JEE Main 2023 · April session

JEE Main 13 April 2023, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 12 were rated hard and 30 easy. Its hard-question count was the 8th 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: 12; 13% of the shift
Chapters asked: 67; 9 questions with a figure

Key findings · 13 Apr 2023, Shift 2

1
12 hard questions (13%): the 8th 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
25 questions tested a new idea, one no earlier year had asked: 35% of the 72 questions tagged to an idea.
4
39 came back from 2022: the same idea had been asked in the 2022 shifts Lumi analysed.
5
21 shared an idea with another 2023 shift (29% 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), Chemical Bonding and Molecular Structure 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 18Medium 12Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 8Medium 19Hard 3

Top chapters

Maths

30 Q · 10 numerical

Easy 4Medium 17Hard 9

Top chapters

Three Dimensional Geometry3 Q
Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Determinants2 Q
Integrals2 Q

Question format

Single correct44 Q
Numerical value30 Q
Two statements6 Q
Assertion–reason5 Q
Other2 Q
Match the list2 Q
Diagram based1 Q

What each question asks you to do

Multi-step29 Q
Calculation28 Q
Application13 Q
Conceptual10 Q
Recall9 Q
Data or graph1 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

Q31
In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=RT$ , $X$ is pressure, $Y$ is volume, R is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:
Units and Measurements
MediumSingle correct
Q32
The distance travelled by an object in time t is given by $s=(2.5)t^2$ . The instantaneous speed of the object at $t=5$ s will be:
Motion in a Straight Line Kinematics in 1D Average vs Instantaneous Velocity
EasySingle correctIdea asked in 3 yearsAsked the year before
Q33
A passenger sitting in a train A moving at $90$ km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is $54$ km/h, then length of train B is:
Motion in a Straight Line Relative Velocity Extended Bodies Overtaking and Crossing
EasySingle correctNew idea
Q34
A vehicle of mass $200$ kg is moving along a levelled curved road of radius $70$ m with angular velocity of $0.2$ rad/s. The centripetal force acting on the vehicle is:
Laws of Motion Circular Motion Centripetal Acceleration
EasySingle correctIdea asked in 4 yearsAsked the year before
Q35
Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the planet. In the…
Gravitation Orbital Mechanics Escape Velocity
EasyTwo statementsIdea asked in 5 yearsAsked the year before
Q36
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius $(5\pm0.1)$ mm having a particular density is falling through a liquid of constant density. The percentage error in…
Mechanical Properties of Fluids Viscosity Terminal Velocity Radius Proportionality
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q37
Two planets A and B of radii R and 1.5 R have densities $\rho$ and $\rho/2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is:
Gravitation
EasySingle correct
Q38
The initial pressure and volume of an ideal gas are $P_0$ and $V_0$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be : (Given $\gamma$ = ratio of specific heats at constant pressure and at constant volume)
Thermodynamics First Law of Thermodynamics Adiabatic P-V Relation
EasySingle correctNew ideaIdea asked in 2 years
Q39
The mean free path of molecules of a certain gas at STP is $1500d$ , where $d$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373K is approximately:
Kinetic Theory Kinetic Theory of Gases Mean Free Path Temperature Dependence
MediumSingle correctNew idea
Q40
A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is:
Oscillations Energy in SHM Kinetic to Potential Energy Ratio
EasySingle correctNew ideaIdea asked in 2 years
Q41
A $10\ \mu$ C charge is divided into two parts and placed at $1$ cm distance so that the repulsive force between them is maximum. The charges of the two parts are:
Electric Charges and Fields Coulomb's Law Maximizing Force via Charge Division
EasySingle correctIdea asked in 2 yearsAsked the year before
Q42
In the network shown below, the charge accumulated in the capacitor in steady state will be:
Current Electricity Kirchhoff's Laws Steady-State Analysis of DC RC Circuits
MediumSingle correct · figureIdea asked in 6 yearsAsked the year before
Q43
An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will experience magnetic force along positive y-axis B. The electron will experience magnetic force along negative…
Moving Charges and Magnetism Lorentz Force Magnetic Force Direction Rules
EasyOtherNew idea
Q44
Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero…
Alternating Current Phasor Diagrams Phase Relations in RLC
MediumTwo statementsIdea asked in 5 yearsAsked the year before
Q45
In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is:
Electromagnetic Waves
EasySingle correct
Q46
In a Young's double slits experiment, the ratio of amplitude of light coming from slits is 2:1. The ratio of the maximum to minimum intensity in the interference pattern is:
Wave Optics Young's Double Slit Resultant Intensity Formula
EasySingle correctIdea asked in 5 yearsAsked the year before
Q47
Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement II : Above the threshold frequency, the maximum…
Dual Nature of Radiation and Matter Photoelectric Effect K_max versus Frequency Graph
EasyTwo statementsNew ideaIdea asked in 2 years
Q48
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170. Reason R :…
Nuclei Nuclear Binding Energy Stability Curve Interpretation
MediumAssertion–reasonNew ideaIdea asked in 2 years
Q49
The output from a NAND gate having inputs A and B given below will be,
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Universal Gates NAND and NOR
MediumDiagram based · figureNew idea
Q50
To radiate EM signal of wavelength $\lambda$ with high efficiency, the antennas should have a minimum size equal to :
Communication Systems
EasySingle correct
Q51
A car accelerates from rest to u m/s. The energy spent in this process is E J. The energy required to accelerate the car from u m/s to 2u m/s is nE J. The value of n is ______ .
Work, Energy and Power Work and Kinetic Energy Kinetic Energy Calculation
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q52
A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be ______ $\mathrm{rad\,s^{-2}}$ .
System of Particles and Rotational Motion Torque and Equilibrium Torque Calculation
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q53
Two plates A and B have thermal conductivities $84\ \mathrm{Wm^{-1}K^{-1}}$ and $126\ \mathrm{Wm^{-1}K^{-1}}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer…
Thermal Properties of Matter Heat Conduction Junction Temperature
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q54
In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is ______ g.
Waves Waves on Strings Sonometer Laws
EasyNumerical valueIdea asked in 4 years
Q55
Three point charges q, $-2q$ and $2q$ are placed on x-axis at a distance $x=0$ , $x=\frac{3}{4}R$ and $x=R$ respectively from origin as shown. If $q=2\times10^{-6}$ C and $R=2$ cm, the magnitude of net force experienced by the charge $-2q$ is ______ N.
Electric Charges and Fields Coulomb's Law Superposition of Forces
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q56
In the circuit shown, the energy stored in the capacitor is $n\ \mu$ J. The value of n is ______.
Current Electricity Wheatstone Bridge DC Bridge with Capacitors
MediumNumerical value · figureNew idea
Q57
A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40$ T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads…
Moving Charges and Magnetism
MediumNumerical value · figure
Q58
An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $24\ \mathrm{cm^2}$ . The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\ \Omega$ . If an externally…
Electromagnetic Induction Faraday's Law Induced Charge Flow
EasyNumerical valueIdea asked in 3 years
Q59
A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ______ D.
Ray Optics and Optical Instruments Lens Maker's Formula Cutting a Thin Lens
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q60
An atom absorbs a photon of wavelength $500$ nm and emits another photon of wavelength $600$ nm. The net energy absorbed by the atom in this process is $n\times10^{-4}$ eV. The value of n is ______. [Assume the atom to be stationary during the absorption and…
Atoms Photoelectric Effect Photon Energy and Momentum
MediumNumerical valueIdea asked in 4 years

Chemistry30 questions

8 easy19 medium3 hard

Q61
Given below are two statements : Statement I : $\mathrm{SO_2}$ and $\mathrm{H_2O}$ both possess V-shaped structure. Statement II : The bond angle of $\mathrm{SO_2}$ is less than that of $\mathrm{H_2O}$ . In the light of the above statements, choose the most…
Chemical Bonding and Molecular Structure VSEPR Theory Bent Geometry (SN=3, 1 LP)
MediumTwo statementsNew idea
Q62
What happens when methane undergoes combustion in systems A and B respectively? System A: Adiabatic system System B: Diathermic container
Thermodynamics (Chemistry)
MediumSingle correct · figure
Q63
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect. Reason R : The…
Solutions Colloids Optical and Kinetic Properties
MediumAssertion–reasonIdea asked in 5 yearsAsked the year before
Q64
The covalency and oxidation state respectively of boron in $[\mathrm{BF_4}]^{-}$ , are
Chemical Bonding and Molecular Structure Redox Reactions Oxidation Number via Coordinate Bonds
MediumSingle correctNew idea
Q65
Given below are two statements related to Ellingham diagram: Statement I : Ellingham diagrams can be constructed for formation of oxides, sulfides and halides of metals. Statement II : It consists of plots of $\Delta_f H^0$ vs T for formation of oxides of…
General Principles and Processes of Isolation of Elements Gibbs Free Energy Ellingham Diagram Basics
MediumTwo statementsNew idea
Q66
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Isotopes of hydrogen have almost same chemical properties, but difference in their rates of reaction. Reason R : Isotopes of hydrogen have…
Hydrogen Hydrogen and Hydrides Kinetic Isotope Effect in Hydrogen
MediumAssertion–reasonIdea asked in 2 years
Q67
Better method for preparation of $\mathrm{BeF_2}$ , among the following is
The s-Block Elements
HardSingle correct
Q68
Identify the correct order of standard enthalpy of formation of sodium halides.
Thermodynamics (Chemistry)
MediumSingle correct
Q69
The correct group of halide ions which can be oxidised by oxygen in acidic medium is
Electrochemistry Group 17 & 18 Reducing Character of Hydrogen Halides
MediumSingle correctNew idea
Q70
Which of the following complexes will exhibit maximum attraction to an applied magnetic field?
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
EasySingle correctIdea asked in 7 yearsAsked the year before
Q71
Which of the following are the Green house gases? A. Water vapour B. Ozone C. $\mathrm{I_2}$ D. Molecular hydrogen Choose the most appropriate answer from the options given below:
Environmental Chemistry Greenhouse Effect
EasyOtherIdea asked in 4 yearsAsked the year before
Q72
The total number of stereoisomers for the complex $[\mathrm{Cr}(ox)_2\mathrm{ClBr}]^{3-}$ (where $ox$ = oxalate) is:
Coordination Compounds Coordination Isomerism Total Isomer Calculation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q73
In the wet tests for detection of various cations by precipitation, $\mathrm{Ba^{2+}}$ cations are detected by obtaining precipitate of
Practical Chemistry (Qualitative Analysis)Cation Analysis Group V Carbonate Precipitation
EasySingle correctNew idea
Q74
Given below are two statements : Statement I : Tropolone is an aromatic compound and has 8 $\pi$ electrons. Statement II : $\pi$ electrons of $>$ C = O group in tropolone is involved in aromaticity. In the light of the above statements, choose the correct…
Organic Chemistry: Some Basic Principles and Techniques Aromatic Hydrocarbons Huckel's Rule (4n+2)
HardTwo statementsIdea asked in 6 yearsAsked the year before
Q75
Match List I with List II 1 - Bromopropane is reacted with reagents in List I to give product in List II LIST I - Reagent | LIST II - Product A. KOH (alc) | I. Nitrile B. KCN (alc) | II. Ester C. $\mathrm{AgNO_2}$ | III. Alkene D. $\mathrm{H_3CCOOAg}$ | IV.…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Ambident Nucleophiles (Cyanide/Nitrite)
MediumMatch the listIdea asked in 3 years
Q76
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Order of acidic nature of the following compounds is A > B > C. [figure: A = cyclohexane ring with OH and an ortho Cl substituent; B =…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
MediumAssertion–reason · figureIdea asked in 3 yearsAsked the year before
Q77
The major product for the following reaction is: $\mathrm{CH_2{=}CH{-}CN}$ + $\mathrm{HO{-}CH_2CH_2{-}SH}$ (arrow)
Aldehydes, Ketones and Carboxylic Acids
MediumSingle correct · figure
Q78
Compound A from the following reaction sequence is: A $\xrightarrow[0-5^\circ\mathrm{C}]{\mathrm{Br_2,\ CS_2}}$ B $\xrightarrow{\mathrm{NaNO_2/HCl}}$ C $\xrightarrow[\Delta]{\mathrm{H_3PO_2}}$ 1,3,5-tribromobenzene
Amines Diazonium Salts Replacement by H or OH
MediumSingle correct · figureIdea asked in 3 years
Q79
The naturally occurring amino acid that contains only one basic functional group in its chemical structure is
Biomolecules
MediumSingle correct
Q80
Match List I with List II LIST I | LIST II A. Weak intermolecular forces of attraction | I. Hexamethylenediamine + adipic acid B. Hydrogen bonding | II. $\mathrm{AlEt_3 + TiCl_4}$ C. Heavily branched polymer | III. 2 - chloro - 1, 3 - butadiene D. High…
Polymers Polymer Classification
MediumMatch the listIdea asked in 3 yearsAsked the year before
Q81
1g of a carbonate ( $\mathrm{M_2CO_3}$ ) on treatment with excess HCl produces 0.01 mol of $\mathrm{CO_2}$ . The molar mass of $\mathrm{M_2CO_3}$ is ______ $\mathrm{g\,mol^{-1}}$ . (Nearest integer)
Some Basic Concepts of Chemistry Stoichiometry Mole-to-Mole Relationships
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q82
Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is ______ $\times10^{-1}$ Å (Nearest integer)
The Solid State Crystal Lattices Edge-Radius Relationships
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q83
The orbital angular momentum of an electron in 3s orbital is $\frac{xh}{2\pi}$ . The value of $x$ is ______ (nearest integer)
Structure of Atom Quantum Numbers Orbital and Spin Angular Momentum
EasyNumerical valueNew ideaIdea asked in 2 years
Q84
Sea water contains 29.25% NaCl and 19% $\mathrm{MgCl_2}$ by weight of solution. The normal boiling point of the sea water is ______ $^\circ$ C (Nearest integer) Assume 100% ionization for both NaCl and $\mathrm{MgCl_2}$ Given :…
Solutions Colligative Properties Boiling Point Elevation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q85
20 mL of 0.1 M NaOH is added to 50 mL of 0.1 M acetic acid solution. The pH of the resulting solution is ______ $\times10^{-2}$ (Nearest integer) Given : $\mathrm{p}K_a(\mathrm{CH_3COOH})=4.76$ $\log 2=0.30$ $\log 3=0.48$
Equilibrium pH and Buffers Buffer Formation via Partial Neutralization
MediumNumerical valueNew idea
Q86
At 298 K, the standard reduction potential for $\mathrm{Cu^{2+}/Cu}$ electrode is 0.34 V. Given : $K_{sp}\ \mathrm{Cu(OH)_2}=1\times10^{-20}$ Take $\frac{2.303RT}{F}=0.059$ V The reduction potential at pH = 14 for the above couple is $(-)x\times10^{-2}$ V.…
Electrochemistry Nernst Equation Nernst Equation and Solubility Product (Ksp)
HardNumerical valueNew idea
Q87
$\mathrm{A(g)\rightarrow 2B(g)+C(g)}$ is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ______ mm Hg. (Nearest integer)
Chemical Kinetics Integrated Rate Equations Gas Kinetics with Complex Stoichiometry
MediumNumerical valueIdea asked in 5 years
Q88
See the following chemical reaction: $\mathrm{Cr_2O_7^{2-}} + X\,\mathrm{H^+} + 6\,\mathrm{Fe^{2+}} \rightarrow Y\,\mathrm{Cr^{3+}} + 6\,\mathrm{Fe^{3+}} + Z\,\mathrm{H_2O}$ The sum of X, Y and Z is ______
Redox Reactions Ion-Electron Acidic
EasyNumerical valueNew ideaIdea asked in 2 years
Q89
If the formula of Borax is $\mathrm{Na_2B_4O_x(OH)_y\cdot zH_2O}$ , then $x+y+z=$ ______
The p-Block Elements Group 13 & 14 Borax and Boric Acid
MediumNumerical valueIdea asked in 2 yearsAsked the year before
Q90
0.400 g of an organic compound (X) gave 0.376 g of AgBr in Carius method for estimation of bromine. % of bromine in the compound (X) is ______ . (Given: Molar mass AgBr = 188 g mol $^{-1}$ Br = 80 g mol $^{-1}$ )
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Gravimetric Precipitation Analysis
EasyNumerical valueIdea asked in 5 yearsAsked the year before

Maths30 questions

4 easy17 medium9 hard

Q1
The range of $f(x)=4\sin^{-1}\left(\frac{x^2}{x^2+1}\right)$ is
Inverse Trigonometric Functions Functions and Domain Range of Inverse Trigonometric Functions
MediumSingle correctNew idea
Q2
Let $S=\{z\in\mathbb{C}: \bar{z}=i(z^2+Re(\bar{z}))\}$ . Then $\sum_{z\in S}|z|^2$ is equal to
Complex Numbers and Quadratic Equations
HardSingle correct
Q3
Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2}x+2=0$ . Then $\alpha^{14}+\beta^{14}$ is equal to
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
If the system of equations $2x+y-z=5$ $2x-5y+\lambda z=\mu$ $x+2y-5z=7$ has infinitely many solutions, then $(\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q5
Let for $A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}$ , $|A|=2$ . If $|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n$ , then $3n+\alpha$ is equal to
Determinants Matrix Inverse Trap involving |adj(A)| vs |A^-1|
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q6
All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is
Permutations and Combinations Lexicographic Rank of a Word
EasySingle correctIdea asked in 4 yearsAsked the year before
Q7
The coefficient of $x^5$ in the expansion of $\left(2x^3-\frac{1}{3x^2}\right)^5$ is
Binomial Theorem
EasySingle correct
Q8
Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the product of its $3^{rd}$ and $5^{th}$ terms be $\frac{1}{9}$ . Then $6(a_2+a_4)(a_4+a_6)$ is equal to
Sequences and Series AP and GP GP General Term
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q9
If $\lim_{x\to0}\dfrac{e^{ax}-\cos(bx)-\dfrac{cxe^{-cx}}{2}}{1-\cos(2x)}=17$ , then $5a^2+b^2$ is equal to
Limits and Derivatives L'Hopital's Rule Choosing Series Expansion over L'Hopital
HardSingle correctIdea asked in 7 yearsAsked the year before
Q10
The value of $\dfrac{e^{-\frac{\pi}{4}}+\int_0^{\frac{\pi}{4}}e^{-x}\tan^{50}x\,dx}{\int_0^{\frac{\pi}{4}}e^{-x}\left(\tan^{49}x+\tan^{51}x\right)dx}$ is
Integrals Definite Integral Properties Reduction Formulae in Definite Integrals
HardSingle correctIdea asked in 4 yearsAsked the year before
Q11
The area of the region $\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\}$ is
Application of Integrals Area Under Curves Area of Inequalities
HardSingle correctIdea asked in 8 yearsAsked the year before
Q12
Let $(\alpha,\beta)$ be the centroid of the triangle formed by the lines $15x-y=82$ , $6x-5y=-4$ and $9x+4y=17$ . Then $\alpha+2\beta$ and $2\alpha-\beta$ are the roots of the equation
Straight Lines
MediumSingle correct
Q13
Let the centre of a circle C be $(\alpha,\beta)$ and its radius $r<8$ . Let $3x+4y=24$ and $3x-4y=32$ be two tangents and $4x+3y=1$ be a normal to C. Then $(\alpha-\beta+r)$ is equal to
Conic Sections Circle Tangents Normal Passes Through Center
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q14
The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$ , also passes through the point
Three Dimensional Geometry Planes in 3D Plane Through Two Points Parallel to a Vector
MediumSingle correctIdea asked in 2 years
Q15
The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$ , is
Three Dimensional Geometry Skew Lines Coplanarity Determinant Test
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q16
Let N be the foot of perpendicular from the point P $(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$ . Then the distance of N from the plane $2x-2y+z+5=0$ is
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
Let $|\vec{a}|=2$ , $|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$ . Then $\left|(\vec{a}+2\vec{b})\times(2\vec{a}-3\vec{b})\right|^2$ is equal to
Vector Algebra Cross Product Anti-commutativity and Distributivity
MediumSingle correctNew idea
Q18
Let for a triangle ABC, $\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}$ $\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ $\overrightarrow{CA}=4\hat{i}+3\hat{j}+\delta\hat{k}$ If $\delta>0$ and the area of the triangle ABC is $5\sqrt{6}$ , then…
Vector Algebra Cross Product Area of Triangles and Parallelograms
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
The random variable X follows binomial distribution B $(n, p)$ , for which the difference of the mean and the variance is $1$ . If $2P(X=2)=3P(X=1)$ , then $n^2P(X>1)$ is equal to
Probability
MediumSingle correct
Q20
The statement $(p\wedge(\sim q))\vee((\sim p)\wedge q)\vee((\sim p)\wedge(\sim q))$ is equivalent to ______
Mathematical Reasoning
EasySingle correct
Q21
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b)\in A\times A: b=|a| \text{ or } b^2=a+1\}$ be a relation on A. Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is ______
Relations and Functions Sets and Relations Counting Reflexive and Symmetric Relations
MediumNumerical valueNew ideaIdea asked in 2 years
Q22
Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______
Permutations and Combinations Fundamental Counting Principle
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q23
The remainder, when $7^{103}$ is divided by 17, is ______
Binomial Theorem
MediumNumerical value
Q24
Let $[\alpha]$ denote the greatest integer $\le\alpha$ . Then $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}]$ is equal to ______
Relations and Functions
MediumNumerical value
Q25
Let $f(x)=\sum_{k=1}^{10}k\,x^k$ , $x\in\mathbb{R}$ . If $2f(2)+f'(2)=119(2)^n+1$ then $n$ is equal to ______
Limits and Derivatives Arithmetico-Geometric Series Derivative Method for AGP Sums
HardNumerical valueNew idea
Q26
Let $f_n=\int_0^{\frac{\pi}{2}}\left(\sum_{k=1}^{n}\sin^{k-1}x\right)\left(\sum_{k=1}^{n}(2k-1)\sin^{k-1}x\right)\cos x\,dx$ , $n\in\mathbb{N}$ . Then $f_{21}-f_{20}$ is equal to ______
Integrals Integration by Substitution Odd Power of Cosine Substitution
HardNumerical valueNew idea
Q27
If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}$ , $x>1$ such that $y(2)=\frac{2}{9}\log_e\left(2+\sqrt{3}\right)$ and…
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q28
The foci of a hyperbola are $(\pm2,0)$ and its eccentricity is $\frac{3}{2}$ . A tangent, perpendicular to the line $2x+3y=6$ , is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are $a$ and…
Conic Sections
HardNumerical value
Q29
The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is ______.
Statistics Variance and SD Correcting Incorrect Variance
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q30
For $x\in(-1,1]$ , the number of solutions of the equation $\sin^{-1}x=2\tan^{-1}x$ is equal to ______.
Inverse Trigonometric Functions Inverse Trig Identities Graphical Root Counting for Mixed Equations
HardNumerical 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.