JEE Main 2024 · April session

JEE Main 5 April 2024, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 9 were rated hard and 33 easy. Its hard-question count was the joint 12th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Aldehydes, Ketones and Carboxylic Acids, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 9; 10% of the shift
Chapters asked: 59; 12 questions with a figure

Key findings · 5 Apr 2024, Shift 2

1
9 hard questions (10%): the joint 12th 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 8 of 30 rated hard; Physics had the most easy questions (20 of 30).
3
18 questions tested a new idea, one no earlier year had asked: 23% of the 78 questions tagged to an idea.
4
34 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
42 shared an idea with another 2024 shift (54% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Moving Charges and Magnetism in Physics (3), Aldehydes, Ketones and Carboxylic Acids in Chemistry (3) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 20Medium 10Hard 0

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 17Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 21Hard 8

Top chapters

Conic Sections3 Q
Complex Numbers and Quadratic Equations2 Q
Continuity and Differentiability2 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q

Question format

Single correct48 Q
Numerical value30 Q
Match the list4 Q
Diagram based4 Q
Two statements3 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step29 Q
Calculation25 Q
Conceptual13 Q
Application12 Q
Recall10 Q
Data or graph1 Q

Most common: Multi-step.

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

20 easy10 medium0 hard

Q31
What is the dimensional formula of $ab^{-1}$ in the equation $\left(P+\frac{a}{V^2}\right)(V-b)=RT$ , where letters have their usual meaning.
Units and Measurements Real Gases Units of VdW Constants
MediumSingle correctIdea asked in 2 years
Q32
A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in m/s $^2$ ) :
Motion in a Plane Circular Motion Centripetal Acceleration
EasySingle correctIdea asked in 4 yearsAsked the year before
Q33
A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :
Laws of Motion Friction Kinetic Friction Calculation
EasySingle correctNew idea
Q34
A particle moves in $x$ - $y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p}(t)=\hat{i}\cos(kt)-\hat{j}\sin(kt)$ . If k is constant, the angle between $\vec{F}$ and $\vec{P}$ will be :
Laws of Motion Newton's Laws of Motion Momentum Formulation (F = dp/dt)
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q35
A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :
Work, Energy and Power Power Kinematics of Constant Power
MediumSingle correctIdea asked in 3 years
Q36
A vernier callipers has 20 divisions on the vernier scale, which coincides with 19 $^{th}$ division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ________ mm.
Units and Measurements
EasySingle correct
Q37
A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given = Radius of geo-stationary orbit for earth is $4.2\times10^4$ km)
Gravitation Orbital Mechanics Geostationary Satellites
MediumSingle correctIdea asked in 2 years
Q38
Match List-I with List-II : List-I List-II (A) A force that restores an elastic body of unit area to its original state (I) Bulk modulus (B) Two equal and opposite forces parallel to opposite faces (II) Young's modulus (C) Forces perpendicular everywhere to…
Mechanical Properties of Solids Elasticity Stress and Strain Types
EasyMatch the listIdea asked in 4 yearsAsked the year before
Q39
If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :
Kinetic Theory Kinetic Theory of Gases Mean Free Path
EasySingle correctIdea asked in 4 years
Q40
The vehicles carrying inflammable fluids usually have metallic chains touching the ground :
Electrostatic Potential and Capacitance Conductors in Fields Earthing of Conductors
EasySingle correctNew idea
Q41
A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L=10 mH) is 31.4 V, then the current in this circuit is ________.
Alternating Current Phasor Diagrams Voltage Phasor Resolution
EasySingle correctNew idea
Q42
The ratio of heat dissipated per second through the resistance $5\ \Omega$ and $10\ \Omega$ in the circuit given below is :
Current Electricity Ohm's Law and Resistance Power Dissipation Ratios in Series vs Parallel
EasySingle correct · figureIdea asked in 5 yearsAsked the year before
Q43
The electrostatic force $\left(\vec{F_1}\right)$ and magnetic force $\left(\vec{F_2}\right)$ acting on a charge q moving with velocity $v$ can be written :
Moving Charges and Magnetism Lorentz Force Lorentz Force Vector Summation
EasySingle correctIdea asked in 3 years
Q44
Match List-I with List-II : List-I (EM-Wave) List-II (Wavelength Range) (A) Infra-red (I) $<10^{-3}$ nm (B) Ultraviolet (II) 400 nm to 1 nm (C) X-rays (III) 1 mm to 700 nm (D) Gamma rays (IV) 1 nm to $10^{-3}$ nm Choose the correct answer from the options…
Electromagnetic Waves
EasyMatch the list
Q45
Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of…
Ray Optics and Optical Instruments Prism Deviation Angular Dispersion
EasyTwo statementsNew idea
Q46
A galvanometer of resistance $100\ \Omega$ when connected in series with $400\ \Omega$ measures a voltage of upto 10 V. The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $x\times10^{-2}\ \Omega$ . The value of $x$ …
Moving Charges and Magnetism Wheatstone Bridge Shunting Galvanometer for Protection
MediumSingle correctNew ideaIdea asked in 2 years
Q47
Which of the following statement is not true about stopping potential ( $V_0$ ) ?
Dual Nature of Radiation and Matter Photoelectric Effect Stopping Potential
EasySingle correctIdea asked in 2 years
Q48
The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron)
Atoms Bohr's Atomic Model Angular Momentum Quantization
EasySingle correctIdea asked in 5 yearsAsked the year before
Q49
During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_P}{C_V}$ for the gas is :
Thermodynamics Thermodynamic Processes Adiabatic T-V and P-T Relations
MediumSingle correctIdea asked in 4 years
Q50
The output (Y) of logic circuit given below is 0 only when :
Semiconductor Electronics: Materials, Devices and Simple Circuits Logic Gates Combinational Logic Circuits
EasySingle correct · figureIdea asked in 7 yearsAsked the year before
Q51
The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ________ m.
Motion in a Plane Projectile Motion Angle of Elevation of Maximum Height
EasyNumerical valueNew idea
Q52
A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ________.
System of Particles and Rotational Motion
MediumNumerical value
Q53
In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be…
Wave Optics Single Slit Diffraction Single Slit Minima Condition
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q54
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain…
Mechanical Properties of Fluids Fluid Statics Pascal's Law
EasyNumerical value · figureIdea asked in 3 yearsAsked the year before
Q55
A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ________ cm.
Waves Waves on Strings Sonometer Laws
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q56
A wire of resistance $20\ \Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final…
Current Electricity Ohm's Law and Resistance Resistance of Cut and Recombined Uniform Wires
MediumNumerical valueIdea asked in 2 years
Q57
A solenoid of length 0.5 m has a radius of 1 cm and is made up of 'm' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28\times10^{-3}$ T then the value of m is ________.
Moving Charges and Magnetism Ampere's Circuital Law Ideal Infinite Solenoid
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q58
The electric field at point p due to an electric dipole is E. The electric field at point R on equatorial line will be $\frac{E}{x}$ . The value of $x$ :
Electric Charges and Fields Electric Dipoles Electric Field on Equatorial Line
MediumNumerical value · figureIdea asked in 3 yearsAsked the year before
Q59
The current in an inductor is given by $I=(3t+8)$ where t is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH.
Electromagnetic Induction Inductance Self-Inductance and Back EMF
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q60
The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915 $\mathrm{\AA}$ . The longest wavelength of spectral lines in the Balmer series will be ________ $\mathrm{\AA}$ .
Atoms Bohr's Atomic Model Shortest and Longest Wavelengths
MediumNumerical valueIdea asked in 5 yearsAsked the year before

Chemistry30 questions

12 easy17 medium1 hard

Q61
The number of moles of methane required to produce 11 g $\mathrm{CO_2(g)}$ after complete combustion is : (Given molar mass of methane in $\mathrm{g\ mol^{-1}}$ : 16)
Some Basic Concepts of Chemistry Stoichiometry Mole-to-Mole Relationships
EasySingle correctIdea asked in 3 yearsAsked the year before
Q62
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $\mathrm{NH_3}$ and $\mathrm{NF_3}$ molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole…
Chemical Bonding and Molecular Structure VSEPR Theory Net Dipole Moment from VSEPR Symmetry
MediumAssertion–reasonIdea asked in 4 yearsAsked the year before
Q63
Given below are two statements : Statement I : On passing $\mathrm{HCl_{(g)}}$ through a saturated solution of $\mathrm{BaCl_2}$ , at room temperature white turbidity appears. Statement II : When HCl gas is passed through a saturated solution of NaCl, sodium…
Equilibrium Solubility Product Common Ion Effect
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q64
For the electro chemical cell $\mathrm{M|M^{2+}||X|X^{2-}}$ If $\mathrm{E^0_{(M^{2+}/M)}} = 0.46\ \mathrm{V}$ and $\mathrm{E^0_{(X/X^{2-})}} = 0.34\ \mathrm{V}$ . Which of the following is correct ?
Electrochemistry Nernst Equation Standard Cell Potential
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q65
The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO_3}$ solution :
Electrochemistry Faraday's Laws of Electrolysis Electrochemical Equivalent (Z) Calculation
EasySingle correctNew idea
Q66
Given below are two statements : Statement I : The metallic radius of Na is $1.86\ \mathrm{A^\circ}$ and the ionic radius of $\mathrm{Na^+}$ is lesser than $1.86\ \mathrm{A^\circ}$ . Statement II : Ions are always smaller in size than the corresponding…
Classification of Elements and Periodicity in Properties Periodic Trends Atomic and Ionic Radii Trends
EasyTwo statementsIdea asked in 3 years
Q67
Match List - I with List - II. List - I List - II (A) ICl (I) T - shape (B) $\mathrm{ICl_3}$ (II) Square pyramidal (C) $\mathrm{ClF_5}$ (III) Pentagonal bipyramidal (D) $\mathrm{IF_7}$ (IV) Linear Choose the correct answer from the options given below :
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number 5 Derivative Shapes
MediumMatch the listIdea asked in 3 years
Q68
The correct statements from the following are : (A) The decreasing order of atomic radii of group 13 elements is Tl > In > Ga > Al > B. (B) Down the group 13 electronegativity decreases from top to bottom. (C) Al dissolves in dil. HCl and liberates…
The p-Block Elements Group 13 & 14 Group 13 Ionization Energy Trend
MediumSingle correctNew ideaIdea asked in 3 years
Q69
The number of ions from the following that have the ability to liberate hydrogen from a dilute acid is ________. $\mathrm{Ti^{2+}}$ , $\mathrm{Cr^{2+}}$ and $\mathrm{V^{2+}}$
The d- and f-Block Elements
MediumSingle correct
Q70
The metal atom present in the complex MABXL (where A, B, X and L are unidentate ligands and M is metal) involves $\mathrm{sp^3}$ hybridization. The number of geometrical isomers exhibited by the complex is :
Coordination Compounds Coordination Isomerism Optical Isomerism in Tetrahedral Complexes
EasySingle correctNew idea
Q71
The number of complexes from the following with no electrons in the $\mathrm{t_2}$ orbital is ________. $\mathrm{TiCl_4}$ , $\mathrm{[MnO_4]^-}$ , $\mathrm{[FeO_4]^{2-}}$ , $\mathrm{[FeCl_4]^-}$ , $\mathrm{[CoCl_4]^{2-}}$
Coordination Compounds Crystal Field Theory Tetrahedral Field Splitting and Delta_t Relation
MediumSingle correctNew ideaIdea asked in 2 years
Q72
While preparing crystals of Mohr's salt, dil $\mathrm{H_2SO_4}$ is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil $\mathrm{H_2SO_4}$ is added here to :
Equilibrium
EasySingle correct
Q73
The correct nomenclature for the following compound is :
Organic Chemistry: Some Basic Principles and Techniques IUPAC Nomenclature Functional Group Priority
MediumDiagram based · figureIdea asked in 6 yearsAsked the year before
Q74
Match List - I with List - II. List - I (Pair of Compounds) List - II (Isomerism) (A) n-propanol and Isopropanol (I) Metamerism (B) Methoxypropane and ethoxyethane (II) Chain Isomerism (C) Propanone and propanal (III) Position Isomerism (D) Neopentane and…
Organic Chemistry: Some Basic Principles and Techniques Structural Isomerism Position Isomerism
EasyMatch the listNew idea
Q75
Identify A and B in the given chemical reaction sequence : Benzene + succinic anhydride (cyclic five-membered anhydride) $\xrightarrow{\mathrm{AlCl_3}}$ A $\xrightarrow[\mathrm{HCl}]{\mathrm{Zn-Hg}}$ B $\xrightarrow{\mathrm{H^+}}$ [benzene ring fused to a…
Hydrocarbons Aromatic Hydrocarbons Friedel-Crafts Acylation and Acylium Ion
MediumDiagram based · figureIdea asked in 2 years
Q76
Which one of the following reactions is NOT possible ?
Alcohols, Phenols and Ethers Alcohols and Phenols Dow Process for Phenol
MediumDiagram based · figureIdea asked in 2 years
Q77
Identify the major product in the following reaction. 1-bromo-1-methylcyclopentane $\xrightarrow[\mathrm{C_2H_5OH}]{\bar{\mathrm{O}}\mathrm{H}}$ Major Product
Haloalkanes and Haloarenes Alkenes and Alkynes Saytzeff vs. Hofmann Elimination
EasyDiagram based · figureIdea asked in 6 years
Q78
$\mathrm{CH_3CH_2-OH}$ $\xrightarrow[\text{(iii) NaOH, CaO, }\Delta]{\text{(i) Jone's Reagent, (ii) }\mathrm{KMnO_4}}$ P Consider the above reaction sequence and identify the major product P.
Aldehydes, Ketones and Carboxylic Acids Alkanes and Free Radicals Soda-Lime Decarboxylation of Carboxylic Acids
MediumSingle correctNew idea
Q79
Consider the given chemical reaction : cyclohexene $\xrightarrow[\text{Heat}]{\mathrm{KMnO_4-H_2SO_4}}$ Product "A" Product "A" is :
Hydrocarbons Alkenes and Alkynes Hot KMnO4 Oxidative Cleavage
EasySingle correct · figureNew idea
Q80
Coagulation of egg, on heating is because of :
Biomolecules
EasySingle correct
Q81
In an atom, total number of electrons having quantum numbers $n=4$ , $|m_l|=1$ and $m_s=-\frac{1}{2}$ is ________.
Structure of Atom Quantum Numbers Magnetic Quantum Number
MediumNumerical valueIdea asked in 4 years
Q82
Number of compounds from the following with zero dipole moment is ________. $\mathrm{HF}$ , $\mathrm{H_2}$ , $\mathrm{H_2S}$ , $\mathrm{CO_2}$ , $\mathrm{NH_3}$ , $\mathrm{BF_3}$ , $\mathrm{CH_4}$ , $\mathrm{CHCl_3}$ , $\mathrm{SiF_4}$ , $\mathrm{H_2O}$ ,…
Chemical Bonding and Molecular Structure VSEPR Theory Net Dipole Moment from VSEPR Symmetry
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q83
Combustion of 1 mole of benzene is expressed at $\mathrm{C_6H_6(l) + \frac{15}{2}\,O_2(g) \rightarrow 6\,CO_2(g) + 3\,H_2O(l)}$ . The standard enthalpy of combustion of 2 mol of benzene is $-$ ' $x$ ' kJ. $x=$ ________. Given : 1. standard Enthalpy of formation…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Formation and Combustion
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q84
Considering acetic acid dissociates in water, its dissociation constant is $6.25\times10^{-5}$ . If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at $-x\times10^{-2}\ ^\circ\mathrm{C}$ , provided pure water freezes at…
Solutions Colligative Properties Freezing Point Depression
HardNumerical valueIdea asked in 4 years
Q85
Consider the following single step reaction in gas phase at constant temperature. $\mathrm{2A_{(g)} + B_{(g)} \rightarrow C_{(g)}}$ The initial rate of the reaction is recorded as $\mathrm{r_1}$ when the reaction starts with 1.5 atm pressure of A and 0.7 atm…
Chemical Kinetics Rate Laws Rate and Stoichiometry
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q86
The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products A and B along with the evolution of $\mathrm{CO_2}$ . The sum of spin-only magnetic moment values of A and B is ________ B.M. (Nearest integer) [Given…
The d- and f-Block Elements d-Block Elements Preparation Steps of Potassium Dichromate
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q87
In the Claisen-Schmidt reaction to prepare 351 g of dibenzalacetone using 87 g of acetone, the amount of benzaldehyde required is ________ g. (Nearest integer)
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Claisen-Schmidt Condensation
MediumNumerical valueNew idea
Q88
Using the given figure, the ratio of $\mathrm{R_f}$ values of sample A and sample C is $x\times10^{-2}$ . Value of $x$ is ________.
Organic Chemistry: Some Basic Principles and Techniques
EasyNumerical value · figure
Q89
The product (C) in the following sequence of reactions has ________ $\pi$ bonds. n-propylbenzene (benzene ring bearing a three-carbon chain) $\xrightarrow[\Delta]{\mathrm{KMnO_4-KOH}}$ (A) $\xrightarrow{\mathrm{H_3O^+}}$ (B)…
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Side-chain Oxidation
MediumNumerical value · figureIdea asked in 5 yearsAsked the year before
Q90
X g of ethanamine was subjected to reaction with $\mathrm{NaNO_2/HCl}$ followed by hydrolysis to liberate $\mathrm{N_2}$ and HCl. The HCl generated was completely neutralised by 0.2 moles of NaOH. X is ________ g.
Amines Reaction of Primary Aliphatic Amines with HNO2
EasyNumerical valueIdea asked in 2 years

Maths30 questions

1 easy21 medium8 hard

Q1
Let the set $S=\{2, 4, 8, 16, \ldots, 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$ . The maximum number of such possible partitions of $S$ is equal to :
Permutations and Combinations Division of Objects into Groups
MediumSingle correctIdea asked in 3 years
Q2
Let $f, g : \mathbf{R} \to \mathbf{R}$ be defined as : $f(x) = |x-1|$ and $g(x) = \begin{cases} e^x, & x \geq 0 \\ x+1, & x \leq 0. \end{cases}$ Then the function $f(g(x))$ is
Relations and Functions
MediumSingle correct
Q3
Let $S_1 = \{z \in C : |z| \leq 5\}$ , $S_2 = \left\{z \in C : \mathrm{Im}\left(\frac{z+1-\sqrt{3}i}{1-\sqrt{3}i}\right) \geq 0\right\}$ and $S_3 = \{z \in C : \mathrm{Re}(z) \geq 0\}$ . Then the area of the region $S_1 \cap S_2 \cap S_3$ is :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Locus of Argument (Ray)
HardSingle correctNew idea
Q4
The values of $m, n$ , for which the system of equations $x+y+z=4$ , $2x+5y+5z=17$ , $x+2y+mz=n$ has infinitely many solutions, satisfy the equation :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q5
Let $\alpha\beta \neq 0$ and $A = \begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{bmatrix}$ . If $B = \begin{bmatrix} 3\alpha & -9 & 3\alpha \\ -\alpha & 7 & -2\alpha \\ -2\alpha & 5 & -2\beta \end{bmatrix}$ is…
Determinants Matrix Inverse Cofactor Matrix and Adjoint
MediumSingle correctIdea asked in 5 years
Q6
60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50^{\text{th}}$ word is :
Permutations and Combinations Lexicographic Rank of a Word
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q7
The coefficients $a, b, c$ in the quadratic equation $ax^2+bx+c=0$ are from the set $\{1, 2, 3, 4, 5, 6\}$ . If the probability of this equation having one real root bigger than the other is $p$ , then $216p$ equals :
Probability
MediumSingle correct
Q8
For $x \geq 0$ , the least value of $K$ , for which $4^{1+x}+4^{1-x}$ , $\frac{K}{2}$ , $16^x+16^{-x}$ are three consecutive terms of an A.P., is equal to :
Sequences and Series AP and GP AM-GM Inequality Application
MediumSingle correctIdea asked in 2 years
Q9
If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2x}{\sqrt[3]{5}}\right)^{12}$ , $x \neq 0$ , is $\alpha \times 2^8 \times \sqrt[5]{3}$ , then $25\alpha$ is equal to :
Binomial Theorem
MediumSingle correct
Q10
Let $f : [-1, 2] \to \mathbf{R}$ be given by $f(x) = 2x^2 + x + [x^2] - [x]$ , where $[t]$ denotes the greatest integer less than or equal to $t$ . The number of points, where $f$ is not continuous, is :
Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q11
Let $\beta(m, n) = \int_0^1 x^{m-1}(1-x)^{n-1}\,dx$ , $m, n > 0$ . If $\int_0^1 (1-x^{10})^{20}\,dx = a \times \beta(b, c)$ , then $100(a+b+c)$ equals ________.
Integrals Definite Integral Properties Beta Function Integrals
MediumSingle correctIdea asked in 2 years
Q12
The area enclosed between the curves $y = x|x|$ and $y = x - |x|$ is :
Application of Integrals Area Under Curves Area with Modulus
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q13
The differential equation of the family of circles passing through the origin and having centre at the line $y=x$ is :
Differential Equations
MediumSingle correct
Q14
Let $ABCD$ and $AEFG$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on the diagonal $AC$ . Then the radius $r$ of the circle passing through the point $F$ and touching the line segments $BC$ and…
Straight Lines Circle Tangents Condition of tangency
MediumSingle correctIdea asked in 4 years
Q15
Let the circle $C_1 : x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1, 0)$ and radius 2. If the line of the common chord of $C_1$ and $C_2$ intersects the $y$ -axis at the point $P$ , then the square of the distance of $P$ from the centre of…
Conic Sections Power of a Point Radical axis of two circles
EasySingle correctIdea asked in 3 yearsAsked the year before
Q16
Let $A(-1, 1)$ and $B(2, 3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $\Delta PAB$ is 10. If the locus of $P$ is $ax+by=15$ , then $5a+2b$ is :
Straight Lines Straight Line Distance Locus of Points at a Fixed Distance
MediumSingle correctIdea asked in 2 years
Q17
Let $(\alpha, \beta, \gamma)$ be the image of the point $(8, 5, 7)$ in the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}$ . Then $\alpha+\beta+\gamma$ is equal to :
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
MediumSingle correctIdea asked in 6 years
Q18
Let $\vec{a} = 2\hat{i}+5\hat{j}-\hat{k}$ , $\vec{b} = 2\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{c}$ be three vectors such that $(\vec{c}+\hat{i}) \times (\vec{a}+\vec{b}+\hat{i}) = \vec{a} \times (\vec{c}+\hat{i})$ . If $\vec{a}\cdot\vec{c} = -29$ , then…
Vector Algebra Cross Product Solving Vector Equations with Cross Products
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
Consider three vectors $\vec{a}, \vec{b}, \vec{c}$ . Let $|\vec{a}| = 2$ , $|\vec{b}| = 3$ and $\vec{a} = \vec{b} \times \vec{c}$ . If $\alpha \in \left[0, \frac{\pi}{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$ , then the minimum value of…
Vector Algebra Cross Product Magnitude and Sine Formula
HardSingle correctIdea asked in 7 yearsAsked the year before
Q20
If $y(\theta) = \frac{2\cos\theta + \cos 2\theta}{\cos 3\theta + 4\cos 2\theta + 5\cos\theta + 2}$ , then at $\theta = \frac{\pi}{2}$ , $y'' + y' + y$ is equal to :
Continuity and Differentiability Chain Rule Second Derivative of Composite Functions
HardSingle correctIdea asked in 2 yearsAsked the year before
Q21
The number of solutions of $\sin^2 x + (2+2x-x^2)\sin x - 3(x-1)^2 = 0$ , where $-\pi \leq x \leq \pi$ , is ________.
Trigonometric Functions General Solutions Graphical Root Counting for Mixed Equations
HardNumerical valueIdea asked in 4 years
Q22
If $1 + \frac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}} + \frac{5-2\sqrt{6}}{18} + \frac{9\sqrt{3}-11\sqrt{2}}{36\sqrt{3}} + \frac{49-20\sqrt{6}}{180} + \ldots$ upto $\propto = 2 + \left(\sqrt{\frac{b}{a}}+1\right)\log_e\left(\frac{a}{b}\right)$ , where $a$ and $b$ are…
Sequences and Series
HardNumerical value
Q23
Let $a > 0$ be a root of the equation $2x^2+x-2=0$ . If $\lim_{x \to \frac{1}{a}} \frac{16\left(1-\cos(2+x-2x^2)\right)}{(1-ax)^2} = \alpha + \beta\sqrt{17}$ , where $\alpha, \beta \in Z$ , then $\alpha+\beta$ is equal to ________.
Limits and Derivatives L'Hopital's Rule Simplifying with Standard Limits Before L'Hopital
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q24
Let the maximum and minimum values of $\left(\sqrt{8x-x^2-12}-4\right)^2 + (x-7)^2$ , $x \in R$ be $M$ and $m$ , respectively. Then $M^2-m^2$ is equal to ________.
Conic Sections Circle Tangents Maximum and Minimum Distance to a Circle
HardNumerical valueIdea asked in 2 years
Q25
If $f(t) = \int_0^{\pi} \frac{2x\,dx}{1-\cos^2 t \sin^2 x}$ , $0 < t < \pi$ , then the value of $\int_0^{\frac{\pi}{2}} \frac{\pi^2\,dt}{f(t)}$ equals ________.
Integrals Definite Integral Properties King's Property
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q26
Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + \frac{2x}{(1+x^2)^2}\,y = x e^{\frac{1}{(1+x^2)}}$ ; $y(0) = 0$ . Then the area enclosed by the curve $f(x) = y(x)\,e^{-\frac{1}{(1+x^2)}}$ and the line $y-x=4$ is ________.
Differential Equations Linear Differential Equations General Solution Formula
MediumNumerical valueIdea asked in 3 years
Q27
Let a line perpendicular to the line $2x-y=10$ touch the parabola $y^2=4(x-9)$ at the point $P$ . The distance of the point $P$ from the centre of the circle $x^2+y^2-14x-8y+56=0$ is ________.
Conic Sections Tangents and Normals Point of Tangency from Given Slope
MediumNumerical valueNew idea
Q28
Let the point $(-1, \alpha, \beta)$ lie on the line of the shortest distance between the lines $\frac{x+2}{-3} = \frac{y-2}{4} = \frac{z-5}{2}$ and $\frac{x+2}{-1} = \frac{y+6}{2} = \frac{z-1}{0}$ . Then $(\alpha-\beta)^2$ is equal to ________.
Three Dimensional Geometry Lines in 3D Equation of Line of Shortest Distance
MediumNumerical valueNew idea
Q29
Let the mean and the standard deviation of the probability distribution | X | $\alpha$ | 1 | 0 | $-3$ | |---|---|---|---|---| | P(X) | $\frac{1}{3}$ | $K$ | $\frac{1}{6}$ | $\frac{1}{4}$ | be $\mu$ and $\sigma$ , respectively. If $\sigma-\mu=2$ , then…
Probability Variance and SD Variance Formula Calculation
MediumNumerical value · figureNew idea
Q30
The number of real solutions of the equation $x|x+5| + 2|x+7| - 2 = 0$ is ________.
Complex Numbers and Quadratic Equations Curve Sketching Graphical Root Counting
MediumNumerical valueIdea asked in 2 yearsAsked the year before

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.