JEE Main 2021 · February session

JEE Main 26 February 2021, Shift 1

88 questions (2 more dropped by NTA): 29 numerical-answer and 59 multiple choice. 3 were rated hard and 44 easy. Its hard-question count was the joint 23rd highest of the 24 2021 shifts Lumi analysed. The biggest chapter was Differential Equations, with 3 questions.

Questions: 88; 2 dropped by NTA
Numerical answer: 29; 33% of the shift
Hard: 3; 3% of the shift
Chapters asked: 66; 12 questions with a figure

Key findings · 26 Feb 2021, Shift 1

1
3 hard questions (3%): the joint 23rd highest count of the 24 2021 shifts Lumi analysed. Across those shifts the hard share ran from 3% to 17%.
2
Physics was the hardest section, with 1 of 29 rated hard; Chemistry had the most easy questions (18 of 30).
3
54 questions tested a new idea, one no earlier year had asked: 78% of the 69 questions tagged to an idea.
4
15 came back from 2020: the same idea had been asked in the 2020 shifts Lumi analysed.
5
38 shared an idea with another 2021 shift (55% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Gravitation in Physics (3), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (3) and Differential Equations in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

29 Q · 10 numerical

Easy 15Medium 13Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 18Medium 11Hard 1

Top chapters

Maths

29 Q · 9 numerical

Easy 11Medium 17Hard 1

Top chapters

Question format

Single correct42 Q
Numerical value29 Q
Diagram based8 Q
Assertion–reason3 Q
Other2 Q
Match the list2 Q
Two statements2 Q

What each question asks you to do

Calculation29 Q
Application20 Q
Multi-step15 Q
Recall13 Q
Conceptual10 Q
Diagram reading1 Q

Most common: Calculation.

Against the other 2021 shifts

This shift next to the 23 other 2021 shifts Lumi analysed

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

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

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

Drill down

What this shift asked, and its history

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

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

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open29 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 88 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

88 of 88 questions

Physics29 questions

15 easy13 medium1 hard

Chemistry30 questions

18 easy11 medium1 hard

Q31
The orbital having two radial as well as two angular nodes is :
Structure of Atom Quantum Numbers Calculation of Radial and Angular Nodes
EasySingle correctNew ideaIdea asked in 5 years
Q32
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Dipole-dipole interactions are the only non-covalent interactions, resulting in hydrogen bond formation. Reason R : Fluorine is the most…
Chemical Bonding and Molecular Structure
EasyAssertion–reason
Q33
Match List-I with List-II. List-I (Electronic configuration of elements) | List-II ( $\Delta_i H$ in kJ mol $^{-1}$ ) (a) $1s^2\ 2s^2$ | (i) 801 (b) $1s^2\ 2s^2\ 2p^4$ | (ii) 899 (c) $1s^2\ 2s^2\ 2p^3$ | (iii) 1314 (d) $1s^2\ 2s^2\ 2p^1$ | (iv) 1402 Choose the…
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
MediumMatch the listNew ideaIdea asked in 4 years
Q34
Match List-I with List-II. List-I (Ore) | List-II (Element Present) (a) Kernite | (i) Tin (b) Cassiterite | (ii) Boron (c) Calamine | (iii) Fluorine (d) Cryolite | (iv) Zinc Choose the most appropriate answer from the options given below :
General Principles and Processes of Isolation of Elements
EasyMatch the list
Q35
Statements about heavy water are given below. A. Heavy water is used in exchange reactions for the study of reaction mechanisms. B. Heavy water is prepared by exhaustive electrolysis of water. C. Heavy water has higher boiling point than ordinary water. D.…
Hydrogen Hydrogen and Hydrides Heavy Water Properties
EasyOtherNew idea
Q36
Find A, B and C in the following reactions : $\mathrm{NH_3 + A + CO_2 \rightarrow (NH_4)_2CO_3}$ $\mathrm{(NH_4)_2CO_3 + H_2O + B \rightarrow NH_4HCO_3}$ $\mathrm{NH_4HCO_3 + NaCl \rightarrow NH_4Cl + C}$
The s-Block Elements s-Block Elements Limitations of the Solvay Process
EasySingle correctNew idea
Q37
Compound A used as a strong oxidizing agent is amphoteric in nature. It is the part of lead storage batteries. Compound A is :
The p-Block Elements
EasySingle correct
Q38
Which one of the following lanthanoids does not form $\mathrm{MO_2}$ ? [M is lanthanoid metal]
The d- and f-Block Elements f-Block Elements Lanthanide Oxidation States
MediumSingle correctNew ideaIdea asked in 3 years
Q39
The presence of ozone in troposphere :
Environmental Chemistry Primary Reactions of Photochemical Smog
EasySingle correctNew ideaIdea asked in 2 years
Q40
Given below are two statements : Statement I : A mixture of chloroform and aniline can be separated by simple distillation. Statement II : When separating aniline from a mixture of aniline and water by steam distillation aniline boils below its boiling…
Organic Chemistry: Some Basic Principles and Techniques
MediumTwo statements
Q41
Which of the following is ‘a’ FALSE statement ?
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q42
For the given reaction : [reaction scheme, see figure_note: structure $\xrightarrow[\text{2. Red hot iron tube, 873 K}]{\text{1. }\mathrm{NaNH_2}}$ (A) (major product)] What is ‘A’ ?
Hydrocarbons Alkenes and Alkynes Cyclic Polymerization of Alkynes
MediumDiagram based · figureNew idea
Q43
For the given reaction : [reaction scheme, see figure_note: structure $\xrightarrow[\text{UV light}]{\mathrm{Br_2}}$ ‘A’ (major product) monobrominated] What is ‘A’?
Hydrocarbons
MediumDiagram based · figure
Q44
$\mathrm{A\ (C_4H_8Cl_2)} \xrightarrow[373\ \mathrm{K}]{\text{Hydrolysis}} \mathrm{B\ (C_4H_8O)}$ B reacts with Hydroxyl amine but does not give Tollen’s test. Identify A and B.
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Ammonia Derivative Addition
MediumSingle correctNew idea
Q45
Identify the major products A and B respectively in the following reactions of phenol : [reaction scheme, see figure_note]
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q46
Given below are two statements : Statement I : $o$ -Nitrophenol is steam volatile due to intramolecular hydrogen bonding. Statement II : $o$ -Nitrophenol has high melting due to hydrogen bonding. In the light of the above statements, choose the most…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Nitration and Steam Volatility
EasyTwo statementsNew ideaIdea asked in 2 years
Q47
An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by ammonolysis of ethyl chloride. The correct structure of amine is :
Amines Hinsberg Test
MediumSingle correct · figureIdea asked in 5 yearsAsked the year before
Q48
The structure of Neoprene is :
Polymers Neoprene Synthesis
EasyDiagram based · figureNew ideaIdea asked in 2 years
Q49
Which of the following vitamin is helpful in delaying the blood clotting ?
Biomolecules
EasySingle correct
Q50
On treating a compound with warm dil. $\mathrm{H_2SO_4}$ , gas X is evolved which turns $\mathrm{K_2Cr_2O_7}$ paper acidified with dil. $\mathrm{H_2SO_4}$ to a green compound Y. X and Y respectively are :
Organic Chemistry: Some Basic Principles and Techniques Anion Analysis Sulfite Dichromate Paper Test
EasySingle correctNew ideaIdea asked in 2 years
Q51
The number of significant figures in $50000.020\times10^{-3}$ is __________.
Some Basic Concepts of Chemistry
EasyNumerical value
Q52
A certain gas obeys $\mathrm{P(V_m - b) = RT}$ . The value of $\left(\frac{\partial Z}{\partial P}\right)_T$ is $\frac{xb}{RT}$ . The value of $x$ is __________. (Integer answer) (Z : compressibility factor)
States of Matter Real Gases High Pressure VdW Limit
MediumNumerical valueNew idea
Q53
For a chemical reaction $\mathrm{A + B \rightleftharpoons C + D}$ ( $\Delta_r H^{\ominus} = 80$ kJ mol $^{-1}$ ) the entropy change $\Delta_r S^{\ominus}$ depends on the temperature T(in K) as $\Delta_r S^{\ominus} = 2T$ (J K $^{-1}$ mol $^{-1}$ ). Minimum…
Thermodynamics (Chemistry)Gibbs Free Energy Temperature Dependence
EasyNumerical valueNew ideaIdea asked in 2 years
Q54
224 mL of $\mathrm{SO_{2(g)}}$ at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution. The non-volatile solute produced is dissolved in 36 g of water. The lowering of vapour pressure of solution (assuming the solution is dilute)…
Solutions Colligative Properties Relative Lowering of VP
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q55
A homogeneous ideal gaseous reaction $\mathrm{AB_{2(g)} \rightleftharpoons A_{(g)} + 2B_{(g)}}$ is carried out in a 25 litre flask at 27°C. The initial amount of $\mathrm{AB_2}$ was 1 mole and the equilibrium pressure was 1.9 atm. The value of $\mathrm{K_p}$ …
Equilibrium Chemical Equilibrium Degree of Dissociation
MediumNumerical valueNew ideaIdea asked in 4 years
Q56
Consider the following reaction $\mathrm{MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{+2} + 4H_2O}$ , $\mathrm{E^\circ} = 1.51$ V. The quantity of electricity required in Faraday to reduce five moles of $\mathrm{MnO_4^-}$ is __________. (Integer answer)
Electrochemistry Faraday's Laws of Electrolysis Charge-Mole Relationship
EasyNumerical valueNew ideaIdea asked in 3 years
Q57
An exothermic reaction $\mathrm{X \rightarrow Y}$ has an activation energy 30 kJ mol $^{-1}$ . If energy change $\Delta E$ during the reaction is $-$ 20 kJ, then the activation energy for the reverse reaction in kJ is __________. (Integer answer)
Chemical Kinetics Arrhenius Equation Forward and Backward Activation Energy Relationship
EasyNumerical valueNew idea
Q58
3.12 g of oxygen is adsorbed on 1.2 g of platinum metal. The volume of oxygen adsorbed per gram of the adsorbent at 1 atm and 300 K in L is __________. [R = 0.0821 L atm K $^{-1}$ mol $^{-1}$ ]
Surface Chemistry
EasyNumerical value
Q59
Dichromate ion is treated with base, the oxidation number of Cr in the product formed is __________.
The d- and f-Block Elements d-Block Elements Chromate-Dichromate pH Equilibrium
EasyNumerical valueNew idea
Q60
Number of bridging CO ligands in $\mathrm{[Mn_2(CO)_{10}]}$ is __________ .
Coordination Compounds
MediumNumerical value

Maths29 questions

11 easy17 medium1 hard

Q61
If $\vec{a}$ and $\vec{b}$ are perpendicular, then $\vec{a}\times(\vec{a}\times(\vec{a}\times(\vec{a}\times\vec{b})))$ is equal to :
Vector Algebra Triple Products VTP with Repeated Vectors
EasySingle correctNew ideaIdea asked in 2 years
Q62
If $(1, 5, 35)$ , $(7, 5, 5)$ , $(1, \lambda, 7)$ and $(2\lambda, 1, 2)$ are coplanar, then the sum of all possible values of $\lambda$ is :
Three Dimensional Geometry Triple Products Coplanarity of Four Points
MediumSingle correctNew ideaIdea asked in 3 years
Q63
The intersection of three lines $x-y=0$ , $x+2y=3$ and $2x+y=6$ is a :
Straight Lines
EasySingle correct
Q64
The value of $\begin{vmatrix}(a+1)(a+2) & a+2 & 1\\ (a+2)(a+3) & a+3 & 1\\ (a+3)(a+4) & a+4 & 1\end{vmatrix}$ is :
Determinants
EasySingle correct
Q65
The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time $t=0$ . The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after…
Differential Equations Variable Separable Form Proportional Rate Problems
MediumSingle correctNew ideaIdea asked in 2 years
Q66
In the circle given below, let $OA = 1$ unit, $OB = 13$ unit and $PQ \perp OB$ . Then, the area of the triangle $PQB$ (in square units) is :
Conic Sections Power of a Point Secant-Tangent Power Theorem
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q67
The value of $\lim_{h\to 0} 2\left\{\frac{\sqrt{3}\sin\left(\frac{\pi}{6}+h\right)-\cos\left(\frac{\pi}{6}+h\right)}{\sqrt{3}h\left(\sqrt{3}\cos h-\sin h\right)}\right\}$ is :
Limits and Derivatives L'Hopital's Rule Trigonometric Pre-Simplification
MediumSingle correctNew idea
Q68
The maximum slope of the curve $y=\frac{1}{2}x^4-5x^3+18x^2-19x$ occurs at the point :
Application of Derivatives Maxima and Minima Second Derivative Test
MediumSingle correctNew idea
Q69
The value of $\int_{-\pi/2}^{\pi/2}\frac{\cos^2 x}{1+3^x}\,dx$ is :
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
MediumSingle correctNew ideaIdea asked in 5 years
Q70
The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :
Permutations and Combinations Distribution of Identical Objects
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q71
The maximum value of the term independent of 't' in the expansion of $\left(tx^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{10}$ where $x\in(0,1)$ is :
Binomial Theorem
HardSingle correct
Q72
Let $R=\{(P, Q)\mid P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1, -1)$ is the set :
Relations and Functions Sets and Relations Equivalence Relations
EasySingle correctNew ideaIdea asked in 4 years
Q73
Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of $A^2$ is 1, then the possible number of such matrices is :
Matrices Matrix Multiplication Trace of A times A Transpose
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q74
Let $f$ be any function defined on $\mathbf{R}$ and let it satisfy the condition : $|f(x)-f(y)|\le|(x-y)^2|,\ \forall\,(x, y)\in\mathbf{R}$ If $f(0)=1$ , then :
Continuity and Differentiability Differentiability via Functional Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q75
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :
Probability
EasySingle correct
Q76
If $\frac{\sin^{-1}x}{a}=\frac{\cos^{-1}x}{b}=\frac{\tan^{-1}y}{c}$ ; $0<x<1$ , then the value of $\cos\left(\frac{\pi c}{a+b}\right)$ is :
Inverse Trigonometric Functions Inverse Trig Identities Complementary Identities
MediumSingle correctNew ideaIdea asked in 3 years
Q77
In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is 25. Then, the sum of $4^{\text{th}}$ , $6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to :
Sequences and Series AP and GP GP General Term
MediumSingle correctNew ideaIdea asked in 5 years
Q78
The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\ldots\ldots$ is equal to :
Sequences and Series Arithmetico-Geometric Series Sum of Infinite AGP
EasySingle correctNew ideaIdea asked in 4 years
Q79
Consider the three planes $P_1 : 3x+15y+21z=9$ , $P_2 : x-3y-z=5$ , and $P_3 : 2x+10y+14z=5$ Then, which one of the following is true ?
Three Dimensional Geometry Planes in 3D Equation of a Parallel Plane
EasySingle correctNew idea
Q80
The value of $\sum_{n=1}^{100}\int_{n-1}^{n} e^{x-[x]}\,dx$ , where $[x]$ is the greatest integer $\le x$ , is :
Integrals Definite Integral Properties Fractional Part Function Integrals
EasySingle correctIdea asked in 2 yearsAsked the year before
Q81
The difference between degree and order of a differential equation that represents the family of curves given by $y^2=a\left(x+\frac{\sqrt{a}}{2}\right)$ , $a>0$ is _________.
Differential Equations
MediumNumerical value
Q82
The sum of $162^{\text{th}}$ power of the roots of the equation $x^3-2x^2+2x-1=0$ is _________.
Complex Numbers and Quadratic Equations Roots of Unity Sum of p-th Powers of Roots
MediumNumerical valueNew ideaIdea asked in 2 years
Q84
If $y=y(x)$ is the solution of the equation $e^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x$ , $y(0)=0$ ; then $1+y\left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2}y\left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}}y\left(\frac{\pi}{4}\right)$ is equal to…
Differential Equations Linear Differential Equations Generalized Substitution for LDEs
MediumNumerical valueNew ideaIdea asked in 4 years
Q85
The number of solutions of the equation $\log_4(x-1)=\log_2(x-3)$ is _________.
Relations and Functions Functions and Domain Logarithmic Function Domain
MediumNumerical valueNew idea
Q86
The number of integral values of 'k' for which the equation $3\sin x+4\cos x=k+1$ has a solution, $k\in\mathbf{R}$ is _________.
Trigonometric Functions General Solutions Parametric Solvability Conditions
EasyNumerical valueNew idea
Q87
Let $(\lambda, 2, 1)$ be a point on the plane which passes through the point $(4, -2, 2)$ . If the plane is perpendicular to the line joining the points $(-2, -21, 29)$ and $(-1, -16, 23)$ , then $\left(\frac{\lambda}{11}\right)^2-\frac{4\lambda}{11}-4$ is…
Three Dimensional Geometry Planes in 3D Normal and Point Form
MediumNumerical valueNew idea
Q88
The value of the integral $\int_0^{\pi}|\sin 2x|\,dx$ is _________.
Integrals Definite Integral Properties Modulus Function Interval Splitting
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q89
If $\sqrt{3}(\cos^2 x)=(\sqrt{3}-1)\cos x+1$ , the number of solutions of the given equation when $x\in\left[0,\frac{\pi}{2}\right]$ is _________.
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
EasyNumerical valueNew ideaIdea asked in 5 years
Q90
Let $m, n\in\mathbf{N}$ and $\gcd(2, n)=1$ . If $30\binom{30}{0}+29\binom{30}{1}+\ldots..+2\binom{30}{28}+1\binom{30}{29}=n\cdot 2^m$ , then $n+m$ is equal to _________. (Here $\binom{n}{k}={}^nC_k$ )
Binomial Theorem Binomial Coefficients AP-Weighted Coefficient Sums
MediumNumerical valueNew ideaIdea asked in 2 years

Dropped from the final key and left out of every count: Q13, Q83.

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.