JEE Main 2021 · March session

JEE Main 17 March 2021, Shift 1

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 7 were rated hard and 35 easy. Its hard-question count was the joint 16th highest of the 24 2021 shifts Lumi analysed. The biggest chapter was System of Particles and Rotational Motion, with 4 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 7; 8% of the shift
Chapters asked: 63; 17 questions with a figure

Key findings · 17 Mar 2021, Shift 1

1
7 hard questions (8%): the joint 16th 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 4 of 29 rated hard; Chemistry had the most easy questions (15 of 30).
3
44 questions tested a new idea, one no earlier year had asked: 61% of the 72 questions tagged to an idea.
4
27 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
43 shared an idea with another 2021 shift (60% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: System of Particles and Rotational Motion in Physics (4), Aldehydes, Ketones and Carboxylic Acids in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Maths

29 Q · 10 numerical

Easy 8Medium 17Hard 4

Top chapters

Question format

Single correct44 Q
Numerical value30 Q
Diagram based12 Q
Two statements2 Q
Other1 Q

What each question asks you to do

Calculation30 Q
Multi-step23 Q
Conceptual13 Q
Application9 Q
Recall9 Q
Diagram reading4 Q
Data or graph1 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
Open29 this shift3065 · 33%33%8/829299715710354533200225

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

Every question

All 89 questions of this shift

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

Subject

Difficulty

Idea

Find

89 of 89 questions

Physics30 questions

12 easy16 medium2 hard

Q1
A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is :
Motion in a Straight Line Kinematics in 1D Acceleration-Deceleration Motion Profiles
MediumSingle correctNew ideaIdea asked in 2 years
Q2
A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed $v$ . If the coefficient of static friction between the tyres and the track is $\mu_s$ , then the magnitude of negative lift $F_L$ acting…
Laws of Motion Circular Motion Banking of Roads
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q3
A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :
Thermodynamics Heat Engines and Refrigerators Carnot Efficiency Limit
EasySingle correctNew ideaIdea asked in 3 years
Q4
A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is : (permeability of free space $=4\pi\times10^{-7}$ H/m)
Moving Charges and Magnetism Ampere's Circuital Law Ideal Infinite Solenoid
EasySingle correctNew ideaIdea asked in 4 years
Q5
A current of 10 A exists in a wire of crosssectional area of 5 mm $^2$ with a drift velocity of $2\times10^{-3}$ ms $^{-1}$ . The number of free electrons in each cubic meter of the wire is __________.
Current Electricity Ohm's Law and Resistance Drift Velocity and Current
MediumSingle correctNew ideaIdea asked in 3 years
Q6
A mass M hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity…
System of Particles and Rotational Motion Angular Momentum Angular Momentum of Conical Pendulum
HardDiagram based · figureIdea asked in 2 yearsAsked the year before
Q7
An AC current is given by $I=I_1\sin\omega t+I_2\cos\omega t$ . A hot wire ammeter will give a reading :
Alternating Current RMS and Peak Values AC Measuring Instruments
EasySingle correctNew ideaIdea asked in 2 years
Q8
A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$ ?
Kinetic Theory Kinetic Theory of Gases Gamma and Degrees of Freedom
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q9
When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :
Mechanical Properties of Fluids Surface Tension Common Interface of Coalescing Bubbles
MediumSingle correctNew idea
Q10
A triangular plate is shown. A force $\vec{F}=4\hat{i}-3\hat{j}$ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :
System of Particles and Rotational Motion Torque and Equilibrium 3D Torque Components
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q11
Two identical metal wires of thermal conductivities $K_1$ and $K_2$ respectively are connected in series. The effective thermal conductivity of the combination is :
Thermal Properties of Matter Heat Conduction Equivalent Thermal Conductivity in Series
EasySingle correctNew idea
Q12
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms $^{-1}$ . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now ?
Work, Energy and Power Work and Kinetic Energy Kinetic Energy Calculation
EasySingle correctNew ideaIdea asked in 4 years
Q13
The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is $2\times10^{8}$ ms $^{-1}$ . The focal length of the lens is __________.
Ray Optics and Optical Instruments Lens Maker's Formula Plano-Convex Lens Focal Length
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q14
Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom ?
Atoms Bohr's Atomic Model Scaling for Hydrogenic Ions
EasySingle correctNew ideaIdea asked in 2 years
Q15
Two ideal polyatomic gases at temperatures $T_1$ and $T_2$ are mixed so that there is no loss of energy. If $F_1$ and $F_2$ , $m_1$ and $m_2$ , $n_1$ and $n_2$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the…
Kinetic Theory Kinetic Theory of Gases Internal Energy of Gas Mixtures
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q16
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?
Oscillations Energy in SHM Fractional Energy Displacements
EasySingle correctNew ideaIdea asked in 2 years
Q17
The output of the given combination gates represents :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q18
An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)
Dual Nature of Radiation and Matter Matter Waves Matter Wave vs Photon Energy Scaling
MediumSingle correctNew idea
Q19
The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measurement is __________…
Units and Measurements
EasySingle correct
Q20
If an electron is moving in the n $^{th}$ orbit of the hydrogen atom, then its velocity ( $v_n$ ) for the n $^{th}$ orbit is given as :
Atoms Bohr's Atomic Model Electron Velocity in Orbit
EasySingle correctNew ideaIdea asked in 2 years
Q21
For VHF signal broadcasting, __________ km $^2$ of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (Take $\pi$ as 3.14)
Communication Systems
MediumNumerical value
Q22
If $2.5\times10^{-6}$ N average force is exerted by a light wave on a non - reflecting surface of 30 cm $^2$ area during 40 minutes of time span, the energy flux of light just before it falls on the surface is __________ W/cm $^2$ . (Round off to the Nearest…
Electromagnetic Waves
MediumNumerical value
Q23
Four identical rectangular plates with length, $l=2$ cm and breadth, $b=\frac{3}{2}$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $\frac{x\varepsilon_0}{d}$ . The value of $x$ is __________. (Round off to the Nearest…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q24
The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is __________. (Round off to the Nearest Integer)
Current Electricity
MediumNumerical value
Q25
A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate…
Electrostatic Potential and Capacitance Dielectrics Dielectric with Battery Disconnected
HardNumerical valueNew ideaIdea asked in 3 years
Q26
The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is __________ .
Gravitation Gravitational Potential Escape Velocity and Potential Relation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q27
The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is __________. (Assuming the acceleration to be uniform).
System of Particles and Rotational Motion Kinematics in 2D Kinematic Equations for Angular Motion
EasyNumerical valueNew idea
Q28
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is…
Oscillations SHM Equations Springs in Series
EasyNumerical value · figureNew ideaIdea asked in 3 years
Q29
The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of…
System of Particles and Rotational Motion
MediumNumerical value · figure
Q30
Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$ . Then the maximum horizontal force that can be applied on the larger block…
Laws of Motion Friction Two-Block Friction Systems
MediumNumerical value · figureNew ideaIdea asked in 2 years

Chemistry30 questions

15 easy14 medium1 hard

Q31
A central atom in a molecule has two lone pairs of electrons and forms three single bonds. The shape of this molecule is :
Chemical Bonding and Molecular Structure VSEPR Theory T-Shaped Geometry (SN=5, 2 LP)
EasySingle correctNew ideaIdea asked in 2 years
Q32
A colloidal system consisting of a gas dispersed in a solid is called a/an :
Surface Chemistry Colloids Colloid Classification by State
EasySingle correctIdea asked in 4 yearsAsked the year before
Q33
The absolute value of the electron gain enthalpy of halogens satisfies :
Classification of Elements and Periodicity in Properties Periodic Trends Electron Gain Enthalpy
EasySingle correctNew ideaIdea asked in 5 years
Q34
The point of intersection and sudden increase in the slope, in the diagram given below, respectively, indicates :
General Principles and Processes of Isolation of Elements Gibbs Free Energy Ellingham Diagram Phase Changes
MediumDiagram based · figureNew idea
Q35
The INCORRECT statement(s) about heavy water is (are) (A) used as a moderator in nuclear reactor (B) obtained as a by-product in fertilizer industry (C) used for the study of reaction mechanism (D) has a higher dielectric constant than water Choose the…
Hydrogen Hydrogen and Hydrides Heavy Water Properties
EasyOtherNew idea
Q36
The correct order of conductivity of ions in water is :
Electrochemistry Periodic Trends Hydration Enthalpy and Ionic Mobility
MediumSingle correctNew idea
Q37
Which of the following compound CANNOT act as a Lewis base ?
Chemical Bonding and Molecular Structure
MediumSingle correct
Q38
What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous solution ?
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
EasySingle correctIdea asked in 6 yearsAsked the year before
Q39
Given below are two statements : Statement I : Potassium permanganate on heating at 573 K forms potassium manganate. Statement II : Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature. In the light of the above…
The d- and f-Block Elements d-Block Elements Permanganate Reactions
MediumTwo statementsNew ideaIdea asked in 3 years
Q40
Reducing smog is a mixture of :
Environmental Chemistry Classical vs Photochemical Smog
EasySingle correctNew ideaIdea asked in 3 years
Q41
Given below are two statements : Statement I : Retardation factor ( $\mathrm{R_f}$ ) can be measured in meter/centimeter. Statement II : $\mathrm{R_f}$ value of a compound remains constant in all solvents. Choose the most appropriate answer from the options…
Organic Chemistry: Some Basic Principles and Techniques
EasyTwo statements
Q42
Which of the following is an aromatic compound ?
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Huckel's Rule (4n+2)
EasyDiagram based · figureNew ideaIdea asked in 6 years
Q43
[reaction drawn: see figure_note] Product “A” in the above chemical reaction is :
Hydrocarbons Alkenes and Alkynes Carbocation Rearrangements
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q44
[reaction drawn: see figure_note] The above reaction requires which of the following reaction conditions ?
Haloalkanes and Haloarenes Alcohols and Phenols Dow Process for Phenol
EasyDiagram based · figureNew ideaIdea asked in 2 years
Q45
Mesityl oxide is a common name of :
Aldehydes, Ketones and Carboxylic Acids
MediumSingle correct
Q46
Hoffmann bromomide degradation of benzamide gives product A, which upon heating with $\mathrm{CHCl_3}$ and NaOH gives product B. The structures of A and B are :
Amines Hofmann Bromamide Degradation
EasyDiagram based · figureNew ideaIdea asked in 5 years
Q47
[reaction drawn: see figure_note] The product “A” in the above reaction is :
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Cyclic Acetal Protection
MediumDiagram based · figureNew idea
Q48
Which of the following reaction is an example of ammonolysis ?
Amines Ammonolysis of Alkyl Halides
EasySingle correctNew ideaIdea asked in 2 years
Q49
With respect to drug-enzyme interaction, identify the wrong statement.
Chemistry in Everyday Life Competitive vs Allosteric Enzyme Inhibition
MediumSingle correctNew ideaIdea asked in 2 years
Q50
Which of the following is correct structure of tyrosine ?
Biomolecules
MediumDiagram based · figure
Q51
The mole fraction of a solute in a 100 molal aqueous solution is __________ $\times 10^{-2}$ . (Round off to the Nearest Integer). [Given : Atomic masses : H : 1.0 u, O : 16.0 u]
Solutions Mole Concept Molality Calculation
MediumNumerical valueNew ideaIdea asked in 2 years
Q52
The pressure exerted by a non-reactive gaseous mixture of 6.4 g of methane and 8.8 g of carbon dioxide in a 10 L vessel at $27^\circ$ C is __________ kPa. (Round off to the Nearest Integer). [Assume gases are ideal, $R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$ …
States of Matter Ideal Gas Laws Dalton's Law
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q53
A certain orbital has $n = 4$ and $m_L = -3$ . The number of radial nodes in this orbital is __________. (Round off to the Nearest Integer).
Structure of Atom Quantum Numbers Calculation of Radial and Angular Nodes
MediumNumerical valueNew ideaIdea asked in 5 years
Q54
The standard enthalpies of formation of $\mathrm{Al_2O_3}$ and CaO are $-1675\ \mathrm{kJ\ mol^{-1}}$ and $-635\ \mathrm{kJ\ mol^{-1}}$ respectively. For the reaction $\mathrm{3CaO + 2Al \rightarrow 3Ca + Al_2O_3}$ the standard reaction enthalpy…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Standard Enthalpy of Reaction
EasyNumerical valueNew ideaIdea asked in 2 years
Q55
The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility of oxygen in water is __________ $\times 10^{-5}\ \mathrm{mol\ dm^{-3}}$ . (Round off to the Nearest Integer). [Given : Henry’s law constant…
Solutions
MediumNumerical value
Q56
0.01 moles of a weak acid HA ( $K_a = 2.0 \times 10^{-6}$ ) is dissolved in 1.0 L of 0.1 M HCl solution. The degree of dissociation of HA is __________ $\times 10^{-5}$ (Round off to the Nearest Integer). [Neglect volume change on adding HA. Assume degree of…
Equilibrium pH and Buffers Common Ion Effect on Weak Acid pH
MediumNumerical valueNew idea
Q57
15 mL of aqueous solution of $\mathrm{Fe^{2+}}$ in acidic medium completely reacted with 20 mL of 0.03 M aqueous $\mathrm{Cr_2O_7^{2-}}$ . The molarity of the $\mathrm{Fe^{2+}}$ solution is __________ $\times 10^{-2}$ M. (Round off to the Nearest Integer).
Redox Reactions Law of Chemical Equivalence in Redox
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q58
For a certain first order reaction 32% of the reactant is left after 570 s. The rate constant of this reaction is __________ $\times 10^{-3}\ \mathrm{s^{-1}}$ . (Round off to the Nearest Integer). [Given : $\log_{10}2 = 0.301$ , $\ln 10 = 2.303$ ]
Chemical Kinetics Integrated Rate Equations First Order Integrated Rate Law
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q59
The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of product ‘A’. The reaction of 1 mol of ‘A’ with excess of $\mathrm{AgNO_3}$ in aqueous medium gives __________ mol(s) of Ag. (Round off to the Nearest…
The p-Block Elements Group 15 & 16 Phosphorus Oxoacids
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q60
[reaction drawn: see figure_note] In the above reaction, 3.9 g of benzene on nitration gives 4.92 g of nitrobenzene. The percentage yield of nitrobenzene in the above reaction is __________%. (Round off to the Nearest Integer). (Given atomic mass : C : 12.0…
Some Basic Concepts of Chemistry Stoichiometry Theoretical and Percent Yield
EasyNumerical value · figureNew ideaIdea asked in 2 years

Maths29 questions

8 easy17 medium4 hard

Q61
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement ?
Relations and Functions Sets and Relations Venn Diagrams
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q62
The area of the triangle with vertices A( $z$ ), B( $iz$ ) and C( $z+iz$ ) is :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Area of Rotated Complex Triangles
EasySingle correctNew idea
Q63
If A $=\begin{pmatrix}0 & \sin\alpha\\ \sin\alpha & 0\end{pmatrix}$ and $\det\left(A^{2}-\frac{1}{2}I\right)=0$ , then a possible value of $\alpha$ is :
Determinants Matrix Multiplication Determinant of Product
EasySingle correctIdea asked in 4 yearsAsked the year before
Q64
The system of equations $kx+y+z=1$ , $x+ky+z=k$ and $x+y+zk=k^{2}$ has no solution if k is equal to :
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
Team ‘A’ consists of 7 boys and n girls and Team ‘B’ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :
Permutations and Combinations Combinations of Distinct Objects
EasySingle correctIdea asked in 8 yearsAsked the year before
Q66
If the fourth term in the expansion of $(x+x^{\log_{2}x})^{7}$ is 4480, then the value of $x$ where $x\in\mathbf{N}$ is equal to :
Binomial Theorem
MediumSingle correct
Q67
The value of $4+\cfrac{1}{5+\cfrac{1}{4+\cfrac{1}{5+\cfrac{1}{4+.....\infty}}}}$ is :
Sequences and Series
MediumSingle correct
Q68
If $\cot^{-1}(\alpha)=\cot^{-1}2+\cot^{-1}8+\cot^{-1}18+\cot^{-1}32+.....$ upto 100 terms, then $\alpha$ is :
Inverse Trigonometric Functions Inverse Trig Identities Telescoping Series with cot-1
MediumSingle correctNew ideaIdea asked in 2 years
Q69
The inverse of $y=5^{\log x}$ is :
Relations and Functions Functions and Domain Domain and Range of Inverse Functions
EasySingle correctNew ideaIdea asked in 2 years
Q70
The value of $\lim_{x\to0^{+}}\frac{\cos^{-1}(x-[x]^{2})\cdot\sin^{-1}(x-[x]^{2})}{x-x^{3}}$ , where $[x]$ denotes the greatest integer $\leq x$ is :
Limits and Derivatives L'Hopital's Rule Handling Greatest Integer Functions
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q72
Which of the following is true for $y(x)$ that satisfies the differential equation $\frac{dy}{dx}=xy-1+x-y$ ; $y(0)=0$ :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q73
In a triangle PQR, the co-ordinates of the points P and Q are $(-2, 4)$ and $(4, -2)$ respectively. If the equation of the perpendicular bisector of PR is $2x-y+2=0$ , then the centre of the circumcircle of the $\Delta$ PQR is :
Straight Lines
MediumSingle correct
Q74
The line $2x-y+1=0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x-2y=4$ . Then, the radius of the circle is :
Conic Sections Circle Tangents Normal Passes Through Center
MediumSingle correctNew ideaIdea asked in 3 years
Q75
Choose the incorrect statement about the two circles whose equations are given below : $x^{2}+y^{2}-10x-10y+41=0$ and $x^{2}+y^{2}-16x-10y+80=0$
Conic Sections Circle Tangents Number of Common Tangents
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q76
The equation of the plane which contains the $y$ -axis and passes through the point $(1, 2, 3)$ is :
Three Dimensional Geometry Planes in 3D Plane Containing a Line and a Point
EasySingle correctNew ideaIdea asked in 3 years
Q77
If the Boolean expression $(p\Rightarrow q)\Leftrightarrow(q * (\sim p))$ is a tautology, then the Boolean expression $p * (\sim q)$ is equivalent to :
Mathematical Reasoning
MediumSingle correct
Q78
Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$ and $\vec{b}=7\hat{i}+\hat{j}-6\hat{k}$ . If $\vec{r}\times\vec{a}=\vec{r}\times\vec{b}$ , $\vec{r}\cdot(\hat{i}+2\hat{j}+\hat{k})=-3$ , then $\vec{r}\cdot(2\hat{i}-3\hat{j}+\hat{k})$ is equal to :
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q79
Two dices are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :
Probability
EasySingle correct
Q80
The sum of possible values of $x$ for $\tan^{-1}(x+1)+\cot^{-1}\left(\frac{1}{x-1}\right)=\tan^{-1}\left(\frac{8}{31}\right)$ is :
Inverse Trigonometric Functions Inverse Trig Identities Tan-1 Sum and Difference
HardSingle correctNew ideaIdea asked in 3 years
Q81
The maximum value of $z$ in the following equation $z=6xy+y^{2}$ , where $3x+4y\leq100$ and $4x+3y\leq75$ for $x\geq0$ and $y\geq0$ is __________.
Application of Derivatives
MediumNumerical value
Q82
If A $=\begin{bmatrix}2 & 3\\ 0 & -1\end{bmatrix}$ , then the value of $\det(A^{4})+\det\left(A^{10}-(\mathrm{Adj}(2A))^{10}\right)$ is equal to __________.
Determinants Matrix Inverse Cofactor Matrix and Adjoint
MediumNumerical valueIdea asked in 5 years
Q83
If $(2021)^{3762}$ is divided by 17, then the remainder is __________.
Binomial Theorem
MediumNumerical value
Q84
If the function $f(x)=\frac{\cos(\sin x)-\cos x}{x^{4}}$ is continuous at each point in its domain and $f(0)=\frac{1}{k}$ , then k is __________.
Continuity and Differentiability Limits via Series Expansion for Continuity
MediumNumerical valueNew ideaIdea asked in 3 years
Q85
If [ $\cdot$ ] represents the greatest integer function, then the value of $\left|\int_{0}^{\sqrt{\frac{\pi}{2}}}\left[[x^{2}]-\cos x\right]dx\right|$ is __________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q86
The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on one circle and point $P_2$ on the other circle for the given circles’ equations $x^{2}+y^{2}-10x-10y+41=0$ $x^{2}+y^{2}-24x-10y+160=0$ is __________.
Conic Sections Circle Tangents Number of Common Tangents
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q87
If the equation of the plane passing through the line of intersection of the planes $2x-7y+4z-3=0$ , $3x-5y+4z+11=0$ and the point $(-2, 1, 3)$ is $ax+by+cz-7=0$ , then the value of $2a+b+c-7$ is __________.
Three Dimensional Geometry Planes in 3D Family of Planes
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q88
Let there be three independent events $E_1$ , $E_2$ and $E_3$ . The probability that only $E_1$ occurs is $\alpha$ , only $E_2$ occurs is $\beta$ and only $E_3$ occurs is $\gamma$ . Let ‘p’ denote the probability of none of events occurs that satisfies the…
Probability Conditional Probability Independence Criterion
HardNumerical valueNew ideaIdea asked in 3 years
Q89
If $f(x)=\sin\left(\cos^{-1}\left(\frac{1-2^{2x}}{1+2^{2x}}\right)\right)$ and its first derivative with respect to $x$ is $-\frac{b}{a}\log_{e}2$ when $x=1$ , where a and b are integers, then the minimum value of $|a^{2}-b^{2}|$ is __________.
Continuity and Differentiability Chain Rule Pre-simplification via Trig Substitution
HardNumerical valueIdea asked in 2 yearsAsked the year before
Q90
If $\vec{a}=\alpha\hat{i}+\beta\hat{j}+3\hat{k}$ , $\vec{b}=-\beta\hat{i}-\alpha\hat{j}-\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}-\hat{k}$ such that $\vec{a}\cdot\vec{b}=1$ and $\vec{b}\cdot\vec{c}=-3$ , then…
Vector Algebra Triple Products STP Definition and Determinant
MediumNumerical valueIdea asked in 2 yearsAsked the year before

Dropped from the final key and left out of every count: Q71.

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.