JEE Main 2024 · April session

JEE Main 6 April 2024, Shift 2

89 questions (1 more dropped by NTA): 29 numerical-answer and 60 multiple choice. 13 were rated hard and 31 easy. Its hard-question count was the 4th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Coordination Compounds, with 3 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 29; 33% of the shift
Hard: 13; 15% of the shift
Chapters asked: 60; 11 questions with a figure

Key findings · 6 Apr 2024, Shift 2

1
13 hard questions (15%): the 4th 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 29 rated hard; Physics had the most easy questions (15 of 30).
3
21 questions tested a new idea, one no earlier year had asked: 28% of the 76 questions tagged to an idea.
4
29 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 (53% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Atoms in Physics (2), Coordination Compounds in Chemistry (3) and Complex Numbers and Quadratic Equations in Maths (2).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 12Hard 3

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Maths

29 Q · 9 numerical

Easy 4Medium 17Hard 8

Top chapters

Question format

Single correct46 Q
Numerical value29 Q
Match the list4 Q
Other4 Q
Diagram based4 Q
Two statements2 Q

What each question asks you to do

Calculation35 Q
Multi-step29 Q
Application11 Q
Recall7 Q
Conceptual6 Q
Data or graph1 Q

Most common: Calculation.

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
Open29 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 89 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

89 of 89 questions

Physics30 questions

15 easy12 medium3 hard

Q31
A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking $30^\circ$ . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely : ( $g=10\ \mathrm{m/s^2}$ , $\sqrt{3}=1.73$ )
Laws of Motion Friction Friction on a Banked Road
MediumSingle correctNew idea
Q32
Given below are two statements : Statement (I) : Dimensions of specific heat is $[\mathrm{L^2T^{-2}K^{-1}}]$ . Statement (II) : Dimensions of gas constant is $[\mathrm{M\,L^2\,T^{-1}K^{-1}}]$ . In the light of the above statements, choose the most appropriate…
Units and Measurements
MediumTwo statements
Q33
A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$ . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$ . Time required to reach the ground,…
Motion in a Straight Line Kinematics in 1D Free Fall Time and Speed Symmetry
MediumSingle correctIdea asked in 2 years
Q34
A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if $g=10\ \mathrm{m/s^2}$ ) :
Laws of Motion Newton's Laws of Motion Static Tension in a Massive String
EasySingle correctNew idea
Q35
Match List-I with List-II : List-I (Y vs X) (A) Y = magnetic susceptibility, X = magnetising field (B) Y = magnetic field, X = distance from centre of a current carrying wire for $x<a$ (where $a$ = radius of wire) (C) Y = magnetic field, X = distance from…
Magnetism and Matter
MediumMatch the list · figure
Q36
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :
Work, Energy and Power Work and Kinetic Energy Momentum and Kinetic Energy Relation
EasySingle correctIdea asked in 4 yearsAsked the year before
Q37
Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at $R/4$ depth under surface of earth ?
Gravitation
EasySingle correct
Q38
Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $R$ = Radius of bubble, $S$ = Surface tension of bubble)
Mechanical Properties of Fluids Surface Tension Excess Pressure in Soap Bubbles
EasySingle correctIdea asked in 4 years
Q39
A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^\circ\mathrm{C}$ . The work done by the gas is : Given, $R=8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}$ .
Thermodynamics First Law of Thermodynamics First Law Energy Balance
EasySingle correctIdea asked in 3 yearsAsked the year before
Q40
In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text{th}}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and…
Units and Measurements
MediumSingle correct
Q41
Energy of 10 non rigid diatomic molecules at temperature $T$ is :
Kinetic Theory Kinetic Theory of Gases Vibrational Degrees of Freedom
MediumSingle correctIdea asked in 2 years
Q42
Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force 16 N. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $P$ and…
Electric Charges and Fields Coulomb's Law Charge Redistribution via Conduction
MediumSingle correctIdea asked in 3 years
Q43
The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : (Given $e=1.6\times10^{-19}\ \mathrm{C}$ )
Current Electricity Ohm's Law and Resistance Electron Count Rate from Current
EasySingle correctNew idea
Q44
In a coil, the current changes from $-2$ A to $+2$ A in 0.2 s and induces an emf of 0.1 V. The self inductance of the coil is :
Electromagnetic Induction Inductance Self-Inductance and Back EMF
EasySingle correctIdea asked in 5 yearsAsked the year before
Q45
In the given electromagnetic wave $E_y=600\sin(\omega t-kx)\ \mathrm{Vm^{-1}}$ , intensity of the associated light beam is (in $\mathrm{W/m^2}$ ) : (Given $\epsilon_0=9\times10^{-12}\ \mathrm{C^2N^{-1}m^{-2}}$ )
Electromagnetic Waves
MediumSingle correct
Q46
For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of the material is :
Ray Optics and Optical Instruments Lens Maker's Formula Lens Maker's Equation
EasySingle correctNew ideaIdea asked in 3 years
Q47
When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV, electron emission takes place. The stopping potential is : (Given $hc=1240\ \mathrm{eV\,nm}$ )
Dual Nature of Radiation and Matter Photoelectric Effect Stopping Potential
EasySingle correctIdea asked in 2 years
Q48
The longest wavelength associated with Paschen series is : (Given $R_H=1.097\times10^7$ SI unit)
Atoms Bohr's Atomic Model Shortest and Longest Wavelengths
EasySingle correctIdea asked in 5 yearsAsked the year before
Q49
The acceptor level of a p-type semiconductor is 6 eV. The maximum wavelength of light which can create a hole would be : Given $hc=1242\ \mathrm{eV\,nm}$ .
Semiconductor Electronics: Materials, Devices and Simple Circuits
MediumSingle correct
Q50
In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49 MSD; 20 divisions on main scale in each cm For mark on paper MSR = 8.45 cm, VC = 26 For mark on paper seen through…
Ray Optics and Optical Instruments Refraction and Snell's Law Apparent Depth and Shift
HardSingle correctIdea asked in 3 yearsAsked the year before
Q51
Two open organ pipes of lengths 60 cm and 90 cm resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is ________ Hz. (Velocity of sound in air $=333\ \mathrm{m/s}$ )
Waves Resonance in Air Columns Open Organ Pipe Harmonics
EasyNumerical valueIdea asked in 2 yearsAsked the year before
Q52
A capacitor of $10\ \mu\mathrm{F}$ capacitance whose plates are separated by 10 mm through air and each plate has area $4\ \mathrm{cm}^2$ is now filled equally with two dielectric media of $K_1=2$ , $K_2=3$ respectively as shown in figure. If new force…
Electrostatic Potential and Capacitance Dielectrics Partial and Multiple Slabs
HardNumerical value · figureIdea asked in 6 yearsAsked the year before
Q53
In the given figure an ammeter $A$ consists of a $240\ \Omega$ coil connected in parallel to a $10\ \Omega$ shunt. The reading of the ammeter is ________ mA.
Current Electricity Kirchhoff's Laws Ammeter Voltage Drop Error
MediumNumerical value · figureNew idea
Q54
Two coherent monochromatic light beams of intensities $I$ and $4I$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $xI$ . The value of $x$ is ________.
Wave Optics Young's Double Slit Resultant Intensity Formula
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q55
In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given $hc=1245\ \mathrm{eV\,nm}$ ,…
Atoms Bohr's Atomic Model Excitation and Ionization Potentials
EasyNumerical valueNew idea
Q56
Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be…
System of Particles and Rotational Motion Moment of Inertia MOI of Discrete Particles
MediumNumerical valueIdea asked in 3 years
Q57
A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$ . Its acceleration at any time $t$ is $x^{-n}$ where $n=$ ________.
Motion in a Straight Line Kinematics in 1D Calculus in Kinematics
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q58
A coil having 100 turns, area of $5\times10^{-3}\ \mathrm{m^2}$ , carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^\circ$ …
Moving Charges and Magnetism Magnetic Dipole Moment Work done in rotating a dipole
EasyNumerical valueIdea asked in 3 years
Q59
For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of $200\ \Omega$ and 100 mH inductor is being used in the given circuit. The frequency of ac source is ________ $\times10^3$ …
Alternating Current LCR Resonance Resonant Frequency Calculation
EasyNumerical valueIdea asked in 4 years
Q60
A wire of cross sectional area $A$ , modulus of elasticity $2\times10^{11}\ \mathrm{Nm^{-2}}$ and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle…
Mechanical Properties of Solids Elasticity Hooke's Law
HardNumerical value · figureIdea asked in 3 yearsAsked the year before

Chemistry30 questions

12 easy16 medium2 hard

Q61
Molality ( $m$ ) of 3 M aqueous solution of NaCl is : (Given : Density of solution $=1.25\ \mathrm{g\,mL^{-1}}$ , Molar mass in $\mathrm{g\,mol^{-1}}$ : Na-23, Cl-35.5)
Solutions Mole Concept Molarity and Molality Interconversion
EasySingle correctIdea asked in 3 years
Q62
Given below are two statements : Statement I : $\mathrm{PF_5}$ and $\mathrm{BrF_5}$ both exhibit $sp^3d$ hybridisation. Statement II : Both $\mathrm{SF_6}$ and $[\mathrm{Co(NH_3)_6}]^{3+}$ exhibit $sp^3d^2$ hybridisation. In the light of the above…
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumTwo statementsIdea asked in 6 yearsAsked the year before
Q63
The ratio $\frac{K_P}{K_C}$ for the reaction : $\mathrm{CO_{(g)}+\frac{1}{2}O_{2(g)}\rightleftharpoons CO_{2(g)}}$ is :
Equilibrium Chemical Equilibrium Kc and Kp Relationship
EasySingle correctIdea asked in 2 years
Q64
Match List - I with List - II. List - I (Reaction) (A) $\mathrm{N_{2(g)}+O_{2(g)}\rightarrow 2NO_{(g)}}$ (B) $\mathrm{2Pb(NO_3)_{2(s)}\rightarrow 2PbO_{(s)}+4NO_{2(g)}+O_{2(g)}}$ (C) $\mathrm{2Na_{(s)}+2H_2O_{(l)}\rightarrow 2NaOH_{(aq.)}+H_{2(g)}}$ (D)…
Redox Reactions Disproportionation Balancing
EasyMatch the listIdea asked in 3 years
Q65
How can an electrochemical cell be converted into an electrolytic cell ?
Electrochemistry
EasySingle correct
Q66
Match List - I with List - II. List - I (Alkali Metal) (A) Li (B) Na (C) Rb (D) Cs List - II (Emission Wavelength in nm) (I) 589.2 (II) 455.5 (III) 670.8 (IV) 780.0 Choose the correct answer from the options given below :
The s-Block Elements s-Block Elements Flame Coloration
HardMatch the listIdea asked in 4 yearsAsked the year before
Q67
The number of ions from the following that are expected to behave as oxidising agent is : $\mathrm{Sn^{4+}, Sn^{2+}, Pb^{2+}, Tl^{3+}, Pb^{4+}, Tl^{+}}$
The p-Block Elements Group 13 & 14 Inert Pair Effect
MediumOtherIdea asked in 5 years
Q68
Evaluate the following statements related to group 14 elements for their correctness. (A) Covalent radius decreases down the group from C to Pb in a regular manner. (B) Electronegativity decreases from C to Pb down the group gradually. (C) Maximum covalance…
The p-Block Elements Periodic Trends Anomalous Behavior of Second Period Elements
MediumOtherNew ideaIdea asked in 2 years
Q69
Arrange the following elements in the increasing order of number of unpaired electrons in it. (A) Sc (B) Cr (C) V (D) Ti (E) Mn Choose the correct answer from the options given below :
Classification of Elements and Periodicity in Properties Quantum Numbers Counting Unpaired Electrons
EasyOtherIdea asked in 2 years
Q70
The correct IUPAC name of $[\mathrm{PtBr_2(PMe_3)_2}]$ is :
Coordination Compounds Coordination Nomenclature Complex Numerical Prefixes (Bis/Tris)
EasySingle correctNew idea
Q71
Match List - I with List - II. List - I (Tetrahedral Complex) (A) $\mathrm{TiCl_4}$ (B) $[\mathrm{FeO_4}]^{2-}$ (C) $[\mathrm{FeCl_4}]^{-}$ (D) $[\mathrm{CoCl_4}]^{2-}$ List - II (Electronic configuration) (I) $e^2, t_2^0$ (II) $e^4, t_2^3$ (III)…
Coordination Compounds Crystal Field Theory Tetrahedral Field Splitting and Delta_t Relation
MediumMatch the listNew ideaIdea asked in 2 years
Q72
During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in $\mathrm{NH_4OH}$ solution when sodium carbonate extract was first acidified with dil. $\mathrm{HNO_3}$ and then $\mathrm{AgNO_3}$ …
Organic Chemistry: Some Basic Principles and Techniques Anion Analysis Halide Confirmatory Tests
EasySingle correctNew idea
Q73
The correct statement among the following, for a "chromatography" purification method is :
Organic Chemistry: Some Basic Principles and Techniques Adsorption Adsorption Chromatography Principle
MediumSingle correctIdea asked in 2 years
Q74
Four aromatic compounds are shown: (I) toluene (benzene ring with $\mathrm{CH_3}$ ), (II) benzene, (III) anisole (benzene ring with $\mathrm{OCH_3}$ ), (IV) benzotrifluoride (benzene ring with $\mathrm{CF_3}$ ). The correct arrangement for decreasing order of…
Hydrocarbons Aromatic Hydrocarbons Ranking Activating Groups
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q75
The incorrect statement regarding the geometrical isomers of 2-butene is :
Hydrocarbons Stereoisomerism Physical Properties of Geometrical Isomers
EasySingle correctNew ideaIdea asked in 2 years
Q76
Chemical reaction: (1-chloropropyl)cyclohexane [cyclohexyl ring attached to CHCl-CH2-CH3] $+$ NaOH $\xrightarrow{\mathrm{H_2O}}$ Major Product "A". Consider the above chemical reaction. Product "A" is :
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Carbocation Rearrangements in SN1
MediumDiagram based · figureIdea asked in 3 yearsAsked the year before
Q77
Identify the product (A) in the following reaction. Aniline (benzene ring with $\mathrm{NH_2}$ ) $\xrightarrow{\text{(i) NaNO}_2+\text{HCl; (ii) Cu}_2\text{Cl}_2\text{; (iii) NaOH, 623 K, 300 atm; (iv) H}^+}$ (A)
Amines Diazonium Salts Sandmeyer Reaction
MediumDiagram based · figureIdea asked in 4 yearsAsked the year before
Q78
Consider the given reaction, identify the major product P. $\mathrm{CH_3-COOH}$ $\xrightarrow{\text{(i) LiAlH}_4\ \text{(ii) PCC}\ \text{(iii) HCN/}\overline{\mathrm{O}}\mathrm{H}\ \text{(iv) H}_2\mathrm{O}/\overline{\mathrm{O}}\mathrm{H},\ \Delta}$ "P"
Aldehydes, Ketones and Carboxylic Acids Nucleophilic Addition Cyanohydrin Formation
MediumSingle correctIdea asked in 2 years
Q79
The major products formed : Anisole (benzene ring with $\mathrm{OCH_3}$ ) $\xrightarrow{\mathrm{HNO_3,\ H_2SO_4}}$ 'A' $\xrightarrow[\mathrm{Fe}]{\mathrm{Br_2\ (excess)}}$ 'B' A and B respectively are :
Haloalkanes and Haloarenes Aromatic Hydrocarbons Synergic Directing Effects in Di-substituted Benzenes
MediumDiagram based · figureNew ideaIdea asked in 2 years
Q80
The incorrect statements regarding enzymes are : (A) Enzymes are biocatalysts. (B) Enzymes are non-specific and can catalyse different kinds of reactions. (C) Most Enzymes are globular proteins. (D) Enzyme - oxidase catalyses the hydrolysis of maltose into…
Biomolecules
EasyOther
Q81
For hydrogen atom, energy of an electron in first excited state is $-3.4$ eV, K.E. of the same electron of hydrogen atom is $x$ eV. Value of $x$ is ________ $\times 10^{-1}$ eV. (Nearest integer)
Structure of Atom Bohr's Atomic Theory Total, Kinetic, and Potential Energy
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q82
Total number of species from the following with central atom utilising $\mathrm{sp^2}$ hybrid orbitals for bonding is ________. $\mathrm{NH_3, SO_2, SiO_2, BeCl_2, C_2H_2, C_2H_4, BCl_3, HCHO, C_6H_6, BF_3, C_2H_4Cl_2}$
Chemical Bonding and Molecular Structure VSEPR Theory Steric Number Calculation
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q83
For the reaction at 298 K, $2A + B \rightarrow C$ , $\Delta H = 400$ kJ mol $^{-1}$ and $\Delta S = 0.2$ kJ mol $^{-1}$ K $^{-1}$ . The reaction will become spontaneous above ________ K.
Thermodynamics (Chemistry)Gibbs Free Energy Temperature Dependence
EasyNumerical valueIdea asked in 2 years
Q84
When ' $x$ ' $\times 10^{-2}$ mL methanol (molar mass $= 32$ g; density $= 0.792$ g/cm $^3$ ) is added to 100 mL water (density $= 1$ g/cm $^3$ ), the following diagram is obtained. $x =$ ________ (nearest integer). [Given : Molal freezing point depression…
Solutions Colligative Properties Freezing Point Depression
MediumNumerical value · figureIdea asked in 4 years
Q85
Consider the two different first order reactions given below $A + B \rightarrow C$ (Reaction 1) $P \rightarrow Q$ (Reaction 2) The ratio of the half life of Reaction 1 : Reaction 2 is 5 : 2. If $t_1$ and $t_2$ represent the time taken to complete…
Chemical Kinetics Rate Laws First-Order Kinetics
MediumNumerical valueIdea asked in 2 years
Q86
Among $\mathrm{VO_2^+}$ , $\mathrm{MnO_4^-}$ and $\mathrm{Cr_2O_7^{2-}}$ , the spin-only magnetic moment value of the species with least oxidising ability is ________ BM (Nearest integer). (Given atomic member V $=23$ , Mn $=25$ , Cr $=24$ )
The d- and f-Block Elements d-Block Elements Spin-only Magnetism
MediumNumerical valueIdea asked in 6 years
Q87
Consider the following reactions $\mathrm{NiS + HNO_3 + HCl \rightarrow A + NO + S + H_2O}$ $\mathrm{A + NH_4OH + H_3C-C{=}N-OH / H_3C-C{=}N-OH \rightarrow B + NH_4Cl + H_2O}$ (dimethylglyoxime, two $\mathrm{H_3C-C=N-OH}$ units, one drawn below the other)…
Coordination Compounds Cation Analysis Nickel DMG Complex
HardNumerical valueIdea asked in 2 years
Q88
Number of carbocations from the following that are not stabilized by hyperconjugation is ________.
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Hyperconjugation
MediumNumerical value · figureNew ideaIdea asked in 3 years
Q89
Reaction: ethoxybenzene (benzene ring with $\mathrm{OC_2H_5}$ ) $\xrightarrow{\mathrm{HNO_3,\ H_2SO_4}}$ P (major product) $\xrightarrow{\mathrm{2Br_2,\ Fe}}$ Q (major product) The ratio of number of oxygen atoms to bromine atoms in the product Q is ________…
Haloalkanes and Haloarenes Aromatic Hydrocarbons Synergic Directing Effects in Di-substituted Benzenes
MediumNumerical value · figureNew ideaIdea asked in 2 years
Q90
An amine (X) is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to it the solution remains clear. Molar mass of the amine (X) formed is ________ g mol $^{-1}$ . (Given molar mass in g mol $^{-1}$ C : 12, H : 1, O : 16, N : 14)
Amines Ammonolysis of Alkyl Halides
MediumNumerical valueIdea asked in 2 years

Maths29 questions

4 easy17 medium8 hard

Q1
Let $f(x)=\frac{1}{7-\sin 5x}$ be a function defined on $\mathbb{R}$ . Then the range of the function $f(x)$ is equal to :
Relations and Functions Functions and Domain Range of a*sin(x) + b*cos(x) Forms
EasySingle correctNew idea
Q2
Let $A=\{1,2,3,4,5\}$ . Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le 5y$ . Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A\times A$ that are required to be added to $R$ to make it a symmetric…
Relations and Functions Sets and Relations Counting Relations
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q3
If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2$ , then
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
HardSingle correctIdea asked in 5 yearsAsked the year before
Q4
If $A$ is a square matrix of order 3 such that $\det(A)=3$ and $\det(\operatorname{adj}(-4\operatorname{adj}(-3\operatorname{adj}(3\operatorname{adj}((2A)^{-1}))))) = 2^m 3^n$ , then $m+2n$ is equal to :
Determinants Matrix Inverse Inverse Relation to Double Adjoint
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q5
If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text{th}}$ position in this arrangement is :
Permutations and Combinations Lexicographic Rank of a Word
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q6
Let $0\le r\le n$ . If $^{n+1}C_{r+1}:{}^{n}C_r:{}^{n-1}C_{r-1}=55:35:21$ , then $2n+5r$ is equal to :
Permutations and Combinations Pascal's Rule and nCr Properties
MediumSingle correctNew idea
Q7
A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to…
Sequences and Series AP and GP AP Sum of n terms
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q8
If the function $f(x)=\left(\frac{1}{x}\right)^{2x}$ ; $x>0$ attains the maximum value at $x=\frac{1}{e}$ then :
Application of Derivatives Maxima and Minima Extrema of x^x and x^(1/x)
HardSingle correctNew idea
Q9
$\lim_{n\to\infty}\frac{(1^2-1)(n-1)+(2^2-2)(n-2)+\cdots+((n-1)^2-(n-1))\cdot 1}{(1^3+2^3+\cdots+n^3)-(1^2+2^2+\cdots+n^2)}$ is equal to :
Limits and Derivatives
MediumSingle correct
Q10
Suppose for a differentiable function $h$ , $h(0)=0$ , $h(1)=1$ and $h'(0)=h'(1)=2$ . If $g(x)=h(e^x)e^{h(x)}$ , then $g'(0)$ is equal to :
Continuity and Differentiability Continuity and Differentiability of Composite Functions
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q11
If the area of the region $\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\}$ is $(\log_e 2)-\frac{1}{7}$ then the value of $7a-3$ is equal to :
Application of Integrals Area Under Curves Finding Unknown Parameters from Area
MediumSingle correctIdea asked in 2 years
Q12
If $\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}$ , then the maximum value of $a\sin x+b\cos x$ , is :
Integrals Integration by Substitution Dividing by Cosine Squared Substitution
MediumSingle correctNew idea
Q13
Suppose the solution of the differential equation $\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}$ represents a circle passing through origin. Then the radius of this circle is :
Differential Equations Homogeneous Equations Shift of Origin Method for Reducible Equations
HardSingle correctNew idea
Q14
If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$ , is $ax^2+by^2+cxy+dx+ey+170=0$ , then the value of $a^2+2b+3c+4d+e$ is equal to :
Straight Lines Straight Line Distance Locus of Constant Distance Ratio
MediumSingle correctNew idea
Q15
If $P(6,1)$ be the orthocentre of the triangle whose vertices are $A(5,-2)$ , $B(8,3)$ and $C(h,k)$ , then the point $C$ lies on the circle :
Straight Lines
MediumSingle correct
Q16
Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $ABC$ and the same process is repeated infinitely many times. If $P$ is the sum of perimeters and $Q$ is be the sum of areas of all the…
Sequences and Series AP and GP Infinite GP Sum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the point $(2,5,-1)$ . If the area of the triangle $PQR$ is $\lambda$ and $\lambda^2=14K$ , then $K$ is equal to :
Three Dimensional Geometry Lines in 3D Image of a Point in a Line
HardSingle correctIdea asked in 6 years
Q18
Let $\vec{a}=2\hat{i}+\hat{j}-\hat{k}$ , $\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}$ . Then the square of the projection of $\vec{a}$ on $\vec{b}$ is :
Vector Algebra Triple Products VTP with Repeated Vectors
MediumSingle correctIdea asked in 2 years
Q19
Let $\vec{a}=6\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . If $\vec{c}$ is a vector such that $|\vec{c}|\ge 6$ , $\vec{a}\cdot\vec{c}=6|\vec{c}|$ , $|\vec{c}-\vec{a}|=2\sqrt{2}$ and the angle between $\vec{a}\times\vec{b}$ and $\vec{c}$ is…
Vector Algebra Cross Product Magnitude and Sine Formula
HardSingle correctIdea asked in 7 yearsAsked the year before
Q20
If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :
Probability
EasySingle correct
Q21
Let $\alpha,\beta$ be roots of $x^2+\sqrt{2}x-8=0$ . If $U_n=\alpha^n+\beta^n$ , then $\frac{U_{10}+\sqrt{2}U_9}{2U_8}$ is equal to ________.
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
EasyNumerical valueIdea asked in 7 yearsAsked the year before
Q22
If the system of equations $2x+7y+\lambda z=3$ $3x+2y+5z=4$ $x+\mu y+32z=-1$ has infinitely many solutions, then $(\lambda-\mu)$ is equal to ________ :
Determinants Cramer's Rule Condition for Infinite Solutions
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q23
If $S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\cdots+60(1+x)^{60}$ , $x\ne 0$ , and $(60)^2 S(60)=a(b)^b+b$ , where $a,b\in\mathbb{N}$ , then $(a+b)$ equal to ________.
Binomial Theorem
HardNumerical value
Q24
Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f:[0,\infty)\to\mathbb{R}$ be a function defined by $f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]$ . Let $S$ be the set of all points in the interval $[0,8]$ at which $f$ is not continuous.…
Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Let $[t]$ denote the largest integer less than or equal to $t$ . If $\int_0^3\left([x^2]+\left[\frac{x^2}{2}\right]\right)dx=a+b\sqrt{2}-\sqrt{3}-\sqrt{5}+c\sqrt{6}-\sqrt{7}$ , where $a,b,c\in\mathbb{Z}$ , then $a+b+c$ is equal to ________.
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q26
If the solution $y(x)$ of the given differential equation $(e^y+1)\cos x\,dx+e^y\sin x\,dy=0$ passes through the point $\left(\frac{\pi}{2},0\right)$ , then the value of $e^{y\left(\frac{\pi}{6}\right)}$ is equal to ________.
Differential Equations Variable Separable Form Separability Check
EasyNumerical valueIdea asked in 2 years
Q28
If the shortest distance between the lines $\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4}$ is $\frac{44}{\sqrt{30}}$ , then the largest possible value of $|\lambda|$ is equal to ________.
Three Dimensional Geometry Skew Lines Finding an Unknown Parameter from Shortest Distance
MediumNumerical valueIdea asked in 3 years
Q29
From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is…
Probability
HardNumerical value
Q30
In a triangle $ABC$ , $BC=7$ , $AC=8$ , $AB=\alpha\in\mathbb{N}$ and $\cos A=\frac{2}{3}$ . If $49\cos(3C)+42=\frac{m}{n}$ , where $\gcd(m,n)=1$ , then $m+n$ is equal to ________.
Trigonometric Functions Properties of Triangles Cosine Rule Application
MediumNumerical valueNew idea

Dropped from the final key and left out of every count: Q27.

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.