JEE Main 2023 · April session

JEE Main 11 April 2023, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 14 were rated hard and 31 easy. Its hard-question count was the joint 5th highest of the 12 2023 shifts Lumi analysed. The biggest chapter was Coordination Compounds, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 14; 16% of the shift
Chapters asked: 69; 15 questions with a figure

Key findings · 11 Apr 2023, Shift 1

1
14 hard questions (16%): the joint 5th highest count of the 12 2023 shifts Lumi analysed. Across those shifts the hard share ran from 9% to 24%.
2
Maths was the hardest section, with 9 of 30 rated hard; Physics had the most easy questions (18 of 30).
3
18 questions tested a new idea, one no earlier year had asked: 25% of the 71 questions tagged to an idea.
4
38 came back from 2022: the same idea had been asked in the 2022 shifts Lumi analysed.
5
31 shared an idea with another 2023 shift (44% 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), Coordination Compounds in Chemistry (4) and Three Dimensional Geometry in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 18Medium 12Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 10Medium 15Hard 5

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 18Hard 9

Top chapters

Three Dimensional Geometry3 Q
Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Integrals2 Q
Matrices2 Q

Question format

Single correct42 Q
Numerical value30 Q
Diagram based10 Q
Two statements5 Q
Match the list2 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step30 Q
Calculation23 Q
Application14 Q
Recall9 Q
Conceptual8 Q
Data or graph5 Q
Diagram reading1 Q

Most common: Multi-step.

Against the other 2023 shifts

This shift next to the 11 other 2023 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
6 Apr, Shift 1	90	31%	11%	33%	30%	27%
6 Apr, Shift 2	89	33%	17%	34%	25%	20%
8 Apr, Shift 1	89	38%	9%	34%	29%	21%
8 Apr, Shift 2	89	42%	16%	34%	23%	30%
10 Apr, Shift 1	88	39%	9%	33%	12%	25%
10 Apr, Shift 2	90	38%	12%	33%	20%	21%
11 Apr, Shift 1	90	34%	16%	33%	25%	33%
11 Apr, Shift 2	88	24%	18%	34%	28%	39%
12 Apr, Shift 1	89	30%	24%	34%	29%	35%
13 Apr, Shift 1	89	24%	19%	34%	21%	37%
13 Apr, Shift 2	90	33%	13%	33%	35%	32%
15 Apr, Shift 1	90	43%	14%	33%	18%	30%

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

18 easy12 medium0 hard

Chemistry30 questions

10 easy15 medium5 hard

Q61
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than…
Structure of Atom
MediumAssertion–reason
Q62
Match List-I with List-II : List-I Species | List-II Geometry/Shape A. $\mathrm{H_3O^+}$ | I. Tetrahedral B. Acetylide anion | II. Linear C. $\mathrm{NH_4^+}$ | III. Pyramidal D. $\mathrm{ClO_2^-}$ | IV. Bent Choose the correct answer from the options given…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 4 Shapes
EasyMatch the listIdea asked in 3 yearsAsked the year before
Q63
25 mL of silver nitrate solution (1M) is added dropwise to 25 mL of potassium iodide (1.05 M) solution. The ion(s) present in very small quantity in the solution is/are
Equilibrium Solubility Product Precipitation Condition
MediumSingle correctIdea asked in 4 years
Q64
For elements B, C, N, Li, Be, O and F, the correct order of first ionization enthalpy is
Classification of Elements and Periodicity in Properties Periodic Trends p-Block Ionization Enthalpy Inversions
EasySingle correctIdea asked in 4 yearsAsked the year before
Q65
In the extraction process of copper, the product obtained after carrying out the reactions (i) $\mathrm{2Cu_2S + 3O_2 \rightarrow 2Cu_2O + 2SO_2}$ (ii) $\mathrm{2Cu_2O + Cu_2S \rightarrow 6Cu + SO_2}$ is called
General Principles and Processes of Isolation of Elements Metallurgical Extraction Blister Copper Formation
EasySingle correctNew idea
Q66
Given below are two statements: Statement-I : Methane and steam passed over a heated Ni catalyst produces hydrogen gas. Statement-II : Sodium nitrite reacts with $\mathrm{NH_4Cl}$ to give $\mathrm{H_2O}$ , $\mathrm{N_2}$ and NaCl. In the light of the above…
Hydrogen Hydrogen and Hydrides Syngas Production via Reforming
EasyTwo statementsIdea asked in 2 years
Q67
Match List-I with List-II: List-I | List-II A. K | I. Thermonuclear reactions B. KCl | II. Fertilizer C. KOH | III. Sodium potassium pump D. Li | IV. Absorbent of $\mathrm{CO_2}$ Choose the correct answer from the options given below :
The s-Block Elements s-Block Elements Biological Role of Na and K
MediumMatch the listNew idea
Q68
For compound having the formula $\mathrm{GaAlCl_4}$ , the correct option from the following is
The p-Block Elements
MediumSingle correct
Q69
Which of the following complex has a possibility to exist as meridional isomer?
Coordination Compounds Coordination Isomerism Facial and Meridional Isomerism in MA3B3
EasySingle correctIdea asked in 3 years
Q70
The set which does not have ambidentate ligand(s) is
Coordination Compounds Coordination Isomerism Ambidentate Ligands in Linkage Isomerism
EasySingle correctIdea asked in 3 yearsAsked the year before
Q71
Given below are two statements: Statement I: If BOD is 4 ppm and dissolved oxygen is 8 ppm, then it is a good quality water. Statement II: If the concentration of zinc and nitrate salts are 5 ppm each, then it can be a good quality water. In the light of the…
Environmental Chemistry Water Quality BOD and COD
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q72
Thin layer chromatography of a mixture shows the following observation: The correct order of elution in the silica gel column chromatography is
Organic Chemistry: Some Basic Principles and Techniques Adsorption Adsorption Chromatography Principle
MediumDiagram based · figureIdea asked in 2 yearsAsked the year before
Q73
Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction (a) 1-tetralol: tetralin with OH on the saturated carbon attached to the benzene ring (b) tetralin with OH on the aromatic ring carbon adjacent to the…
Haloalkanes and Haloarenes Aromatic Hydrocarbons Ranking Activating Groups
HardDiagram based · figureIdea asked in 3 yearsAsked the year before
Q74
[figure: Reaction (I): 4-methoxybenzyl chloride ( $\mathrm{MeO{-}C_6H_4{-}CH_2Cl}$ ) + Nu gives 4-methoxybenzyl-Nu. Reaction (II): 4-nitrobenzyl chloride ( $\mathrm{O_2N{-}C_6H_4{-}CH_2Cl}$ ) + Nu gives 4-nitrobenzyl-Nu.] Where Nu = Nucleophile Find out the…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN1
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q75
[figure: 2-alkylcyclohexanone (R on the ring carbon adjacent to C=O, R = alkyl)] $\xrightarrow{\mathrm{KMnO_4}}$ 'A' (Major Product) $\xrightarrow[\text{(ii) } \mathrm{H_3O^+}]{\text{(i) } \mathrm{NH_2NH_2,\ KOH}}$ 'B' (Major Product) (R = alkyl) 'A' and 'B'…
Aldehydes, Ketones and Carboxylic Acids
HardDiagram based · figure
Q76
The complex that dissolves in water is
Coordination Compounds
HardSingle correct
Q77
o-Phenylenediamine $\xrightarrow{\mathrm{HNO_2}}$ 'X' (Major Product) 'X' is
Amines
MediumDiagram based · figure
Q78
The polymer X - consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. The polymer X is-
Polymers HDPE vs LDPE and Ziegler-Natta Catalyst
EasySingle correctNew idea
Q79
L-isomer of tetrose X ( $\mathrm{C_4H_8O_4}$ ) gives positive Schiff's test and has two chiral carbons. On acetylation, 'X' yields triacetate. 'X' also undergoes following reactions 'A' $\xleftarrow{\mathrm{HNO_3}}$ 'X' $\xrightarrow{\mathrm{NaBH_4}}$ 'B'…
Biomolecules Carbohydrates D and L Configuration of Sugars
HardDiagram based · figureNew ideaIdea asked in 3 years
Q80
When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ring was formed whereas on treatment with neutral $\mathrm{FeCl_3}$ , it gave deep red colour which disppeared on boiling…
Practical Chemistry (Qualitative Analysis)Anion Analysis Acetate Neutral FeCl3 Test
EasySingle correctIdea asked in 2 yearsAsked the year before
Q81
A solution of sugar is obtained by mixing 200g of its 25% solution and 500g of its 40% solution (both by mass). The mass percentage of the resulting sugar solution is __________ (Nearest integer)
Solutions Mole Concept PPM and Mass Percentage
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q82
An atomic substance A of molar mass $12\ \mathrm{g\ mol^{-1}}$ has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is __________. (Nearest integer) Given the density of A is $3.0\ \mathrm{g\ mL^{-1}}$ and…
The Solid State Crystal Lattices Unit Cell Density
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q83
Solid fuel used in rocket is a mixture of $\mathrm{Fe_2O_3}$ and Al (in ratio 1:2). The heat evolved (kJ) per gram of the mixture is __________ (Nearest integer) Given: $\Delta \mathrm{H_f^{\theta}(Al_2O_3)} = -1700\ \mathrm{kJ\ mol^{-1}}$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Standard Enthalpy of Reaction
MediumNumerical valueIdea asked in 2 years
Q84
0.004 M $\mathrm{K_2SO_4}$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of $\mathrm{K_2SO_4}$ is ____________ (Nearest integer)
Solutions Colligative Properties Isotonic Solutions
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q85
A mixture of 1 mole of $\mathrm{H_2O}$ and 1 mole of CO is taken in a 10 litre container and heated to 725 K. At equilibrium 40% of water by mass reacts with carbon monoxide according to the equation:…
Equilibrium Chemical Equilibrium Degree of Dissociation
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q86
In an electrochemical reaction of lead, at standard temperature, if $\mathrm{E^{\circ}(Pb^{2+}/Pb)} = m$ Volt and $\mathrm{E^{\circ}(Pb^{4+}/Pb)} = n$ Volt, then the value of $\mathrm{E^{\circ}(Pb^{2+}/Pb^{4+})}$ is given by $m - xn$ . The value of x is…
Electrochemistry Nernst Equation Latimer Diagrams and E0
MediumNumerical valueNew ideaIdea asked in 2 years
Q87
$\mathrm{KClO_3 + 6FeSO_4 + 3H_2SO_4 \rightarrow KCl + 3Fe_2(SO_4)_3 + 3H_2O}$ The above reaction was studied at 300 K by monitoring the concentration of $\mathrm{FeSO_4}$ in which initial concentration was 10 M and after half an hour became 8.8 M. The rate…
Chemical Kinetics Rate Laws Rate and Stoichiometry
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q88
The ratio of spin-only magnetic moment values $\mu_{\mathrm{eff}}\,\mathrm{[Cr(CN)_6]^{3-}} / \mu_{\mathrm{eff}}\,\mathrm{[Cr(H_2O)_6]^{3+}}$ is _________.
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q89
[figure: bicyclic (hydrindane-type) skeleton: cyclohexane fused to cyclopentane; Me at the ring-fusion carbon, adjacent cyclopentane carbon bearing OH] $\xrightarrow{\mathrm{HBr}}$ 'A' (Major Product) The number of hyperconjugation structures involved to…
Haloalkanes and Haloarenes Resonance and Hyperconjugation Counting Alpha-Hydrogens
HardNumerical value · figureNew idea
Q90
[figure: 4-hydroxybutanal, $\mathrm{OHC{-}CH_2CH_2CH_2{-}OH}$ (y mole)] $\xrightarrow[\mathrm{H_3O^+}]{x\ \text{mol of MeMgBr}}$ [figure: $\mathrm{CH_3CH(OH)CH_2CH_2CH_2OH}$ ] The ratio x/y on completion of the above reaction is ___________.
Alcohols, Phenols and Ethers Alcohols and Phenols Grignard Synthesis of Alcohols
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before

Maths30 questions

3 easy18 medium9 hard

Q1
An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
Relations and Functions Sets and Relations Inclusion-Exclusion for Three Sets
EasySingle correctIdea asked in 4 yearsAsked the year before
Q2
Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is equal to
Three Dimensional Geometry Planes in 3D Image of a Point in a Plane
MediumSingle correctIdea asked in 2 years
Q3
Consider ellipses $E_k : kx^2 + k^2y^2 = 1,\ k = 1, 2, \ldots, 20$ . Let $C_k$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $E_k$ . If $r_k$ is the radius of the circle $C_k$ ,…
Conic Sections
HardSingle correct
Q4
The number of triplets $(x, y, z)$ , where $x, y, z$ are distinct non negative integers satisfying $x + y + z = 15$ , is
Permutations and Combinations Distribution of Identical Objects
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
The number of integral solutions $x$ of $\log_{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2x-3}\right)^2 \ge 0$ is
Sequences and Series Functions and Domain Domain of Variable Base Logarithms
HardSingle correctNew idea
Q6
Let $A$ be a $2 \times 2$ matrix with real entries such that $A' = \alpha A + I$ , where $\alpha \in \mathbb{R} - \{-1, 1\}$ . If $\det(A^2 - A) = 4$ , then the sum of all possible values of $\alpha$ is equal to
Matrices Matrix Multiplication Transpose Reversal Law
MediumSingle correctNew idea
Q7
Let $f(x) = [x^2 - x] + |-x + [x]|$ , where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ is
Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q8
If equation of the plane that contains the point $(-2, 3, 5)$ and is perpendicular to each of the planes $2x + 4y + 5z = 8$ and $3x - 2y + 3z = 5$ is $\alpha x + \beta y + \gamma z + 97 = 0$ then $\alpha + \beta + \gamma =$
Three Dimensional Geometry Planes in 3D Plane Perpendicular to Two Planes
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q9
Area of the region $\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}$ is
Application of Integrals Area Under Curves Area of Inequalities
MediumSingle correctIdea asked in 8 yearsAsked the year before
Q10
Let $f : [2, 4] \to \mathbb{R}$ be a differentiable function such that $(x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]$ with $f(2) = \frac{1}{2}$ and $f(4) = \frac{1}{4}$ . Consider the following two statements : (A) : $f(x) \le 1$ , for all…
Application of Derivatives Monotonicity Proving Inequalities
HardTwo statementsNew idea
Q11
Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\ \hat{i}+\hat{k}$ and $\hat{i}-\hat{j},\ \hat{j}-\hat{k}$ . If $\theta$ is the angle between the vector $\vec{a}$ and the vector…
Vector Algebra Cross Product Magnitude and Sine Formula
HardSingle correctIdea asked in 7 yearsAsked the year before
Q12
For any vector $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ , with $10|a_i| < 1,\ i = 1, 2, 3$ , consider the following statements : (A) : $\max\{|a_1|, |a_2|, |a_3|\} \le |\vec{a}|$ (B) : $|\vec{a}| \le 3\max\{|a_1|, |a_2|, |a_3|\}$
Vector Algebra
MediumTwo statements
Q13
Let $x_1, x_2, \ldots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to 200. If $y_i = i(x_i - i),\ 1 \le i \le 100$ , then the mean of $y_1, y_2, \ldots, y_{100}$ is
Statistics Variance and SD Mean of Discrete Data
MediumSingle correctIdea asked in 4 years
Q14
Let $w_1$ be the point obtained by the rotation of $z_1 = 5 + 4i$ about the origin through a right angle in the anticlockwise direction, and $w_2$ be the point obtained by the rotation of $z_2 = 3 + 5i$ about the origin through a right angle in the clockwise…
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form 90-Degree Rotation via 'i'
MediumSingle correctNew idea
Q15
The value of the integral $\int_{-\log_e 2}^{\log_e 2} e^x\left(\log_e\left(e^x + \sqrt{1+e^{2x}}\right)\right)dx$ is equal to
Integrals Integration by Parts Logarithm of Quadratic Roots
HardSingle correctNew ideaIdea asked in 2 years
Q16
The number of elements in the set $S = \{\theta \in [0, 2\pi] : 3\cos^4\theta - 5\cos^2\theta - 2\sin^6\theta + 2 = 0\}$ is
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q17
Let $S = \{M = [a_{ij}],\ a_{ij} \in \{0, 1, 2\},\ 1 \le i, j \le 2\}$ be a sample space and $A = \{M \in S : M \text{ is invertible}\}$ be an event. Then $P(A)$ is equal to
Probability
HardSingle correct
Q18
Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of…
Statistics Variance and SD Combined Variance of Two Sets
MediumSingle correctIdea asked in 3 years
Q19
Let R be a rectangle given by the lines $x = 0$ , $x = 2$ , $y = 0$ and $y = 5$ . Let $A(\alpha, 0)$ and $B(0, \beta)$ , $\alpha \in [0, 2]$ and $\beta \in [0, 5]$ , be such that the line segment AB divides the area of the rectangle R in the ratio $4:1$ . Then,…
Straight Lines
MediumSingle correct
Q20
Let $y = y(x)$ be a solution curve of the differential equation. $(1 - x^2y^2)\,dx = y\,dx + x\,dy$ . If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$ , then a value of $\alpha$ …
Differential Equations Variable Separable Form Substitution of Product (u = xy)
MediumSingle correctNew idea
Q21
The mean of the coefficients of $x, x^2, \ldots, x^7$ in the binomial expansion of $(2+x)^9$ is ______________.
Binomial Theorem Binomial Coefficients Sum of all Coefficients
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q22
Let a line $l$ pass through the origin and be perpendicular to the lines $l_1 : \vec{r} = (\hat{i} - 11\hat{j} - 7\hat{k}) + \lambda(\hat{i} + 2\hat{j} + 3\hat{k}),\ \lambda \in \mathbb{R}$ and…
Three Dimensional Geometry Lines in 3D Line Perpendicular to Two Given Lines
HardNumerical valueIdea asked in 5 years
Q23
The number of ordered triplets of the truth values of $p$ , $q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge (p \vee r) \Rightarrow (q \vee r)$ is True, is equal to __________
Mathematical Reasoning
EasyNumerical value
Q24
If $a$ and $b$ are the roots of the equation $x^2 - 7x - 1 = 0$ , then the value of $\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}$ is equal to ___________.
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q25
Let $S = 109 + \frac{108}{5} + \frac{107}{5^2} + \ldots + \frac{2}{5^{107}} + \frac{1}{5^{108}}$ . Then the value of $(16S - (25)^{-54})$ is equal to ___________.
Sequences and Series Arithmetico-Geometric Series Sum of Finite AGP
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q26
For $m, n > 0$ , let $\alpha(m, n) = \int_0^2 t^m(1+3t)^n\,dt$ . If $11\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6$ , then $p$ is equal to ______________.
Integrals Integration by Parts Algebraic Reduction Formulas
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q27
The number of integral terms in the expansion of $\left(3^{\frac{1}{2}} + 5^{\frac{1}{4}}\right)^{680}$ is equal to
Binomial Theorem
MediumNumerical value
Q28
Let $H_n : \frac{x^2}{1+n} - \frac{y^2}{3+n} = 1,\ n \in \mathbb{N}$ . Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_k$ is a rational number. If $l$ is the length of the latus rectum of $H_k$ , then $21l$ is equal to…
Conic Sections
MediumNumerical value
Q29
Let $A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}$ , where $a, c \in \mathbb{R}$ . If $A^3 = A$ and the positive value of $a$ belongs to the interval $(n-1, n]$ , where $n \in \mathbb{N}$ , then $n$ is equal to ______________.
Matrices Matrix Multiplication Powers of Square Matrices
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q30
In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is ________________.
Permutations and Combinations Derangements
EasyNumerical valueNew idea

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 2023 shifts.