JEE Main 2020 · January session

JEE Main 9 January 2020, Shift 1

75 questions: 15 numerical-answer and 60 multiple choice. 12 were rated hard and 17 easy. Its hard-question count was the joint highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Integrals, with 4 questions.

Questions: 75; none dropped
Numerical answer: 15; 20% of the shift
Hard: 12; 16% of the shift
Chapters asked: 56; 16 questions with a figure

Key findings · 9 Jan 2020, Shift 1

1
12 hard questions (16%): the joint highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
65 questions tested a new idea, one no earlier year had asked: 98% of the 66 questions tagged to an idea.
3
1 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
4
21 shared an idea with another 2020 shift (32% of tagged questions). Shifts in the same year can test the same idea in a new setting.
5
Biggest chapters: Dual Nature of Radiation and Matter in Physics (2), Hydrocarbons in Chemistry (3) and Integrals in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

25 Q · 5 numerical

Easy 7Medium 13Hard 5

Top chapters

Chemistry

25 Q · 5 numerical

Easy 6Medium 15Hard 4

Top chapters

Maths

25 Q · 5 numerical

Easy 4Medium 18Hard 3

Top chapters

Integrals4 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Continuity and Differentiability2 Q
Determinants2 Q
Trigonometric Functions2 Q

Question format

Single correct47 Q
Numerical value15 Q
Diagram based10 Q
Other3 Q

What each question asks you to do

Multi-step30 Q
Calculation29 Q
Conceptual8 Q
Application3 Q
Recall3 Q
Diagram reading1 Q
Data or graph1 Q

Most common: Multi-step.

Against the other 2020 shifts

This shift next to the 11 other 2020 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
8 Jan, Shift 1	74	22%	11%	20%	92%	34%
8 Jan, Shift 2	75	28%	11%	20%	92%	39%
9 Jan, Shift 1	75	23%	16%	20%	99%	40%
9 Jan, Shift 2	73	27%	7%	21%	95%	48%
2 Sep, Shift 1	75	28%	5%	20%	95%	40%
2 Sep, Shift 2	75	20%	7%	20%	97%	32%
3 Sep, Shift 1	74	32%	12%	20%	91%	37%
3 Sep, Shift 2	75	21%	16%	20%	98%	29%
4 Sep, Shift 1	75	20%	16%	20%	98%	37%
4 Sep, Shift 2	75	32%	13%	20%	97%	39%
5 Sep, Shift 1	75	36%	7%	20%	94%	31%
6 Sep, Shift 2	75	31%	13%	20%	97%	41%

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

Open25 this shift3092 · 33%33%8/830299720720358540200225
Open25 this shift3084 · 33%33%8/830298716720359538199224
Open25 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 75 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

75 of 75 questions

Physics25 questions

7 easy13 medium5 hard

Chemistry25 questions

6 easy15 medium4 hard

Q26
The de Broglie wavelength of an electron in the $4^{\mathrm{th}}$ Bohr orbit is :
Structure of Atom Bohr's Atomic Theory Angular Momentum Quantization
EasySingle correctNew ideaIdea asked in 3 years
Q27
If the magnetic moment of a dioxygen species is 1.73 B.M, it may be :
Chemical Bonding and Molecular Structure Molecular Orbital Theory Magnetic Property Prediction
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q28
If enthalpy of atomisation for $\mathrm{Br_{2(l)}}$ is $x$ kJ/mol and bond enthalpy for $\mathrm{Br_2}$ is $y$ kJ/mol, the relation between them :
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy of Atomization
MediumSingle correctNew idea
Q29
For following reactions $\mathrm{A \xrightarrow{700\ K} Product}$ $\mathrm{A \xrightarrow[catalyst]{500\ K} Product}$ it was found that the $\mathrm{E_a}$ is decreased by 30 kJ/mol in the presence of catalyst. If the rate remains unchanged, the activation…
Chemical Kinetics Arrhenius Equation Catalyst Effect on Arrhenius Parameters
MediumSingle correctNew ideaIdea asked in 3 years
Q30
The $\mathrm{K_{sp}}$ for the following dissociation is $1.6\times10^{-5}$ $\mathrm{PbCl_{2(s)} \rightleftharpoons Pb^{2+}_{(aq)} + 2Cl^{-}_{(aq)}}$ Which of the following choices is correct for a mixture of 300 mL 0.134 M $\mathrm{Pb(NO_3)_2}$ and 100 mL…
Equilibrium Solubility Product Precipitation Condition
MediumSingle correctNew ideaIdea asked in 4 years
Q31
‘X’ melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is :
The Solid State
EasySingle correct
Q32
B has a smaller first ionization enthalpy than Be. Consider the following statements : (I) it is easier to remove 2p electron than 2s electron (II) 2p electron of B is more shielded from the nucleus by the inner core of electrons than the 2s electrons of Be…
Classification of Elements and Periodicity in Properties Periodic Trends Ionization Enthalpy Trends
MediumOtherNew ideaIdea asked in 6 years
Q33
According to the following diagram, A reduces $\mathrm{BO_2}$ when the temperature is :
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Intersections
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q34
The acidic, basic and amphoteric oxides, respectively, are :
Classification of Elements and Periodicity in Properties Periodic Trends Acidic and Basic Character of Oxides
EasySingle correctNew ideaIdea asked in 4 years
Q35
The compound that cannot act both as oxidising and reducing agent is :
Redox Reactions Identifying Redox Agents
EasySingle correctNew ideaIdea asked in 3 years
Q36
The electronic configurations of bivalent europium and trivalent cerium are : (atomic number : Xe = 54, Ce = 58, Eu = 63)
The d- and f-Block Elements f-Block Elements Lanthanide Electronic Configuration
MediumSingle correctNew ideaIdea asked in 5 years
Q37
Complex X of composition $\mathrm{Cr(H_2O)_6Cl_n}$ has a spin only magnetic moment of 3.83 BM. It reacts with $\mathrm{AgNO_3}$ and shows geometrical isomerism. The IUPAC nomenclature of X is :
Coordination Compounds Coordination Nomenclature IUPAC Ligand Naming
HardSingle correctNew idea
Q38
$[\mathrm{Pd(F)(Cl)(Br)(I)}]^{2-}$ has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of $[\mathrm{Fe(CN)_6}]^{n-6}$ , respectively, are : [Note : Ignore the pairing energy]
Coordination Compounds Coordination Isomerism Square Planar MABCD Geometrical Isomers
MediumSingle correctNew idea
Q39
Which of these will produce the highest yield in Friedel Crafts reaction ?
Hydrocarbons Aromatic Hydrocarbons Friedel-Crafts Failure on Deactivated Rings
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q40
The increasing order of basicity for the following intermediates is (from weak to strong)
Organic Chemistry: Some Basic Principles and Techniques Inductive and Electromeric Effects Carbanion Stability
MediumDiagram based · figureNew ideaIdea asked in 3 years
Q41
A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following observations : (i) A and D both form blue-violet colour with ninhydrin. (ii) Lassaigne extract of C gives…
Chemistry in Everyday Life Artificial Sweetener Structural Properties and Stability
HardOtherNew ideaIdea asked in 3 years
Q42
The major product Z obtained in the following reaction scheme is : (drawn starting material) $\xrightarrow[\text{273-278 K}]{\mathrm{NaNO_2/HCl}}$ X $\xrightarrow{\mathrm{Cu_2Br_2}}$ Y $\xrightarrow[\mathrm{H_2SO_4}]{\mathrm{HNO_3}}$ Z
Amines Diazonium Salts Sandmeyer Reaction
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q43
The major product (Y) in the following reactions is : $\mathrm{CH_3-CH(CH_3)-C{\equiv}CH}$ $\xrightarrow[\mathrm{H_2O}]{\mathrm{HgSO_4,\ H_2SO_4}}$ X X $\xrightarrow[\text{(ii) Conc. } \mathrm{H_2SO_4}/\Delta]{\text{(i) } \mathrm{C_2H_5MgBr,\ H_2O}}$ Y
Hydrocarbons Alkenes and Alkynes Kucherov Alkyne Hydration
MediumDiagram based · figureNew ideaIdea asked in 4 years
Q44
The correct order of heat of combustion for following alkadienes is : (a) [drawn structure] (b) [drawn structure] (c) [drawn structure]
Hydrocarbons Resonance and Hyperconjugation Heat of Hydrogenation
HardDiagram based · figureNew idea
Q45
Identify (A) in the following reaction sequence : (A) Gives Positive iodoform test $\xrightarrow[\text{(iii) Conc. } \mathrm{H_2SO_4}/\Delta]{\text{(i) } \mathrm{CH_3MgBr}\ \text{(ii) } \mathrm{H^+, H_2O}}$ (B) $\xrightarrow{\mathrm{O_3/Zn, H_2O}}$ (drawn…
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Grignard Reagent Addition
HardDiagram based · figureNew ideaIdea asked in 4 years
Q46
The molarity of $\mathrm{HNO_3}$ in a sample which has density 1.4 g/mL and mass percentage of 63% is ________. (Molecular Weight of $\mathrm{HNO_3} = 63$ )
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasyNumerical valueNew ideaIdea asked in 5 years
Q47
How much amount of NaCl should be added to 600 g of water ( $\rho = 1.00$ g/mL) to decrease the freezing point of water to $-0.2^\circ\mathrm{C}$ ? ________. (The freezing point depression constant for water $= 2\ \mathrm{K\ kg\ mol^{-1}}$ )
Solutions Colligative Properties Freezing Point Depression
MediumNumerical valueNew ideaIdea asked in 4 years
Q48
108 g of silver (molar mass 108 g $\mathrm{mol^{-1}}$ ) is deposited at cathode from $\mathrm{AgNO_3(aq)}$ solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water by the same quantity of…
Electrochemistry Faraday's Laws of Electrolysis Gas Evolution Volume
MediumNumerical valueNew ideaIdea asked in 3 years
Q49
The hardness of a water sample containing $10^{-3}$ M $\mathrm{MgSO_4}$ expressed as $\mathrm{CaCO_3}$ equivalents (in ppm) is ________. (molar mass of $\mathrm{MgSO_4}$ is 120.37 g/mol)
Hydrogen Hydrogen and Hydrides Causes of Temporary and Permanent Hardness
MediumNumerical valueNew ideaIdea asked in 2 years
Q50
The mass percentage of nitrogen in histamine is ________.
Some Basic Concepts of Chemistry
EasyNumerical value

Maths25 questions

4 easy18 medium3 hard

Q51
If for all real triplets (a, b, c), $f(x)=a+bx+cx^2$ ; then $\int_0^1 f(x)\,\mathrm{d}x$ is equal to :
Integrals
MediumSingle correct
Q52
The number of real roots of the equation, $\mathrm{e}^{4x}+\mathrm{e}^{3x}-4\mathrm{e}^{2x}+\mathrm{e}^{x}+1=0$ is :
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
HardSingle correctNew ideaIdea asked in 4 years
Q53
Let $z$ be a complex number such that $\left|\frac{z-i}{z+2i}\right|=1$ and $|z|=\frac{5}{2}$ . Then the value of $|z+3i|$ is :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
MediumSingle correctNew ideaIdea asked in 5 years
Q54
If the matrices $\mathrm{A}=\begin{bmatrix}1&1&2\\1&3&4\\1&-1&3\end{bmatrix}$ , $\mathrm{B}=\mathrm{adj}\,\mathrm{A}$ and $\mathrm{C}=3\mathrm{A}$ , then $\frac{|\mathrm{adj}\,\mathrm{B}|}{|\mathrm{C}|}$ is equal to :
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumSingle correctNew ideaIdea asked in 6 years
Q55
If for some $\alpha$ and $\beta$ in $\mathbf{R}$ , the intersection of the following three planes $x+4y-2z=1$ $x+7y-5z=\beta$ $x+5y+\alpha z=5$ is a line in $\mathbf{R}^3$ , then $\alpha+\beta$ is equal to :
Determinants Cramer's Rule Evaluating Parameters for Consistency
MediumSingle correctNew ideaIdea asked in 6 years
Q56
If the number of five digit numbers with distinct digits and 2 at the $10^{\mathrm{th}}$ place is 336 k, then k is equal to :
Permutations and Combinations Permutations of Distinct Objects
MediumSingle correctNew ideaIdea asked in 4 years
Q57
The product $2^{\frac{1}{4}}\cdot 4^{\frac{1}{16}}\cdot 8^{\frac{1}{48}}\cdot 16^{\frac{1}{128}}\cdot\ldots$ to $\infty$ is equal to :
Sequences and Series Arithmetico-Geometric Series Infinite Product Reduction to AGP
MediumSingle correctNew idea
Q58
If $f(x)=\begin{cases}\dfrac{\sin(a+2)x+\sin x}{x} & ;\,x<0\\[1ex] \mathrm{b} & ;\,x=0\\[1ex] \dfrac{(x+3x^2)^{1/3}-x^{1/3}}{x^{4/3}} & ;\,x>0\end{cases}$ is continuous at $x=0$ , then a + 2b is equal to :
Continuity and Differentiability Continuity at a Point
MediumSingle correctNew ideaIdea asked in 4 years
Q59
A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of $50\,\mathrm{cm}^3/\mathrm{min}$ . When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is :
Application of Derivatives Chain Rule Chain Rule in Related Rates
MediumSingle correctNew ideaIdea asked in 2 years
Q60
Let $f$ be any function continuous on [a, b] and twice differentiable on (a, b). If for all $x\in(\mathrm{a, b})$ , $f'(x)>0$ and $f''(x)<0$ , then for any $\mathrm{c}\in(\mathrm{a, b})$ , $\frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{b})-f(\mathrm{c})}$ is…
Continuity and Differentiability Mean Value Theorem Proving Inequalities via LMVT
HardSingle correctNew idea
Q61
If $f'(x)=\tan^{-1}(\sec x+\tan x)$ , $-\frac{\pi}{2}<x<\frac{\pi}{2}$ , and $f(0)=0$ , then $f(1)$ is equal to :
Integrals Inverse Trig Identities Periodic Reduction of tan-1(tan x) and cot-1(cot x)
HardSingle correctNew ideaIdea asked in 2 years
Q62
The integral $\int\frac{\mathrm{d}x}{(x+4)^{8/7}(x-3)^{6/7}}$ is equal to : (where C is a constant of integration)
Integrals Integration by Substitution Rational Powers Summing to Two Substitution
MediumSingle correctNew ideaIdea asked in 2 years
Q63
The value of $\int_0^{2\pi}\frac{x\sin^8 x}{\sin^8 x+\cos^8 x}\,\mathrm{d}x$ is equal to :
Integrals Definite Integral Properties King's Property
MediumSingle correctNew ideaIdea asked in 6 years
Q64
Let C be the centroid of the triangle with vertices (3, $-1$ ), (1, 3) and (2, 4). Let P be the point of intersection of the lines $x+3y-1=0$ and $3x-y+1=0$ . Then the line passing through the points C and P also passes through the point :
Straight Lines
EasySingle correct
Q65
A circle touches the $y$ -axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?
Conic Sections Circle Tangents Condition of tangency
MediumSingle correctNew ideaIdea asked in 4 years
Q66
If $\mathrm{e}_1$ and $\mathrm{e}_2$ are the eccentricities of the ellipse, $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola, $\frac{x^2}{9}-\frac{y^2}{4}=1$ respectively and $(\mathrm{e}_1, \mathrm{e}_2)$ is a point on the ellipse,…
Conic Sections Ellipse Eccentricity Eccentricity calculation
EasySingle correctNew ideaIdea asked in 6 years
Q67
In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears…
Probability
MediumSingle correct
Q68
Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum_{i=1}^{10}(x_i-5)=10$ and $\sum_{i=1}^{10}(x_i-5)^2=40$ . If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x_1-3, x_2-3, \ldots., x_{10}-3$ , then the ordered pair…
Statistics Variance and SD Effect of Linear Transformations
MediumSingle correctNew ideaIdea asked in 2 years
Q69
The value of $\cos^3\left(\frac{\pi}{8}\right)\cdot\cos\left(\frac{3\pi}{8}\right)+\sin^3\left(\frac{\pi}{8}\right)\cdot\sin\left(\frac{3\pi}{8}\right)$ is :
Trigonometric Functions Trigonometric Identities Product to Sum Formulas
MediumSingle correctNew ideaIdea asked in 2 years
Q70
Negation of the statement : ‘ $\sqrt{5}$ is an integer or 5 is irrational’ is :
Mathematical Reasoning
EasySingle correct
Q71
The coefficient of $x^4$ in the expansion of $(1+x+x^2)^{10}$ is __________.
Binomial Theorem
MediumNumerical value
Q72
The number of distinct solutions of the equation, $\log_{\frac{1}{2}}|\sin x|=2-\log_{\frac{1}{2}}|\cos x|$ in the interval [0, $2\pi$ ], is __________.
Trigonometric Functions General Solutions Logarithmic Trigonometric Equations
MediumNumerical valueNew idea
Q73
If the vectors, $\vec{p}=(a+1)\hat{i}+a\hat{j}+a\hat{k}$ , $\vec{q}=a\hat{i}+(a+1)\hat{j}+a\hat{k}$ and $\vec{r}=a\hat{i}+a\hat{j}+(a+1)\hat{k}$ $(a\in\mathbf{R})$ are coplanar and $3(\vec{p}\cdot\vec{q})^2-\lambda|\vec{r}\times\vec{q}|^2=0$ , then the value…
Vector Algebra Triple Products Solving for Unknown in Coplanarity
MediumNumerical valueNew ideaIdea asked in 4 years
Q74
If for $x\ge 0$ , $y=y(x)$ is the solution of the differential equation, $(x+1)\mathrm{d}y=((x+1)^2+y-3)\mathrm{d}x$ , $y(2)=0$ , then $y(3)$ is equal to __________.
Differential Equations Linear Differential Equations Integrating Factor Calculation
MediumNumerical valueNew ideaIdea asked in 7 years
Q75
The projection of the line segment joining the points (1, $-1$ , 3) and (2, $-4$ , 11) on the line joining the points ( $-1$ , 2, 3) and (3, $-2$ , 10) is __________.
Three Dimensional Geometry Dot Product Scalar and Vector Projection
EasyNumerical valueNew ideaIdea asked in 5 years

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 2020 shifts.