JEE Main 2023 · April session

JEE Main 10 April 2023, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 11 were rated hard and 34 easy. Its hard-question count was the 9th highest of the 12 2023 shifts Lumi analysed. The biggest chapter was Three Dimensional Geometry, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 11; 12% of the shift
Chapters asked: 70; 14 questions with a figure

Key findings · 10 Apr 2023, Shift 2

1
11 hard questions (12%): the 9th 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 (19 of 30).
3
15 questions tested a new idea, one no earlier year had asked: 20% of the 74 questions tagged to an idea.
4
44 came back from 2022: the same idea had been asked in the 2022 shifts Lumi analysed.
5
28 shared an idea with another 2023 shift (38% 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), Alcohols, Phenols and Ethers in Chemistry (2) and Three Dimensional Geometry in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 19Medium 11Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 14Medium 14Hard 2

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 20Hard 9

Top chapters

Question format

Single correct44 Q
Numerical value30 Q
Diagram based5 Q
Assertion–reason4 Q
Other3 Q
Two statements2 Q
Match the list2 Q

What each question asks you to do

Calculation33 Q
Multi-step19 Q
Conceptual17 Q
Recall9 Q
Application8 Q
Diagram reading2 Q
Data or graph2 Q

Most common: Calculation.

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

19 easy11 medium0 hard

Q31
The distance between two plates of a capacitor is d and its capacitance is $C_1$ , when air is the medium between the plates. If a metal sheet of thickness $\frac{2d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Inserted Conducting Slab
EasySingle correctIdea asked in 2 yearsAsked the year before
Q32
For a periodic motion represented by the equation $y = \sin \omega t + \cos \omega t$ the amplitude of the motion is
Oscillations SHM Equations Collinear Superposition of SHMs
EasySingle correctIdea asked in 4 yearsAsked the year before
Q33
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,
Kinetic Theory Kinetic Theory of Gases Internal Energy of Gas Mixtures
EasySingle correctIdea asked in 5 yearsAsked the year before
Q34
A gas is compressed adiabatically, which one of the following statement is NOT true.
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
EasySingle correctIdea asked in 7 yearsAsked the year before
Q35
Young's moduli of the material of wires A and B are in the ratio of 1:4, while its area of cross sections are in the ratio of 1:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the…
Mechanical Properties of Solids Elasticity Elastic Moduli
EasySingle correctIdea asked in 7 yearsAsked the year before
Q36
Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.…
Gravitation Orbital Mechanics Effect of Earth's Rotation on Launch Velocity
EasyTwo statementsNew idea
Q37
The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given $g = \pi^2$ m/s $^2$ , R = radius of earth)
Gravitation Orbital Mechanics Orbital Time Period
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q38
Two projectiles are projected at $30^\circ$ and $60^\circ$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
Motion in a Plane Projectile Motion Ground-to-Ground Parameters
EasySingle correctIdea asked in 6 yearsAsked the year before
Q39
In an experiment with vernier calipers of least count 0.1 mm, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the…
Units and Measurements
MediumSingle correct
Q40
A person travels $x$ distance with velocity $v_1$ and then $x$ distance with velocity $v_2$ in the same direction. The average velocity of the person is v, then the relation between v, $v_1$ and $v_2$ will be.
Motion in a Straight Line Kinematics in 1D Average Speed Special Cases
EasySingle correctIdea asked in 4 yearsAsked the year before
Q41
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R : Fan continues to rotate due to inertia of…
Laws of Motion Newton's Laws of Motion Newton's First Law
EasyAssertion–reasonNew idea
Q42
A message signal of frequency 3kHz is used to modulate a carrier signal of frequency 1.5 MHz. The bandwidth of the amplitude modulated wave is
Communication Systems
EasySingle correct
Q43
If each diode has a forward bias resistance of 25 $\Omega$ in the below circuit, which of the following options is correct:
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Forward and Reverse Biasing
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q44
The half life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$ th part of its original mass will be:
Nuclei Radioactive Decay Half-Life Calculations
EasySingle correctIdea asked in 4 yearsAsked the year before
Q45
The variation of stopping potential ( $V_0$ ) as a function of the frequency ( $\nu$ ) of the incident light for a metal is shown in figure. The work function of the surface is
Dual Nature of Radiation and Matter Photoelectric Effect Stopping Potential vs Frequency Graph
MediumDiagram based · figureIdea asked in 2 years
Q46
A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will
Electromagnetic Induction Lenz's Law Bar Magnet and Loop Interaction
MediumSingle correctIdea asked in 2 years
Q47
The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $\pi/3$ and $\pi/2$ , respectively are
Wave Optics Young's Double Slit Resultant Intensity Formula
EasySingle correctIdea asked in 5 yearsAsked the year before
Q48
The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $6.0\times10^{-7}$ T. The maximum value of electric field in the electromagnetic wave is
Electromagnetic Waves
EasySingle correct
Q49
Given below are two statements: Statement I : For diamagnetic substance, $-1 \leq \chi < 0$ , where $\chi$ is the magnetic susceptibility. Statement II : Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker…
Magnetism and Matter
EasyTwo statements
Q50
In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor
Current Electricity Ohm's Law and Resistance Drift Velocity and Current
EasySingle correctIdea asked in 3 yearsAsked the year before
Q51
A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s. The maximum force exerted by spring on block is __________N
Oscillations SHM Equations SHM Definition and Force Law
EasyNumerical valueIdea asked in 4 years
Q52
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm $^2$ . The area of cross section at the outlet is 10 mm $^2$ . If the piston is pushed at a speed of 4 cm s $^{-1}$ , the speed of outgoing fluid is ______ cm…
Mechanical Properties of Fluids Fluid Dynamics Equation of Continuity
EasyNumerical value · figureNew ideaIdea asked in 2 years
Q53
A force of $-P\hat{k}$ acts on the origin of the coordinate system. The torque about the point (2, -3) is $P(a\hat{i} + b\hat{j})$ . The ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of x is -
System of Particles and Rotational Motion Torque and Equilibrium Torque Calculation
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q54
If the maximum load carried by an elevator is 1400 kg (600 kg - Passengers + 800 kg - elevator), which is moving up with a uniform speed of 3 m s $^{-1}$ and the frictional force acting on it is 2000 N, then the maximum power used by the motor is __________…
Work, Energy and Power Power Instantaneous Power
MediumNumerical valueIdea asked in 2 years
Q55
An electron revolves around an infinite cylindrical wire having uniform linear charge density $2\times10^{-8}$ C m $^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is…
Electric Charges and Fields Gauss's Law Cylindrical Field
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q56
If 917 $\mathrm{\AA}$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ____________ $\mathrm{\AA}$ .
Atoms Bohr's Atomic Model Shortest and Longest Wavelengths
EasyNumerical valueIdea asked in 5 years
Q57
A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses $L_1$ and $L_2$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens $L_1$ as shown in the…
Ray Optics and Optical Instruments Lens Maker's Formula Thin Lens Formula
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q58
A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5A and angular frequency 700 rad s $^{-1}$ . The central axes of the loop and solenoid coincide. The…
Electromagnetic Induction Faraday's Law Magnetic Flux Calculation
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q59
A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc. is ________ $\times10^{-4}$ T
Moving Charges and Magnetism Biot-Savart Law Field at center of circular arc
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q60
A rectangular parallelopiped is measured as 1 cm $\times$ 1 cm $\times$ 100 cm. If its specific resistance is $3\times10^{-7}\ \Omega$ m, then the resistance between its two opposite rectangular faces will be ____________ $\times10^{-7}\ \Omega$ .
Current Electricity Ohm's Law and Resistance Resistivity and Geometry
EasyNumerical valueIdea asked in 4 yearsAsked the year before

Chemistry30 questions

14 easy14 medium2 hard

Q61
Match List I with List II LIST I A. 16 g of $\mathrm{CH_4}$ (g) B. 1 g of $\mathrm{H_2}$ (g) C. 1 mole of $\mathrm{N_2}$ (g) D. 0.5 mol of $\mathrm{SO_2}$ (g) LIST II I. Weighs 28g II. $60.2 \times 10^{23}$ electrons III. Weighs 32 g IV. Occupies 11.4 L…
Some Basic Concepts of Chemistry Mole Concept Mole and Avogadro Calculations
EasyMatch the listIdea asked in 5 yearsAsked the year before
Q62
The correct relationships between unit cell edge length 'a' and radius of sphere 'r' for face-centred and body-centred cubic structures respectively are:
The Solid State Crystal Lattices Edge-Radius Relationships
EasySingle correctIdea asked in 2 yearsAsked the year before
Q63
Ferric chloride is applied to stop bleeding because -
Surface Chemistry Colloids Hardy-Schulze Rule
EasySingle correctIdea asked in 3 years
Q64
The correct order of metallic character is =
Classification of Elements and Periodicity in Properties Periodic Trends Metallic and Non-Metallic Character Trends
EasySingle correctIdea asked in 3 yearsAsked the year before
Q65
Gibbs energy vs T plot for the formation of oxides is given below. For the given diagram, the correct statement is -
General Principles and Processes of Isolation of Elements Gibbs Free Energy Ellingham Diagram Reduction Feasibility
MediumDiagram based · figureNew idea
Q66
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Physical properties of isotopes of hydrogen are different. Reason R : Mass difference between isotopes of hydrogen is very large. In the light…
Hydrogen Hydrogen and Hydrides Isotopes of Hydrogen
EasyAssertion–reasonIdea asked in 4 yearsAsked the year before
Q67
Number of water molecules in washing soda and soda ash respectively are:
The s-Block Elements
EasySingle correct
Q68
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The energy required to form $\mathrm{Mg^{2+}}$ from Mg is much higher than that required to produce $\mathrm{Mg^+}$ Reason R :…
Classification of Elements and Periodicity in Properties
MediumAssertion–reason
Q69
The correct order of the number of unpaired electrons in the given complexes is A. $[\mathrm{Fe(CN)_6}]^{3-}$ B. $[\mathrm{FeF_6}]^{3-}$ C. $[\mathrm{CoF_6}]^{3-}$ D. $[\mathrm{Cr(oxalate)_3}]^{3-}$ E. $[\mathrm{Ni(CO)_4}]$ Choose the correct answer from the…
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumOtherIdea asked in 7 yearsAsked the year before
Q70
Match List I with List II LIST I (Complex) A. $[\mathrm{Ti(H_2O)_6}]^{2+}$ B. $[\mathrm{V(H_2O)_6}]^{2+}$ C. $[\mathrm{Mn(H_2O)_6}]^{3+}$ D. $[\mathrm{Fe(H_2O)_6}]^{3+}$ LIST II (Crystal Field splitting energy ( $\Delta_0$ )) I. $-1.2$ II. $-0.6$ III. $0$ IV.…
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumMatch the listIdea asked in 6 yearsAsked the year before
Q71
The delicate balance of $\mathrm{CO_2}$ and $\mathrm{O_2}$ is NOT disturbed by
Environmental Chemistry
EasySingle correct
Q72
In Carius tube, an organic compound 'X' is treated with sodium peroxide to form a mineral acid 'Y'. The solution of $\mathrm{BaCl_2}$ is added to 'Y' to form a precipitate 'Z'. 'Z' is used for the quantitative estimation of an extra element. 'X' could be
Organic Chemistry: Some Basic Principles and Techniques
MediumSingle correct
Q73
The decreasing order of hydride affinity for following carbocations is: A. $\mathrm{CH_2=CH-\overset{+}{C}(CH_3)-CH_3}$ (carbocation carbon bearing vinyl and two methyl groups) B. $\mathrm{C_6H_5-\overset{+}{C}(C_6H_5)-C_6H_5}$ (triphenylmethyl cation) C.…
Organic Chemistry: Some Basic Principles and Techniques Inductive and Electromeric Effects Carbocation Stability
HardOther · figureIdea asked in 4 yearsAsked the year before
Q74
The major product 'P' formed in the given reaction is:
Haloalkanes and Haloarenes Aromatic Hydrocarbons Friedel-Crafts Alkylation
HardDiagram based · figureIdea asked in 5 yearsAsked the year before
Q75
Incorrect method of preparation for alcohols from the following is:
Alcohols, Phenols and Ethers Alkenes and Alkynes Hydroboration-Oxidation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q76
The correct order for acidity of the following hydroxyl compound is : A. $\mathrm{CH_3OH}$ B. $\mathrm{(CH_3)_3COH}$ C. phenol ( $\mathrm{C_6H_5-OH}$ ) D. $\mathrm{MeO-C_6H_4-OH}$ (para) E. $\mathrm{O_2N-C_6H_4-OH}$ (para) Choose the correct answer from the…
Alcohols, Phenols and Ethers Organic Acidity and Basicity Phenol Acidity
MediumOther · figureNew ideaIdea asked in 2 years
Q77
In the reaction given below : [figure: $\mathrm{H_2N-C(=O)-CH(CH_3)-C(=CH_2)-C(=O)-CH_2CH_3}$ ] $\xrightarrow{\text{(i) LiAlH}_4,\ \text{(ii) H}_3\mathrm{O}^+}$ 'X' The product 'X' is :
Amines Alcohols and Phenols NaBH4 vs LiAlH4 Chemoselectivity
MediumDiagram based · figureNew idea
Q78
Buna-S can be represented as:
Polymers Buna-S (SBR) Monomers
EasySingle correctIdea asked in 2 years
Q79
The reaction used for preparation of soap from fat is :
Biomolecules
EasySingle correct
Q80
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : 3.1500g of hydrated oxalic acid dissolved in water to make 250.0 mL solution will result in 0.1 M oxalic acid solution. Reason R : Molar mass…
Some Basic Concepts of Chemistry Mole Concept Molarity Calculation
EasyAssertion–reasonIdea asked in 5 yearsAsked the year before
Q81
The electron in the $n^{th}$ orbit of $\mathrm{Li^{2+}}$ is excited to $(n + 1)$ orbit using the radiation of energy $1.47 \times 10^{-17}$ J (as shown in the diagram). The value of n is ________. Given: $R_H = 2.18 \times 10^{-18}$ J
Structure of Atom Bohr's Atomic Theory Ionization and Excitation Energy
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q82
The number of molecules from the following which contain only two lone pair of electrons is ___________ $\mathrm{H_2O}$ , $\mathrm{N_2}$ , CO, $\mathrm{XeF_4}$ , $\mathrm{NH_3}$ , NO, $\mathrm{CO_2}$ , $\mathrm{F_2}$
Chemical Bonding and Molecular Structure VSEPR Theory Geometry vs Shape Distinction
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q83
The number of endothermic process/es from the following is ____________ A. $\mathrm{I_2}$ (g) $\rightarrow$ 2I (g) B. HCl (g) $\rightarrow$ H(g) + Cl(g) C. $\mathrm{H_2O}$ (l) $\rightarrow$ $\mathrm{H_2O}$ (g) D. C(s) + $\mathrm{O_2}$ (g) $\rightarrow$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Sign Conventions for Heat Flow
EasyNumerical valueIdea asked in 2 years
Q84
An aqueous solution of volume 300 $\mathrm{cm^3}$ contains 0.63 g of protein. The osmotic pressure of the solution at 300 K is 1.29 mbar. The molar mass of the protein is ____________ g $\mathrm{mol^{-1}}$ Given: R = 0.083 L bar $\mathrm{K^{-1}}$ …
Solutions Colligative Properties Osmotic Pressure
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
$\mathrm{A}(g) \rightleftharpoons 2\mathrm{B}(g) + \mathrm{C}(g)$ For the given reaction, if the initial pressure is 450 mm Hg and the pressure at time t is 720 mm Hg at a constant temperature T and constant volume V. The fraction of A(g) decomposed under…
Equilibrium Chemical Equilibrium Dalton's Law in Kp Calculations
MediumNumerical valueNew ideaIdea asked in 3 years
Q86
The specific conductance of 0.0025 M acetic acid is $5 \times 10^{-5}$ $\mathrm{S\ cm^{-1}}$ at a certain temperature. The dissociation constant of acetic acid is ____________ $\times 10^{-7}$ . (Nearest integer) Consider limiting molar conductivity of…
Electrochemistry
MediumNumerical value
Q87
The number of incorrect statement/s from the following is ____________ A. The successive half lives of zero order reactions decreases with time. B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction C. Order and…
Chemical Kinetics Integrated Rate Equations Zero Order Half-Life
MediumNumerical valueNew ideaIdea asked in 3 years
Q88
The difference in the oxidation state of Xe between the oxidised product of Xe formed on complete hydrolysis of $\mathrm{XeF_4}$ and $\mathrm{XeF_4}$ is ____________
The p-Block Elements Group 17 & 18 Xenon Fluorides
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q89
For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ____________ number of unpaired electrons.
The d- and f-Block Elements Quantum Numbers Spin-Only Magnetic Moment
EasyNumerical valueNew idea
Q90
In alkaline medium, the reduction of permanganate anion involves a gain of ____________ electrons.
Redox Reactions Permanganate n-Factor Across Media
EasyNumerical valueIdea asked in 3 yearsAsked the year before

Maths30 questions

1 easy20 medium9 hard

Q1
Let $A = \{2, 3, 4\}$ and $B = \{8, 9, 12\}$ . Then the number of elements in the relation $R = \{((a_1, b_1), (a_2, b_2)) \in (A \times B, A \times B) : a_1 \text{ divides } b_2 \text{ and } a_2 \text{ divides } b_1\}$ is
Relations and Functions Sets and Relations Cartesian Products
MediumSingle correctNew idea
Q2
Let $S = \left\{x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10\right\}$ and $\beta = \sum_{x \in S} \tan^2\left(\frac{x}{3}\right)$ , then $\frac{1}{6}(\beta - 14)^2$ is equal to
Trigonometric Functions General Solutions Quadratic Substitution in Trigonometry
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q3
Let $S = \left\{z = x + iy : \frac{2z - 3i}{4z + 2i} \text{ is a real number}\right\}$ . Then which of the following is NOT correct?
Complex Numbers and Quadratic Equations
MediumSingle correct
Q4
If $A = \frac{1}{5!\,6!\,7!}\begin{bmatrix} 5! & 6! & 7! \\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}$ , then $|\mathrm{adj}(\mathrm{adj}(2A))|$ is equal to
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is
Permutations and Combinations Distribution of Distinct Objects into Distinct Boxes
MediumSingle correctIdea asked in 3 years
Q6
If the coefficients of $x$ and $x^2$ in $(1+x)^p (1-x)^q$ are $4$ and $-5$ respectively, then $2p + 3q$ is equal to
Binomial Theorem
MediumSingle correct
Q7
Let the number $(22)^{2022} + (2022)^{22}$ leave the remainder $\alpha$ when divided by $3$ and $\beta$ when divided by $7$ . Then $(\alpha^2 + \beta^2)$ is equal to
Binomial Theorem
MediumSingle correct
Q8
If $S_n = 4 + 11 + 21 + 34 + 50 + \ldots$ to $n$ terms, then $\frac{1}{60}(S_{29} - S_9)$ is equal to
Sequences and Series AP and GP Method of Differences for Telescoping Series
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q9
Let $g(x) = f(x) + f(1-x)$ and $f''(x) > 0,\ x \in (0,1)$ . If $g$ is decreasing in the interval $(0, \alpha)$ and increasing in the interval $(\alpha, 1)$ , then…
Application of Derivatives Monotonicity Strict Monotonicity
HardSingle correctNew idea
Q10
For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$ , if…
Integrals Integration by Substitution Exponential Factor Manipulation
HardSingle correctIdea asked in 4 yearsAsked the year before
Q11
Let $f$ be a continuous function satisfying $\int_0^{t^2} (f(x) + x^2)\, dx = \frac{4}{3}t^3,\ \forall t > 0$ . Then $f\left(\frac{\pi^2}{4}\right)$ is equal to
Integrals Leibniz Rule Solving Integral Equations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q12
Let A be the point $(1, 2)$ and B be any point on the curve $x^2 + y^2 = 16$ . If the centre of the locus of the point P, which divides the line segment AB in the ratio $3:2$ is the point $C(\alpha, \beta)$ , then the length of the line segment AC is
Conic Sections
MediumSingle correct
Q13
Let a circle of radius $4$ be concentric to the ellipse $15x^2 + 19y^2 = 285$ . Then the common tangents are inclined to the minor axis of the ellipse at the angle
Conic Sections Circle Tangents Common Tangent to Circle and Conic
HardSingle correctIdea asked in 3 yearsAsked the year before
Q14
Let the image of the point $P(1, 2, 6)$ in the plane passing through the points $A(1, 2, 0)$ , $B(1, 4, 1)$ and $C(0, 5, 1)$ be $Q(\alpha, \beta, \gamma)$ . Then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to
Three Dimensional Geometry Planes in 3D Image of a Point in a Plane
MediumSingle correctIdea asked in 2 years
Q15
Let the line $\frac{x}{1} = \frac{6-y}{2} = \frac{z+8}{5}$ intersect the lines $\frac{x-5}{4} = \frac{y-7}{3} = \frac{z+2}{1}$ and $\frac{x+3}{6} = \frac{3-y}{3} = \frac{z-6}{1}$ at the points A and B respectively. Then the distance of the mid-point of the…
Three Dimensional Geometry Lines in 3D Point of Intersection Calculation
HardSingle correctIdea asked in 6 yearsAsked the year before
Q16
Let $\vec{a} = 2\hat{i} + 7\hat{j} - \hat{k},\ \vec{b} = 3\hat{i} + 5\hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + 2\hat{k}$ . Let $\vec{d}$ be a vector which is perpendicular to both $\vec{a}$ and $\vec{b}$ , and $\vec{c} \cdot \vec{d} = 12$ . Then…
Vector Algebra Cross Product Unit Normal Vector Calculation
MediumSingle correctIdea asked in 2 years
Q17
If the points P and Q are respectively the circumcenter and the orthocentre of a $\Delta ABC$ , then $\overrightarrow{PA} + \overrightarrow{PB} + \overrightarrow{PC}$ is equal to
Vector Algebra Dot Product Orthocenter Position Vector Relations
MediumSingle correctNew idea
Q18
Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$ , then $k$ is equal to.
Probability
MediumSingle correct
Q19
Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution $x_i$ : $0$ , $1$ , $2$ , $3$ , $4$ , $5$ $f_i$ : $k+2$ , $2k$ , $k^2-1$ , $k^2-1$ , $k^2+1$ , $k-3$ where $\sum f_i = 62$ . If $[x]$ denotes the greatest integer $\leq x$ , then…
Statistics Variance and SD Variance of Discrete Frequency Distribution
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q20
The statement $\sim[p \vee (\sim(p \wedge q))]$ is equivalent to
Mathematical Reasoning
EasySingle correct
Q21
If the domain of the function $f(x) = \sec^{-1}\left(\frac{2x}{5x+3}\right)$ is $[\alpha, \beta) \cup (\gamma, \delta]$ , then $|3\alpha + 10(\beta + \gamma) + 21\delta|$ is equal to ________.
Inverse Trigonometric Functions Functions and Domain Domain of Inverse Secant and Cosecant
MediumNumerical valueIdea asked in 2 years
Q22
Let S be the set of values of $\lambda$ , for which the system of equations $6\lambda x - 3y + 3z = 4\lambda^2$ , $2x + 6\lambda y + 4z = 1$ , $3x + 2y + 3\lambda z = \lambda$ has no solution. Then $12\sum_{\lambda \in S} |\lambda|$ is equal to ____________.
Determinants Cramer's Rule Condition for No Solution
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q23
The sum of all the four-digit numbers that can be formed using all the digits $2, 1, 2, 3$ is equal to ___________.
Permutations and Combinations Sum of Numbers Formed by Given Digits
MediumNumerical valueIdea asked in 2 years
Q24
Suppose $a_1, a_2, 2, a_3, a_4$ be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is $2$ and the sum of all $5$ terms of the arithmetico-geometric progression is $\frac{49}{2}$ , then $a_4$ is equal to…
Sequences and Series Arithmetico-Geometric Series AGP General Term
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q25
Let the quadratic curve passing through the point $(-1, 0)$ and touching the line $y = x$ at $(1, 1)$ be $y = f(x)$ . Then the $x$ -intercept of the normal to the curve at the point $(\alpha, \alpha + 1)$ in the first quadrant is _________.
Application of Derivatives Tangents and Normals Intercepts of Tangent and Normal
MediumNumerical valueIdea asked in 3 years
Q26
If the area of the region $\{(x, y) : |x^2 - 2| \leq y \leq x\}$ is A, then $6A + 16\sqrt{2}$ is equal to ______.
Application of Integrals Area Under Curves Area with Modulus
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q27
Let the tangent at any point P on a curve passing through the points $(1, 1)$ and $\left(\frac{1}{10}, 100\right)$ , intersect positive $x$ - axis and $y$ -axis at the points A and B respectively. If $PA : PB = 1 : k$ and $y = y(x)$ is the solution of the…
Differential Equations Variable Separable Form Substitution of Ratio (u = y/x)
HardNumerical valueNew idea
Q28
Let the equations of two adjacent sides of a parallelogram ABCD be $2x - 3y = -23$ and $5x + 4y = 23$ . If the equation of its one diagonal AC is $3x + 7y = 23$ and the distance of A from the other diagonal is d, then $50\,d^2$ is equal to ___________.
Straight Lines Straight Line Distance Area of Parallelogram via Parallel Distances
HardNumerical valueNew idea
Q29
Let the foot of perpendicular from the point A $(4, 3, 1)$ on the plane P : $x - y + 2z + 3 = 0$ be N. If B $(5, \alpha, \beta)$ , $\alpha, \beta \in \mathbb{Z}$ is a point on plane P such that the area of the triangle ABN is $3\sqrt{2}$ , then…
Three Dimensional Geometry Point-Plane Distance Foot of Perpendicular
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q30
In the figure, $\theta_1 + \theta_2 = \frac{\pi}{2}$ and $\sqrt{3}\,(BE) = 4(AB)$ . If the area of $\Delta CAB$ is $2\sqrt{3} - 3$ unit $^2$ , when $\frac{\theta_2}{\theta_1}$ is the largest, then the perimeter (in unit) of $\Delta CED$ is equal to ___________.
Trigonometric Functions Properties of Triangles Sine Rule Application
HardNumerical value · figureIdea asked in 2 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 2023 shifts.