JEE Main 2024 · April session

JEE Main 9 April 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 28 easy. Its hard-question count was the joint 8th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Organic Chemistry: Some Basic Principles and Techniques, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 10; 11% of the shift
Chapters asked: 56; 14 questions with a figure

Key findings · 9 Apr 2024, Shift 1

1
10 hard questions (11%): the joint 8th highest count of the 18 2024 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 6 of 30 rated hard; Chemistry had the most easy questions (13 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
30 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
40 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: Alternating Current in Physics (2), Organic Chemistry: Some Basic Principles and Techniques in Chemistry (4) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 12Medium 15Hard 3

Top chapters

Chemistry

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 3Medium 21Hard 6

Top chapters

Conic Sections3 Q
Application of Derivatives2 Q
Binomial Theorem2 Q
Complex Numbers and Quadratic Equations2 Q
Determinants2 Q
Differential Equations2 Q

Question format

Single correct53 Q
Numerical value30 Q
Two statements3 Q
Assertion–reason3 Q
Other1 Q

What each question asks you to do

Multi-step45 Q
Calculation16 Q
Conceptual10 Q
Recall9 Q
Application9 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

12 easy15 medium3 hard

Q31
The dimensional formula of latent heat is :
Units and Measurements
EasySingle correct
Q32
A particle moving in a straight line covers half the distance with speed $6$ m/s. The other half is covered in two equal time intervals with speeds $9$ m/s and $15$ m/s respectively. The average speed of the particle during the motion is :
Motion in a Straight Line Kinematics in 1D Average Speed Special Cases
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q33
A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is :
System of Particles and Rotational Motion Torque and Equilibrium Rotational Equilibrium
EasySingle correctIdea asked in 2 years
Q34
A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m_2}{m_1}$ is :
Laws of Motion Newton's Laws of Motion Standard Atwood Machine
EasySingle correctIdea asked in 3 years
Q35
A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v=\alpha\sqrt{x}$ , where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from…
Work, Energy and Power Work and Kinetic Energy Work-Energy Theorem
EasySingle correctIdea asked in 6 yearsAsked the year before
Q36
An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5$ km. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x\frac{GM_em}{21R_e}$ . The…
Gravitation Orbital Mechanics Energy of Orbiting Bodies
MediumSingle correctIdea asked in 3 years
Q37
A sphere of relative density $\sigma$ and diameter D has concentric cavity of diameter d. The ratio of $\frac{D}{d}$ , if it just floats on water in a tank is :
Mechanical Properties of Fluids Fluid Statics Law of Floatation
MediumSingle correctIdea asked in 3 years
Q38
A sample of $1$ mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma=\frac{3}{2}$ , then the work done by the gas in the process is :
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q39
The volume of an ideal gas ( $\gamma=1.5$ ) is changed adiabatically from $5$ litres to $4$ litres. The ratio of initial pressure to final pressure is :
Thermodynamics Thermodynamic Processes Adiabatic Process Analysis
EasySingle correctIdea asked in 7 yearsAsked the year before
Q40
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is :
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
MediumSingle correct · figureIdea asked in 6 yearsAsked the year before
Q41
The equivalent resistance between A and B is :
Current Electricity Kirchhoff's Laws Identifying False Junctions
MediumSingle correct · figureIdea asked in 2 years
Q42
Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's…
Electromagnetic Waves
HardTwo statements
Q43
A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :
Alternating Current Phasor Diagrams Impedance Triangle Construction
MediumSingle correctIdea asked in 4 years
Q44
A plane EM wave is propagating along $x$ direction. It has a wavelength of $4$ mm. If electric field is in $y$ direction with the maximum magnitude of $60\ \mathrm{Vm^{-1}}$ , the equation for magnetic field is :
Electromagnetic Waves
MediumSingle correct
Q45
Given below are two statements : Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side. Statement (II) : Concave lens always forms a virtual and erect…
Ray Optics and Optical Instruments Lens Maker's Formula Thin Lens Formula
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q46
A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :
Dual Nature of Radiation and Matter Matter Waves Wavelength from Kinetic Energy
EasySingle correctIdea asked in 4 yearsAsked the year before
Q47
The energy equivalent of $1$ g of substance is :
Nuclei Nuclear Binding Energy Total Binding Energy
EasySingle correctIdea asked in 2 years
Q48
A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $1.42$ eV. The wavelength of light emitted from the LED is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes LED Bandgap and Emission Wavelength
EasySingle correctIdea asked in 3 years
Q49
One main scale division of a vernier caliper is equal to m units. If $n^{th}$ division of main scale coincides with $(n+1)^{th}$ division of vernier scale, the least count of the vernier caliper is :
Units and Measurements
MediumSingle correct
Q50
A galvanometer has a coil of resistance $200\ \Omega$ with a full scale deflection at $20\ \mu$ A. The value of resistance to be added to use it as an ammeter of range $(0\text{-}20)$ mA is :
Moving Charges and Magnetism Wheatstone Bridge Shunting Galvanometer for Protection
EasySingle correctNew ideaIdea asked in 2 years
Q51
If $\vec{a}$ and $\vec{b}$ makes an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}\,|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ . The integer value of n is ________.
Motion in a Plane
MediumNumerical value
Q52
A string is wrapped around the rim of a wheel of moment of inertia $0.40\ \mathrm{kgm^2}$ and radius $10$ cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $40$ N. The angular velocity of…
System of Particles and Rotational Motion Torque and Equilibrium Torque Calculation
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q53
Two persons pull a wire towards themselves. Each person exerts a force of $200$ N on the wire. Young's modulus of the material of wire is $1\times10^{11}\ \mathrm{N\,m^{-2}}$ . Original length of the wire is $2$ m and the area of cross section is…
Mechanical Properties of Solids Elasticity Elastic Moduli
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q54
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4$ m, $2\ \mathrm{ms^{-1}}$ and $16\ \mathrm{ms^{-2}}$ at a certain instant. The amplitude of the motion is $\sqrt{x}$ m where $x$ is…
Oscillations SHM Equations Velocity and Accel vs Position
MediumNumerical valueIdea asked in 4 years
Q55
At the centre of a half ring of radius $R=10$ cm and linear charge density $4\ \mathrm{nC\,m^{-1}}$ , the potential is $x\pi$ V. The value of $x$ is ________.
Electrostatic Potential and Capacitance Electric Potential Potential of a Semi-Circular Ring
EasyNumerical valueNew idea
Q56
The current flowing through the $1\ \Omega$ resistor is $\frac{n}{10}$ A. The value of n is ________.
Current Electricity Kirchhoff's Laws Kirchhoff's Voltage Law (KVL)
MediumNumerical value · figureIdea asked in 6 yearsAsked the year before
Q57
A square loop of edge length $2$ m carrying current of $2$ A is placed with its edges parallel to the $x$ - $y$ axis. A magnetic field is passing through the $x$ - $y$ plane and expressed as $\vec{B}=B_0(1+4x)\hat{k}$ , where $B_0=5$ T. The net magnetic force…
Moving Charges and Magnetism Magnetic Dipole Moment Force on Dipole in 1D Field Gradient
HardNumerical valueNew idea
Q58
When a coil is connected across a $20$ V dc supply, it draws a current of $5$ A. When it is connected across $20$ V, $50$ Hz ac supply, it draws a current of $4$ A. The self inductance of the coil is ________ mH. (Take $\pi=3$ )
Alternating Current Phasor Diagrams Real Inductor (Choke Coil) Phasors
MediumNumerical valueIdea asked in 3 years
Q59
In a Young's double slit experiment, the intensity at a point is $\left(\frac{1}{4}\right)^{th}$ of the maximum intensity, the minimum distance of the point from the central maximum is ________ $\mu$ m. (Given : $\lambda=600$ nm, $d=1.0$ mm, $D=1.0$ m)
Wave Optics Young's Double Slit Intensity at Fractional Path Differences
MediumNumerical valueIdea asked in 3 years
Q60
A star has $100\%$ helium composition. It starts to convert three ${}^4\mathrm{He}$ into one ${}^{12}\mathrm{C}$ via triple alpha process as ${}^4\mathrm{He}+{}^4\mathrm{He}+{}^4\mathrm{He}\to{}^{12}\mathrm{C}+Q$ . The mass of the star is $2.0\times10^{32}$ …
Nuclei Fission and Fusion Q-Value of a Reaction
HardNumerical valueNew idea

Chemistry30 questions

13 easy16 medium1 hard

Q61
Compare the energies of following sets of quantum numbers for multielectron system. (A) $n=4, l=1$ (B) $n=4, l=2$ (C) $n=3, l=1$ (D) $n=3, l=2$ (E) $n=4, l=0$ Choose the correct answer from the options given below :
Structure of Atom Quantum Numbers Aufbau Principle and n+l Rule
EasySingle correctIdea asked in 5 years
Q62
In which one of the following pairs the central atoms exhibit $sp^2$ hybridization ?
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
EasySingle correctIdea asked in 6 yearsAsked the year before
Q63
$0.05\mathrm{M}\ \mathrm{CuSO_4}$ when treated with $0.01\mathrm{M}\ \mathrm{K_2Cr_2O_7}$ gives green colour solution of $\mathrm{Cu_2Cr_2O_7}$ . The two solutions are separated as shown below : [SPM : Semi Permeable Membrane] [figure: container divided by…
Solutions Colligative Properties Hypertonic and Hypotonic Solutions
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q64
The molar conductivity for electrolytes A and B are plotted against $C^{1/2}$ as shown below. Electrolytes A and B respectively are :
Electrochemistry
EasySingle correct · figure
Q65
Given below are two statements : Statement (I) : The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule. Statement (II) : $p\pi-p\pi$ …
Redox Reactions Oxidation Number Assignment
MediumTwo statementsIdea asked in 4 yearsAsked the year before
Q66
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Both rhombic and monoclinic sulphur exist as $\mathrm{S_8}$ while oxygen exists as $\mathrm{O_2}$ . Reason (R) : Oxygen forms…
The p-Block Elements Periodic Trends pπ-pπ Multiple Bonding in Second Period
MediumAssertion–reasonNew idea
Q67
The $\mathrm{F^-}$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula.
Environmental Chemistry Drinking Water Standards: Fluoride Limits
MediumSingle correctIdea asked in 3 years
Q68
The electronic configuration of Cu(II) is $3d^9$ whereas that of Cu(I) is $3d^{10}$ . Which of the following is correct ?
The d- and f-Block Elements d-Block Elements Aqueous Stability of Cu+ vs Cu2+
EasySingle correctIdea asked in 2 years
Q69
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The total number of geometrical isomers shown by $[\mathrm{Co(en)_2Cl_2}]^+$ complex ion is three. Reason (R) :…
Coordination Compounds Coordination Isomerism Optical Activity in M(AA)2B2 Complexes
MediumAssertion–reasonNew idea
Q70
Methods used for purification of organic compounds are based on :
Organic Chemistry: Some Basic Principles and Techniques
EasySingle correct
Q71
Relative stability of the contributing structures is : (I) $\mathrm{CH_2=CH-\overset{\ddot{O}:}{\overset{\|}{C}}-H}$ $\longleftrightarrow$ (II) $\mathrm{{}^+CH_2-CH=C(-\ddot{O}:^-)-H}$ $\longleftrightarrow$ (III) $\mathrm{{}^-{:}CH_2-CH=C(-\ddot{O}^+{:})-H}$
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Relative Stability
MediumSingle correct · figureIdea asked in 2 years
Q72
[figure: benzene + succinic anhydride (cyclic five-membered anhydride) $\xrightarrow{\mathrm{AlCl_3}}$ A $\xrightarrow[\mathrm{HCl}]{\mathrm{Zn-Hg}}$ B $\xrightarrow{\mathrm{Conc.\ H_2SO_4}}$ C] What is the structure of C ?
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Intramolecular Friedel-Crafts
MediumSingle correct · figureIdea asked in 2 years
Q73
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $\mathrm{S_N2}$ reaction of $\mathrm{C_6H_5CH_2Br}$ occurs more readily than the $\mathrm{S_N2}$ reaction of $\mathrm{CH_3CH_2Br}$ .…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN2
EasyAssertion–reasonIdea asked in 2 years
Q74
In the following sequence of reaction, the major products B and C respectively are : [figure: Cl-cyclobutane-Br (1,3-disubstituted cyclobutane) $\xrightarrow{\mathrm{Na/Et_2O}}$ A; A $\xrightarrow[\mathrm{(ii)\ D_2O}]{\mathrm{(i)\ Mg/Et_2O}}$ B; A…
Organic Chemistry: Some Basic Principles and Techniques Alkanes and Free Radicals Wurtz Reaction Limitations
HardSingle correct · figureNew idea
Q75
Identify major product "X" formed in the following reaction : [figure: benzene $\xrightarrow[\mathrm{Anhydrous\ AlCl_3/CuCl}]{\mathrm{CO,\ HCl}}$ X (Major Product)]
Aldehydes, Ketones and Carboxylic Acids Aromatic Hydrocarbons Gattermann-Koch Formylation
EasySingle correct · figureIdea asked in 3 years
Q76
Identify the product A and product B in the following set of reactions. [figure: $\mathrm{CH_3-CH=CH_2}$ $\xrightarrow{\mathrm{H_2O,\ H^+}}$ major Product A; $\mathrm{CH_3-CH=CH_2}$ $\xrightarrow[\mathrm{H_2O,\ H_2O_2,\ \overline{O}H}]{\mathrm{(BH_3)_2}}$ …
Alcohols, Phenols and Ethers Alkenes and Alkynes Hydroboration-Oxidation
EasySingle correct · figureIdea asked in 4 yearsAsked the year before
Q77
For the given compounds, the correct order of increasing $\mathrm{pK_a}$ value : (A) phenol (B) 4-nitrophenol ( $\mathrm{O_2N}$ and OH para on benzene ring) (C) 3-methoxyphenol (HO and $\mathrm{OCH_3}$ meta) (D) 3-nitrophenol (OH and $\mathrm{NO_2}$ meta) (E)…
Alcohols, Phenols and Ethers Alcohols and Phenols Phenol Acidity Comparison
MediumSingle correct · figureIdea asked in 3 yearsAsked the year before
Q78
Correct order of basic strength of Pyrrole (five-membered ring with NH), Pyridine (six-membered aromatic ring with N) and Piperidine (saturated six-membered ring with NH) is :
Amines Basicity of Nitrogen Heterocycles
MediumSingle correct · figureIdea asked in 3 years
Q79
On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed ?
The p-Block Elements
MediumSingle correct
Q80
Identify the incorrect statements regarding primary standard of titrimetric analysis. (A) It should be purely available in dry form. (B) It should not undergo chemical change in air. (C) It should be hygroscopic and should react with another chemical…
Some Basic Concepts of Chemistry
MediumOther
Q81
Molarity (M) of an aqueous solution containing $x$ g of anhyd. $\mathrm{CuSO_4}$ in 500 mL solution at 32 $^\circ$ C is $2\times10^{-1}$ M. Its molality will be ________ $\times 10^{-3}$ m. (nearest integer). [Given density of the solution = 1.25 g/mL]
Solutions Mole Concept Molarity and Molality Interconversion
MediumNumerical valueIdea asked in 3 years
Q82
The total number of species from the following in which one unpaired electron is present, is ________. $\mathrm{N_2, O_2, C_2^-, O_2^-, O_2^{2-}, H_2^+, CN^-, He_2^+}$
Chemical Bonding and Molecular Structure Molecular Orbital Theory Magnetic Property Prediction
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q83
The heat of solution of anhydrous $\mathrm{CuSO_4}$ and $\mathrm{CuSO_4\cdot5H_2O}$ are $-70$ kJ mol $^{-1}$ and $+12$ kJ mol $^{-1}$ respectively. The heat of hydration of $\mathrm{CuSO_4}$ to $\mathrm{CuSO_4\cdot5H_2O}$ is $-x$ kJ. The value of $x$ is…
Thermodynamics (Chemistry)Enthalpy and Hess's Law Enthalpy of Solution and Hydration
EasyNumerical valueNew ideaIdea asked in 2 years
Q84
When equal volume of 1M HCl and 1M $\mathrm{H_2SO_4}$ are separately neutralised by excess volume of 1M NaOH solution, $x$ and $y$ kJ of heat is liberated respectively. The value of $y/x$ is ________.
Thermodynamics (Chemistry)Enthalpy and Hess's Law Neutralization Enthalpy of Polybasic Acids
EasyNumerical valueNew idea
Q85
The standard reduction potentials at 298 K for the following half cells are given below : $\mathrm{Cr_2O_7^{2-}} + 14\mathrm{H^+} + 6e^- \rightarrow 2\mathrm{Cr^{3+}} + 7\mathrm{H_2O}$ , $E^\circ = 1.33$ V $\mathrm{Fe^{3+}(aq)} + 3e^- \rightarrow \mathrm{Fe}$ …
Electrochemistry Nernst Equation Standard Cell Potential
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q86
Given below are two statements : Statement I : The rate law for the reaction $\mathrm{A + B \rightarrow C}$ is rate $(r) = k[\mathrm{A}]^2[\mathrm{B}]$ . When the concentration of both A and B is doubled, the reaction rate is increased " $x$ " times. Statement…
Chemical Kinetics Integrated Rate Equations Zero Order Integrated Rate Law
EasyNumerical value · figureNew ideaIdea asked in 2 years
Q87
Number of colourless lanthanoid ions among the following is ________. $\mathrm{Eu^{3+}, Lu^{3+}, Nd^{3+}, La^{3+}, Sm^{3+}}$
The d- and f-Block Elements f-Block Elements Identifying Colorless Lanthanide Ions
MediumNumerical valueNew idea
Q88
Number of ambidentate ligands among the following is ________. $\mathrm{NO_2^-, SCN^-, C_2O_4^{2-}, NH_3, CN^-, SO_4^{2-}, H_2O}$ .
Coordination Compounds Coordination Isomerism Ambidentate Ligands in Linkage Isomerism
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q89
How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects ? [figure: eight structures: anisole ( $\mathrm{OCH_3}$ on benzene); $\mathrm{(CH_3)_2CH-CH=CH-C(=O)-CH_3}$ (skeletal enone); benzene;…
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Mesomeric Effect
MediumNumerical value · figureIdea asked in 3 years
Q90
Total number of essential amino acid among the given list of amino acids is ________. Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline
Biomolecules
EasyNumerical value

Maths30 questions

3 easy21 medium6 hard

Q1
If the domain of the function $f(x)=\sin^{-1}\left(\frac{x-1}{2x+3}\right)$ is $\mathbf{R}-(\alpha,\beta)$ , then $12\alpha\beta$ is equal to :
Relations and Functions Inverse Trig Domains Domain of Inverse Trig with Rational Arguments
MediumSingle correctNew idea
Q2
Let $\alpha,\beta$ be the roots of the equation $x^2+2\sqrt{2}\,x-1=0$ . The quadratic equation, whose roots are $\alpha^4+\beta^4$ and $\frac{1}{10}\left(\alpha^6+\beta^6\right)$ , is :
Complex Numbers and Quadratic Equations Quadratic Roots Equation Formation
MediumSingle correctIdea asked in 2 years
Q3
Let $\lambda,\mu\in\mathbf{R}$ . If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many solutions, then $\mu+2\lambda$ is equal to :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q4
The coefficient of $x^{70}$ in $x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}$ is ${}^{99}C_p-{}^{46}C_q$ . Then a possible value of $p+q$ is :
Binomial Theorem Binomial Coefficients Geometric Progression of Expansions
HardSingle correctIdea asked in 2 years
Q5
If the sum of the series $\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)}$ is equal to $5$ , then $50d$ is equal to :
Sequences and Series AP and GP Method of Differences (Vn Method)
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q6
Let $f(x)=ax^3+bx^2+cx+41$ be such that $f(1)=40$ , $f'(1)=2$ and $f''(1)=4$ . Then $a^2+b^2+c^2$ is equal to :
Application of Derivatives
EasySingle correct
Q7
A variable line L passes through the point $(3,5)$ and intersects the positive coordinate axes at the points A and B. The minimum area of the triangle OAB, where O is the origin, is :
Straight Lines Maxima and Minima Optimization Problems
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q8
Let $\int\frac{2-\tan x}{3+\tan x}\,dx=\frac{1}{2}\left(\alpha x+\log_e|\beta\sin x+\gamma\cos x|\right)+C$ , where C is the constant of integration. Then $\alpha+\frac{\gamma}{\beta}$ is equal to :
Integrals Integration by Substitution Numerator-Denominator Derivative Matching
MediumSingle correctIdea asked in 2 years
Q9
The parabola $y^2=4x$ divides the area of the circle $x^2+y^2=5$ in two parts. The area of the smaller part is equal to :
Application of Integrals Area Under Curves Ratio of Divided Areas
MediumSingle correctIdea asked in 2 years
Q10
The solution of the differential equation $(x^2+y^2)dx-5xy\,dy=0$ , $y(1)=0$ , is :
Differential Equations Homogeneous Equations Substitution y = vx
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q11
The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$ , passing through the point $(0,1)$ is a conic, whose vertex lies on the line :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q12
Let $f(x)=x^2+9$ , $g(x)=\frac{x}{x-9}$ and $a=f\circ g(10)$ , $b=g\circ f(3)$ . If $e$ and $l$ denote the eccentricity and the length of the latus rectum of the ellipse $\frac{x^2}{a}+\frac{y^2}{b}=1$ , then $8e^2+l^2$ is equal to.
Conic Sections Ellipse Eccentricity Length of Latus Rectum
EasySingle correctIdea asked in 6 yearsAsked the year before
Q13
Let a circle passing through $(2,0)$ have its centre at the point $(h,k)$ . Let $(x_c,y_c)$ be the point of intersection of the lines $3x+5y=1$ and $(2+c)x+5c^2y=1$ . If $h=\lim_{c\to1}x_c$ and $k=\lim_{c\to1}y_c$ , then the equation of the circle is :
Conic Sections
MediumSingle correct
Q14
A ray of light coming from the point $P(1,2)$ gets reflected from the point Q on the $x$ -axis and then passes through the point $R(4,3)$ . If the point $S(h,k)$ is such that PQRS is a parallelogram, then $hk^2$ is equal to :
Straight Lines Straight Line Distance Image of a point in a line
MediumSingle correctIdea asked in 4 years
Q15
Let the line L intersect the lines $x-2=-y=z-1$ , $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}$ . Then which of the following points lies on L?
Three Dimensional Geometry Lines in 3D Line Intersecting Two Skew Lines Parallel to a Third
MediumSingle correctNew idea
Q16
The shortest distance between the lines $\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$ and $\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
EasySingle correctIdea asked in 6 yearsAsked the year before
Q17
Let $\overrightarrow{OA}=2\vec{a}$ , $\overrightarrow{OB}=6\vec{a}+5\vec{b}$ and $\overrightarrow{OC}=3\vec{b}$ , where O is the origin. If the area of the parallelogram with adjacent sides $\overrightarrow{OA}$ and $\overrightarrow{OC}$ is $15$ sq. units,…
Vector Algebra Cross Product Area of Quadrilateral via Diagonals
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q18
Let three vectors $\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}$ , $\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}$ , $\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}$ form a triangle such that $\vec{c}=\vec{a}-\vec{b}$ and the area of the triangle is $5\sqrt{6}$ . If $\alpha$ is a positive…
Vector Algebra Cross Product Area of Triangles and Parallelograms
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q19
The frequency distribution of the age of students in a class of 40 students is given below. | Age | 15 | 16 | 17 | 18 | 19 | 20 | |---|---|---|---|---|---|---| | No of Students | 5 | 8 | 5 | 12 | $x$ | $y$ | If the mean deviation about the median is $1.25$ ,…
Statistics
HardSingle correct
Q20
Let $\left|\cos\theta\cos(60^\circ-\theta)\cos(60^\circ+\theta)\right|\le\frac{1}{8}$ , $\theta\in[0,2\pi]$ . Then, the sum of all $\theta\in[0,2\pi]$ , where $\cos3\theta$ attains its maximum value, is :
Trigonometric Functions Trigonometric Identities Cosine Product Identity with 60 Degrees
MediumSingle correctNew idea
Q21
Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$ . Let R be a relation defined on $A\times B$ by $(a_1,b_1)\,R\,(a_2,b_2)$ if and only if $a_1+a_2=b_1+b_2$ . Then the number of elements in R is ________.
Relations and Functions Sets and Relations Counting Relations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
The sum of the square of the modulus of the elements in the set $\{z=a+ib:\ a,b\in\mathbf{Z},\ z\in\mathbf{C},\ |z-1|\le1,\ |z-5|\le|z-5i|\}$ is ________.
Complex Numbers and Quadratic Equations
MediumNumerical value
Q23
Let A be a non-singular matrix of order 3. If $\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10}$ and $\det(3\,\mathrm{adj}(2A))=2^m\cdot3^n$ , then $|3m+2n|$ is equal to ________.
Determinants Matrix Inverse Inverse Relation to Double Adjoint
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q24
Let $f:(0,\pi)\to\mathbf{R}$ be a function given by $f(x)=\begin{cases}\left(\frac{8}{7}\right)^{\frac{\tan 8x}{\tan 7x}}, & 0<x<\frac{\pi}{2}\\ a-8, & x=\frac{\pi}{2}\\ (1+|\cot x|)^{\frac{b}{a}|\tan x|}, & \frac{\pi}{2}<x<\pi\end{cases}$ where…
Continuity and Differentiability Finding Unknown Constants for Continuity
HardNumerical valueIdea asked in 3 years
Q25
The remainder when $428^{2024}$ is divided by $21$ is ________.
Binomial Theorem
MediumNumerical value
Q26
If a function $f$ satisfies $f(m+n)=f(m)+f(n)$ for all $m,n\in\mathbf{N}$ and $f(1)=1$ , then the largest natural number $\lambda$ such that $\sum_{k=1}^{2022}f(\lambda+k)\le(2022)^2$ is equal to ________.
Sequences and Series AP and GP AP Sum of n terms
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q27
Let the set of all positive values of $\lambda$ , for which the point of local minimum of the function $(1+x(\lambda^2-x^2))$ satisfies $\frac{x^2+x+2}{x^2+5x+6}<0$ , be $(\alpha,\beta)$ . Then $\alpha^2+\beta^2$ is equal to ________.
Application of Derivatives Maxima and Minima First Derivative Test
MediumNumerical valueIdea asked in 3 years
Q28
Let $\lim_{n\to\infty}\left(\frac{n}{\sqrt{n^4+1}}-\frac{2n}{(n^2+1)\sqrt{n^4+1}}+\frac{n}{\sqrt{n^4+16}}-\frac{8n}{(n^2+4)\sqrt{n^4+16}}+\ldots+\frac{n}{\sqrt{n^4+n^4}}-\frac{2n\cdot n^2}{(n^2+n^2)\sqrt{n^4+n^4}}\right)$ be $\frac{\pi}{k}$ , using only the…
Integrals Integral as Limit of Sum Summation to Riemann Form
HardNumerical valueIdea asked in 4 yearsAsked the year before
Q29
Let the centre of a circle, passing through the points $(0,0)$ , $(1,0)$ and touching the circle $x^2+y^2=9$ , be $(h,k)$ . Then for all possible values of the coordinates of the centre $(h,k)$ , $4(h^2+k^2)$ is equal to ________.
Conic Sections Circle Tangents Common Tangent of Touching Circles
HardNumerical valueIdea asked in 4 years
Q30
Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1,2,3,4$ . If the probability that $ax^2+bx+c=0$ has all real roots is $\frac{m}{n}$ , $\gcd(m,n)=1$ , then $m+n$ is equal to ________.
Probability
MediumNumerical value

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.