JEE Main 2021 · February session

JEE Main 25 February 2021, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 21 easy. Its hard-question count was the joint 8th 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: 10; 11% of the shift
Chapters asked: 65; 14 questions with a figure

Key findings · 25 Feb 2021, Shift 1

1
10 hard questions (11%): the joint 8th 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 (10 of 30).
3
53 questions tested a new idea, one no earlier year had asked: 65% of the 82 questions tagged to an idea.
4
27 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
50 shared an idea with another 2021 shift (61% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Gravitation in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Application of Derivatives in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 10Medium 18Hard 2

Top chapters

Chemistry

30 Q · 10 numerical

Easy 9Medium 19Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 2Medium 22Hard 6

Top chapters

Application of Derivatives3 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Determinants2 Q
Integrals2 Q
Permutations and Combinations2 Q

Question format

Single correct46 Q
Numerical value30 Q
Diagram based8 Q
Two statements3 Q
Assertion–reason2 Q
Match the list1 Q

What each question asks you to do

Multi-step27 Q
Calculation24 Q
Application24 Q
Conceptual7 Q
Recall5 Q
Data or graph3 Q

Most common: Multi-step.

Against the other 2021 shifts

This shift next to the 23 other 2021 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
24 Feb, Shift 1	90	36%	7%	33%	68%	24%
24 Feb, Shift 2	88	43%	5%	32%	63%	21%
25 Feb, Shift 1	90	23%	11%	33%	65%	30%
25 Feb, Shift 2	89	35%	10%	34%	67%	24%
26 Feb, Shift 1	88	50%	3%	33%	78%	17%
26 Feb, Shift 2	90	27%	12%	33%	80%	29%
16 Mar, Shift 2	90	31%	7%	33%	69%	33%
17 Mar, Shift 1	89	39%	8%	34%	61%	26%
17 Mar, Shift 2	89	36%	17%	34%	66%	32%
18 Mar, Shift 1	90	40%	9%	33%	74%	24%
18 Mar, Shift 2	90	34%	9%	33%	63%	28%
22 Jul, Shift 2	90	40%	12%	33%	67%	28%
25 Jul, Shift 1	90	31%	13%	33%	56%	34%
25 Jul, Shift 2	90	48%	3%	33%	63%	27%
3 Aug, Shift 1	90	32%	11%	33%	68%	21%
3 Aug, Shift 2	90	32%	7%	33%	61%	24%
4 Aug, Shift 1	90	40%	8%	33%	62%	29%
4 Aug, Shift 2	90	32%	7%	33%	65%	41%
26 Aug, Shift 1	89	27%	15%	34%	66%	30%
26 Aug, Shift 2	89	21%	9%	34%	60%	28%
27 Aug, Shift 1	90	27%	13%	33%	63%	34%
27 Aug, Shift 2	90	29%	9%	33%	72%	29%
31 Aug, Shift 1	90	27%	11%	33%	70%	24%
31 Aug, Shift 2	90	30%	13%	33%	72%	31%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open30 this 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

10 easy18 medium2 hard

Q1
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason R : The product of their mass and radius must be…
Gravitation Gravitational Potential Escape Velocity and Potential Relation
EasyAssertion–reasonIdea asked in 6 yearsAsked the year before
Q2
Match List - I with List - II : List - I List - II (a) h (Planck's constant) (i) $[M\,L\,T^{-1}]$ (b) E (kinetic energy) (ii) $[M\,L^{2}\,T^{-1}]$ (c) V (electric potential) (iii) $[M\,L^{2}\,T^{-2}]$ (d) P (linear momentum) (iv) $[M\,L^{2}\,I^{-1}\,T^{-3}]$ …
Units and Measurements
EasyMatch the list
Q3
If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :
Oscillations Pendulums Simple Pendulum Period
EasySingle correctNew ideaIdea asked in 2 years
Q4
A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of…
Waves Resonance in Air Columns End Correction Concept
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q5
In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}+\overrightarrow{AG}+\overrightarrow{AH}$ , if, $\overrightarrow{AO}=2\hat{i}+3\hat{j}-4\hat{k}$
Motion in a Plane
EasyDiagram based · figure
Q6
Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If $T_A$ and $T_B$ are the time periods of A and B respectively then the value of $T_B - T_A$ : [ Given : radius of earth = 6400…
Gravitation Orbital Mechanics Orbital Time Period
MediumSingle correct · figureIdea asked in 6 yearsAsked the year before
Q7
A 5 V battery is connected across the points X and Y. Assume $D_1$ and $D_2$ to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Ideal vs. Practical Diode Circuit Analysis
MediumDiagram based · figureIdea asked in 7 yearsAsked the year before
Q8
Given below are two statements : Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz. Statement II : The side band frequencies are 1002 kHz and 998 kHz. In the light of the…
Communication Systems
MediumTwo statements
Q9
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light…
Thermal Properties of Matter Thermal Expansion Thermal Stress
EasyAssertion–reasonIdea asked in 3 years
Q10
The current ( $i$ ) at time t=0 and t= $\infty$ respectively for the given circuit is :
Electromagnetic Induction Inductance Current Continuity in Inductors
HardDiagram based · figureNew ideaIdea asked in 2 years
Q11
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first…
Units and Measurements
MediumSingle correct
Q12
An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are $\lambda_\alpha$ and $\lambda_p$ respectively. The ratio $\frac{\lambda_p}{\lambda_\alpha}$ is :
Dual Nature of Radiation and Matter Matter Waves Wavelength Ratios of Different Particles
EasySingle correctIdea asked in 6 yearsAsked the year before
Q13
Two coherent light sources having intensity in the ratio $2x$ produce an interference pattern. The ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be :
Wave Optics Young's Double Slit Fringe Visibility and Contrast
MediumSingle correctNew idea
Q14
An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity $v$ . The velocity with which middle point of the train passes the signal post is :
Motion in a Straight Line Kinematics in 1D Uniform Acceleration Equations
MediumSingle correctNew ideaIdea asked in 4 years
Q15
A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is __________ and their speed is __________, in the ratio.
Moving Charges and Magnetism Lorentz Force Magnetic Force Vector Calculation
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q16
Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is __________.
Moving Charges and Magnetism Biot-Savart Law Field on axis of circular loop
MediumSingle correctNew ideaIdea asked in 2 years
Q17
The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.
Alternating Current Phasor Diagrams Series Phasor Addition
HardDiagram based · figureNew ideaIdea asked in 2 years
Q18
A diatomic gas, having $C_P=\frac{7}{2}R$ and $C_V=\frac{5}{2}R$ , is heated at constant pressure. The ratio dU : dQ : dW :
Thermodynamics First Law of Thermodynamics Heat in Isochoric and Isobaric Processes
EasySingle correctNew ideaIdea asked in 4 years
Q19
Two radioactive substances X and Y originally have $N_1$ and $N_2$ nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio $\frac{N_1}{N_2}$ will be equal to :
Nuclei Radioactive Decay Integer Half-Life Shortcuts
MediumSingle correctNew ideaIdea asked in 2 years
Q20
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force $F_1$ . Now a spherical cavity of radius $\left(\frac{R}{2}\right)$ is made in the sphere (as shown in figure) and the force becomes $F_2$ . The value of…
Gravitation Gravitational Potential Potential Inside a Spherical Cavity
MediumDiagram based · figureNew idea
Q21
A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R=gas constant) is $\frac{x}{3R}$ . Value of $x$ is __________.
Kinetic Theory Kinetic Theory of Gases Kinetic Energy and Temp
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q22
512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is __________ V.
Electrostatic Potential and Capacitance Electric Potential Potential of a Solid Non-Conducting Sphere
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q23
A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V=3t volt. (where t is in second). If the voltage is applied when t=0, then the energy stored in the coil after 4 s is __________ J.
Electromagnetic Induction Inductance Energy Stored in Inductors
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q24
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is __________ m/s. (Take g=10 m/s $^2$ )
Work, Energy and Power Circular Motion Vertical Circular Motion
MediumNumerical valueNew ideaIdea asked in 2 years
Q25
The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as $U=\frac{\alpha}{r^{10}}-\frac{\beta}{r^{5}}-3$ where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be…
Work, Energy and Power Work and Kinetic Energy Potential Energy Curves and Equilibrium
MediumNumerical valueNew ideaIdea asked in 2 years
Q26
The electric field in a region is given by $\vec{E}=\left(\frac{3}{5}E_0\hat{i}+\frac{4}{5}E_0\hat{j}\right)\frac{N}{C}$ . The ratio of flux of reported field through the rectangular surface of area 0.2 m $^2$ (parallel to $y-z$ plane) to that of the surface…
Electric Charges and Fields Gauss's Law Electric Flux Calculation
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q27
A transmitting station releases waves of wavelength 960 m. A capacitor of $2.56\ \mu$ F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ $\times10^{-8}$ H.
Alternating Current LCR Resonance Resonant Frequency Calculation
EasyNumerical valueNew ideaIdea asked in 4 years
Q28
The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is __________ cm.
Ray Optics and Optical Instruments Lens Maker's Formula Lens Magnification
MediumNumerical valueNew ideaIdea asked in 2 years
Q29
In a certain thermodynamical process, the pressure of a gas depends on its volume as $kV^{3}$ . The work done when the temperature changes from $100^{\circ}$ C to $300^{\circ}$ C will be __________ nR, where n denotes number of moles of a gas.
Thermodynamics Thermodynamic Processes Polytropic Process Analysis
MediumNumerical valueNew ideaIdea asked in 2 years
Q30
In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than $E_1$ and $E_2$ as well. For key $K_1$ (closed), the jockey is adjusted to touch the wire at point $J_1$ so that there is no deflection in the…
Current Electricity Potentiometer Comparing EMF of Two Cells
EasyNumerical value · figureNew ideaIdea asked in 2 years

Chemistry30 questions

9 easy19 medium2 hard

Q31
The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below : (A), (B), (C), (D) [plots shown in figure] The correct plot for $3s$ orbital is :
Structure of Atom Quantum Numbers Interpreting Radial Probability Distribution Graphs
MediumDiagram based · figureNew idea
Q32
According to molecular orbital theory, the species among the following that does not exist is :
Chemical Bonding and Molecular Structure Molecular Orbital Theory Bond Order Calculation
MediumSingle correctNew ideaIdea asked in 3 years
Q33
The solubility of AgCN in a buffer solution of $\mathrm{pH}=3$ is $x$ . The value of $x$ is : [Assume : No cyano complex is formed ; $\mathrm{K_{sp}(AgCN)}=2.2\times10^{-16}$ and $\mathrm{K_a(HCN)}=6.2\times10^{-10}$ ]
Equilibrium Solubility Product pH Effect on Solubility
HardSingle correctNew idea
Q34
In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $\left(\frac{x}{m}\right)$ is directly proportional to $\mathrm{P^x}$ . The value of $x$ is :
Surface Chemistry Adsorption Freundlich Isotherm Equation
EasySingle correctNew idea
Q35
Ellingham diagram is a graphical representation of :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Basics
EasySingle correctIdea asked in 3 yearsAsked the year before
Q36
Which of the following equation depicts the oxidizing nature of $\mathrm{H_2O_2}$ ?
Hydrogen Hydrogen and Hydrides Oxidizing Action of H2O2
EasySingle correctNew ideaIdea asked in 2 years
Q37
The correct statement about $\mathrm{B_2H_6}$ is :
The p-Block Elements Group 13 & 14 Diborane Structure
MediumSingle correctNew ideaIdea asked in 2 years
Q38
Given below are two statements : Statement I : $\mathrm{CeO_2}$ can be used for oxidation of aldehydes and ketones. Statement II : Aqueous solution of $\mathrm{EuSO_4}$ is a strong reducing agent. In the light of the above statements, choose the correct…
The d- and f-Block Elements f-Block Elements Cerium(IV) as an Oxidizing Agent
MediumTwo statementsNew ideaIdea asked in 3 years
Q39
In which of the following pairs, the outer most electronic configuration will be the same ?
The d- and f-Block Elements d-Block Elements Electronic Configuration
MediumSingle correctNew ideaIdea asked in 4 years
Q40
The hybridization and magnetic nature of $\mathrm{[Mn(CN)_6]^{4-}}$ and $\mathrm{[Fe(CN)_6]^{3-}}$ , respectively are :
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q41
Given below are two statements : Statement I : An allotrope of oxygen is an important intermediate in the formation of reducing smog. Statement II : Gases such as oxides of nitrogen and sulphur present in troposphere contribute to the formation of…
Environmental Chemistry Classical vs Photochemical Smog
MediumTwo statementsNew ideaIdea asked in 3 years
Q42
Complete combustion of 1.80 g of an oxygen containing compound ( $\mathrm{C_xH_yO_z}$ ) gave 2.64 g of $\mathrm{CO_2}$ and 1.08 g of $\mathrm{H_2O}$ . The percentage of oxygen in the organic compound is :
Some Basic Concepts of Chemistry Stoichiometry Empirical Formula from Combustion Data
EasySingle correctNew ideaIdea asked in 4 years
Q43
Identify A in the given chemical reaction.
Hydrocarbons Alkanes and Free Radicals Aromatization (Reforming) of Alkanes
MediumDiagram based · figureNew idea
Q44
Identify A and B in the chemical reaction.
Haloalkanes and Haloarenes Alkenes and Alkynes Markovnikov's Rule Application
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q45
The major product of the following chemical reaction is : $\mathrm{CH_3CH_2CN}$ $\xrightarrow[\text{3) Pd/BaSO}_4\text{, H}_2]{\text{1) H}_3\text{O}^+\text{, }\Delta\ \ \text{2) SOCl}_2}$ ?
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Rosenmund Reduction
EasySingle correctIdea asked in 4 yearsAsked the year before
Q46
Which one of the following reactions will not form acetaldehyde ?
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives DIBAL-H Selective Reduction
MediumSingle correctIdea asked in 3 years
Q47
Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are : A = [structure] B = [structure] C = [structure]
Aldehydes, Ketones and Carboxylic Acids Organic Acidity and Basicity Exceptional Acidity of Picric Acid
MediumSingle correct · figureNew idea
Q48
Which of the following reaction/s will not give $p$ -aminoazobenzene ? A - [benzene ring with $\mathrm{NO_2}$ ] $\xrightarrow[\mathrm{iii)\ Aniline}]{\mathrm{i)\ Sn/HCl,\ ii)\ HNO_2}}$ B - [benzene ring with $\mathrm{NO_2}$ ]…
Amines Diazonium Salts Azo Coupling Reactions
MediumSingle correct · figureNew ideaIdea asked in 5 years
Q49
Which statement is correct ?
Polymers Buna-S (SBR) Monomers
MediumSingle correctNew ideaIdea asked in 2 years
Q50
Which of the glycosidic linkage between galactose and glucose is present in lactose ?
Biomolecules Carbohydrates Lactose Structure and Linkage
EasySingle correctIdea asked in 2 yearsAsked the year before
Q51
0.4 g mixture of NaOH, $\mathrm{Na_2CO_3}$ and some inert impurities was first titrated with $\frac{\mathrm{N}}{10}$ HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrated. 1.5…
Some Basic Concepts of Chemistry Stoichiometry Composition of Solid Mixtures
HardNumerical valueNew idea
Q52
A car tyre is filled with nitrogen gas at 35 psi at $27^\circ$ C. It will burst if pressure exceeds 40 psi. The temperature in $^\circ$ C at which the car tyre will burst is ________. (Rounded-off to the nearest integer)
States of Matter Ideal Gas Laws Gay-Lussac's Law
EasyNumerical valueNew ideaIdea asked in 2 years
Q53
The reaction of cyanamide, $\mathrm{NH_2CN_{(s)}}$ with oxygen was run in a bomb calorimeter and $\Delta U$ was found to be $-742.24$ kJ mol $^{-1}$ . The magnitude of $\Delta H_{298}$ for the reaction…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Bomb Calorimetry Calculations
MediumNumerical valueNew ideaIdea asked in 6 years
Q54
1 molal aqueous solution of an electrolyte $\mathrm{A_2B_3}$ is 60% ionised. The boiling point of the solution at 1 atm is ________ K. (Rounded-off to the nearest integer) [Given $\mathrm{K_b}$ for $\mathrm{(H_2O)} = 0.52$ K kg mol $^{-1}$ ]
Solutions Colligative Properties Van't Hoff Factor (i)
MediumNumerical valueNew ideaIdea asked in 4 years
Q55
In basic medium $\mathrm{CrO_4^{2-}}$ oxidises $\mathrm{S_2O_3^{2-}}$ to form $\mathrm{SO_4^{2-}}$ and itself changes into $\mathrm{Cr(OH)_4^{-}}$ . The volume of 0.154 M $\mathrm{CrO_4^{2-}}$ required to react with 40 mL of 0.25 M $\mathrm{S_2O_3^{2-}}$ is…
Redox Reactions Law of Chemical Equivalence in Redox
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q56
For the reaction, $a\mathrm{A} + b\mathrm{B} \rightarrow c\mathrm{C} + d\mathrm{D}$ , the plot of $\log k$ vs $\frac{1}{\mathrm{T}}$ is given below : The temperature at which the rate constant of the reaction is $10^{-4}$ s $^{-1}$ is ________ K. (Rounded-off…
Chemical Kinetics Arrhenius Equation Log Base 10 Arrhenius Plot Slope
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q57
The ionization enthalpy of $\mathrm{Na^+}$ formation from $\mathrm{Na_{(g)}}$ is 495.8 kJ mol $^{-1}$ , while the electron gain enthalpy of Br is $-325.0$ kJ mol $^{-1}$ . Given the lattice enthalpy of NaBr is $-728.4$ kJ mol $^{-1}$ . The energy for the formation…
Classification of Elements and Periodicity in Properties Enthalpy and Hess's Law Born-Haber Cycle for Lattice Enthalpy
EasyNumerical valueNew idea
Q58
Among the following, the number of halide(s) which is/are inert to hydrolysis is ________. (A) $\mathrm{BF_3}$ (B) $\mathrm{SiCl_4}$ (C) $\mathrm{PCl_5}$ (D) $\mathrm{SF_6}$
The p-Block Elements Group 15 & 16 Sulfur Fluorides Steric Hindrance
MediumNumerical valueNew idea
Q59
Consider the following chemical reaction. $\mathrm{CH{\equiv}CH}$ $\xrightarrow[\text{2) CO, HCl, AlCl}_3]{\text{1) Red hot Fe tube, 873 K}}$ Product The number of $sp^2$ hybridized carbon atom(s) present in the product is ________.
Hydrocarbons Aromatic Hydrocarbons Gattermann-Koch Formylation
MediumNumerical valueNew ideaIdea asked in 3 years
Q60
Using the provided information in the following paper chromatogram : Fig : Paper chromatography for compounds A and B. the calculated $\mathrm{R_f}$ value of A ________ $\times10^{-1}$ .
Organic Chemistry: Some Basic Principles and Techniques
EasyNumerical value · figure

Maths30 questions

2 easy22 medium6 hard

Q61
Let $f, g : \mathrm{N} \to \mathrm{N}$ such that $f(\mathrm{n}+1) = f(\mathrm{n}) + f(1)\ \forall\ \mathrm{n} \in \mathrm{N}$ and $g$ be any arbitrary function. Which of the following statements is NOT true ?
Relations and Functions
MediumSingle correct
Q62
Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ , (here $i^2 = -1$ ) be normal to a circle C. If the line $iz + \bar{z} + 1 + i = 0$ is tangent to this circle C, then its radius is :
Complex Numbers and Quadratic Equations Circle Tangents Normal Passes Through Center
HardSingle correctNew ideaIdea asked in 3 years
Q63
The integer 'k', for which the inequality $x^2 - 2(3k-1)x + 8k^2 - 7 > 0$ is valid for every $x$ in R, is :
Complex Numbers and Quadratic Equations Quadratic Roots Always Positive Condition
MediumSingle correctNew ideaIdea asked in 2 years
Q64
If $0 < \theta, \phi < \frac{\pi}{2}$ , $x = \sum_{n=0}^{\infty} \cos^{2n}\theta$ , $y = \sum_{n=0}^{\infty} \sin^{2n}\phi$ and $z = \sum_{n=0}^{\infty} \cos^{2n}\theta \cdot \sin^{2n}\phi$ then :
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q65
If Rolle's theorem holds for the function $f(x) = x^3 - ax^2 + bx - 4$ , $x \in [1, 2]$ with $f'\left(\frac{4}{3}\right) = 0$ , then ordered pair (a, b) is equal to :
Application of Derivatives Rolle's Theorem Parameter Evaluation
MediumSingle correctNew idea
Q66
$\lim_{n \to \infty}\left(1 + \frac{1 + \frac{1}{2} + ....... + \frac{1}{n}}{n^2}\right)^n$ is equal to :
Limits and Derivatives L'Hopital's Rule e-Power Shortcut for 1^infinity Forms
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q67
The value of the integral $\int \frac{\sin\theta . \sin 2\theta\ (\sin^6\theta + \sin^4\theta + \sin^2\theta)\sqrt{2\sin^4\theta + 3\sin^2\theta + 6}}{1 - \cos 2\theta}\, d\theta$ is : (where c is a constant of integration)
Integrals Integration by Substitution Composite Function Substitution
HardSingle correctNew ideaIdea asked in 3 years
Q68
The value of $\int_{-1}^{1} x^2 e^{[x^3]}dx$ , where [t] denotes the greatest integer $\leq$ t, is :
Integrals Definite Integral Properties Greatest Integer Function Integrals
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q69
If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^2 - 4x + y + 8}{x - 2}$ , then this curve also passes through the point :
Differential Equations Linear Differential Equations General Solution Formula
HardSingle correctNew ideaIdea asked in 3 years
Q70
The image of the point (3, 5) in the line $x - y + 1 = 0$ , lies on :
Straight Lines Straight Line Distance Image of a point in a line
EasySingle correctIdea asked in 4 yearsAsked the year before
Q71
A tangent is drawn to the parabola $y^2 = 6x$ which is perpendicular to the line $2x + y = 1$ . Which of the following points does NOT lie on it ?
Conic Sections General Conic Section Condition for Line Tangency
MediumSingle correctNew idea
Q72
If the curves, $\frac{x^2}{a} + \frac{y^2}{b} = 1$ and $\frac{x^2}{c} + \frac{y^2}{d} = 1$ intersect each other at an angle of $90^\circ$ , then which of the following relations is TRUE ?
Application of Derivatives Tangents and Normals Orthogonal Intersection of Curves
MediumSingle correctNew idea
Q73
Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l + m - n = 0$ and $l^2 + m^2 - n^2 = 0$ . Then the value of $\sin^4\alpha + \cos^4\alpha$ is :
Three Dimensional Geometry Angle Between Lines Angle from Linear and Quadratic DC Equations
MediumSingle correctNew idea
Q74
The equation of the line through the point (0, 1, 2) and perpendicular to the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{-2}$ is :
Three Dimensional Geometry Lines in 3D Cartesian Symmetric Form
MediumSingle correctNew idea
Q75
When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$ . If three missiles are fired independently from the ship,…
Probability Conditional Probability Multiplication Rule of Probability
EasySingle correctNew idea
Q76
The coefficients a, b and c of the quadratic equation, $ax^2 + bx + c = 0$ are obtained by throwing a dice three times. The probability that this equation has equal roots is :
Probability Quadratic Roots Nature of Roots
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q77
All possible values of $\theta \in [0, 2\pi]$ for which $\sin 2\theta + \tan 2\theta > 0$ lie in :
Trigonometric Functions General Solutions Trigonometric Inequality Intervals
MediumSingle correctNew idea
Q78
The total number of positive integral solutions $(x, y, z)$ such that $xyz = 24$ is :
Permutations and Combinations Distribution of Identical Objects
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q79
A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is $30^\circ$ (Ignore man's height). After sailing for 20 seconds,…
Trigonometric Functions
MediumSingle correct
Q80
The statement $\mathrm{A} \to (\mathrm{B} \to \mathrm{A})$ is equivalent to :
Mathematical Reasoning
MediumSingle correct
Q81
If $\mathrm{A} = \begin{bmatrix} 0 & -\tan\left(\frac{\theta}{2}\right) \\ \tan\left(\frac{\theta}{2}\right) & 0 \end{bmatrix}$ and…
Matrices Matrix Inverse Inverse of Skew-Symmetric Matrices
HardNumerical valueNew idea
Q82
Let $\mathrm{A} = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix}$ , where $x$ , $y$ and $z$ are real numbers such that $x + y + z > 0$ and $xyz = 2$ . If $\mathrm{A}^2 = \mathrm{I}_3$ , then the value of $x^3 + y^3 + z^3$ is_________.
Determinants Matrix Multiplication Powers of Square Matrices
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q83
If the system of equations $kx + y + 2z = 1$ $3x - y - 2z = 2$ $-2x - 2y - 4z = 3$ has infinitely many solutions, then k is equal to __________.
Determinants Cramer's Rule Condition for Infinite Solutions
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q84
The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is __________.
Permutations and Combinations Permutations of Distinct Objects
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
Let $\mathrm{A}_1, \mathrm{A}_2, \mathrm{A}_3, .....$ be squares such that for each $\mathrm{n} \geq 1$ , the length of the side of $\mathrm{A}_\mathrm{n}$ equals the length of diagonal of $\mathrm{A}_{\mathrm{n}+1}$ . If the length of $\mathrm{A}_1$ is 12 cm,…
Sequences and Series AP and GP GP General Term
MediumNumerical valueNew ideaIdea asked in 5 years
Q86
The number of points, at which the function $f(x) = |2x+1| - 3|x+2| + |x^2 + x - 2|$ , $x \in \mathrm{R}$ is not differentiable, is __________.
Continuity and Differentiability Differentiability of Modulus Functions
MediumNumerical valueNew ideaIdea asked in 5 years
Q87
Let $f(x)$ be a polynomial of degree 6 in $x$ , in which the coefficient of $x^6$ is unity and it has extrema at $x = -1$ and $x = 1$ . If $\lim_{x \to 0} \frac{f(x)}{x^3} = 1$ , then $5 \cdot f(2)$ is equal to __________.
Application of Derivatives Maxima and Minima Critical vs Stationary Points
HardNumerical valueNew ideaIdea asked in 3 years
Q88
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then $\mathrm{A}^4$ is equal to __________.
Application of Integrals Area Under Curves Area Between Trigonometric Curves
MediumNumerical valueNew idea
Q89
The locus of the point of intersection of the lines $(\sqrt{3})\mathrm{k}x + \mathrm{k}y - 4\sqrt{3} = 0$ and $\sqrt{3}\,x - y - 4(\sqrt{3})\,\mathrm{k} = 0$ is a conic, whose eccentricity is __________.
Conic Sections General Conic Section Condition for a Hyperbola
MediumNumerical valueNew idea
Q90
Let $\vec{a} = \hat{i} + 2\hat{j} - \hat{k}$ , $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a} = \vec{c} \times \vec{a}$ and…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumNumerical valueIdea asked in 6 yearsAsked the year before

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.