JEE Main 2021 · March session

JEE Main 18 March 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 8 were rated hard and 36 easy. Its hard-question count was the joint 12th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Aldehydes, Ketones and Carboxylic Acids, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 8; 9% of the shift
Chapters asked: 66; 13 questions with a figure

Key findings · 18 Mar 2021, Shift 1

1
8 hard questions (9%): the joint 12th 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 6 of 30 rated hard; Chemistry had the most easy questions (16 of 30).
3
51 questions tested a new idea, one no earlier year had asked: 74% of the 69 questions tagged to an idea.
4
18 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
38 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: Work, Energy and Power in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 14Medium 16Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 16Medium 12Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 6Medium 18Hard 6

Top chapters

Conic Sections3 Q
Integrals3 Q
Sequences and Series3 Q
Straight Lines3 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q

Question format

Single correct46 Q
Numerical value30 Q
Diagram based6 Q
Match the list6 Q
Assertion–reason1 Q
Other1 Q

What each question asks you to do

Calculation31 Q
Multi-step22 Q
Application13 Q
Recall12 Q
Conceptual8 Q
Data or graph3 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
Open30 this shift3065 · 33%33%8/829299715710354533200225

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

Every question

All 90 questions of this shift

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

Subject

Difficulty

Idea

Find

90 of 90 questions

Physics30 questions

14 easy16 medium0 hard

Q1
An oil drop of radius 2 mm with a density 3 g cm $^{-3}$ is held stationary under a constant electric field $3.55\times10^{5}$ V m $^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess ? Consider…
Electric Charges and Fields
MediumSingle correct
Q2
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :
Work, Energy and Power Power Kinematics of Constant Power
EasySingle correctIdea asked in 3 yearsAsked the year before
Q3
Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3 T, the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of…
Moving Charges and Magnetism Ampere's Circuital Law Ideal Infinite Solenoid
MediumSingle correct · figureNew ideaIdea asked in 4 years
Q4
The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use $\gamma = 1.4$ ) :
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
MediumSingle correct · figureIdea asked in 7 yearsAsked the year before
Q5
The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :
Motion in a Straight Line Kinematics in 1D Uniform Acceleration Equations
EasyDiagram based · figureNew ideaIdea asked in 4 years
Q6
An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :
Alternating Current RMS and Peak Values Time from Peak to RMS
EasySingle correctNew ideaIdea asked in 2 years
Q7
In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light…
Wave Optics Young's Double Slit YDSE Fringe Width
EasySingle correctIdea asked in 5 yearsAsked the year before
Q8
A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q9
The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}}$ . The measured value of the length of pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s…
Units and Measurements
MediumSingle correct
Q10
Imagine that the electron in a hydrogen atom is replaced by a muon ( $\mu$ ). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :
Atoms Bohr's Atomic Model Reduced Mass Effect
MediumSingle correctNew idea
Q11
A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life, $T_{1/2}$ of the nuclei is :
Nuclei Radioactive Decay Parallel Decay Branching
MediumSingle correctNew ideaIdea asked in 2 years
Q12
A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.
Moving Charges and Magnetism Magnetic Dipole Moment Stable and unstable equilibrium states
MediumSingle correctNew idea
Q13
In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity…
Units and Measurements
MediumSingle correct
Q14
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :
Gravitation Orbital Mechanics Kepler's Laws
EasySingle correctNew ideaIdea asked in 4 years
Q15
In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :
Alternating Current LCR Resonance Resistance Effect on Resonance Curve
MediumSingle correctNew ideaIdea asked in 2 years
Q16
Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :
Ray Optics and Optical Instruments Optical Instruments Astigmatism and Cylindrical Lenses
MediumSingle correctNew idea
Q17
What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? ( $k_B$ is Boltzmann constant)
Kinetic Theory Kinetic Theory of Gases Law of Equipartition
EasySingle correctNew ideaIdea asked in 4 years
Q18
Match List - I with List - II. List - I (a) 10 km height over earth's surface (b) 70 km height over earth's surface (c) 180 km height over earth's surface (d) 270 km height over earth's surface List - II (i) Thermosphere (ii) Mesosphere (iii) Stratosphere…
Communication Systems
EasyMatch the list
Q19
A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the $x$ -direction. At a particular point in space and time, $\vec{B} = 2.0\times10^{-8}\,\hat{k}$ T. (where, $\hat{k}$ is unit vector along $z$ -direction) What is $\vec{E}$ at…
Electromagnetic Waves
MediumSingle correct
Q20
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $\omega$ . Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :
System of Particles and Rotational Motion Angular Momentum Conservation of Angular Momentum
EasySingle correctIdea asked in 5 yearsAsked the year before
Q21
An npn transistor operates as a common emitter amplifier with a power gain of $10^6$ . The input circuit resistance is 100 $\Omega$ and the output load resistance is 10 k $\Omega$ . The common emitter current gain ' $\beta$ ' will be __________. (Round off to the…
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors CE Amplifier Voltage Gain
MediumNumerical valueNew ideaIdea asked in 3 years
Q22
A ball of mass 10 kg moving with a velocity $10\sqrt{3}$ m/s along the $x$ -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts…
System of Particles and Rotational Motion Collisions Momentum in Explosions
MediumNumerical value · figureNew ideaIdea asked in 3 years
Q23
The voltage across the 10 $\Omega$ resistor in the given circuit is $x$ volt. The value of 'x' to the nearest integer is __________.
Current Electricity Kirchhoff's Laws Voltage Divider Rule
EasyNumerical value · figureNew ideaIdea asked in 2 years
Q24
As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is $x$ m/s. (Take $g = 10$ m/s $^2$ ) The value of 'x' to…
Work, Energy and Power Work and Kinetic Energy Conservation of Mechanical Energy
EasyNumerical value · figureNew ideaIdea asked in 4 years
Q25
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a}$ s. The value of 'a' to the nearest integer is __________.
Oscillations SHM Equations Phasor Diagram Technique
MediumNumerical valueNew ideaIdea asked in 3 years
Q26
The circuit shown in the figure consists of a charged capacitor of capacity 3 $\mu$ F and a charge of 30 $\mu$ C. At time $t=0$ , when the key is closed, the value of current flowing through the 5 M $\Omega$ resistor is ' $x$ ' $\mu$ A. The value of ' $x$ ' to the…
Electromagnetic Induction RC Circuits Initial Rate of Charging
EasyNumerical value · figureNew idea
Q27
A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is ' $x$ ' m/s. The value of ' $x$ ' to the nearest integer is __________.
Motion in a Plane Relative Velocity River-Boat Drift Analysis
EasyNumerical valueNew idea
Q28
Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of wire A. The length of the wires A and B are…
Mechanical Properties of Solids Elasticity Elastic Moduli
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q29
A parallel plate capacitor has plate area 100 m $^2$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is ' $x$ ' pF. The value of…
Electrostatic Potential and Capacitance Dielectrics Partial and Multiple Slabs
MediumNumerical valueNew ideaIdea asked in 6 years
Q30
A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of…
Work, Energy and Power Work and Kinetic Energy Work Done by Non-Conservative Forces
EasyNumerical valueNew ideaIdea asked in 2 years

Chemistry30 questions

16 easy12 medium2 hard

Q31
In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is :
The Solid State Crystal Lattices Empirical Formula from Void Occupation
EasySingle correctNew idea
Q32
A certain orbital has no angular nodes and two radial nodes. The orbital is :
Structure of Atom Quantum Numbers Calculation of Radial and Angular Nodes
EasySingle correctNew ideaIdea asked in 5 years
Q33
Match List - I with List - II : List - I (Process) (a) Deacon's process (b) Contact process (c) Cracking of hydrocarbons (d) Hydrogenation of vegetable oils List - II (Catalyst) (i) ZSM-5 (ii) $\mathrm{CuCl_2}$ (iii) Particles 'Ni' (iv) $\mathrm{V_2O_5}$ …
Surface Chemistry d-Block Elements Specific d-Block Industrial Catalysts
MediumMatch the listNew ideaIdea asked in 3 years
Q34
The ionic radius of $\mathrm{Na^+}$ ion is 1.02 Å. The ionic radii (in Å) of $\mathrm{Mg^{2+}}$ and $\mathrm{Al^{3+}}$ , respectively, are :
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasySingle correctIdea asked in 5 yearsAsked the year before
Q35
The chemical that is added to reduce the melting point of the reaction mixture during the extraction of aluminium is :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Hall-Heroult Process
EasySingle correctNew ideaIdea asked in 3 years
Q36
Given below are two Statements : One is labelled as Assertion A and the other is labelled as Reason R : Assertion A : During the boiling of water having temporary hardness, $\mathrm{Mg(HCO_3)_2}$ is converted to $\mathrm{MgCO_3}$ . Reason R : The solubility…
Hydrogen Hydrogen and Hydrides Temporary Hardness and Clark's Method
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q37
Match List - I with List - II : List - I (a) $\mathrm{Ca(OCl)_2}$ (b) $\mathrm{CaSO_4\cdot\frac{1}{2}H_2O}$ (c) CaO (d) $\mathrm{CaCO_3}$ List - II (i) Antacid (ii) Cement (iii) Bleach (iv) Plaster of Paris Choose the most appropriate answer from the options…
The s-Block Elements s-Block Elements Gypsum and Plaster of Paris
EasyMatch the listNew idea
Q38
The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is :
The p-Block Elements
HardSingle correct
Q39
Match List - I with List - II : List - I (a) Chlorophyll (b) Vitamin - $\mathrm{B_{12}}$ (c) Anticancer drug (d) Grubbs catalyst List - II (i) Ruthenium (ii) Platinum (iii) Cobalt (iv) Magnesium Choose the most appropriate answer from the options given below :
Coordination Compounds
EasyMatch the list
Q40
The correct structures of trans- $\mathrm{[NiBr_2(PPh_3)_2]}$ and meridional- $\mathrm{[Co(NH_3)_3(NO_2)_3]}$ , respectively, are :
Coordination Compounds Coordination Isomerism Square Planar Geometry
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q41
The statements that are TRUE : (A) methane leads to both global warming and photochemical smog (B) methane is generated from paddy fields (C) methane is a stronger global warming gas than $\mathrm{CO_2}$ (D) methane is a part of reducing smog. Choose the…
Environmental Chemistry Greenhouse Effect
MediumOtherIdea asked in 4 yearsAsked the year before
Q42
Compound with molecular formula $\mathrm{C_3H_6O}$ can show :
Organic Chemistry: Some Basic Principles and Techniques Structural Isomerism Functional Isomerism
EasySingle correctNew idea
Q43
Match List - I with List - II : List - I (Chemicals) (a) Alcoholic potassium hydroxide (b) Pd/ $\mathrm{BaSO_4}$ (c) BHC (Benzene hexachloride) (d) Polyacetylene List - II (Use/Preparation/Constituent) (i) electrodes in batteries (ii) obtained by addition…
Haloalkanes and Haloarenes
MediumMatch the list
Q44
Reaction of Grignard reagent, $\mathrm{C_2H_5MgBr}$ with $\mathrm{C_8H_8O}$ followed by hydrolysis gives compound "A" which reacts instantly with Lucas reagent to give compound B, $\mathrm{C_{10}H_{13}Cl}$ . The Compound B is :
Alcohols, Phenols and Ethers Alcohols and Phenols Grignard Synthesis of Alcohols
MediumDiagram based · figureNew idea
Q45
[figure: cyclohexyl-C#N --(H2O/H+)--> "A" (Major Product) --(H2O/H+, heat)--> cyclohexyl-COOH] Consider the above chemical reaction and identify product "A" :
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Hydrolysis of Nitriles
EasyDiagram based · figureNew ideaIdea asked in 2 years
Q46
[figure: p-methylanisole (benzene ring with CH3 at top and OCH3 at bottom, para) --(Alkaline KMnO4, then H+)--> "X"] Considering the above chemical reaction, identify the product "X" :
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Side-Chain Oxidation of Alkylbenzenes
EasyDiagram based · figureNew ideaIdea asked in 2 years
Q47
[figure: aniline --(NaNO2, HCl, 273 K - 278 K)--> "X" (Major Product) --(N,N-dimethylaniline)--> "Y" (Major Product)] Considering the above reaction, X and Y respectively are :
Amines Diazonium Salts Regioselectivity in Azo Coupling
EasyDiagram based · figureNew idea
Q48
Match List - I with List - II : List - I (Class of Drug) (a) Antacid (b) Artificial Sweetener (c) Antifertility (d) Tranquilizers List - II (Example) (i) Novestrol (ii) Cimetidine (iii) Valium (iv) Alitame Choose the most appropriate match :
Chemistry in Everyday Life Therapeutic Drug Classes
EasyMatch the listIdea asked in 3 yearsAsked the year before
Q49
A non-reducing sugar "A" hydrolyses to give two reducing mono saccharides. Sugar A is :
Biomolecules Carbohydrates Non-Reducing Nature of Sucrose
EasySingle correctNew ideaIdea asked in 2 years
Q50
Reagent, 1-naphthylamine and sulphanilic acid in acetic acid is used for the detection of :
Organic Chemistry: Some Basic Principles and Techniques
MediumSingle correct
Q51
Complete combustion of 3 g of ethane gives $x\times10^{22}$ molecules of water. The value of $x$ is __________. (Round off to the Nearest Integer). [Use : $N_A = 6.023\times10^{23}$ ; Atomic masses in u : C : 12.0 ; O : 16.0 ; H : 1.0]
Some Basic Concepts of Chemistry Mole Concept Mole and Avogadro Calculations
EasyNumerical valueNew ideaIdea asked in 5 years
Q52
AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on Molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is __________. (Round off to the Nearest Integer).
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
MediumNumerical valueNew ideaIdea asked in 3 years
Q53
For the reaction $\mathrm{C_2H_6 \rightarrow C_2H_4 + H_2}$ the reaction enthalpy $\Delta_rH =$ __________ kJ mol $^{-1}$ . (Round off to the Nearest Integer). [Given : Bond enthalpies in kJ mol $^{-1}$ : C-C : 347, C=C : 611; C-H : 414, H-H : 436]
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bond Enthalpy Calculations
EasyNumerical valueNew ideaIdea asked in 4 years
Q54
2 molal solution of a weak acid HA has a freezing point of 3.885°C. The degree of dissociation of this acid is __________ $\times10^{-3}$ . (Round off to the Nearest Integer). [Given : Molal depression constant of water = 1.85 K kg mol $^{-1}$ Freezing point…
Solutions Colligative Properties Freezing Point Depression
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q55
In order to prepare a buffer solution of pH 5.74, sodium acetate is added to acetic acid. If the concentration of acetic acid in the buffer is 1.0 M, the concentration of sodium acetate in the buffer is __________ M. (Round off to the Nearest Integer).…
Equilibrium pH and Buffers Acidic Buffer pH Calculation
EasyNumerical valueNew ideaIdea asked in 3 years
Q56
For the reaction $\mathrm{2Fe^{3+}(aq) + 2I^-(aq) \rightarrow 2Fe^{2+}(aq) + I_2(s)}$ the magnitude of the standard molar free energy change, $\Delta_rG^\circ_m = -$ __________ kJ (Round off to the Nearest Integer).…
Electrochemistry Gibbs Free Energy Standard Gibbs Energy and Standard Cell Potential
HardNumerical valueNew ideaIdea asked in 2 years
Q57
$\mathrm{2\,NO(g) + Cl_2(g) \rightleftharpoons 2\,NOCl(s)}$ This reaction was studied at $-10$ °C and the following data was obtained run | $[\mathrm{NO}]_0$ | $[\mathrm{Cl_2}]_0$ | $r_0$ 1 | 0.10 | 0.10 | 0.18 2 | 0.10 | 0.20 | 0.35 3 | 0.20 | 0.20 | 1.40…
Chemical Kinetics Rate Laws Initial Rates Method
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q58
The total number of unpaired electrons present in the complex $\mathrm{K_3[Cr(oxalate)_3]}$ is __________.
Coordination Compounds Crystal Field Theory High and Low Spin States
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q59
__________ grams of 3-Hydroxy propanal (MW = 74) must be dehydrated to produce 7.8 g of acrolein (MW = 56) ( $\mathrm{C_3H_4O}$ ) if the percentage yield is 64. (Round off to the Nearest Integer). [Given : Atomic masses : C : 12.0 u, H : 1.0 u, O : 16.0 u]
Aldehydes, Ketones and Carboxylic Acids Stoichiometry Reverse Yield Calculation
MediumNumerical valueNew idea
Q60
A reaction of 0.1 mole of Benzylamine with bromomethane gave 23 g of Benzyl trimethyl ammonium bromide. The number of moles of bromomethane consumed in this reaction are $n\times10^{-1}$ , when $n =$ __________. (Round off to the Nearest Integer). [Given :…
Amines Hofmann Exhaustive Methylation and Elimination
MediumNumerical valueNew idea

Maths30 questions

6 easy18 medium6 hard

Q61
If the functions are defined as $f(x)=\sqrt{x}$ and $g(x)=\sqrt{1-x}$ , then what is the common domain of the following functions : $f+g,\ f-g,\ f/g,\ g/f,\ g-f$ where $(f\pm g)(x) = f(x)\pm g(x),\ (f/g)(x) = \frac{f(x)}{g(x)}$
Relations and Functions Functions and Domain Intersection of Domains
EasySingle correctNew ideaIdea asked in 2 years
Q62
If the equation $a|z|^2 + \bar{\alpha}z + \alpha\bar{z} + d = 0$ represents a circle where a, d are real constants, then which of the following condition is correct ?
Complex Numbers and Quadratic Equations
MediumSingle correct
Q63
Let $A+2B=\begin{bmatrix}1&2&0\\6&-3&3\\-5&3&1\end{bmatrix}$ and $2A-B=\begin{bmatrix}2&-1&5\\2&-1&6\\0&1&2\end{bmatrix}$ . If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) $-$ Tr(B) has value equal to :
Matrices
EasySingle correct
Q64
Let $\alpha,\beta,\gamma$ be the real roots of the equation, $x^3+ax^2+bx+c=0$ , ( $a,b,c\in\mathbf{R}$ and $a,b\ne0$ ). If the system of equations (in $u,v,w$ ) given by $\alpha u+\beta v+\gamma w=0$ ; $\beta u+\gamma v+\alpha w=0$ ; $\gamma u+\alpha v+\beta w=0$ …
Determinants Cramer's Rule Parameter Evaluation in Homogeneous Systems
HardSingle correctIdea asked in 5 yearsAsked the year before
Q65
The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :
Permutations and Combinations Sum of Numbers Formed by Given Digits
MediumSingle correctNew ideaIdea asked in 2 years
Q66
Let $(1+x+2x^2)^{20} = a_0 + a_1x + a_2x^2 + \ldots + a_{40}x^{40}$ . Then, $a_1 + a_3 + a_5 + \ldots + a_{37}$ is equal to :
Binomial Theorem Binomial Coefficients Sum of Even and Odd Coefficients
HardSingle correctNew ideaIdea asked in 3 years
Q67
The value of $3+\cfrac{1}{4+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{3+\cdots\infty}}}}$ is equal to :
Sequences and Series
MediumSingle correct
Q68
$\frac{1}{3^2-1}+\frac{1}{5^2-1}+\frac{1}{7^2-1}+\ldots+\frac{1}{(201)^2-1}$ is equal to :
Sequences and Series AP and GP Method of Differences for Telescoping Series
MediumSingle correctNew ideaIdea asked in 6 years
Q69
If $\alpha,\beta$ are natural numbers such that $100^{\alpha}-199\beta=(100)(100)+(99)(101)+(98)(102)+\ldots+(1)(199)$ , then the slope of the line passing through $(\alpha,\beta)$ and origin is :
Straight Lines
MediumSingle correct
Q70
If $f(x)=\begin{cases}\dfrac{1}{|x|} & ;\ |x|\ge1\\ ax^2+b & ;\ |x|<1\end{cases}$ is differentiable at every point of the domain, then the values of a and b are respectively :
Continuity and Differentiability Finding Unknowns using Differentiability
MediumSingle correctNew ideaIdea asked in 3 years
Q71
The real valued function $f(x)=\dfrac{\mathrm{cosec}^{-1}x}{\sqrt{x-[x]}}$ , where $[x]$ denotes the greatest integer less than or equal to $x$ , is defined for all $x$ belonging to :
Inverse Trigonometric Functions Functions and Domain Domain of Inverse Secant and Cosecant
MediumSingle correctNew ideaIdea asked in 2 years
Q72
If $\lim_{x\to0}\dfrac{\sin^{-1}x-\tan^{-1}x}{3x^3}$ is equal to L, then the value of $(6L+1)$ is :
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q73
The integral $\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx$ is equal to : (where c is a constant of integration)
Integrals Integration by Substitution Composite Function Substitution
MediumSingle correctNew ideaIdea asked in 3 years
Q74
The differential equation satisfied by the system of parabolas $y^2=4a(x+a)$ is :
Differential Equations
MediumSingle correct
Q75
Choose the correct statement about two circles whose equations are given below : $x^2+y^2-10x-10y+41=0$ $x^2+y^2-22x-10y+137=0$
Conic Sections Circle Tangents Number of Common Tangents
EasySingle correctIdea asked in 4 yearsAsked the year before
Q76
For the four circles M, N, O and P, following four equations are given : Circle M : $x^2+y^2=1$ Circle N : $x^2+y^2-2x=0$ Circle O : $x^2+y^2-2x-2y+1=0$ Circle P : $x^2+y^2-2y=0$ If the centre of circle M is joined with centre of the circle N, further centre…
Conic Sections
EasySingle correct
Q77
The number of integral values of m so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is :
Straight Lines Cramer's Rule Conditions for Integer Solutions
MediumSingle correctNew idea
Q78
The equation of one of the straight lines which passes through the point (1, 3) and makes an angle $\tan^{-1}(\sqrt{2})$ with the straight line, $y+1=3\sqrt{2}\,x$ is :
Straight Lines
MediumSingle correct
Q79
The solutions of the equation $\begin{vmatrix}1+\sin^2x & \sin^2x & \sin^2x\\ \cos^2x & 1+\cos^2x & \cos^2x\\ 4\sin2x & 4\sin2x & 1+4\sin2x\end{vmatrix}=0$ , $(0<x<\pi)$ , are :
Determinants
MediumSingle correct
Q80
A vector $\vec{a}$ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $\vec{a}$ has components $p+1$ and…
Vector Algebra Dot Product Dot Product Invariance Under Rotation
MediumSingle correctNew idea
Q81
Let $z_1, z_2$ be the roots of the equation $z^2+az+12=0$ and $z_1, z_2$ form an equilateral triangle with origin. Then, the value of $|a|$ is __________.
Complex Numbers and Quadratic Equations Roots of Unity Equilateral Triangle Condition via Omega
MediumNumerical valueNew ideaIdea asked in 2 years
Q82
Let $f(x)$ and $g(x)$ be two functions satisfying $f(x^2)+g(4-x)=4x^3$ and $g(4-x)+g(x)=0$ , then the value of $\int_{-4}^{4}f(x^2)\,dx$ is __________.
Integrals Definite Integral Properties Even and Odd Functions
HardNumerical valueNew ideaIdea asked in 3 years
Q83
If $f(x)=\int\dfrac{5x^8+7x^6}{(x^2+1+2x^7)^2}\,dx$ , $(x\ge0)$ , $f(0)=0$ and $f(1)=\dfrac{1}{K}$ , then the value of K is __________.
Integrals Integration by Substitution Quotient Rule Differential Recognition
HardNumerical valueNew idea
Q84
A square ABCD has all its vertices on the curve $x^2y^2=1$ . The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is __________.
Conic Sections
HardNumerical value
Q85
Let the plane $ax+by+cz+d=0$ bisect the line joining the points $(4,-3,1)$ and $(2,3,-5)$ at the right angles. If a, b, c, d are integers, then the minimum value of $(a^2+b^2+c^2+d^2)$ is __________.
Three Dimensional Geometry Planes in 3D Perpendicular Bisector Plane
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q86
The equation of the planes parallel to the plane $x-2y+2z-3=0$ which are at unit distance from the point $(1,2,3)$ is $ax+by+cz+d=0$ . If $(b-d)=K(c-a)$ , then the positive value of K is __________.
Three Dimensional Geometry Point-Plane Distance Generating Parallel Planes at a Given Distance
MediumNumerical valueNew idea
Q87
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher…
Statistics Variance and SD Mean of Discrete Data
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q88
The number of times the digit 3 will be written when listing the integers from 1 to 1000 is __________.
Permutations and Combinations
MediumNumerical value
Q89
The missing value in the following figure is __________.
Sequences and Series
HardNumerical value · figure
Q90
The number of solutions of the equation $|\cot x|=\cot x+\dfrac{1}{\sin x}$ in the interval $[0,2\pi]$ is __________.
Trigonometric Functions
MediumNumerical value

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.