JEE Main 2021 · August session

JEE Main 26 August 2021, Shift 2

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 8 were rated hard and 19 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: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 8; 9% of the shift
Chapters asked: 63; 18 questions with a figure

Key findings · 26 Aug 2021, Shift 2

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; Physics had the most easy questions (9 of 29).
3
48 questions tested a new idea, one no earlier year had asked: 60% of the 80 questions tagged to an idea.
4
32 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
47 shared an idea with another 2021 shift (59% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

29 Q · 10 numerical

Easy 9Medium 18Hard 2

Top chapters

Current Electricity2 Q
Electrostatic Potential and Capacitance2 Q
Laws of Motion2 Q
Motion in a Plane2 Q
Moving Charges and Magnetism2 Q
Oscillations2 Q

Chemistry

30 Q · 10 numerical

Easy 7Medium 23Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 21Hard 6

Top chapters

Question format

Single correct39 Q
Numerical value30 Q
Diagram based12 Q
Assertion–reason4 Q
Match the list2 Q
Two statements2 Q

What each question asks you to do

Calculation28 Q
Multi-step25 Q
Application19 Q
Recall13 Q
Conceptual2 Q
Diagram reading1 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 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

9 easy18 medium2 hard

Q1
Match List - I with List - II : List - I List - II (a) Magnetic Induction (i) $\mathrm{ML^2T^{-2}A^{-1}}$ (b) Magnetic Flux (ii) $\mathrm{M^0L^{-1}A}$ (c) Magnetic Permeability (iii) $\mathrm{MT^{-2}A^{-1}}$ (d) Magnetization (iv) $\mathrm{MLT^{-2}A^{-2}}$ …
Units and Measurements Biot-Savart Law Dimensions of Permeability
MediumMatch the listNew ideaIdea asked in 2 years
Q2
A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is the range of communication for Line of Sight (LoS) mode ? [use radius of earth $=6400$ km]
Communication Systems
EasySingle correct
Q3
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :
Oscillations Pendulums Thermal Expansion Effects on Clocks
MediumSingle correctNew idea
Q4
Four NOR gates are connected as shown in figure. The truth table for the given figure is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q5
A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
Motion in a Plane Relative Velocity Observer-Dependent Trajectory Shapes
EasySingle correctNew idea
Q6
At time $t=0$ , a material is composed of two radioactive atoms A and B, where $\mathrm{N_A(0)=2N_B(0)}$ . The decay constant of both kind of radioactive atoms is $\lambda$ . However, A disintegrates to B and B disintegrates to C. Which of the following figures…
Nuclei Radioactive Decay Successive Decay Chains
HardDiagram based · figureNew ideaIdea asked in 2 years
Q7
The angle between vector $\left(\vec{A}\right)$ and $\left(\vec{A}-\vec{B}\right)$ is :
Motion in a Plane
MediumDiagram based · figure
Q8
The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$ . How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value ?
Dual Nature of Radiation and Matter Matter Waves Wavelength from Kinetic Energy
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q9
A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $\mathrm{r}=\frac{L}{\sqrt{2}}$ . The speed of particle will be :
Laws of Motion Circular Motion Conical Pendulum Dynamics
EasySingle correctNew idea
Q10
The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m $^2$ .
System of Particles and Rotational Motion Moment of Inertia Parallel Axis Theorem
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q11
A light beam is described by $\mathrm{E}=800\,\sin\omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right)$ . An electron is allowed to move normal to the propagation of light beam with a speed of $3\times10^{7}\ \mathrm{ms^{-1}}$ . What is the maximum magnetic…
Electromagnetic Waves
MediumSingle correct
Q12
The temperature of equal masses of three different liquids $x$ , $y$ and $z$ are $10^\circ$ C, $20^\circ$ C and $30^\circ$ C respectively. The temperature of mixture when $x$ is mixed with $y$ is $16^\circ$ C and that when $y$ is mixed with $z$ is $26^\circ$ C.…
Thermal Properties of Matter Calorimetry Specific Heat Capacity
MediumSingle correctNew ideaIdea asked in 2 years
Q13
Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi}\times10^{2}\ \mathrm{Nm^{-2}}$ . What is the minimum radius of the wire ? (take $\mathrm{g}=10\ \mathrm{ms^{-2}}$ )
Mechanical Properties of Solids Elasticity Breaking Stress and Breaking Force
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q14
A refrigerator consumes an average 35 W power to operate between temperature $-10^\circ$ C to $25^\circ$ C. If there is no loss of energy then how much average heat per second does it transfer ?
Thermodynamics Heat Engines and Refrigerators Refrigerator COP
EasySingle correctNew idea
Q16
A cylindrical container of volume $4.0\times10^{-3}\ \mathrm{m^3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is : [Take gas constant as 8.3 J mol $^{-1}$ …
Kinetic Theory Kinetic Theory of Gases Microscopic Dalton's Law
EasySingle correctNew idea
Q17
An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.
Current Electricity Ohm's Law and Resistance Joule Heating and Power
EasySingle correctIdea asked in 6 yearsAsked the year before
Q18
A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant $\mathrm{K_1}$ and $\mathrm{K_2}$ of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance…
Electrostatic Potential and Capacitance Dielectrics Partial and Multiple Slabs
MediumDiagram based · figureNew ideaIdea asked in 6 years
Q19
If you are provided a set of resistances $2\ \Omega$ , $4\ \Omega$ , $6\ \Omega$ and $8\ \Omega$ . Connect these resistances so as to obtain an equivalent resistance of $\frac{46}{3}\ \Omega$ .
Current Electricity
EasySingle correct
Q20
The two thin coaxial rings, each of radius ‘a’ and having charges $+Q$ and $-Q$ respectively are separated by a distance of ‘s’. The potential difference between the centres of the two rings is :
Electrostatic Potential and Capacitance Electric Potential Axial Potential of Ring
MediumSingle correctNew idea
Q21
The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is __________ N. (take $\mathrm{g}=10\ \mathrm{ms^{-2}}$ )
Laws of Motion Friction Two-Block Friction Systems
MediumNumerical value · figureNew ideaIdea asked in 2 years
Q22
For the given circuit, the power across zener diode is __________ mW.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Regulation
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q23
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass ‘m’ to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the…
Units and Measurements
MediumNumerical value
Q24
Two simple harmonic motions are represented by the equations $x_1=5\sin\left(2\pi t+\frac{\pi}{4}\right)$ and $x_2=5\sqrt{2}(\sin2\pi t+\cos2\pi t)$ . The amplitude of second motion is __________ times the amplitude in first motion.
Oscillations SHM Equations Collinear Superposition of SHMs
EasyNumerical valueNew ideaIdea asked in 4 years
Q25
If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is __________.…
Moving Charges and Magnetism Lorentz Force Cyclotron Frequency and Energy
MediumNumerical valueNew ideaIdea asked in 3 years
Q26
A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids $\mathrm{P_1}$ and $\mathrm{P_2}$ are so placed in between the source of light and screen that the intensity of light on screen is I/2. $\mathrm{P_2}$ …
Wave Optics Polarization Intensity Halving of Unpolarized Light
MediumNumerical valueNew idea
Q27
An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and…
Ray Optics and Optical Instruments Lens Maker's Formula Lens and Curved Mirror Coincidence
HardNumerical value · figureNew idea
Q28
A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s $^{-1}$ in a uniform horizontal magnetic field of $3.0\times10^{-2}$ T. The maximum emf induced the coil will be __________ $\times10^{-2}$ …
Electromagnetic Induction Faraday's Law AC Generator Principle
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q29
A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its…
Moving Charges and Magnetism Magnetic Dipole Moment Torque on a dipole in uniform field
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q30
Two waves are simultaneously passing through a string and their equations are : $y_1=\mathrm{A_1}\sin k(x-vt)$ , $y_2=\mathrm{A_2}\sin k(x-vt+x_0)$ . Given amplitudes $\mathrm{A_1}=12$ mm and $\mathrm{A_2}=5$ mm, $x_0=3.5$ cm and wave number…
Waves Waves on Strings Superposition of Traveling Waves
MediumNumerical valueIdea asked in 3 yearsAsked the year before

Chemistry30 questions

7 easy23 medium0 hard

Q31
The interaction energy of London forces between two particles is proportional to $r^x$ , where r is the distance between the particles. The value of $x$ is :
Chemical Bonding and Molecular Structure
EasySingle correct
Q32
The bond order and magnetic behaviour of $\mathrm{O_2^-}$ ion are, respectively :
Chemical Bonding and Molecular Structure Molecular Orbital Theory Oxygen Ion Series Comparison
MediumSingle correctNew ideaIdea asked in 3 years
Q33
The sol given below with negatively charged colloidal particles is :
Surface Chemistry Colloids Zeta Potential and Helmholtz Double Layer
MediumSingle correctNew ideaIdea asked in 2 years
Q34
Chalcogen group elements are :
The p-Block Elements
EasySingle correct
Q35
Given below are two statements : Statement I : Sphalerite is a sulphide ore of zinc and copper glance is a sulphide ore of copper. Statement II : It is possible to separate two sulphide ores by adjusting proportion of oil to water or by using ‘depressants’…
General Principles and Processes of Isolation of Elements Adsorption Adsorption in Froth Flotation
MediumTwo statementsNew 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) : Heavy water is used for the study of reaction mechanism. Reason (R) : The rate of reaction for the cleavage of $\mathrm{O-H}$ bond is…
Hydrogen Hydrogen and Hydrides Kinetic Isotope Effect in Hydrogen
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q37
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Barium carbonate is insoluble in water and is highly stable. Reason (R) : The thermal stability of the carbonates increases with…
The s-Block Elements s-Block Elements Thermal Stability Trends
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q38
The number of non-ionisable hydrogen atoms present in the final product obtained from the hydrolysis of $\mathrm{PCl_5}$ is :
The p-Block Elements Group 15 & 16 Hydrolysis of Phosphorus Halides
MediumSingle correctNew idea
Q39
Arrange the following Cobalt complexes in the order of increasing Crystal Field Stabilization Energy (CFSE) value. Complexes : $[\mathrm{CoF_6}]^{3-}$ , $[\mathrm{Co(H_2O)_6}]^{2+}$ , $[\mathrm{Co(NH_3)_6}]^{3+}$ and $[\mathrm{Co(en)_3}]^{3+}$ (the letters A,…
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q40
Indicate the complex/complex ion which did not show any geometrical isomerism :
Coordination Compounds Coordination Isomerism Octahedral Geometrical
MediumSingle correctNew ideaIdea asked in 2 years
Q41
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Photochemical smog causes cracking of rubber. Reason (R) : Presence of ozone, nitric oxide, acrolein, formaldehyde and peroxyacetyl…
Environmental Chemistry Secondary Pollutants in Photochemical Smog
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q42
Which one of the following compounds is not aromatic ?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q43
The number of stereoisomers possible for 1,2-dimethyl cyclopropane is :
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Geometrical Isomerism in Cycloalkanes
MediumSingle correctNew idea
Q44
[reaction scheme] drawn structure --( $\mathrm{Br_2}$ / $\mathrm{AlBr_3}$ $(\mathrm{C_2H_5})_2\mathrm{O}$ )--> ‘A’ (Major Product) Consider the given reaction, the Product $\mathbf{A}$ is :
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Ortho-Para vs Meta Directing
MediumDiagram based · figureNew ideaIdea asked in 5 years
Q45
Match List - I with List - II. List - I (Chemical Reaction) (a) $\mathrm{CH_3COOCH_2CH_3} \rightarrow \mathrm{CH_3CH_2OH}$ (b) $\mathrm{CH_3COOCH_3} \rightarrow \mathrm{CH_3CHO}$ (c) $\mathrm{CH_3C \equiv N} \rightarrow \mathrm{CH_3CHO}$ (d)…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Reduction of Acids
MediumMatch the list · figureIdea asked in 5 yearsAsked the year before
Q46
[reaction scheme] drawn structure (a skeletal chain with a branch, ending in a C=O group with H) --“X”, HCN, $\mathrm{H_2O}$ --> drawn structure (same chain; the carbon bears OH above, CN to the right and H below) -- $\mathrm{LiAlH_4}$ , $\mathrm{H_3O^+}$ -->…
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Reduction of Cyanohydrins
MediumDiagram based · figureNew idea
Q47
[reaction scheme] drawn structure: benzene ring with a $\mathrm{CH_2}$ bonded to $\mathrm{NH_2}$ and, on another ring carbon (meta-type position as drawn), a C(=O) bonded to $\mathrm{NH_2}$ --( $\mathrm{(CH_3CO)_2O}$ )--> $\mathbf{P}$ (Major Product) The Major…
Amines Protection of Aniline for Mono-Substitution
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q48
[structure drawn, labelled Chlordiazepoxide] The class of drug to which chlordiazepoxide with above structure belongs is :
Chemistry in Everyday Life Therapeutic Drug Classes
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q49
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Sucrose is a disaccharide and a non-reducing sugar. Reason (R) : Sucrose involves glycosidic linkage between $\mathrm{C_1}$ of…
Biomolecules Carbohydrates Sucrose Structure and Linkage
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q50
Which one of the following phenols does not give colour when condensed with phthalic anhydride in presence of conc. $\mathrm{H_2SO_4}$ ?
Alcohols, Phenols and Ethers Alcohols and Phenols Phthalein Dye Test
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q51
100 mL of $\mathrm{Na_3PO_4}$ solution contains 3.45 g of sodium. The molarity of the solution is __________ $\times 10^{-2}$ mol $\mathrm{L^{-1}}$ . (Nearest integer) [Atomic Masses - Na : 23.0 u, O : 16.0 u, P : 31.0 u]
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q52
A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 10^{14}$ Hz. The velocity of ejected electron is __________ $\times 10^5$ $\mathrm{ms^{-1}}$ . (Nearest integer) [Use : h =…
Structure of Atom Photoelectric Effect Einstein's Photoelectric Equation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q53
For water $\Delta_{\mathrm{vap}}H$ = 41 kJ $\mathrm{mol^{-1}}$ at 373 K and 1 bar pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is __________…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Relation Between ΔH and ΔU
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q54
83 g of ethylene glycol dissolved in 625 g of water. The freezing point of the solution is __________ K. (Nearest integer) [Use : Molal Freezing point depression constant of water = 1.86 K kg $\mathrm{mol^{-1}}$ Freezing point of water = 273 K Atomic masses…
Solutions Colligative Properties Freezing Point Depression
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q55
The equilibrium constant $\mathrm{K_c}$ at 298 K for the reaction $\mathrm{A + B \rightleftharpoons C + D}$ is 100. Starting with an equimolar solution with concentrations of A, B, C and D all equal to 1 M, the equilibrium concentration of D is __________…
Equilibrium Chemical Equilibrium ICE Table Construction
MediumNumerical valueNew ideaIdea asked in 3 years
Q56
For the galvanic cell, $\mathrm{Zn(s) + Cu^{2+}}$ (0.02 M) $\rightarrow \mathrm{Zn^{2+}}$ (0.04 M) $+ \mathrm{Cu(s)}$ , $\mathrm{E_{cell}}$ = __________ $\times 10^{-2}$ V. (Nearest integer) [Use : $\mathrm{E^0_{Cu/Cu^{2+}}}$ = $-0.34$ V,…
Electrochemistry Nernst Equation Full Cell Nernst Equation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q57
The reaction rate for the reaction $[\mathrm{PtCl_4}]^{2-} + \mathrm{H_2O} \rightleftharpoons [\mathrm{Pt(H_2O)Cl_3}]^- + \mathrm{Cl^-}$ was measured as a function of concentrations of different species. It was observed that…
Chemical Kinetics Chemical Equilibrium Equilibrium Constant from Rate Constants
MediumNumerical valueNew idea
Q58
The overall stability constant of the complex ion $[\mathrm{Cu(NH_3)_4}]^{2+}$ is $2.1 \times 10^{13}$ . The overall dissociation constant is $y \times 10^{-14}$ . Then $y$ is __________. (Nearest integer)
Coordination Compounds
MediumNumerical value
Q59
In the sulphur estimation, 0.471 g of an organic compound gave 1.44 g of barium sulfate. The percentage of sulphur in the compound is __________%. (Nearest integer) (Atomic Mass of Ba = 137 u)
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Gravimetric Precipitation Analysis
MediumNumerical valueNew ideaIdea asked in 5 years
Q60
A chloro compound “A”. (i) forms aldehydes on ozonolysis followed by the hydrolysis. (ii) when vaporized completely 1.53 g of A, gives 448 mL of vapour at STP. The number of carbon atoms in a molecule of compound $\mathbf{A}$ is __________.
Haloalkanes and Haloarenes Alkenes and Alkynes Reductive Ozonolysis Products
MediumNumerical valueIdea asked in 7 yearsAsked the year before

Maths30 questions

3 easy21 medium6 hard

Q61
The domain of the function $\mathrm{cosec}^{-1}\left(\frac{1+x}{x}\right)$ is :
Inverse Trigonometric Functions Inverse Trig Domains Sec-1 and Csc-1 Domains
EasySingle correctNew idea
Q62
If $(\sqrt{3}+i)^{100}=2^{99}(\mathrm{p}+i\mathrm{q})$ , then p and q are roots of the equation :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form De Moivre's Theorem for Integer Powers
MediumSingle correctNew idea
Q63
Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$ , and a system of linear equations $x+y+z=5$ $x+2y+3z=\mu$ $x+3y+\lambda z=1$ is constructed. If p is the probability that the system has a unique solution and q is the probability…
Determinants Cramer's Rule Probability in Linear Systems
MediumSingle correctNew idea
Q64
Let $\mathrm{A}=\begin{pmatrix}1&0&0\\0&1&1\\1&0&0\end{pmatrix}$ . Then $\mathrm{A}^{2025}-\mathrm{A}^{2020}$ is equal to :
Matrices Matrix Multiplication Powers of Square Matrices
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
$\lim_{x\to2}\left(\sum_{\mathrm{n}=1}^{9}\frac{x}{\mathrm{n}(\mathrm{n}+1)x^2+2(2\mathrm{n}+1)x+4}\right)$ is equal to :
Limits and Derivatives AP and GP Method of Differences for Telescoping Series
MediumSingle correctNew ideaIdea asked in 6 years
Q66
The local maximum value of the function $f(x)=\left(\frac{2}{x}\right)^{x^2}$ , $x>0$ , is :
Application of Derivatives Maxima and Minima Extrema of Variable-Base Exponentials
MediumSingle correctNew ideaIdea asked in 2 years
Q67
The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1+\sin^2 x}{1+\pi^{\sin x}}\right)\mathrm{d}x$ is :
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctNew ideaIdea asked in 5 years
Q68
Let $y(x)$ be the solution of the differential equation $2x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0$ , $x>0$ . If $y(\mathrm{e})=1$ , then $y(1)$ is equal to :
Differential Equations Linear Differential Equations Generalized Substitution for LDEs
HardSingle correctNew ideaIdea asked in 4 years
Q69
A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that $\mathrm{PC}=\sqrt{5}$ inches and $\angle\mathrm{PCB}=\tan^{-1}(2)$ . The acute angle through which the pencil must be rotated about C so…
Trigonometric Functions Straight Line Distance Perpendicular distance from point
MediumSingle correct · figureIdea asked in 3 yearsAsked the year before
Q70
A hall has a square floor of dimension $10\ \mathrm{m}\times10\ \mathrm{m}$ (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $\cos^{-1}\frac{1}{5}$ , then the height of the hall (in meters) is :
Three Dimensional Geometry Angle Between Lines Angle via Direction Ratios
MediumSingle correct · figureNew idea
Q71
A circle C touches the line $x=2y$ at the point $(2,\ 1)$ and intersects the circle $C_1:x^2+y^2+2y-5=0$ at two points P and Q such that PQ is a diameter of $C_1$ . Then the diameter of C is :
Conic Sections Circle Tangents Family of Circles Touching a Line
HardSingle correctIdea asked in 5 yearsAsked the year before
Q72
The point $\mathrm{P}(-2\sqrt{6},\sqrt{3})$ lies on the hyperbola $\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{b}^2}=1$ having eccentricity $\frac{\sqrt{5}}{2}$ . If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and…
Conic Sections General Conic Section Tangent to General Conic (T=0)
HardSingle correctIdea asked in 3 yearsAsked the year before
Q73
The locus of the mid points of the chords of the hyperbola $x^2-y^2=4$ , which touch the parabola $y^2=8x$ , is :
Conic Sections General Conic Section Chord Bisected at a Given Point (T=S1)
HardSingle correctNew ideaIdea asked in 3 years
Q74
If the value of the integral $\int_0^5\frac{x+[x]}{\mathrm{e}^{x-[x]}}\,\mathrm{d}x=\alpha\mathrm{e}^{-1}+\beta$ , where $\alpha,\beta\in\mathbf{R}$ , $5\alpha+6\beta=0$ , and $[x]$ denotes the greatest integer less than or equal to $x$ ; then the value of…
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q75
Consider the two statements : (S1) : $(\mathrm{p}\to\mathrm{q})\vee(\sim\mathrm{q}\to\mathrm{p})$ is a tautology. (S2) : $(\mathrm{p}\wedge\sim\mathrm{q})\wedge(\sim\mathrm{p}\vee\mathrm{q})$ is a fallacy. Then :
Relations and Functions
EasyTwo statements
Q76
Let $[t]$ denote the greatest integer less than or equal to t. Let $f(x)=x-[x]$ , $g(x)=1-x+[x]$ , and $h(x)=\min\{f(x),g(x)\}$ , $x\in[-2,2]$ . Then h is :
Continuity and Differentiability Differentiability of Max/Min Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q77
If $\sum_{\mathrm{r}=1}^{50}\tan^{-1}\frac{1}{2\mathrm{r}^2}=\mathrm{p}$ , then the value of $\tan\mathrm{p}$ is :
Inverse Trigonometric Functions Inverse Trig Identities Telescoping Inverse Trig Series
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q78
A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability $\mathrm{P}(\mathrm{X}\geq5\,|\,\mathrm{X}>2)$ is :
Probability Conditional Probability Conditional Probability Definition
MediumSingle correctNew ideaIdea asked in 2 years
Q79
Let P be the plane passing through the point $(1,2,3)$ and the line of intersection of the planes $\vec{\mathbf{r}}\cdot(\hat{i}+\hat{j}+4\hat{k})=16$ and $\vec{\mathbf{r}}\cdot(-\hat{i}+\hat{j}+\hat{k})=6$ . Then which of the following points does NOT lie on…
Three Dimensional Geometry Planes in 3D Family of Planes
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q80
The value of $2\sin\left(\frac{\pi}{8}\right)\sin\left(\frac{2\pi}{8}\right)\sin\left(\frac{3\pi}{8}\right)\sin\left(\frac{5\pi}{8}\right)\sin\left(\frac{6\pi}{8}\right)\sin\left(\frac{7\pi}{8}\right)$ is :
Trigonometric Functions Trigonometric Identities Product to Sum Formulas
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q81
Let $\lambda\neq0$ be in $\mathbf{R}$ . If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+2\lambda=0$ , and $\alpha$ and $\gamma$ are the roots of the equation $3x^2-10x+27\lambda=0$ , then $\frac{\beta\gamma}{\lambda}$ is equal to __________.
Complex Numbers and Quadratic Equations Quadratic Roots Common Root Condition
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q82
Let A be a $3\times3$ real matrix. If $\det(2\,\mathrm{Adj}(2\,\mathrm{Adj}(\mathrm{Adj}\,(2\mathrm{A}))))=2^{41}$ , then the value of $\det(\mathrm{A}^2)$ equals __________.
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
MediumNumerical valueNew ideaIdea asked in 6 years
Q83
Let $\binom{\mathrm{n}}{\mathrm{k}}$ denote ${}^{\mathrm{n}}\mathrm{C}_{\mathrm{k}}$ and…
Binomial Theorem Binomial Coefficients Vandermonde's Identity
HardNumerical valueNew idea
Q84
The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit “1” and they all are multiple of 11, is __________.
Permutations and Combinations Sum of Numbers Formed by Given Digits
MediumNumerical valueNew ideaIdea asked in 2 years
Q85
Let a and b respectively be the points of local maximum and local minimum of the function $f(x)=2x^3-3x^2-12x$ . If A is the total area of the region bounded by $y=f(x)$ , the $x$ -axis and the lines $x=\mathrm{a}$ and $x=\mathrm{b}$ , then $4\,\mathrm{A}$ is…
Application of Integrals Area Under Curves Area with X-Axis
MediumNumerical valueNew idea
Q86
Let the mean and variance of four numbers 3, 7, $x$ and $y$ ( $x>y$ ) be 5 and 10 respectively. Then the mean of four numbers $3+2x$ , $7+2y$ , $x+y$ and $x-y$ is __________.
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q87
If the projection of the vector $\hat{i}+2\hat{j}+\hat{k}$ on the sum of the two vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and $-\lambda\hat{i}+2\hat{j}+3\hat{k}$ is 1, then $\lambda$ is equal to __________.
Vector Algebra Dot Product Scalar and Vector Projection
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q88
The least positive integer n such that $\frac{(2i)^{\mathrm{n}}}{(1-i)^{\mathrm{n}-2}}$ , $i=\sqrt{-1}$ , is a positive integer, is __________.
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form De Moivre's Theorem for Integer Powers
MediumNumerical valueNew idea
Q89
Let Q be the foot of the perpendicular from the point $\mathrm{P}(7,-2,13)$ on the plane containing the lines $\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}$ and $\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7}$ . Then $(\mathrm{PQ})^2$ , is equal to __________.
Three Dimensional Geometry Point-Plane Distance Foot of Perpendicular
HardNumerical valueNew ideaIdea asked in 3 years
Q90
Let $\mathrm{a}_1,\mathrm{a}_2,\ldots,\mathrm{a}_{10}$ be an AP with common difference $-3$ and $\mathrm{b}_1,\mathrm{b}_2,\ldots,\mathrm{b}_{10}$ be a GP with common ratio 2. Let $\mathrm{c}_{\mathrm{k}}=\mathrm{a}_{\mathrm{k}}+\mathrm{b}_{\mathrm{k}}$ ,…
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical valueIdea asked in 7 yearsAsked the year before

Dropped from the final key and left out of every count: Q15.

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.