JEE Main 2024 · January session

JEE Main 27 January 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 8 were rated hard and 45 easy. Its hard-question count was the joint 15th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 8; 9% of the shift
Chapters asked: 60; 11 questions with a figure

Key findings · 27 Jan 2024, Shift 1

1
8 hard questions (9%): the joint 15th highest count of the 18 2024 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 6 of 30 rated hard; Chemistry had the most easy questions (21 of 30).
3
21 questions tested a new idea, one no earlier year had asked: 29% of the 73 questions tagged to an idea.
4
23 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
38 shared an idea with another 2024 shift (52% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (3), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 19Medium 10Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 21Medium 8Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 5Medium 19Hard 6

Top chapters

Question format

Single correct48 Q
Numerical value30 Q
Two statements6 Q
Diagram based4 Q
Other1 Q
Assertion–reason1 Q

What each question asks you to do

Calculation28 Q
Multi-step26 Q
Conceptual15 Q
Application12 Q
Recall8 Q
Diagram reading1 Q

Most common: Calculation.

Against the other 2024 shifts

This shift next to the 17 other 2024 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
27 Jan, Shift 1	90	50%	9%	33%	29%	29%
29 Jan, Shift 1	89	38%	10%	34%	28%	34%
30 Jan, Shift 1	90	37%	11%	33%	22%	17%
30 Jan, Shift 2	89	42%	10%	34%	32%	29%
31 Jan, Shift 1	90	39%	12%	33%	31%	34%
31 Jan, Shift 2	89	28%	13%	34%	23%	30%
1 Feb, Shift 1	90	36%	11%	33%	21%	19%
1 Feb, Shift 2	88	40%	8%	34%	19%	21%
4 Apr, Shift 1	89	26%	20%	33%	26%	36%
4 Apr, Shift 2	90	33%	18%	33%	13%	26%
5 Apr, Shift 1	90	40%	8%	33%	22%	27%
5 Apr, Shift 2	90	37%	10%	33%	23%	32%
6 Apr, Shift 1	88	43%	11%	34%	18%	22%
6 Apr, Shift 2	89	35%	15%	33%	28%	33%
8 Apr, Shift 1	90	31%	9%	33%	19%	37%
8 Apr, Shift 2	90	33%	12%	33%	19%	28%
9 Apr, Shift 1	90	31%	11%	33%	20%	50%
9 Apr, Shift 2	90	31%	16%	33%	27%	39%

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

19 easy10 medium1 hard

Chemistry30 questions

21 easy8 medium1 hard

Q61
Choose the polar molecule from the following :
Chemical Bonding and Molecular Structure VSEPR Theory VSEPR Symmetry and Dipole Moments
EasySingle correctNew ideaIdea asked in 2 years
Q62
A solution of two miscible liquids showing negative deviation from Raoult's law will have :
Solutions
EasySingle correct
Q63
Given below are two statements : Statement (I) : Aqueous solution of ammonium carbonate is basic. Statement (II) : Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $\mathrm{K_a}$ and $\mathrm{K_b}$ value of acid and the…
Equilibrium pH and Buffers pH of Weak Acid-Weak Base Salts
EasyTwo statementsIdea asked in 3 years
Q64
Given below are two statements : Statement (I) : The $4f$ and $5f$ - series of elements are placed separately in the Periodic table to preserve the principle of classification. Statement (II) : s-block elements can be found in pure form in nature. In the…
Classification of Elements and Periodicity in Properties
EasyTwo statements
Q65
Element not showing variable oxidation state is :
Classification of Elements and Periodicity in Properties Group 17 & 18 Anomalous Properties of Fluorine
EasySingle correctIdea asked in 2 years
Q66
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Melting point of Boron (2453 K) is unusually high in group 13 elements. Reason (R) : Solid Boron has very strong crystalline lattice.…
The p-Block Elements
EasyAssertion–reason
Q67
Which of the following electronic configuration would be associated with the highest magnetic moment ?
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
EasySingle correctIdea asked in 6 years
Q68
The electronic configuration for Neodymium is : [Atomic Number for Neodymium 60]
The d- and f-Block Elements f-Block Elements Lanthanide Electronic Configuration
EasySingle correctIdea asked in 5 years
Q69
Consider the following complex ions $\mathrm{P=[FeF_6]^{3-}}$ $\mathrm{Q=[V(H_2O)_6]^{2+}}$ $\mathrm{R=[Fe(H_2O)_6]^{2+}}$ The correct order of the complex ions, according to their spin only magnetic moment values (in B.M.) is :
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q70
IUPAC name of following compound (P) is :
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Cyclic Compound Naming
EasySingle correct · figureNew ideaIdea asked in 2 years
Q71
Cyclohexene [figure: cyclohexene ring] is __________ type of an organic compound.
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct · figure
Q72
Which of the following has highly acidic hydrogen ?
Aldehydes, Ketones and Carboxylic Acids Organic Acidity and Basicity Acidity of Active Methylene Compounds
EasyDiagram based · figureIdea asked in 2 years
Q73
The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is :
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms SN2 Transition State
EasySingle correctIdea asked in 2 years
Q74
Given below are two statements : Statement (I) : p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol. Statement (II) : Ethanol will give immediate turbidity with Lucas reagent. In the light of the above statements, choose the correct answer…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
EasyTwo statementsIdea asked in 3 yearsAsked the year before
Q75
The ascending order of acidity of $-$ OH group in the following compounds is : (A) Bu $-$ OH (B) [p-nitrophenol: $\mathrm{O_2N}$ at para position of phenol] (C) [p-methoxyphenol: MeO at para position of phenol] (D) [phenol] (E) [2,4-dinitrophenol:…
Alcohols, Phenols and Ethers Organic Acidity and Basicity Phenol Acidity
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q76
Highest enol content will be shown by :
Aldehydes, Ketones and Carboxylic Acids Structural Isomerism Aromaticity-Driven Enolization
HardDiagram based · figureNew idea
Q77
Which of the following is strongest Bronsted base ?
Amines Basicity of Nitrogen Heterocycles
EasyDiagram based · figureIdea asked in 3 years
Q78
Two nucleotides are joined together by a linkage known as :
Biomolecules
EasySingle correct
Q79
Yellow compound of lead chromate gets dissolved on treatment with hot NaOH solution. The product of lead formed is a :
Coordination Compounds Group 13 & 14 Amphoterism of Tin and Lead Oxides
MediumSingle correctNew idea
Q80
NaCl reacts with conc. $\mathrm{H_2SO_4}$ and $\mathrm{K_2Cr_2O_7}$ to give reddish fumes (B), which react with NaOH to give yellow solution (C). (B) and (C) respectively are :
The d- and f-Block Elements d-Block Elements Chromyl Chloride Test Reactions
MediumSingle correctNew idea
Q81
Mass of methane required to produce 22 g of $\mathrm{CO_2}$ after complete combustion is __________ g. (Given Molar mass in $\mathrm{g\ mol^{-1}}$ C = 12.0 H = 1.0 O = 16.0)
Some Basic Concepts of Chemistry Stoichiometry Mass-Mass Stoichiometry
EasyNumerical valueIdea asked in 3 years
Q82
The number of electrons present in all the completely filled subshells having $n = 4$ and $s = +\frac{1}{2}$ is __________. (Where $n$ = principal quantum number and $s$ = spin quantum number)
Structure of Atom Quantum Numbers Maximum Electrons in a Subshell
MediumNumerical valueNew idea
Q83
Sum of bond order of CO and $\mathrm{NO^+}$ is __________.
Chemical Bonding and Molecular Structure Molecular Orbital Theory Isoelectronic Bond Order Shortcut
EasyNumerical valueNew idea
Q84
If three moles of an ideal gas at 300 K expand isothermally from $30\ \mathrm{dm^3}$ to $45\ \mathrm{dm^3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is __________ J.
Thermodynamics (Chemistry)
MediumNumerical value
Q85
From the given list, the number of compounds with +4 oxidation state of Sulphur is __________. $\mathrm{SO_3,\ H_2SO_3,\ SOCl_2,\ SF_4,\ BaSO_4,\ H_2S_2O_7}$
Redox Reactions Oxidation Number Assignment
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q86
The mass of silver (Molar mass of Ag : $108\ \mathrm{g\ mol^{-1}}$ ) displaced by a quantity of electricity which displaces 5600 mL of $\mathrm{O_2}$ at S.T.P. will be __________ g.
Electrochemistry Faraday's Laws of Electrolysis Gas Evolution Volume
EasyNumerical valueIdea asked in 3 years
Q87
Consider the following data for the given reaction $\mathrm{2\ HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}}$ | 1 | 2 | 3 $\mathrm{HI\ (mol\ L^{-1})}$ | 0.005 | 0.01 | 0.02 $\mathrm{Rate\ (mol\ L^{-1}s^{-1})}$ | $7.5\times10^{-4}$ | $3.0\times10^{-3}$ |…
Chemical Kinetics Rate Laws Initial Rates Method
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q88
Among the following, total number of meta directing functional groups is __________. (Integer based) $\mathrm{-OCH_3,\ -NO_2,\ -CN,\ -CH_3,\ -NHCOCH_3,\ -COR,\ -OH,\ -COOH,\ -Cl}$
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Ortho-Para vs Meta Directing
EasyNumerical valueIdea asked in 5 years
Q89
Among the given organic compounds, the total number of aromatic compounds is __________. (A) [figure] (B) [figure] (C) [figure] (D) [figure]
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Huckel's Rule (4n+2)
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q90
3-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product (A). The number of possible stereoisomers for 'A' is __________.
Haloalkanes and Haloarenes Alkenes and Alkynes Peroxide Effect (Anti-Markovnikov)
MediumNumerical valueIdea asked in 3 years

Maths30 questions

5 easy19 medium6 hard

Q1
Let $S=\{1,2,3,\ldots,10\}$ . Suppose M is the set of all the subsets of S, then the relation $R=\{(A,B): A\cap B\neq\phi;\ A,B\in M\}$ is :
Relations and Functions Sets and Relations Relation Types
EasySingle correctIdea asked in 5 yearsAsked the year before
Q2
The function $f:\mathbf{N}-\{1\}\to\mathbf{N}$ ; defined by $f(n)=$ the highest prime factor of n, is :
Relations and Functions
EasySingle correct
Q3
If $S=\{z\in\mathbf{C}: |z-i|=|z+i|=|z-1|\}$ , then, n(S) is :
Complex Numbers and Quadratic Equations
MediumSingle correct
Q4
Consider the matrix $f(x)=\begin{bmatrix}\cos x & -\sin x & 0\\ \sin x & \cos x & 0\\ 0 & 0 & 1\end{bmatrix}$ . Given below are two statements : Statement I : $f(-x)$ is the inverse of the matrix $f(x)$ . Statement II : $f(x)\,f(y)=f(x+y)$ . In the light of the…
Matrices Matrix Inverse Inverse of Orthogonal Matrices
EasyTwo statementsNew idea
Q5
${}^{n-1}\mathrm{C}_r=(k^2-8)\,{}^{n}\mathrm{C}_{r+1}$ if and only if :
Permutations and Combinations Pascal's Rule and nCr Properties
MediumSingle correctNew idea
Q6
If A denotes the sum of all the coefficients in the expansion of $(1-3x+10x^2)^n$ and B denotes the sum of all the coefficients in the expansion of $(1+x^2)^n$ , then :
Binomial Theorem Binomial Coefficients Sum of all Coefficients
EasySingle correctIdea asked in 4 yearsAsked the year before
Q7
The number of common terms in the progressions $4, 9, 14, 19, \ldots\ldots$ , up to $25^{th}$ term and $3, 6, 9, 12, \ldots\ldots$ , up to $37^{th}$ term is :
Sequences and Series AP and GP Counting Common Terms of Finite APs
MediumSingle correctIdea asked in 3 years
Q8
Consider the function. $f(x)=\begin{cases}\dfrac{a(7x-12-x^2)}{b|x^2-7x+12|}, & x<3\\[2mm] 2^{\frac{\sin(x-3)}{x-[x]}}, & x>3\\[2mm] b, & x=3\end{cases}$ , where $[x]$ denotes the greatest integer less than or equal to $x$ . If S denotes the set of all ordered…
Continuity and Differentiability Continuity involving GIF and Fractional Part
HardSingle correctIdea asked in 6 yearsAsked the year before
Q9
If $a=\lim_{x\to0}\dfrac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}$ and $b=\lim_{x\to0}\dfrac{\sin^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$ , then the value of $ab^3$ is :
Limits and Derivatives L'Hopital's Rule Conjugation vs L'Hopital for Radicals
MediumSingle correctIdea asked in 3 years
Q10
If the shortest distance of the parabola $y^2=4x$ from the centre of the circle $x^2+y^2-4x-16y+64=0$ is d, then $d^2$ is equal to :
Conic Sections Normals to Conics Shortest Distance from Point to Parabola
MediumSingle correctNew idea
Q11
If $\displaystyle\int_0^1\dfrac{1}{\sqrt{3+x}+\sqrt{1+x}}\,dx=a+b\sqrt{2}+c\sqrt{3}$ , where a, b, c are rational numbers, then $2a+3b-4c$ is equal to :
Integrals
MediumSingle correct
Q12
If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2)$ , $(2, 3)$ and $(3, 1)$ , and $I_1=\int_a^b x\sin(4x-x^2)\,dx$ , $I_2=\int_a^b \sin(4x-x^2)\,dx$ , then $36\dfrac{I_1}{I_2}$ is equal to :
Integrals Definite Integral Properties King's Property
HardSingle correctIdea asked in 6 yearsAsked the year before
Q13
Let $x=x(t)$ and $y=y(t)$ be solutions of the differential equations $\dfrac{dx}{dt}+ax=0$ and $\dfrac{dy}{dt}+by=0$ respectively, $a, b\in\mathbf{R}$ . Given that $x(0)=2$ ; $y(0)=1$ and $3y(1)=2x(1)$ , the value of t, for which $x(t)=y(t)$ , is :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q14
Four distinct points $(2k, 3k)$ , $(1, 0)$ , $(0, 1)$ and $(0, 0)$ lie on a circle for k equal to :
Conic Sections
MediumSingle correct
Q15
The portion of the line $4x+5y=20$ in the first quadrant is trisected by the lines $L_1$ and $L_2$ passing through the origin. The tangent of an angle between the lines $L_1$ and $L_2$ is :
Straight Lines Straight Line Distance Section Ratio by a Line
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
The length of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ , whose mid point is $\left(1, \dfrac{2}{5}\right)$ , is equal to :
Conic Sections General Conic Section Chord Bisected at a Given Point (T=S1)
HardSingle correctIdea asked in 3 years
Q17
The distance, of the point $(7, -2, 11)$ from the line $\dfrac{x-6}{1}=\dfrac{y-4}{0}=\dfrac{z-8}{3}$ along the line $\dfrac{x-5}{2}=\dfrac{y-1}{-3}=\dfrac{z-5}{6}$ , is :
Three Dimensional Geometry Lines in 3D General Point Parameterization
MediumSingle correctIdea asked in 2 years
Q18
If the shortest distance between the lines $\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3}$ and $\dfrac{x-\lambda}{2}=\dfrac{y+1}{4}=\dfrac{z-2}{-5}$ is $\dfrac{6}{\sqrt{5}}$ , then the sum of all possible values of $\lambda$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$ , $\vec{b}=3(\hat{i}-\hat{j}+\hat{k})$ . Let $\vec{c}$ be the vector such that $\vec{a}\times\vec{c}=\vec{b}$ and $\vec{a}\cdot\vec{c}=3$ . Then $\vec{a}\cdot\left((\vec{c}\times\vec{b})-\vec{b}-\vec{c}\right)$ is equal to :
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q20
Let $a_1, a_2, \ldots a_{10}$ be 10 observations such that $\sum_{k=1}^{10}a_k=50$ and $\sum_{\forall k<j}a_k\cdot a_j=1100$ . Then the standard deviation of $a_1, a_2, \ldots, a_{10}$ is equal to :
Statistics Variance and SD Variance Formula Calculation
MediumSingle correctNew idea
Q21
If $\alpha$ satisfies the equation $x^2+x+1=0$ and $(1+\alpha)^7=A+B\alpha+C\alpha^2$ , $A, B, C\geq 0$ , then $5(3A-2B-C)$ is equal to ________.
Complex Numbers and Quadratic Equations Roots of Unity Periodicity of Omega Powers
MediumNumerical valueIdea asked in 3 years
Q22
Let $A=\begin{bmatrix}2&0&1\\1&1&0\\1&0&1\end{bmatrix}$ , $B=[B_1, B_2, B_3]$ , where $B_1, B_2, B_3$ are column matrices, and $AB_1=\begin{bmatrix}1\\0\\0\end{bmatrix}$ , $AB_2=\begin{bmatrix}2\\3\\0\end{bmatrix}$ , $AB_3=\begin{bmatrix}3\\2\\1\end{bmatrix}$ If…
Determinants Matrix Multiplication Determinant of Product
MediumNumerical valueIdea asked in 4 years
Q23
Let for a differentiable function $f:(0,\infty)\to\mathbf{R}$ , $f(x)-f(y)\geq \log_e\left(\dfrac{x}{y}\right)+x-y$ , $\forall x, y\in(0,\infty)$ . Then $\sum_{n=1}^{20}f'\left(\dfrac{1}{n^2}\right)$ is equal to ________.
Continuity and Differentiability
HardNumerical value
Q24
If $8=3+\dfrac{1}{4}(3+p)+\dfrac{1}{4^2}(3+2p)+\dfrac{1}{4^3}(3+3p)+\cdots\cdots\infty$ , then the value of p is ________.
Sequences and Series Arithmetico-Geometric Series Sum of Infinite AGP
MediumNumerical valueIdea asked in 4 years
Q25
Let $f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)$ , $x\in\mathbf{R}$ . Then $f'(10)$ is equal to ________.
Continuity and Differentiability
MediumNumerical value
Q26
Let the area of the region $\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\}$ be $\dfrac{m}{n}$ , where m and n are coprime numbers. Then $m+n$ is equal to ________.
Application of Integrals Area Under Curves Area of Inequalities
MediumNumerical valueIdea asked in 8 yearsAsked the year before
Q27
If the solution of the differential equation $(2x+3y-2)\,dx+(4x+6y-7)\,dy=0$ , $y(0)=3$ , is $\alpha x+\beta y+3\log_e|2x+3y-\gamma|=6$ , then $\alpha+2\beta+3\gamma$ is equal to ________.
Differential Equations Variable Separable Form Reducible to Separable (Parallel Lines Case)
HardNumerical valueNew idea
Q28
The least positive integral value of $\alpha$ , for which the angle between the vectors $\alpha\hat{i}-2\hat{j}+2\hat{k}$ and $\alpha\hat{i}+2\alpha\hat{j}-2\hat{k}$ is acute, is ________.
Vector Algebra Dot Product Acute and Obtuse Angle Conditions
EasyNumerical valueIdea asked in 2 years
Q29
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let $a=P(X=3)$ , $b=P(X\geq3)$ and $c=P(X\geq6\,|\,X>3)$ . Then $\dfrac{b+c}{a}$ is equal to ________.
Probability Conditional Probability Memoryless Property in Discrete Trials
MediumNumerical valueNew idea
Q30
Let the set of all $a\in\mathbf{R}$ such that the equation $\cos 2x+a\sin x=2a-7$ has a solution be $[p, q]$ and $r=\tan 9^\circ-\tan 27^\circ-\dfrac{1}{\cot 63^\circ}+\tan 81^\circ$ , then $pqr$ is equal to ________.
Trigonometric Functions Trigonometric Identities Values of Non-Standard Specific Angles
HardNumerical valueIdea asked in 3 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 2024 shifts.