{11} + H_2O \xrightarrow{Enzyme\ A} C_6H_{12}O_6 + C_6H_{12}O_6}$ Sucrose Glucose Fructose $\mathrm{C_6H_{12}O_6 \xrightarrow{Enzyme\ B} 2C_2H_5OH + 2CO_2}$ Glucose In the above reactions, the enzyme A and enzyme B respectively are :
Biomolecules Carbohydrates Inversion of Cane Sugar
EasySingle correctNew ideaIdea asked in 2 years
Q47
$\mathrm{C_7H_7N_2OCl + C_2H_5OH} \longrightarrow$ [structure] $+ \mathrm{N_2} + \text{"X"} + \text{"Y"}$ (A) In the above reaction, the structural formula of (A), "X" and "Y" respectively are :
Amines Diazonium Salts Reduction to Benzene via Ethanol
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q48
Primary, secondary and tertiary amines can be separated using :
Amines Hinsberg Test
EasySingle correctIdea asked in 5 yearsAsked the year before
Q49
Match List - I with List - II. List - I Chemical Compound List - II Used as (a) Sucralose (i) Synthetic detergent (b) Glyceryl ester of stearic acid (ii) Artificial sweetener (c) Sodium benzoate (iii) Antiseptic (d) Bithionol (iv) Food preservative Choose…
Chemistry in Everyday Life Food Additives
EasyMatch the listNew idea
Q50
Fructose is an example of :
Biomolecules Carbohydrates Hydrolysis-Based Classification of Carbohydrates
EasySingle correctNew ideaIdea asked in 2 years
Q51
The number of chlorine atoms in 20 mL of chlorine gas at STP is __________ $10^{21}$ . (Round off to the Nearest Integer). [Assume chlorine is an ideal gas at STP $R = 0.083\ \mathrm{L\ bar\ mol^{-1}\ K^{-1}}$ , $\mathrm{N_A} = 6.023 \times 10^{23}$ ]
Some Basic Concepts of Chemistry Mole Concept Mole and Avogadro Calculations
EasyNumerical valueNew ideaIdea asked in 5 years
Q52
KBr is doped with $10^{-5}$ mole percent of $\mathrm{SrBr_2}$ . The number of cationic vacancies in 1 g of KBr crystal is __________ $10^{14}$ . (Round off to the Nearest Integer). [Atomic Mass : K : 39.1 u, Br : 79.9 u $\mathrm{N_A} = 6.023 \times 10^{23}$ ]
The Solid State Solid State Defects Impurity Defects and Doping
MediumNumerical valueNew idea
Q53
In the ground state of atomic Fe( $Z = 26$ ), the spin-only magnetic moment is __________ $\times 10^{-1}$ BM. (Round off to the Nearest Integer). [Given : $\sqrt{3} = 1.73$ , $\sqrt{2} = 1.41$ ]
Structure of Atom Quantum Numbers Counting Unpaired Electrons
EasyNumerical valueNew ideaIdea asked in 2 years
Q54
A 1 molal $\mathrm{K_4Fe(CN)_6}$ solution has a degree of dissociation of 0.4. Its boiling point is equal to that of another solution which contains 18.1 weight percent of a non electrolytic solute A. The molar mass of A is __________ u. (Round off to the…
Solutions Colligative Properties Degree of Dissociation from Van't Hoff Factor
MediumNumerical valueNew ideaIdea asked in 5 years
Q55
Consider the reaction $\mathrm{N_2O_4(g) \rightleftharpoons 2NO_2(g)}$ . The temperature at which $\mathrm{K_C} = 20.4$ and $\mathrm{K_P} = 600.1$ , is __________ K. (Round off to the Nearest Integer). [Assume all gases are ideal and…
Equilibrium Chemical Equilibrium Kc and Kp Relationship
EasyNumerical valueNew ideaIdea asked in 2 years
Q56
A KCl solution of conductivity $0.14\ \mathrm{S\ m^{-1}}$ shows a resistance of $4.19\ \Omega$ in a conductivity cell. If the same cell is filled with an HCl solution, the resistance drops to $1.03\ \Omega$ . The conductivity of the HCl solution is…
Electrochemistry
EasyNumerical value
Q57
The reaction $\mathrm{2A + B_2 \rightarrow 2AB}$ is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of __________. (Round off to the…
Chemical Kinetics Rate Laws Order vs Molecularity
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q58
On complete reaction of $\mathrm{FeCl_3}$ with oxalic acid in aqueous solution containing KOH, resulted in the formation of product A. The secondary valency of Fe in the product A is __________. (Round off to the Nearest Integer).
Coordination Compounds
MediumNumerical value
Q59
The total number of C-C sigma bond/s in mesityl oxide ( $\mathrm{C_6H_{10}O}$ ) is __________. (Round off to the Nearest Integer).
Organic Chemistry: Some Basic Principles and Techniques
EasyNumerical value
Q60
[reaction scheme] Consider the above reaction. The percentage yield of amide product is __________. (Round off to the Nearest Integer). (Given : Atomic mass : C : 12.0 u, H : 1.0 u, N : 14.0 u, O : 16.0 u, Cl : 35.5 u)
Amines Stoichiometry Theoretical and Percent Yield
MediumNumerical value · figureNew ideaIdea asked in 2 years

Maths30 questions

3 easy17 medium10 hard

Q61
The number of solutions of the equation $\sin^{-1}\left[x^2+\frac{1}{3}\right]+\cos^{-1}\left[x^2-\frac{2}{3}\right]=x^2$ , for $x\in[-1, 1]$ , and $[x]$ denotes the greatest integer less than or equal to $x$ , is :
Inverse Trigonometric Functions Inverse Trig Domains Inverse Trig with GIF and Fractional Part
HardSingle correctNew ideaIdea asked in 2 years
Q62
If the Boolean expression $(p\wedge q)\circledast(p\otimes q)$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by :
Mathematical Reasoning
EasySingle correct
Q63
Let O be the origin. Let $\overrightarrow{OP}=x\hat{i}+y\hat{j}-\hat{k}$ and $\overrightarrow{OQ}=-\hat{i}+2\hat{j}+3x\hat{k}$ , $x, y\in\mathbf{R}$ , $x>0$ , be such that $\left|\overrightarrow{PQ}\right|=\sqrt{20}$ and the vector $\overrightarrow{OP}$ is…
Vector Algebra Triple Products STP Definition and Determinant
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q64
If $x, y, z$ are in arithmetic progression with common difference d, $x\neq 3d$ , and the determinant of the matrix $\begin{bmatrix}3 & 4\sqrt{2} & x\\ 4 & 5\sqrt{2} & y\\ 5 & k & z\end{bmatrix}$ is zero, then the value of $k^2$ is :
Determinants Cramer's Rule Arithmetic Progression Coefficients Trick
MediumSingle correctNew idea
Q65
The value of the limit $\lim_{\theta\to 0}\frac{\tan(\pi\cos^2\theta)}{\sin(2\pi\sin^2\theta)}$ is equal to :
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
MediumSingle correctNew ideaIdea asked in 6 years
Q66
If the integral $\int_0^{10}\frac{[\sin 2\pi x]}{e^{x-[x]}}dx=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma$ , where $\alpha, \beta, \gamma$ are integers and $[x]$ denotes the greatest integer less than or equal to $x$ , then the value of $\alpha+\beta+\gamma$ …
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardSingle correctIdea asked in 7 yearsAsked the year before
Q67
If the curve $y=y(x)$ is the solution of the differential equation $2(x^2+x^{5/4})dy-y(x+x^{1/4})dx=2x^{9/4}dx$ , $x>0$ which passes through the point $\left(1, 1-\frac{4}{3}\log_e 2\right)$ , then the value of $y(16)$ is equal to :
Differential Equations Linear Differential Equations Standard Linear Form Identification
HardSingle correctIdea asked in 3 yearsAsked the year before
Q68
Let $y=y(x)$ be the solution of the differential equation $\cos x(3\sin x+\cos x+3)dy=(1+y\sin x(3\sin x+\cos x+3))dx$ , $0\leq x\leq\frac{\pi}{2}$ , $y(0)=0$ . Then, $y\left(\frac{\pi}{3}\right)$ is equal to :
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q69
Consider the function $f:\mathbf{R}\to\mathbf{R}$ defined by $f(x)=\begin{cases}\left(2-\sin\left(\frac{1}{x}\right)\right)|x|, & x\neq 0\\ 0, & x=0\end{cases}$ . Then $f$ is :
Application of Derivatives Monotonicity First Derivative Test
HardSingle correctIdea asked in 3 yearsAsked the year before
Q70
The value of $\lim_{n\to\infty}\frac{[r]+[2r]+\ldots+[nr]}{n^2}$ , where r is a non-zero real number and $[r]$ denotes the greatest integer less than or equal to r, is equal to :
Limits and Derivatives Integral as Limit of Sum Greatest Integer Function Sums
MediumSingle correctNew idea
Q71
Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$ . Then the probability that…
Probability Conditional Probability Multiplication Rule of Probability
MediumSingle correctNew idea
Q72
If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :
Permutations and Combinations Triangles from Points with Collinearity
EasySingle correctNew ideaIdea asked in 3 years
Q73
Let the tangent to the circle $x^2+y^2=25$ at the point R(3, 4) meet $x$ -axis and $y$ -axis at points P and Q, respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then $r^2$ is…
Conic Sections Straight Line Distance Incenter via Equidistance
MediumSingle correctNew ideaIdea asked in 3 years
Q74
Let $S_1$ , $S_2$ and $S_3$ be three sets defined as $S_1=\{z\in\mathbb{C}:|z-1|\leq\sqrt{2}\}$ $S_2=\{z\in\mathbb{C}:\mathrm{Re}((1-\mathrm{i})z)\geq 1\}$ $S_3=\{z\in\mathbb{C}:\mathrm{Im}(z)\leq 1\}$ Then the set $S_1\cap S_2\cap S_3$
Complex Numbers and Quadratic Equations
MediumSingle correct
Q75
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=e^{-x}\sin x$ . If $F:[0, 1]\to\mathbf{R}$ is a differentiable function such that $F(x)=\int_0^x f(t)\,dt$ , then the value of $\int_0^1(F'(x)+f(x))e^x dx$ lies in the interval
Integrals Definite Integral Properties Bounding and Estimation Property
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q76
The value of $\sum_{r=0}^{6}\left({}^6C_r\cdot{}^6C_{6-r}\right)$ is equal to :
Binomial Theorem Binomial Coefficients Sum of Squares of Binomial Coefficients
EasySingle correctNew idea
Q77
If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line $\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}$ and containing the line $\frac{x-2}{3}=\frac{1-y}{2}=\frac{z+1}{1}$ is $\alpha x+\beta y+\gamma z=24$ , then…
Three Dimensional Geometry Planes in 3D Plane Containing a Line and a Point
HardSingle correctNew ideaIdea asked in 3 years
Q78
Two tangents are drawn from a point P to the circle $x^2+y^2-2x-4y+4=0$ , such that the angle between these tangents is $\tan^{-1}\left(\frac{12}{5}\right)$ , where $\tan^{-1}\left(\frac{12}{5}\right)\in(0, \pi)$ . If the centre of the circle is denoted by C…
Conic Sections Circle Tangents Area of Tangent-Chord Triangle
MediumSingle correctNew ideaIdea asked in 2 years
Q79
The number of solutions of the equation $x+2\tan x=\frac{\pi}{2}$ in the interval $[0, 2\pi]$ is :
Trigonometric Functions General Solutions Graphical Root Counting for Mixed Equations
MediumSingle correctNew ideaIdea asked in 4 years
Q80
Let L be a tangent line to the parabola $y^2=4x-20$ at (6, 2). If L is also a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{b}=1$ , then the value of b is equal to :
Conic Sections General Conic Section Condition for Line Tangency
MediumSingle correctNew idea
Q81
Let $I_n=\int_1^e x^{19}(\log|x|)^n dx$ , where $n\in\mathbf{N}$ . If $(20)I_{10}=\alpha I_9+\beta I_8$ , for natural numbers $\alpha$ and $\beta$ , then $\alpha-\beta$ equals to __________.
Integrals Integration by Parts Algebraic Reduction Formulas
MediumNumerical valueNew ideaIdea asked in 3 years
Q82
Let $\tan\alpha$ , $\tan\beta$ and $\tan\gamma$ ; $\alpha, \beta, \gamma\neq\frac{(2n-1)\pi}{2}$ , $n\in\mathbf{N}$ be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $\Delta$ ABC coincides with origin and…
Trigonometric Functions Trigonometric Identities Triple Angle Formulas
HardNumerical valueNew ideaIdea asked in 2 years
Q83
If 1, $\log_{10}(4^x-2)$ and $\log_{10}\left(4^x+\frac{18}{5}\right)$ are in arithmetic progression for a real number $x$ , then the value of the determinant $\begin{vmatrix}2\left(x-\frac{1}{2}\right) & x-1 & x^2\\ 1 & 0 & x\\ x & 1 & 0\end{vmatrix}$ is…
Determinants
MediumNumerical value
Q84
Consider a set of $3n$ numbers having variance 4. In this set, the mean of first $2n$ numbers is 6 and the mean of the remaining $n$ numbers is 3. A new set is constructed by adding 1 into each of first $2n$ numbers, and subtracting 1 from each of the…
Statistics Variance and SD Combined Variance of Two Sets
HardNumerical valueNew ideaIdea asked in 3 years
Q85
Let $f:[-1, 1]\to\mathbf{R}$ be defined as $f(x)=ax^2+bx+c$ for all $x\in[-1, 1]$ , where $a, b, c\in\mathbf{R}$ such that $f(-1)=2$ , $f'(-1)=1$ and for $x\in(-1, 1)$ the maximum value of $f''(x)$ is $\frac{1}{2}$ . If $f(x)\leq\alpha$ , $x\in[-1, 1]$ , then the…
Application of Derivatives Maxima and Minima Closed Interval Extrema
MediumNumerical valueNew ideaIdea asked in 6 years
Q86
Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^2}\right)^n$ , $x\neq 0$ , be in the ratio 12 : 8 : 3. Then the term independent of $x$ in the expansion, is equal to __________.
Binomial Theorem Binomial Coefficients Ratio of Consecutive Coefficients
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q87
Let $f:[-3, 1]\to\mathbf{R}$ be given as $f(x)=\begin{cases}\min\{(x+6), x^2\}, & -3\leq x\leq 0\\ \max\{\sqrt{x}, x^2\}, & 0\leq x\leq 1.\end{cases}$ If the area bounded by $y=f(x)$ and $x$ -axis is A, then the value of $6A$ is equal to __________.
Application of Integrals Area Under Curves Area Involving Max/Min Functions
MediumNumerical valueNew ideaIdea asked in 6 years
Q88
Let P be an arbitrary point having sum of the squares of the distances from the planes $x+y+z=0$ , $lx-nz=0$ and $x-2y+z=0$ , equal to 9. If the locus of the point P is $x^2+y^2+z^2=9$ , then the value of $l-n$ is equal to __________.
Three Dimensional Geometry
HardNumerical value
Q89
Let $\overrightarrow{x}$ be a vector in the plane containing vectors $\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{b}=\hat{i}+2\hat{j}-\hat{k}$ . If the vector $\overrightarrow{x}$ is perpendicular to…
Vector Algebra Dot Product Scalar and Vector Projection
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q90
Let $A=\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ and $B=\begin{bmatrix}\alpha\\ \beta\end{bmatrix}\neq\begin{bmatrix}0\\ 0\end{bmatrix}$ such that $AB=B$ and $a+d=2021$ , then the value of $ad-bc$ is equal to __________.
Matrices Cramer's Rule Eigenvalue-Type Homogeneous Systems
MediumNumerical valueNew idea

Dropped from the final key and left out of every count: Q17.

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.