Sure shot 60
JEE 2024 is around the corner
JEE MAIN CUT-OFF
Previous year JEE Main Qualifying Cut Off
Category
2023
2022
2021
2020
2019
General
90.7788642
88.4121383
87.8992241
90.3765335
89.7548849
EWS
75.6229025
63.1114141
66.2214845
70.2435518
78.2174869
OBC-NCL
73.6114227
67.0090297
68.0234447
72.8887969
74.3166557
SC
51.9776027
43.0820954
46.8825338
50.1760245
54.0128155
ST
37.2348772
26.7771328
34.6728999
39.0696101
44.3345172
PwD
0.0013527
0.0031029
0.0096375
0.0618524
0.11371730
Percentile
January 23
April 23
June 22
July 22
99
192
200
206
213
95
134
141
134
149
90
106
110
145
116
We know the important chapters
We know the important chapters
We know the important chapters
What are the type of questions going
to be asked from that…..
Let’s have the analysis of the
topics today
Chemistry
Chapter Name
Question Type
Periodic Properties
Ionisation enthalpy and
Electron gain enthalpy
Chemical Bonding
Molecular Orbital Theory, VSEPR Theory and Hybridisation
S block
Flame colour
P-Block
Oxoacids of P and S
D and f block
Magnetic Moment
Coordination compounds
spin magnetic moment
Mole concept
Stoichiometry based problems
Atomic structure
Quantum numbers
Chemical Equilibrium
equilibrium Constant
Thermodynamics
Reaction based
Solutions
ΔTf and ΔTb
Electrochemistry
Conductance
Chemical Kinetics
Activation Energy
General Organic Chemistry
Aromaticity and resonance
Environmental Chemistry
Smog
Chemistry
15 questions in total
Chemistry
15 questions in total
The mark you can get from these
topics are ≈ 60
Physics
Chapter Name
Question Type
Units & Measurements
Dimensions
Projectile Motion
Range & Velocity
Rotation
Moment of inertia
Gravitation
Variation in g
Solids
Young's Modulus
Thermodynamics
Heat Engine
Simple harmonic motion
Time period
Electrostatics
Electric Field
Capacitors
Dielectrics
Magnetic Field
Straight Wire & Circular Coil
Alternating current
Series RLC Circuit
EM Waves
E/B=C
Wave Optics
Young's Double Slit Experiment
MODERN PHYSICS
Half Life , Photoelectric Effect , De Broglie
& Electronic Transition
Semiconductors
Diode & Logic Gates
Physics
17 questions in total
Physics
17 questions in total
The marks you can get from these
topics are ≈ 68
Math
Chapter Name
Question Type
Quadratic equations
No. of roots and roots & coefficients
Sequence and Series
Arithmetic Progression/Vn Method
Binomial Theorem
Finding remainder/ General term (Coefficients)
Matrices and Determinants
Properties of Adjoint/System of linear equations
3D Geometry
Shortest distance between lines
Differential equations
Linear Differential Equations
Mathematical Reasoning
logical equivalent and Tautology
Area under the Curve
Area under parabola and line
Parabola
Tangent to parabola
Math
9 questions in total
Math
9 questions in total
The marks you can get from these
topics are ≈ 36
≈ 164 marks in total
NIT CSE with 164 marks
NIT DURGAPUR (HS)
NIT Manipur (OS)
NIT JALANDHAR (HS)
NIT Hamirpur (HS)
NIT SILCHAR (os)
NIT Uttarakhand (OS)
NIT RAIPUR (os)
NIT Puducherry (OS)
NIT GOA
NIT Arunachal Pradesh (OS)
NIT PATNA (OS)
NIT Sikkim (OS)
NIT MEGHALAYA (os)
NIT AGARTALA (OS)
NIT SRINAGAR (OS)
NIT Mizoram (OS)
NIT Nagaland (OS)
NIT Andhra Pradesh (OS)
≈ 164 marks in total
A few more steps to 99%ile
Now, let’s have a look to these questions
Chemistry
Ionisation enthalpy and Electron gain enthalpy
JEE Main 25th January 2023 S-1
JEE Main 25th July 2022 S-2
Q. Inert gases have positive electron
gain enthalpy. Its correct order is
(A) Xe < Kr < Ne < He
(B) He < Ne < Kr < Xe
(C) He < Xe < Kr < Ne
(D) He < Kr < Xe < Ne
Q. The first ionization enthalpies of Be, B,
N and O follow the order
(A) O < N < B < Be
(B) Be < B < N < O
(C) B < Be < N < O
(D) B < Be < O < N
JEE Main 25th June 2022 S-2
Q. The correct order of electron gain
enthalpies of Cl, F, Te and Po is
(A) F < Cl < Te < Po
(B) Po < Te < F < Cl
(C) Te < Po < Cl < F
(D) Cl < F < Te < Po
JEE Main 01th February 2023 S-2
Q. For electron gain enthalpies of the
elements denoted as ΔegH, the incorrect
option is:
(A) ΔegH(Cl) < ΔegH(F)
(B) ΔegH(Se) < ΔegH(S)
(C) ΔegH(I)< ΔegH(At)
(D) ΔegH(Te) < ΔegH(Po)
Ionisation enthalpy and Electron gain enthalpy
JEE Main 29th June 2022 S-2
Q. Given below are two statements. One
is labelled as Assertion A and the order
is labelled as Reason R.
Assertion A: The first ionization enthalpy
for oxygen is lower than that of nitrogen.
Reason R: The four electrons in 2p
orbitals of oxygen experience more
electron-electron repulsion.
In the light of the above statements,
choose the correct answer from the
options given below.
(A) Both A and R are correct and R is the
correct explanation of A.
(B) Both A and R are correct but R is NOT
the correct explanation of A.
(C) A is correct but R is not correct.
(D) A is not correct but R is correct.
JEE Main 27th July 2022 S-2
Q. Outermost electronic configurations
of four elements A, B, C, D are given
below:
(A) 3s2
(B) 3s23p1
(C) 3s23p3
(D) 3s23p4
The correct order of first ionization
enthalpy for them is :
(A) (A) < (B) < (C) < (D)
(B) (B) < (A) < (D) < (C)
(C) (B) < (D) < (A) < (C)
(D) (B) < (A) < (C) < (D)
Ionisation enthalpy and Electron gain enthalpy
JEE Main 25th January 2023 S-1
Q. Given below are two statements: one
is labelled as Assertion (A) and the
other is labelled as Reason (R)
Assertion A: The first ionization enthalpy
of 3d series elements is more than that
of group 2 metals
Reason R: In 3d series of elements
successive filling of d-orbitals takes
place.
In the light of the above statements,
choose the correct answer from the
options given below:
(A) Both A and R are true and R is the
correct explanation of A
(B) Both A and R are true but R is not the
correct explanation of A
(C) A is false but R is true
(D) A is true but R is false
Molecular Orbital Theory
JEE Main 24th June 2022 S-2
JEE Main 25th July 2022 S-1
Q. The correct order of bond orders of C22-, N22and O22- is, respectively.
(A) C22- < N22- < O22-
(B) O22- < N22- < C22-
(C) C22- < O22- < N22-
(D) N22- < C22- < O22-
JEE Main 25th June 2022 S-1
Q. Bonding in which of the following diatomic
molecule(s) become(s) stronger, on the basis of
MO Theory, by removal of an electron?
(A) NO (B) N2
(C) O2
(D) C2 (E) B2
Q. Among the following species
N2, N2+, N2-, N22-, O2, O2+, O2-, O22the number of species showing diamagnetism
is
JEE Main 27th July 2022 S-1
Q. Amongst the following the number of
oxide(s) which are paramagnetic in nature is
Na2O, KO2, NO2, N2O, ClO2, NO, SO2, Cl2O
JEE Main 27th July 2022 S-1
Q. According to MO theory, number of
species/ions from the following having identical
bond order is___:
CN- , NO+ , O2 , O2+ , O22+
Molecular Orbital Theory
JEE Main 24th Jan 2023 S-2
JEE Main 26th June 2022 S-1
Q. What is the number of unpaired electrons(s)
in the highest occupied molecular orbital of the
following species: N2 ; N2+ ; O2; O2+ ?
(A) 0, 1, 2, 1 (B) 2, 1, 2, 1 (C) 0, 1, 0, 1 (D) 2, 1, 0, 1
Q. Consider the ions/molecule
JEE Main 29th Jan 2023 S-2
Q. According to MO theory the bond orders for
O22-, CO and NO+ respectively are
(A) 1, 3, and 3
(B) 1, 3, and 2
(C) 1, 2, and 3
(D) 2, 3 and 3
JEE Main 25th June 2022 S-1
Q. The number of paramagnetic species
among the following is____.
B2, Li2, C2, C2-, O22-, O2+ and He2+
O2+, O2, O2-, O22-
For increasing bond order the correct option is:
(A) O22- < O2- < O2 < O2+ (B) O2- < O22- < O2 < O2+
(C) O2- < O22- < O2+ < O2 (D) O2- < O2+ < O22- < O2
VSEPR Theory and Hybridisation
JEE Main 24th June 2022 S-2
JEE Main 25th July 2022 S-2
Q. Amongst SF4, XeF4, CF4 and H2O, the number
of species with two lone pairs of electrons___.
Q. The sum of number of lone pairs of electrons
present on the central atoms of
XeO3, XeOF4 and XeF6 is____
JEE Main 27th June 2022 S-1
Q. Based upon VSEPR theory, match the shape
(geometry) of the molecules in List - I with the
molecules in List - II and select the most
appropriate option
List - I
List-II
(Shape)
(Molecules)
(A) T-shaped
(I) XeF4
(B) Trigonal planar
(II) SF4
(C) Square planar
(III) ClF3
(D) See-saw
(IV) BF3
(A) (A)-I, (B)-II, (C)-III, (D)-IV
(B) (A)-III, (B)-IV, (C)-I, (D)-III
(C) (A)-III, (B)-IV, (C)-II, (D)-I
(D) (A)-IV, (B)-III, (C)-I, (D)-II
JEE Main 25th July 2022 S-2
Q. The sum of number of lone pairs of electrons
present on the central atoms of
XeO3, XeOF4 and XeF6 is____
JEE Main 29th July 2022 S-2
Q. Consider, PF5, BrF5, PCl3, SF6, [ICl4]-, ClF3 and
IF5.
Amongst the above molecule(s)/ion(s), the
number of molecules(s)/ion(s) having sp3d2
hybridization is____.
VSEPR Theory and Hybridisation
JEE Main 27th June 2022 S-2
JEE Main 28th June 2022 S-2
Q. Identify the incorrect statement for PCl5 from
the following.
(A) In this molecule, orbitals of phosphorus are
assumed to undergo sp3d hybridization
(B) The geometry of PCl5 is trigonal
bipyramidal.
(C) PCl5 has two axial bonds stronger than
three equatorial bonds
(D) The three equatorial bonds of PCl5 lie in a
plane.
Q. In the structure of SF4, the lone pair of
electrons on S is in.
(A) Equatorial position and there are two Ione
pair-bond pair repulsions at 90°
(B) Equatorial position and there are three lone
pair-bond pair repulsions at 90°
(C) Axial position and there are three lone pairbond pair repulsion at 90°
(D) Axial position and there are two lone pairbond pair repulsion at 90°
JEE Main 27th July 2022 S-2
Q. The number of molecule(s) or ions(s) from
the following having non-planar structure is__.
NO3-, H2O2, BF3, PCl3, XeF4,
SF4, XeO3, PH4+, SO3 [Al(OH)4]-
VSEPR Theory and Hybridisation
JEE Main 28th June 2022 S-1
JEE Main 29th June 2022 S-2
Q. The hybridization of P exhibited in PF5 is spxdy.
The value of y is____.
Q. Consider the species CH4, NH4+ and BH4-. Choose
the correct option with respect to the there species:
(A) They are isoelectronic and only two have
tetrahedral structures
(B) They are isoelectronic and all have tetrahedral
structures
(C) Only two are isoelectronic and all have
tetrahedral structures
(D) Only two are isoelectronic and only two have
tetrahedral structures
JEE Main 29th July 2022 S-1
Q. Number of lone pairs of electrons in the
central atom of SCl2, O3, ClF3 and SF6,
respectively, are:
(A) 0, 1, 2 and 2
(B) 2, 1, 2
and 0
(C) 1, 2, 2 and 0
(D) 2, 1, 2
and 0
JEE Main 29th June 2022 S-2
Q. Number of lone pair (s) of electrons on
central atom and the shape of BrF3 molecule
respectively, are:
(A) 0, triangular planar
(B) 1, pyramidal
(C) 2, bent T-shape
(D) 1, bent T-shape
VSEPR Theory and Hybridisation
JEE Main 26th July 2022 S-1
Q. Match List-I with List-II
List-I
List-II
(Compound)
(Shape)
(A) BrF5
(I) bent
(B) [CrF6]3(II) Square pyramidal
(C) O3
(III) Trigonal
bipyramidal
(D) PCl5
(IV) Octahedral
Choose the correct answer from the options
given below:
(A) A-I, B-II, C-III, D-IV (B) A-IV, B-III, C-II, D-I
(C) A-II, B-IV, C-I, D-III (D) A-III, B-IV, C-II, D-I
JEE Main 25th July 2022 S-2
Q. Match List-I with List-II:
List-I
List-II
(A) XeO3
(I) sp3d; linear
(B) XeF2
(II) sp3; pyramidal
(C) XeOF4 (III) sp3d3; distorted octahedral
(D) XeF6
(IV) sp3d2; square pyramidal
Choose the correct answer from the options
given below:
(A) A-II, B-I, C-IV, D-III
(B) A-II, B-IV, C-III, D-I
(C) A-IV, B-II, C-III, D-I
(D) A-IV, B-II, C-I, D-III
JEE Main 31th Jan 2023 S-2
Q. Amongst the following, the number of
species having the linear shape is___.
XeF2, I3+, C3O2, I3-, CO2, SO2, BeCl2 and BCl2Θ
VSEPR Theory and Hybridisation
JEE Main 30th Jan 2023 S-1
Q. Match List-I with List-II:
List-I
List-II
(Molecule/ions)
(No. of lone pairs of eon
central atom)
(A) IF7
(I) Three
(B) ICl4(II) One
(C) XeF6
(III) Two
(D) XeF2
(IV) Zero
Choose the correct from the options given
below:
(A) A-II, B-III, C-IV, D-I (B) A-IV, B-III, C-II, D-I
(C) A-II, B-I, C-IV, D-III (D) A-IV, B-1, C-II, D-III
JEE Main 31th Jan 2023 S-1
Q. Match List-I with List-II:
List-I
List-II
(A) XeF4
(I) See - Saw
(B) SF4
(II) Square planar
+
(C) NH4
(III) Bent T-shaped
(D) BrF3
(IV) Tetrahedral
Choose the correct answer from the options
given below:
(A) A-IV, B-IIII, C-II, D-I (B) A-II, B-I, C-III, D-IV
(C) A-IV, B-I, C-II, D-III (D) A-II, B-I, C-IV, D-III
Flame colour – s block
JEE Main 26th June 2022 S-2
Q. S-block element which cannot be
qualitatively confirmed by the flame
test is
(A) Li
(B)
Na
(C) Rb
(D) Be
JEE Main 24th June 2022 S-2
Q. In the flame test of a mixture of salts,
a green flame with blue centre was
observed. Which one of the following
cations may be present?
(A) Cu2+
(B) Sr2+
(C) Ba2
(D) Ca2
JEE Main 07th January 2023 S-2
Q. Given below are two statements, one
is labelled as Assertion A and the other
is labelled as Reason R.
Assertion A:- The alkali metals and their
salts impart characteristic colour to
reducing flame.
Reason R:- Alkali metals can be
detected using flame tests.
In the light of the above statements,
choose the most appropriate answer
form the options given below.
(A) Both A and R are correct but R is not
the correct explanation of A.
(B) A is correct but R is not correct.
(C) A is not correct but R is correct.
(D) Both A and R are correct and R is the
correct explanation of A.
Flame colour – s block
th June 2022 S-1
JEE
Main 29List
Q. Match
I with List II
List-I
II
(Metal)
JEE Main 25th January 2023 S-1
List-
(Emitted light
wavelength (nm))
(I)
(A) Li
670.8
(B) Na
(II) 589.2
(C) Rb
(III) 780.0
(D) Cs
(IV) 455.5
Choose the correct answer from the
options given below:
A. A-I, B-II, C-III, D-IV
B. A-III, B-II, C-I, D-IV
C. A-III, B-I, C-II, D-IV
D. A-IV, B-II, C-I, D-III
Q. Q. Match List I with List II
List-I
List-II
(Elements)
(Colour imparted to
the flame)
(A) K
(I) Brick Red
(B) Ca
(II) Violet
(C) Sr
(III) Apple Green
(D) Ba
(IV) Crimson Red
Choose the correct answer from the options given below:
A
A-II, B-I, C-III, D-IV
B
A-II, B-IV, C-I, D-III
C
A-II, B-I, C-IV, D-III
D
A-IV, B-III, C-II, D-I
Oxoacids of P and S
JEE Main 26th June 2022 S-1
JEE Main 29th June 2022 S-1
Consider the following reaction:
A + alkali → B (Major Product) If B is an
oxoacid of phosphorus with no P–H
bond, then A is
(A) White P4
(B) Red P4
(C) P2O3
(D) H3PO3
The oxoacid of phosphorus
that is easily obtained from a
reaction of alkali and white
phosphorus and has two P-H
bonds, is:
(A) Phosphoric acid
(B) Phosphinic acid
(C) Pyrophosphorus acid
(D) Hypophosphoric acid
JEE Main 28th June 2022 S-2
Which of the following oxoacids of
sulphur contains “S” in two different
oxidation states?
(A) H2S2O3
(B) H2S2O6
(C) H2S2O7
(D) H2S2O8
JEE Main
27th
July 2022 S-1
Which oxoacid of phosphorous
has the highest number of
oxygen atoms present in its
chemical formula?
(A) Pyrophosphorous acid
(B) Hypophosphoric acid
(C) Phosphoric acid
(D) Pyrophosphoric acid
JEE Main 24th Jan 2023 S-1
Which of the phosphorus oxoacid
can create silver mirror from
AgNO3 solution?
(A) (HPO3)n
(B) H4P2O5
(C) H4P2O6
(D) H4P2O7
JEE Main 31th Jan 2023 S-1
The oxidation state of phosphorus
in hypophosphoric acid is
+____ .
Oxoacids of P and S
JEE Main 24th Jan 2023 S-2
Sum of 𝜋-bonds present in
peroxides and pyrosulphuric
acid is
JEE Main 29th July 2022 S-2
Q. Consider the following sulphur based
oxoacids.
H2SO3, H2SO4, H2S2O8 and H2S2O7.
Amongst these oxoacids, the number of those
with peroxo(O-O) bond is___ .
Magnetic Moment - D and f block
JEE Main 24th January 2023 S-1
JEE Main 27th June 2022 S-1
Q. The magnetic moment of a transition
metal compound has been calculated
to be 3.87 B.M. The metal ion is
(A) Cr2+
(B) Mn2+
(C) V2+
(D) Ti2+
Q. Acidified potassium permanganate
solution oxidises oxalic acid. The spinonly magnetic moment of the
manganese product formed from the
above reaction is ______ B.M.
(Nearest integer)
JEE Main 29th June 2022 S-1
Q. An acidified manganate solution
undergoes disproportionation reaction.
The spin-only magnetic moment value
of the product having manganese in
higher oxidation state is ______ B.M.
(Nearest integer)
JEE Main 26th July 2022 S-2
Q. The spin-only magnetic moment
value of the compound with strongest
oxidizing ability among MnF4, MnF3 and
MnF2 is _______ B.M. [nearest
integer].
Magnetic Moment - D and f block
JEE Main 25th July 2022 S-1
JEE Main 25th June 2022 S-2
Q. Among Co3+, Ti2+, V2+ and Cr2+ ions,
one if used as a reagent cannot liberate
H2 from dilute mineral acid solution, its
spin-only magnetic moment in gaseous
state is ______ B.M. (Nearest integer).
Q. The metal ion (in gaseous state) with
lowest spin only magnetic moment
value is
(A) V2+
(B) Ni2+
(C) Cr2+
(D) Fe2+
JEE Main 25th Jan 2023 S-1
JEE Main 26th June 2022 S-1
Q. How many of the following metal ions have
similar value of spin only magnetic moment in
gaseous state?____
(Given: Atomic number: V, 23 ; Cr, 24; Fe, 26; Ni,
28) V3+, Cr3+, Fe2+, Ni3+
Q. The spin-only magnetic moment value of the
most basic oxide of vanadium among V2O3,
V2O4 and V2O5 is _______ B.M. [nearest
integer].
spin magnetic moment
JEE Main 25th June 2022 S-2
JEE Main 27th June 2022 S-2
JEE Main 26th July 2022 S-1
Amongst FeCl3.3H2O, K3[Fe(CN)6] and
[Co(NH3)6]Cl3, the spin-only magnetic
moment value of the inner-orbital
complex that absorbs light at shortest
wavelength is _____ B.M.
Arrange the following
coordination compounds in
the increasing order of
magnetic moments.. (Atomic
numbers : Mn = 25; Fe = 26)
(A) [FeF6]3- (B) [Fe(CN)6]3(C) [MnCl6]3- (D) [Mn(CN)6]3(A) A < B < D < C
(B) B < D < C < A
(C) A < C < D < B
(D) B < D < A < C
The difference between spin
only magnetic moment value
of [Co(H2O)6]Cl2 and
[Cr(H2O)6]Cl3 is ____ .
JEE Main
26th June
2022 S-1
The spin-only magnetic moment value
of an octahedral complex among
CoCl3.4NH3, NiCl2.6H2O and PtCl4.2HCl,
which upon reaction with excess of
AgNO3 gives 2 moles of AgCl is ____
B.M. (Nearest Integer)
JEE Main 27th July 2022 S-2
The spin only magnetic
moment of the complex
present in Fehling’s reagent is
____ B.M.
spin magnetic moment
JEE Main 25th July 2022 S-1
JEE Main 29th June 2022 S-2
Consider the following metal
complexes :
[Co(NH3)]3+
[CoCl(NH3)5]2+
[Co(CN)6]3[Co(NH3)5(H2O)]3+
The spin-only magnetic
moment value of the complex
that absorbs light with shortest
wavelength B.M.
Spin only magnetic moment of
[MnBr6]4- is ___ B.M. (round off to the
closest integer)
JEE Main 01st Feb 2023 S-2
The spin only magnetic moment of
[Mn(H2O)6]2+ complexes is ____ B.M.
(Nearest integer)
JEE Main 29th Jan 2023 S-2
Q. Correct order of spin only magnetic moment
of the following complex ions is:
A
[FeF6]3- > [CoF6]3- > [Co(C2O4)3]3-
B
[Co(C2O4)3]3- > [CoF6]3- > [FeF6]3-
C
[FeF6]3- > [Co(C2O4)3]3- > [CoF6]3-
D
[CoF6]3- >[FeF6]3- > [Co(C2O4)3]3-
Stoichiometry - Mole concept
JEE Main 31th Jan 2023 S-1
JEE Main 31th Jan 2023 S-1
Q. Zinc reacts with hydrochloric acid to give
hydrogen and zinc chloride. The volume of
hydrogen gas produced at STP from the
reaction of 11.5 g of zinc with excess HCl is __N
(Nearest integer)
(Given : Molar mass of Zn is 65.4g mol-1 and
Molar volume of H2 at STP = 22.7L)
Q. Assume carbon burns according to following
equation:
When 12 g carbon is burnt in 48 g of oxygen, the
volume of carbon monoxide produced is___
× 10-1 L at STP [Nearest integer]
[Given: Assume CO as ideal gas, Mass of C is 12
g mol-1, Mass of O is 16 g mol-1 and molar
volume of an ideal gas at STP is 22.7 L mol-1]
JEE Main 31th Jan 2023 S-2
Q. When a hydrocarbon A undergoes complete
combustion it requires 11 equivalents of oxygen
and produces 4 equivalents of water. What is
the molecular formula of A?
(A) C9H8
(B) C11H4
(C) C5H8
(D) C11H8
JEE Main 25th July 2022 S-2
Q. 56.0 L of nitrogen gas is mixed with excess of
hydrogen gas and it is found that 20 L of
ammonia gas is produced. The volume of
unused nitrogen gas is found to be___ L.
Stoichiometry - Mole concept
JEE Main 26th June 2022 S-1
Q. On complete combustion 0.30 g of an
organic compound gave 0.20 g of carbon
dioxide and 0.10 g of water. The percentage of
carbon in the given organic compound is____
(Nearest Integer)
JEE Main 28th July 2022 S-1
Q. On complete combustion of 0.492 g of an
organic compound containing C, H and O,
0.7938g of CO2 and 0.4428 g of H2O was
produced. The % composition of oxygen in the
compound is____.
JEE Main 29th Jan 2023 S-2
Q. When a hydrocarbon A undergoes
combustion in the presence of air, it requires 9.5
equivalents of oxygen and produces 3
equivalents of water. What is the molecular
formula of A?
(A) C8H6
(B) C9H9
(C) C6H6
(D) C9H6
JEE Main 29th Jan 2023 S-2
Q. When 0.01 mol of an organic compound
containing 60% carbon was burnt completely,
4.4 g of CO2 was produced. The molar mass of
compound is ____ g mol-1 (Nearest integer)
Stoichiometry - Mole concept
JEE Main 24th June 2022 S-2
Q. If a rocket runs on a fuel (C15 H30) and liquid
oxygen, the weight of oxygen required and CO2
released for every litre of fuel respectively are:
(Given: density of the fuel is 0.756 g/mL)
(A) 1188 g and 1296 g (B) 2376 and 2592 g
(C) 2592 g and 2376 g (D) 3429 g and 3142 g
JEE Main 29th July 2022 S-2
Q. A 1.84 mg sample of polyhydric alcoholic
compound ‘X’ of molar mass 92.0 g/mol gave
1.344 mL of H2 gas at STP. The number of
alcoholic hydrogens present in compound ‘X’
is____.
Q.
⇌ 2NH
th July
2(g) +
2(g) 2022
3(g)
JEEN
Main
293H
S-1
20 g 5 g
Consider the above reaction, the limiting
reagent of the reaction and number of moles of
NH3 formed respectively are:
(A) H2, 1.42 moles
(B) H2, 0.71
moles
(C) N2, 1.42 moles
(D) N2, 0.71
moles
JEE Main 29th July 2022 S-2
Q. Consider the reaction
4HNO3(l) + 3KCl(s) → Cl2(g) + NOCl(g) +
2H2O(g) + 3KNO3(s)
The amount of HNO3 required to produce 110.0 g
of KNO3 is
(Given: Atomic masses of H, O, N and K are 1, 16,
14 and 39, respectively)
(A) 32.2 g (B) 69.4 g (C) 91.5 g (D) 162.5 g
Stoichiometry - Mole concept
JEE Main 29th Jan 2023 S-2
JEE Main 28th July 2022 S-1
Q. On complete combustion, 0.492 g of an
organic compound gave 0.792 g of CO2.
The % of carbon in the organic compound
is___
(Nearest integer)
Q. In the given reaction,
X + Y + 3Z ⇌ XYZ3
If one mole of each of X and Y with 0.05 mol of Z
gives compound XYZ3. (Given : Atomic masses
of X, Y and Z are 10, 20 and 30 amu,
respectively). The yield of XYZ3 is____g.
(Nearest integer)
JEE Main 26th June 2022 S-2
Q. The mole of methane required to produce 81
g of water after complete combustion is___ ×
10-2 mol. [Nearest Integer]
Quantum numbers
JEE Main
24th Jan
JEE Main 29th June 2022 S-1
2023 S-2
Q. The number of s-electrons present in an ion with
55 protons in its unipositive state is
(A) 8
(B) 9
(C)
12
(D) 10
JEE Main 29th June 2022 S-1
Q. The electronic configuration of Pt (atomic
number 78) is:
(A) [Xe] 4f14 5d9 6s1
(B) [Kr] 4f14 5d10
(C) [Xe] 4f14 5d10
(D) [Xe] 4f14
5d8 6s2
JEE Main 30th Jan 2023 S-2
Q. Maximum number of electrons that can be
accommodated in shell with n = 4 are
(A) 16
(B) 32
(C) 50
72
(D)
Q. Which of the following statements are correct?
(A) The electronic configuration of Cr is [Ar] 3d5 4s1
(B) The magnetic quantum number may have a
negative value.
(C) In the ground state of an atom, the orbitals are
filled in order of their increasing energies.
(D) The total number of nodes are given by n-2
Choose the most appropriate answer from the
options given below:
(A) (A), (C) and (D) only
(B) (A) and (B) only
(C) (A) and (C) only
(D) (A), (B) and (C) only
Quantum numbers
JEE Main 27th June 2022 S-2
Q. Consider the following set of quantum numbers
n
l
m1
A.
3
3
-3
B.
3
2
-2
C.
2
1
+1
D.
2
2
+2
The number of correct sets of quantum numbers is
JEE Main 27th July 2022 S-2
Q. The correct decreasing order of energy, for the
orbitals having, following set of quantum numbers:
(A) n = 3, l = 0, m = 0
(B) n = 4, l = 0, m = 0
(C) n = 3, l = 1, m = 0
(D) n = 3, l = 2, m = 1
(A) D > B > C > A
(B) B > D > C > A
(C) C > B > D > A
(D) B > C > D >
A
JEE Main 27th July 2022 S-1
Q. Given below are two statements. One is labelled
as Assertion A and the other is labelled as Reason
R. Assertion A : Energy of 2 s orbital of hydrogen
atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same
subshell decrease with increase in the atomic
number.
In the light of the above statements, choose the
correct answer from the options given below.
(A) Both A and R are true and R is the correct
explanation of S.
(B) Both A and R are true but R is NOT the correct
explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
Quantum numbers
JEE Main 28th June 2022 S-2
Q. Consider the following statements:
(A) The principal quantum number ‘n’ is a positive
integer with values of ‘n’ = 1, 2, 3, …
(B) The azimuthal quantum number ‘l’ for a given
‘n’ (principal quantum number) can have values as
‘l’ = 0, 1, 2, ….. n
(C) Magnetic orbital number ‘ml’ for a particular ‘l’
(azimuthal quantum number) has (2l + 1) values.
(D) ± ½ are the two possible orientations of electron
spin
(E) For l = 5, there will be a total of 9 orbital.
Which of the above statements are correct?
(A) (A), (B) and (C)
(B) (A), (C), (D) and (E)
(B) (A), (C) and (D)
(D) (A), (B), (C) and (D)
JEE Main 29th July 2022 S-2
Q. Given below are the quantum numbers for 4
electrons.
A. n = 3, l = 2, m1 = 1, ms = + ½
B. n = 4, l = 1, m1 = 0, ms = + ½
C. n = 4, l = 2, m1 = - 2, ms = - ½
D. n = 3, l = 1, m1 = - 1, ms = + ½
The correct order of increasing energy is:
(A) D < B < A < C
(B) D < A < B <
C
(C) B < D < A < C
(D) B < D < C <
A
JEE Main 25th July 2022 S-1
Q. Which of the following sets of quantum numbers
is not allowed?
(A) n = 3, 1 = 2, m1 = 0, s = + ½
(B) n = 3, 1 = 2, m1 = - 2, s = + ½
(C) n = 3, 1 = 3, m1 = - 3, s = - ½
(D) n = 3, 1 = 0, m1 = 0, s = - ½
Equilibrium Constant - Chemical Equilibrium
JEE Main 27th June 2022 S-1
Q. 2NOCl(g) ⇌ 2NO(g) + Cl2(g)
In an experiment, 2.0 moles of NOCl was placed
in a one-litre flask and the concentration of NO
after equilibrium established, was found to be
0.4 mol/L. The equilibrium constant at 30℃ is
______ × 10-4.
JEE Main 28th July 2022 S-2
Q. At 600 K, 2 mol of NO are mixed with 1 mol of O 2.
2NO(g) + O2(g) ⇌ 2NO2(g)
The reaction occurring as above comes to
equilibrium under a total pressure of 1 atm.
Analysis of the system shows that 0.6 mol of
oxygen are present at equilibrium. The equilibrium
constant for the reaction is _____. (Nearest
integer).
JEE Main 26th July 2022 S-1
Q. AT 298 K, the equilibrium constant is 2 × 1015
for the reaction:
Cu(s) + 2Ag+(aq) ⇌ Cu2+(aq) + 2Ag(s)
The equilibrium constant for the reaction
1/2Cu2+(aq) + Ag(s) ⇌ 1/2Cu(s) + Ag+(aq)
is x × 10-8. The value of x is ______ . (Nearest
Integer).
Equilibrium Constant - Chemical Equilibrium
JEE Main 31th January 2023 S-1
Q. For reaction:
Kp = 2 × 1012 at 27℃ and 1 atm pressure. The Kc
for the same reaction is _______ × 1013.
(Nearest integer)
(Given R = 0.082 L atm K-1 mol-1)
JEE Main 29th January 2023 S-2
Q. At 298 K
N2(g) + 3H2(g) ⇌ 2NH3(g), K1 = 4 × 105
N2(g) + O2(g) ⇌ 2NO(g), K2 = 1.6 × 1012
H2(g) + 1/2O2(g) ⇌ H2O(g), K3 = 1.0 × 10-13
Based on above equilibria, the equilibrium
constant of the reaction,
2NH3(g) + 5/2O2(g) ⇌ 2NO(g) + 3H2O(g) is
_____ × 10-33 (Nearest integer)
Q.
For a reaction at equilibrium
JEE Main 24h June 2022 S-1
A(g) ⇌ B(g) + 1/2C(g) the relation between
dissociation constant (K), degree of
dissociation (α) and equilibrium pressure (p)
is given by:
(A)
(C)
JEE Main
(B)
(D)
24th June
2022 S-2
Q. PCl5 dissociates as PCl5(g)⇌ PCl3(g) +
Cl2(g)
5 moles of PCl5 are placed in a 200 litre vessel
which contains 2 moles of N2 and is
maintained at 600 K. The equilibrium pressure
is 2.46 atm. The equilibrium constant Kp for the
dissociation of PCl5 is ______ × 10-3. (nearest
integer)
(Given: R = 0.082 L atm K -1 mol-1; Assume ideal
Reaction based - Thermodynamics
JEE Main 25th June 2022 S-2
At 25oC and 1 atm pressure, the
enthalpy of combustion of benzene (l)
and acetylene (g) re -3268 kJ mol-1 and
-1300 kJ mol-1, respectively. The change
in enthalpy for the reaction
3C2H2 → C6H6(l), is
(A)+324 kJ mol-1
(B) +632 kJ mol-1
(C) -632 kJ mol-1
(D) -732 kJ mol-1
JEE Main 25th July 2022 S-1
The enthalpy of combustion of propane, graphite and dihydrogen
at 298 K are :- 2220.0 kJ mol-1, -393.5 kJ mol-1 and -285.8 kJ mol-1
respectively. The magnitude enthalpy of formation of propane
(C3H8) is _____ kJ mol-1.(Nearest integer)
JEE Main 25th July 2022 S-1
While performing a thermodynamics experiment, a student made
the following observations,
HCl + NaOH → NaCl + H2O , ∆H = - 57.3 kJ mol-1
CH3COOH + NaOH → CH3COONa + H2O , ∆H = -55.3 kJ mol-1
The enthalpy of ionization of CH3COOH as calculated by the
student is _____ kJ mol-1.(Nearest integer)
Reaction based - Thermodynamics
JEE Main 26th June 2022 S-2
JEE Main 21st June 2023 S-1
For complete combustion of methanol
CH3OH(1)+3/2O2(g)→ CO2(g) + 2H2O(l)
The amount of heat produced as
measured by bomb calorimeter is 726
kJ mol-1 at 27oC. The enthalpy of
combustion for the reaction is -x kJ
mol-1, where x is _____. (Nearest
integer)
(Given : R = 8.3 JK-1 mol-1)
The enthalpy change for the conversion
of 1/2Cl2 (g) to Cl-(aq) is (-) _____
Kj mol-1 (Nearest integer)
Given :
JEE Main 25th Jan 2023 S-2
28 L of CO2 is produced on complete
combustion of 16.8 L gaseous mixture of ethene
and methane at 25oC and 1 atm. Heat evolved
during the combustion process is ______ kJ.
Given ∆HC(CH4) = -900 kJ mol-1
∆Hc(C2H4) = -1400 kJ mol-1
Solutions - ΔTf and ΔTb
JEE Main 24th Jan 2023 S-1
Q. In the depression of freezing point experiment
A. Vapour pressure of the solution is less than that
of pure solvent.
B. Vapour pressure of the solution is more than
that of pure solvent.
C. Only solute molecules solidify at the freezing
point.
D. Only solvent molecules solidify at the freezing
point.
(A) A and D only
(B) B and C
only
(C) A and C only
(D) A only
JEE Main 30th Jan 2023 S-1
Q. A solution containing 2 g of a non-volatile
solute in 20 g of water boils at 373.52 K. The
molecular mass of the solute is _____ g mol-1.
(Nearest integer)
Given, water boils at 373 K, Kb for water = 0.52 K kg
mol-1)
JEE Main 30th Jan 2023 S-2
Q. Lead storage battery contains 38% by weight
solution of H2SO4. The van’t Hoff factor is 2.67 at
this concentration. The temperature in Kelvin at
which the solution in the battery will freeze is
____(Nearest integer).
Given Kf=1.8 K kg mol-1
Solutions - ΔTf and ΔTb
JEE Main 29th Jan 2023 S-1
Q. Solid Lead nitrate is dissolved in 1 litre of
water. The solution was found to boil at 100.15℃.
When 0.2 mol of NaCl is added to the resulting
solution, it was observed that the solution froze
at -0.8℃. The solubility product of PbCl2 formed
is _____ × 10-6 at 298 K. (Nearest integer)
Given: Kb = 0.5 K kg mol-1 and Kf = 1.8 kg mol-1.
Assume molarity to be equal to molarity in all
cases.c
JEE Main
25th
June 2022 S-2
Q. Solute A associates in water. When 0.7 g of
solute A is dissolved in 42.0 g of water, it
depresses the freezing point by 0.2℃. The
percentage association of solute A in water, is
[Given: Molar mass of A = 93 g mol-1. Molal
depression constant of water is 1.86 K kg mol-1]
(A) 50%
(B) 60%
(C) 70%
(D) 80%
JEE Main 26th June 2022 S-1
Q. A 0.5 percent solution of potassium chloride
was found to freeze at -0.24℃. The percentage
dissociation of potassium chloride is ______.
(Nearest integer)
(Molar depression constant for water is 1.80 K
kg mol-1 and molar mass of KCl is 74.6 g mol-1).
JEE Main 27th June 2022 S-1
Q. 2g of a non-volatile non-electrolyte solute is
dissolved in 200 g of two different solvents A
and B whose ebullioscopic constants are in the
ratio of 1 : 8. The elevation in boiling points of A
and B are in the ratio x/y(x : y). The value of y is
______ (Nearest integer).
Solutions - ΔTf and ΔTb
JEE Main 29th July 2022 S-2
JEE Main 29th June 2022 S-1
Q. 1.80 g of solute A was dissolved in 62.5 cm3 of
ethanol and freezing point of the solution was
found to be 155.1 K. The molar mass of solute A
is ____ g mol-1.
[Given: Freezing point of ethanol is 156.0 K
Density of ethanol is 0.80 g cm-3. Freezing point
depression constant of ethanol is 2.00 K kg mol1]
Q. 1.2 mL of acetic acid is dissolved in water to
make 2.0 L of solution. The depression in
freezing point observed for this strength of acid
is 0.0198℃. The percentage of dissociation of
the acid is _____(Nearest integer)
[Given: Density of acetic acid is 1.02 g mL-1
Molar mass of acetic acid is 60 g mol-1 Kf(H2O)
= 1.85 K kg mol-1]
JEE Main 27th June 2022 S-2
JEE Main 29th June 2022 S-2
Q. A solution containing 2.5 × 10-3 kg of a solute
dissolved in 75 × 10-3 kg of water boils at
373.535 K. The molar mass of the solute is
____ g mol-1. [nearest integer] (Given : Kb
(H2O) = 0.52 K Kg mol-1, boiling point of water =
373.15 K)
Q. Elevation in boiling point for 1.5 molal solution
of glucose in water is 4K. The depression in
freezing point for 4.5 molar solution of glucose
in water is 4K. The ratio of molal elevation
constant to molal depression constant (Kb/Kf)
is _______ .
Solutions - ΔTf and ΔTb
JEE Main 25th July 2022 S-1
JEE Main 26th July 2022 S-2
Q. The depression in freezing point observed for
a formic acid solution of concentration 0.5 mL L1 is 0.0405℃. Density of formic acid is 1.05 g mL1. The Van’t Hoff factor of the formic acid
solution is nearly: (Given for water Kf = 1.86 K kg
mol-1)
(A) 0.8
(B) 1.1
(C) 1.9
(D) 2.4
Q. The elevation in boiling point for 1 molal
solution of non-volatile solute A is 3K. The
depression in freezing point for 2 molal solution
of A in the same solvent is 6K. The ratio of K b
and Kf i.e., Kb/Kf is 1 : X. The value of X is [nearest
integer].
JEE Main 25th July 2022 S-1
Q. 150 g of acetic acid was contaminated with
10.2 g ascorbic acid (C6H8O6) to lower down its
freezing point by (x × 10-1) ℃. The value of x is
_______. (Nearest integer)
[Given Kf = 3.9 K kg mol-1; Molar mass of
ascorbic acid = 176 g mol-1]
Q. Two solutions A and B are prepared by
dissolving 1 g of non-volatile solutes X and Y.
respectively in 1 kg of water. The ratio of
depression in freezing points for A and B is
found to be 1 : 4. The ratio of molar masses of X
and Y is:
(A) 1 : 4
(B) 1 : 0.25
(C) 1 : 0.20
(D) 1 : 5
JEE Main 28th July 2022 S-1
Conductance - Electrochemistry
JEE Main 29th Jan 2023 S-1
Following figure shows dependence of molar
conductance of two electrolytes on concentration.
Λ0m is the limiting molar conductivity.
JEE Main 24th June 2022 S-2
Q. The resistance of conductivity cell containing
0.01 M KCl solution at 298 K is 1750 𝛺. If the
conductivity of 0.01 M KCl solution at 298 K is 0.152
× 10-3 S cm-1, then the cell constant of the
conductivity cell is ____ × 10-3 cm-1.
JEE Main 31th Jan 2023 S-2
The number of Incorrect statement(s) from the
following is___
(A) Λ0m for electrolyte A is obtained by extrapolation
(B) For electrolyte B, Λm vs √c graph is a straight line
with intercept equal to Λ0m
(C) At infinite dilution, the value of degree of
dissociation approach zero for electrolyte B.
(D) Λ0m for any electrolyte A or B can be calculated
using 𝜆° for individual ions.
Q. The resistivity of a 0.8 M solution of an electrolyte
is 5 × 10-3 𝛺cm. Its molar conductivity is __ × 104 𝛺-1
cm2 mol-1. (Nearest integer)
Conductance - Electrochemistry
JEE Main 27th June 2022 S-1
JEE Main 01st Feb 2023 S-2
Q. The limiting molar conductivities of NaI, NaNO3
and AgNO3 are 12.7, 12.0 and 13.3 mS m2 mol-1,
respectively (all at 25°C). The limiting molar
conductivity of AgI at this temperature is___ mS
m2 mol-1
Q. 1 × 10-5 M AgNO3 is added to 1 L of saturated
solution of AgBr. The conductivity of this solution at
298 K is ___ × 10-8 S m-1.
[Given: Ksp (AgBr) = 4.9 × 10-13 at 298 K
JEE Main 25th July 2022 S-2
Q. The molar conductivity of a conductivity cell
filled with 10 moles of 20 mL NaCl solution is 𝛬m1 and
that of 20 moles another identical cell having 80 mL
NaCl solution is 𝛬m2, The conductivities exhibited by
these two cells are same.
The relationship between 𝛬m2 and 𝛬m1 is
(A) 𝛬m2 = 2𝛬m1
(B) 𝛬m2 = 𝛬m1/2
(C) 𝛬m2 = 𝛬m1
(D) 𝛬m2 = 4𝛬m1
3
Conductance - Electrochemistry
JEE Main 27th July 2022 S-2
Q. Given below are two statements:
Statement I: For KI, molar conductivity increases
steeply with dilution.
Statement II: For carbonic acid, molar conductivity
increases slowly with dilution.
In the light of the above statements, choose the
correct answer from the options given below:
(A) Both Statement I and Statement II are true
(B) Both Statement I and Statement II are false
(C) Statement I is true but Statement II is false
(D) Statement I is false but Statement II is true
JEE Main 29th July 2022 S-1
Q. Resistance of a conductivity cell (cell constant
129 m-1) filled with 74.5 ppm solution of KCl is 100 𝛺
(labelled as solution 1). When the same cell is filled
with KCl solution of 149 ppm, the resistance is 50 𝛺
(labelled as solution 2). The ratio of molar
conductivity of solution 1 and solution 2 is
i.e.
The value of x is___
(Nearest integer)
Given, molar mass of KCl is 74.5 g mol-1
Activation Energy - Chemical Kinetics
JEE Main 24th June 2022 S-1
Q. The rate constants for decomposition of
acetaldehyde have been measured over the
temperature range 700-1000 K. The data has
been analysed by plotting Ink vs 103/T graph.
The value of activation energy for the reaction
is _____ kJ mol-1. (Nearest integer)
(Given : R 8.31 JK-1 mol -1)
JEE Main 26th June 2022 S-2
Q. Catalyst A reduces the activation energy for
a reaction by 10 kJ mol-1 at 300 K. The ratio of
rate constants,
is e x. The value of x
is ______. [Nearest integer]
[Assume that the pre-exponential factor is
same in both the cases. Given R = 8.31 JK -1 mol1]
Activation Energy - Chemical Kinetics
JEE Main 29th June 2022 S-2
JEE Main 27th June 2022 S-2
Q. It has been found that for a chemical
reaction with rise in temperature by 9K the rate
constant gets doubled. Assuming a reaction to
be occurring at 300 K, the value of activation
energy is found to be _____ kJ mol-1 [Nearest
integer]
(Given ln 10 = 2.3, R = 8.3 JK -1mol-1, log2 = 0.30)
JEE Main 29th June 2022 S-1
Q. The activation energy of one of the reactions
in a biochemical process is 532611 J mol-1. When
the temperature falls from 310 K to 300 K, the
change in rate constant observed is
k300 = x × 10-3 k310. The value of x is ______.
[Given: ln 10 = 2.3 , R = 8.3 JK-1 mol-1]
Q. The equation k = (6.5 × 1012 s-1)e-26000K/T
is followed for the decomposition of compound
A. The activation energy for the reaction is
_____ kJ mol-1. [nearest integer]
(Given : R = 8.314 JK-1 mol-1)
JEE Main 28th July 2022 S-2
Q. For a reaction, given below is the graph of
lnk vs 1/T. The activation energy for the reaction
is equal to ______ cal mol-1. (Nearest
integer).
(Given: R = 2 cal K-1 mol-1).
Activation Energy - Chemical Kinetics
JEE Main 31th January 2023 S-1
JEE Main 24th January 2023 S-1
Q. A → B
The rate constants of the above reaction at 200
K and 300 K are 0.03 min-1 and 0.05 min-1
respectively. The activation energy for the
reaction is _______ J (Nearest integer)
(Given: ln10 = 2.3 , R = 8.3 JK -1 mol-1)
log5 = 0.70
log3 = 0.48
log2 = 0.30
Q. The number of correct statement/s from the
following is ______ .
A. Larger the activation energy, smaller is the
value of the rate constant.
B. The higher is the activation energy, higher is
the value of the temperature coefficient.
C. At lower temperatures, increase in
temperature causes more change in the value
of k than at higher temperature.
D. A plot of ln k vs 1/T is a straight line with slope
equal to
Aromaticity and resonance - GOC
JEE Main 24th June 2022 S-2
JEE Main 28th June 2022 S-1
Q. Arrange the following carbocations in
decreasing order of stability.
(A) A > C > B
C
(C) C > B > A
B
Q. Which of the following structures are
aromatic in nature?
(B) A > B >
(A) A, B, C and D
and B
(D) C > A >
(C) Only A and C
C and D
th
Q.
Which
of
the
following
JEE Main 27 June 2022 S-2 is most stable?
(A)
(C)
(B)
(D)
(B) Only A
(D) Only B,
Aromaticity and resonance - GOC
JEE Main 29th June 2022 S-2
Q. Which of the following carbocations is most
stable:
(A)
(C)
JEE Main 01th February 2023 S-1
Q. Resonance in carbonate ion (CO32-) is
(B)
(D)
Which of the following is true?
(1) It is possible to identify each structure
individually by some physical or chemical
method.
(2) All these structures are in dynamic
equilibrium with each other
(3) Each structure exists for equal amount of
time
(4) CO32- has a single structure i.e., resonance
hybrid of the above three structures.
Aromaticity and resonance - GOC
JEE Main 27th July 2022 S-1
JEE Main 24th January 2023 S-1
Q. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A: [6] Annulene [8] Annulene and cis-[10]
annulene, are respectively aromatic, not-aromatic and
aromatic
Q. Increasing order of stability of the resonance
structure is:
[6] Annulene
B.
[8] Annulene
A.
C.
Cis-[10] Annulene
Reason R: Planarity is one of the requirements of
aromatic systems.
In the light of the above statements, choose the most
appropriate answer from the options given below.
(A) Both A and R are correct and R is the correct
explanation of A.
(B) Both A and R are correct but R is NOT the correct
explanation of A.
(C) A is correct but R is not correct.
(D) A is not correct but R is correct.
D.
(1) C, D, B, A
(C) D, C, A, B
(B) C, D, A, B
(D) D, C, B, A
Smog - Environmental Chemistry
JEE Main 27th June 2022 S-1
JEE Main 25th July 2022 S-1
Q. Given below are two statements:
Statement I : Classical smog occurs in cool humid
climate. It is a reducing mixture of smoke, fog and
sulphur dioxide
Statement II : Photochemical smog has components,
ozone, nitric oxide, acrolein, formaldehyde, PAN etc.
In the light of above statements, choose the most
appropriate answer from the options given below
The photochemical smog does not generally
contain:
(A) No
(B) NO2
(C) SO2
(D) HCHO
(A) Both Statement I and Statement II are correct
(B) Both Statement I and Statement II are incorrect
(C) Statement I is correct but Statement II is incorrect
(D) Statement I is incorrect but Statement II is correct
JEE Main 28th June 2022 S-2
Correct statement about photo-chemical smog is:
(A) It occurs in humid climate.
(B) It is a mixture of smoke, fog and SO2
(C) It is reducing smog.
JEE Main 01st Feb 2023 S-1
How can photochemical smog be controlled?
(A) By using tall chimneys
(B) By complete combustion of fuel
(C)By using catalytic converters in the
automobiles/industry
(D) By using catalyst
Smog - Environmental Chemistry
JEE Main 28th June 2022 S-2
JEE Main 29th Jan 2023 S-1
Q. Correct statement about smog is
Correct statement about photo-chemical smog is:
(A) It occurs in humid climate.
(B) It is a mixture of smoke, fog and SO 2
(C) It is reducing smog.
(D) It results from reaction of unsaturated
hydrocarbons.
A
NO2 is present in classical smog
B
Both NO2 and SO2 are present in
classical smog
C
Photochemical smog has high
concentration of oxidizing agents
D
Classical smog also has high
concentration of oxidizing agents
Mathematics
No. of roots and roots & coefficients
JEE Main 31h January 2023 S-2
JEE Main 24th June 2022 S-2
Q. The sum of all the real roots of the equation
(e2x - 4) (6e2x - 5ex + 1) = 0 is
(A) loge3 (B) -loge3 (C) loge6 (D) -loge6
JEE Main 28th July 2022 S-1
Q. The sum of all real values of x for which
is equal to
Q. The equation e4x + 8e3x + 13e2x - 8ex + 1 = 0,
x ∈ R has:
(A) Two solutions and both are negative
(B) No solution
(C) Four solutions two of which are negative
(D) Two solutions and only one of them is
negative.
JEE Main 31th Jan 2023 S-1
Q. The number of real roots of the equation
JEE Main 26th June 2022 S-1
Q. The sum of the cubes of all the roots of the
equation x4 -3x3 - 2x2 +3x + 1 = 10 is ____ .
Is
(A) 0
(B) 1
(C) 3
(D) 2
No. of roots and roots & coefficients
JEE Main 27th June 2022 S-1
Q. If the sum of all the roots of the equation
JEE Main 26th July 2022 S-2
Q. The minimum value of the sum of the
squares of the roots of x3 + (3 - a)x + 1 = 2a is:
(A) 4
(B) 5
(C) 6
(D) 8
Arithmetic Progression
JEE Main 30th Jan 2023 S-1
JEE Main 27th June 2022 S-1
Q. If
then a1 + a2 + … +
a25, is equal to:
(A) 51/144 (B) 49/138 (C) 50/141 (D) 52/147
JEE Main 29th July 2022 S-1
Q. If the sum of the first ten terms of the series
where m and n are co-prime numbers, then
m + n is equal to
JEE Main 25th July 2022 S-2
Q.
Q. The sum
(A) 7/87
co-prime, then m + n is equal to
(B) 7/29
(C) 14/87
(D) 21/29
JEE Main 30th June 2022 S-1
JEE Main 26th July 2022 S-2
Q.
and n are
is equal to
where m
Q.
(A) 20/11
(B) 11/6
(C) 241/132 (D) 21/11
Arithmetic Progression
JEE Main 01th Feb 2023 S-2
JEE Main 01th Feb 2023 S-1
Q. The sum of the common terms of the
following three arithmetic progressions.
3, 7, 11, 15, ……………….., 399,
2, 5, 8, 11, …………………., 359 and
2, 7, 12, 17, ……………….., 197, is equal to______.
Q. Let a1 = 8, a2, a3, …. an be an A.P. If the sum of
its first four terms is 50 and the sum of its last
four terms is 170, then the product of its middle
two terms is_____.
JEE Main 26th July 2022 S-2
Q. Suppose a1,a2,, …, an, … be an arithmetic
progression of natural numbers. If the ratio of
the sum of the first five terms to the sum of first
nine terms of the progression is 5 : 17 and
110 < a15 < 120, then the sum of the first ten terms
of the progression is equal to:
(A) 290
(B) 380
(C) 460
(D) 510
Q. Different A.P.’s are constructed with the first
term 100, the last term 199, and integral
common differences. The sum of the common
differences of all such. A.P.’s having at least 3
terms and at most 33 terms is.
JEE Main 29th June 2022 S-2
Q. Let 3, 6, 9, 12, …. upto 78 terms and 5, 9, 13, 17, …
upto 59 terms be two series. Then, the sum of
the terms common to both the series is equal to
JEE Main 27th July 2022 S-1
JEE Main 30th Jan 2023 S-2
Q. The 8th common term of the series
S1 = 3 + 7 + 11 + 15 + 19 + ….,
S2 = 1 + 6 + 11 + 16 + 21 + …. is ______.
Arithmetic Progression
JEE Main 31st Jan 2023 S-1
JEE Main 25th Jan 2023 S-1
Q. Let a1, a2, …, an be in A.P. If a5 = 2a7 and a11 =18,
Q. Let A1, A2, A3 be the three A.P. with the same
common difference d and having their first
terms as A, A + 1, A + 2, respectively. Let a, b, c
be the 7th, 9th, 17th terms of A1, A2, A3, respectively
JEE Main 27th June 2022 S-2
Q. If a1, a2, a3, … and b1, b2, b3 ….. Are A.P. and
a1 = 2, a10 = 3, a1 b1 = 1 = a10 b10 then a4b4 is equal
to
(A) 35/27 (B) 1
(C) 27/28 (D) 28/27
JEE Main 24th June 2022 S-1
Q. If
where n is an even integer, is an
arithmetic progression with common difference 1
and
(A) 48
then n is equal to:
(B) 96
(C) 92
(D) 104
such that
If a = 29, then the sum of first 20 terms of an AP
whose first term is c - a - b and common
difference is d/12, is equal to_____
Finding remainder/ General term (Coefficients)
JEE Main 24th June 2022 S-1
JEE Main 28th July 2022 S-1
Q. The remainder when 32022 is divided by 5 is
(A) 1
(B) 2
(C) 3
(D) 4
JEE Main 24th June 2022 S-2
JEE Main 25th Jan 2022 S-2
Q. The remainder when 1 + 3 + 32 + 33 + … + 32021
is divided by 50 is_____.
JEE Main 26th June 2022 S-1
(B) 2
Q. The remainder when (2023)2023 is divided by
35 is ____.
JEE Main 31st Jan 2023 S-1
Q. The remainder when (2021)2023 is divided by 7 is:
(A) 1
Q. The remainder when 72022 + 32022 is divided
by 5 is:
(A) 0
(B) 2
(C) 3
(D) 4
(C) 5
(D) 6
JEE Main 27th July 2022 S-1
Q. The remainder when (2021)2022 + (2022)2021 is
divided by 7 is
(A) 0
(B) 1
(C) 2
(D) 6
Q. The remainder on dividing 599 by 11 is___.
JEE Main 01st Feb 2023 S-1
Q. The remainder when 19200 + 23200 is divided
by 49 is_____.
Finding remainder/ General term (Coefficients)
JEE Main 31st Jan 2023 S-2
Q. The coefficient of
x-6,
in the expansion of
JEE Main 31st Jan 2023 S-2
Q. If the constant term in the binomial
expansion of
JEE Main 27th June 2022 S-1
is -84 and the
Q. If the coefficient of x10 in the binomial
coefficient of x-3l is 2⍺ β, where β < 0 is an odd
number. Then |⍺ l + β| is equal to____
expansion of
JEE Main 29th June 2022 S-2
is 5k l, where l,k ∈ N
and l is coprime to 5, then k is equal to__.
JEE Main 29th June 2022 S-1
Q. If the constant term in the expansion of
is 2k. l, where l is an odd
integer, then the value of k is equal to:
Q. Let the coefficients of x-1 and x-3 in the
expansion of
x > 0, be m and n
respectively. If r is a positive integer such
mn2 = 15Cr . 2r, then the value of r is equal to__.
Finding remainder/ General term (Coefficients)
JEE Main 30th Jan 2023 S-1
JEE Main 01st Feb 2023 S-2
Q. If the coefficient of x15 in the expansion of
Q. If the term without x in the expansion of
is equal to the coefficient of
x-15 in the expansion of
JEE Main 27th June 2022 S-2
where a and b are positive real numbers, then
for each such ordered pair (a, b):
(A) a = b
(B) ab = 1
(C) ab = 1 (D) ab = 3
Q. If the sum of the coefficients of all the
positive powers of x, in the binomial expansion
of
is 939, then the sum of all the
possible integral values of n is:
JEE Main 25th July 2022 S-1
Q. If the maximum value of the term
independent of t in the expansion of
x ≥ 0, is K, then 8K is
equal to___.
is 7315, then |⍺| is equal to__
JEE Main 31st Jan 2023 S-1
Q. Let ⍺ > 0, be the smallest number such that
the expansion of
has a term
βx-⍺, β ∈ N. Then ⍺ is equal to____.
Finding remainder/ General term (Coefficients)
JEE Main 28th June 2022 S-2
Q. The term independent of x in the expression
of (1 - x2 + 3x3)
(A)
(B)
x ≠ 0 is
(C)
(D)
JEE Main 26th July 2022 S-1
Q. If the coefficients of x and x2 in the expansion
of (1 + x)p(1 - x)q, p, q ≤ 15, are -3 and -5
respectively, then the coefficient of x3 is equal to
Properties of Adjoint/System of linear equations
JEE Main 27th July 2022 S-2
JEE Main 27th June 2022 S-2
Q. Consider a matrix
where ⍺, β, γ are three distinct natural numbers.
If
JEE Main 27th June 2022 S-1
then the number of such 3- tuples (⍺, β, γ) is__.
JEE Main 28th July 2022 S-1
Q. Let the matrix
Q. Let A and B be two 3 × 3 matrices such that AB = I
and
, then |adj(B adj(2A))| is equal to
(A) 16
(B) 32
(C) 64
(D) 128
Q. The positive value of the determinant of the
matrix A, whose
and the matrix
B0 = A49 + 2A98. If Bn = Adj(Bn-1) for all n ≥ 1, then
det(B4) is equal to:
(A) 328
(B) 330
(C) 332
(D) 336
JEE Main 26th June 2022 S-1
Q. Let A be a 3 × 3 invertible matrix. If
|adj(24A) = adj(3 adj(2A))|, then |A|2 is equal to:
(A) 66
(B) 212
(C) 26
(D) 1
Properties of Adjoint/System of linear equations
JEE Main 24th Jan 2023 S-2
JEE Main 29th June 2022 S-1
Q. If the system of equations x + 2y + 3z = 3,
(A)
(B)
Q. If the system of linear equations
2x + y - z = 7, x - 3y + 2z = 1, x + 4y + δz = k,
where δ, k ∈ R has infinitely many solutions, then
δ + k is equal to:
(A) -3 (B) 3 (C) 6
(D) 9
(C)
(D)
JEE Main 26th June 2022 S-2
4x + 3y - 4z = 4, 8x + 4y - λz = 9 + μ has infinitely
many solutions then the ordered pair (λ, μ) is equal
to___
JEE Main 28th June 2022 S-2
Q. If the system of linear equations
2x - 3y = γ + 5, ⍺x + 5y = β + 1, where ⍺, β, γ ∈ R
has infinitely many solutions, then the value of
|9⍺ + 3β + 5γ| is equal to
Q. If the system of equations ⍺x + y + z = 5,
x + 2y + 3z = 4, x + 3y + 5z = β, has infinitely
many solutions, then the ordered pair (⍺, β) is
equal to:
(A) (1, -3) (B) (-1, 3) (C) (1, 3)
(D) (-1, -3)
Properties of Adjoint/System of linear equations
JEE Main 01st Feb 2023 S-1
JEE Main 24th June 2022 S-1
Q. Let S denote the set of all real values of λ
such that the system of equations λx + y + z = 1,
x + λy + z = 1, x + y + λz = 1 is inconsistent, then
Q. The number of values of ⍺ for which the
system of equations: x + y + z = ⍺,
⍺x + 2⍺y + 3z = -1, x + 3⍺y + 5z = 4 is
inconsistent, is
(A) 0
(B) 1
(C) 2
(D) 3
is equal to
(A) 2
(B) 12
(C) 4
(D) 6
JEE Main 26th June 2022 S-1
Q. The ordered pair (a, b), for which the system of
linear equations 3x - 2y + z = b, 5x - 8y + 9z = 3,
2x + y + az = -1 has no solution, is:
(A) (3, ⅓)
(B) (-3, ⅓) (C) (-3, -⅓) (D) (3, -⅓)
JEE Main 27th June 2022 S-1
Q. Let the system of linear equations
x +2y + z = 2, ⍺x + 3y - z = ⍺, -⍺x + y + 2z = -⍺ be
inconsistent. Then ⍺ is equal to:
(A) 5/2
(B) -5/2
(C) 7/2
(D) -7/2
JEE Main 28th June 2022 S-1
Q. If the system of linear equations
2x + 3y - z = -2, x + y + z = 4, x - y + |λ|z = 4λ - 4
where λ ∈ R, has no solution, then
(A) λ = 7
(B) λ = -7 (C) λ = 8
(D) λ2 = 1
JEE Main 25th July 2022 S-1
Q. The number of θ ∈ (0, 4𝜋) for which the
system of linear equations 3(sin 3θ)x - y + z = 2,
3(cos 2θ)x + 4y + 3z = 3, 6x + 7y + 7z = 9 has no
solution is:
(A) 6
(B) 7
(C) 8
(D) 9
Properties of Adjoint/System of linear equations
JEE Main 30th Jan 2023 S-1
JEE Main 31st Jan 2023 S-1
Q. Let the system of linear equations
x + y + kz = 2, 2x + 3y - z = 1, 3x + 4y + 2z = k
have infinitely many solutions. Then the system
(k + 1)x + (2k - 1)y = 7, (2k + 1)x + (k + 5)y = 10
has:
(A) Infinitely many solutions
(B) Unique solution satisfying x - y = 1
(C) no solution
(D) Unique solution satisfying x + y = 1
Q. For the system of linear equations
x + y + z = 6, ⍺x + βy + 7z = 3, x + 2y + 3z = 14,
which of the following is NOT true?
(A) If ⍺ = β = 7, then the system has no solution
(B) If ⍺ = β and ⍺ ≠ 7 then the system has a
unique solution
(C) There is a unique point (⍺, β) on the line
x + 2y + 18 = 0 for which the system has
infinitely many solutions
(D) For every point (⍺, β) ≠ (7, 7) on the line
x - 2y + 7 = 0, the system has infinitely many
solutions
Shortest distance between lines
JEE Main 24th Jan 2023 S-1
JEE Main 30th Jan 2023 S-1
Q. The shortest distance between the lines
Q. The line l1 passes through the point (2, 6, 2)
and is perpendicular to the plane
2x + y - 2z = 10. Then the shortest distance
between the line l1 and the line
is equal to
JEE Main 01st Feb 2023 S-1
Q. The shortest distance between the lines
(A) 7
(B) 19/3
(C) 19/7
(D) 9
JEE Main 24th Jan 2023 S-2
(A) 7√3
(B) 5√3
(C) 6√3
(D) 4√3
JEE Main 29th Jan 2023 S-2
Q. If the shortest between the lines
Q. Shortest distance between the lines
(A) 2√3
(B) 4√3
(C) 3√3
(D) 5√3
then the square of the sum of all possible
values of 𝞴 is
Shortest distance between lines
JEE Main 25th Jan 2023 S-2
JEE Main 25th July 2022 S-2
Q. If the shortest distance between the line
joining the points (1, 2, 3) and (2, 3, 4), and the
Q. The shortest distance between the lines
line
(A) 2√29
is 𝛂, then 28𝛂2 is
equal to ______
JEE Main 31th Jan 2023 S-1
(B) 1
(C) √37/√29 (D) √29/2
JEE Main 24th June 2022 S-2
Q. If the shortest distance between the lines
Q. Let the shortest distance between the lines
Then the sum of all possible values of λ is:
(A) 16
(B) 6
(C) 12
(D) 15
If (𝛂, 𝜷, 𝛄) lies on L, then which of the following is
NOT possible?
(A) 𝛂 + 2𝛄 = 24
(B) 2𝛂 + 𝛄 = 7
(C) 2𝛂 - 𝛄 = 9
(D) 𝛂 -2 𝛄 = 19
JEE Main 27th June 2022 S-2
Q. The shortest distance between the lines
(A)
(B)
(C)
(D)
Linear Differential Equations
JEE Main 24th Jan 2023 S-1
JEE Main 30th Jan 2022 S-1
Q. Let y = y(x) be the solution of the differential
equation x3 dy + (xy -1) dx = 0, x > 0,
Q. Let the solution curve y = y(x) of the DE
Then y(1) is equal to
(A)1
(B) e
(C) 2 - e
(D) 3
pass through the origin. Then y(1) is equal to :
JEE Main 26th June 2022 S-2
Q. If the solution of the differential equation
satisfies y(0) = 0, then the value of y(2) is___
(A) -1
(B) 1
(C) 0
(D) e
(A)
(B)
(C)
(D)
JEE Main 25th Jan 2023 S-1
Q. Let y = y(x) be the solution curve of the DE
JEE Main 28th June 2022 S-1
Q. Let y = y(x) be the solution of the differential
equation
with y(2) = - 2. Then y(3) is equal to
(A) -18
(B) -12
(C) -6
(D) -3
(A)
(B)
(C)
(D)
Linear Differential Equations
JEE Main 29th Jan 2023 S-2
JEE Main 28th July 2022 S-1
Q. Let y = y(x) be the solution of the differential
equation
(B)
(C)
(D)
JEE Main 01st Feb 2023 S-1
Q. If y = y(x) is the solution curve of the
differential equation
y(0) = 1, then
(A)
(B)
(C)
(D)
be the solution curve of the
differential equation
If y(2) = 2, then y(e) is equal to
(A)
Q. If y = y(x),
is equal to
(a)
(b)
(c)
(d)
JEE Main 24th June 2022 S-1
Q. If x = x(y) is the solution of the differential
equation
then x(e) is equal to:
(A)e3(ee-1)
(B) ee(e3-1)
(C) e2(ee+1)
(D) ee(e2-1)
Linear Differential Equations
JEE Main 29th June 2022 S-1
JEE Main 29th July 2022 S-2
Q. Let y = y(x) be the solution of the differential
Q. Let y = y (x) be the solution curve of the DE
equation
with
If
then the value of 3α2 is
equal to _____ .
Which passes through the point (0,1). Then y(1) is
equal to
(A) 1/2
(B) 3/2
(C) 5/2
(D) 7/2
JEE Main 28th July 2022 S-2
JEE Main 25th Jan 2023 S-2
Q. Let y = y(x) be the solution curve of the
Q. Let y = y(t) be a solution of the differential
differential equation
equation
x > 1 passing through the point
and 𝛾 > 0. Then
is equal to
(a) 11 + 6 loge 3
(b) 19
(c) 12 - 2 loge3
(d) 19 - 6 loge 3
(A) is 0
(C) is 1
where, α > 0, β > 0
(B) Does not exist
(D) is -1
logical equivalent and Tautology
JEE Main 25th June 2022 S-2
JEE Main 27th July 2022 S-2
Q. The negation of the Boolean expression
((~q) ∧ P) ⇒ ((~p) ∨ q) is logically equivalent to
(a) p ⇒ q (b) q ⇒ p (c) ~ (p ⇒ q) (d) ~(q ⇒ p)
Q. (p ∧ r) ⇔ (p ∧ (~q)) is equivalent to (~p) where r is
(A) p
(B) ~p
(C) q
(D) ~q
JEE Main 29th July 2022 S-2
Q. The statement (p ⇒ q) ∨ (p ⇒ r) is NOT
equivalent to:
(a) (p ∧ (~r)) ⇒ q
(b) (~ q) ⇒ ((~ r) ∨ p)
(c) p ⇒ (q ∨ r)
(d) (p ∧ (~ q)) ⇒ r
JEE Main
24th Jan
2023 S-2
Q. Let p and q be two statements.
Then ~(p ⋀ (p ⇒ ~q)) is equivalent to
(A) p V (p ⋀ (~q))
(B) p V ((~p) ⋀ q)
(C) (~p) V q
(D) p V (p ⋀ q)
JEE Main 24th Jan 2023 S-1
Q. The compound statement
(~(P ∧ Q)) ∨ ((~P) ∧ Q) ⇒ ((~ P) ∧ (~ Q)) is equivalent to
(A) ((~ P) ∨ Q) ∧ ((~ Q) ∨ P)
(B) (~ Q) ∨ P
(C) ((~ P) ∨ Q) ∧ (~ Q)
(D) (~ P) ∨ Q
JEE Main 27th June 2022 S-1
Q. The Boolean expression (~(p ⋀ q))Vq is equivalent to:
A. q → (p ⋀ q)
B. p → q
C. p → (p → q)
D. p → (p V q)
logical equivalent and Tautology
JEE Main 30th Jan 2023 S-1
Q. Among the statements:
(S1) ((p V q) ⇒ r) ⇔ (p ⇒ r)
(S2) ((p V q) ⇒ r) ⇔ ((p ⇒ r) V (q ⇒ r))
(A) Only (S1) is a tautology
(B) Neither (S1) nor (S2) is a tautology
(C) Only (S2) is a tautology
(D) Both (S1) and (S2) are tautologies
JEE Main 26th June 2022 S-2
Q. Let r ∈ {p, q, ~p, ~q} be such that the logical
statement r ∨ (~ p) ⇒ (p ∧ q) ∨ r is a tautology.
Then ‘r’ is equal to:
(a) p
(b) q
(c) ~p
(d) ~q
JEE Main 25th July 2022 S-1
Q. Which of the following statements is a
tautology?
(a) ((~ p) ∨ q) ⇒ p
(b) p ⇒ ((~ p) ∨ q)
(c) ((~ p) ∨ q) ⇒ q
(d) q ⇒ (( ~ p) ∨ q)
JEE Main 31th Jan 2023 S-2
Q. The number of values of r ∈ {p, q, ~p, ~q} for
which ((p ∧ q) ⇒ (r ∨ q)) ∧ ((p ∧ r) ⇒ q) is a
tautology, is:
(a) 3
(b) 2
(c) 1
(d) 4
logical equivalent and Tautology
JEE Main 31th Jan 2023 S-1
Q. (S1): (p ⇒ q) ∨ (p ∧ (~q)) is a tautology
(S2): ((~p) ⇒ (~q)) ∧ ((~ p) ∨ q) is a
Contradiction. Then
(a) Only (S2) is correct
(b) Both (S1) and (S2) are correct
(c) Both (S1) and (S2) are wrong
(d) Only (S1) is correct
JEE Main 28th July 2022 S-1
Q. Let the operations *, ⊙ ∈ {⋀, V}.
If (p * q) ⊙ (p ⊙ ～q) is a tautology, then the
ordered pair (*, ⊙) is:
(A) (V, ⋀) (B) (V, V) (C) (⋀, ⋀) (D) (⋀, V)
JEE Main 29th June 2022 S-1
Q. Let Δ ∈ {∧, ∨, ⇒, ⇔} be such that
(p ∧ q) Δ ((p ∨ q) ⇒ q) is a tautology.
Then Δ is equal to:
(a) ∧
(b) ∨
(c) ⇒
(d) ⇔
JEE Main 26th June 2022 S-1
Q. Let Δ, ▽ ∈ {⋀, V} be such that p ▽ q ⇒ ((p ▽ q) ▽ r) is
a tautology. Then (p ▽ q) Δr is logically equivalent to:
(A) (p ▽ r) V q
(B) (p Δ r) ⋀ q
(C) (p ⋀ r) Δ q
(D) (p ▽ r) ⋀ q
JEE Main 25th Jan 2023 S-2
Q. Let Δ, ▽ ∈ {⋀, V} be such that (p → q) Δ (p ▽ q) is a
tautology. Then
(A) Δ = ⋀, ▽ = V
(B) Δ = V, ▽ = ⋀
(C) Δ = V, ▽ = V
(D) Δ = ⋀, ▽ = ⋀
Area under parabola and line
JEE Main 30th Jan 2023 S-1
Q. Let 𝜶 be the area of the larger region
bounded by the curve y2 = 8x and the lines y = x
and x = 2, which lies in the first quadrant. Then
the value of 3𝜶 is equal to_______.
JEE Main 28th June 2022 S-1
Q. The area of the region
S = {(x, y ) : y2 ≤ 8x, y ≥ √2 x, x ≥ 1} is
(A) (13√2)/6 (B) (11√2)/6 (C) (5√2)/6 (D) (19√2)/6
JEE Main 27th July 2022 S-2
JEE Main 26th June 2022 S-2
Q. The area of the region enclosed by y ≤ 4x2,
x2 ≤ 9y and y ≤ 4, is equal to:
(A) 40/3
(B) 56/3
(C) 112/3
(D) 80/3
Q. The area of the region bounded by y2 = 8x and
y2 = 16(3 - x) is equal to:
(A) 32/3
(B) 40/3
(C) 16
(D) 19
JEE Main
24th Jan
2023 S-2
Q. If the area of the region bounded by the
curves y2 - 2y = -x, x + y = 0 is A, then 8A is
equal to
JEE Main 25th Jan 2023 S-1
Q. If the area enclosed by the parabolas
P1 : 2y = 5 x2 and P2 : x2 - y + 6 = 0 is equal to the area
enclosed by P1 and y = ⍺x, ⍺ > 0, then ⍺3 is equal
to____.
Area under parabola and line
JEE Main 26th July 2022 S-2
JEE Main 30th Jan 2023 S-2
Q. The area bounded by the curves y = |x2 - 1|
and y= 1 is
Q. Let q be the maximum integral value of p in [0, 10]
for which the roots of the equation
(A)
(B)
(C)
are rational. Then the area
of the region {(x, y) : 0 ≤ y ≤ (x - q)2, 0 ≤ x ≤ q} is
(D)
(A) 243
JEE Main 25th July 2022 S-1
(b)
(C) 125/3
(D) 164
JEE Main 27th June 2022 S-1
Q. The area of the region given by
A = {(x, y) ; x2 ≤ y ≤ min {x + 2, 4 - 3x}} is:
(a)
(B) 25
(c)
(d)
Q. Let A1 = {(x, y) : |x| ≤ y2, |x| +2y ≤ 8} and
A2 = {(x, y) : |x| + |y| ≤ k}. If 27 (Area A 1) = 5 (Area A2),
then k is equal to:
JEE Main 26th June 2022 S-1
JEE Main 31st Jan 2023 S-2
Q. Let the area of the region
{(x, y) : |2x - 1| ≤ y ≤ | x2 - x|, 0 ≤ x ≤ 1} be A. Then
(6A + 11)2 is equal to__
Q. The area bounded by the curve y = |x2 - 9| and
the line y = 3 is:
(A) 4(2√3 + √6 - 4}
(B) 4(4√3 + √6 - 4)
(C) 8(4√3 + 3√6 - 9) (D) 8(4√3 + √6 - 9)
Tangent to parabola
JEE Main 29th June 2022 S-2
JEE Main 25th Jan 2023 S-1
Q. Let P : y2 = 4ax, a > 0 be parabola with focus S.
Let the tangents to the parabola P make an angle
of 𝞹/4 with the line y = 3x + 5 touch the parabola P
at A and B. Then the value of a for which A, B and S
are collinear is:
(A) 8 only (B) 2 only (C) ¼ only (D) any a>0
Q. The distance of the point (6, -2√2) from the
common tangent y = mx + c, m > 0, of the curves x
= 2y2 and x = 1 + y2 is
(A) 1/3
(B) 5
(C) 14/3
(D) 5√3
JEE Main 31st Jan 2023 S-2
Q. Let S be the set of all a ∈ N such that the area of
the triangle formed by the tangent at the point
P(b, c), b, c ∈ N, on the parabola y2 = 2ax and the
lines x = b, y = 0 is 16 unit2, then
Is equal to____.
JEE Main 24th June 2022 S-1
Q. If two tangents drawn from a point (⍺, β) lying
on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x
are such that the slope of one tangent is four
times the other, then the value of (10⍺ + 5)2 + (16β2
+ 50)2 equals_____.
JEE Main 24th Jan 2023 S-2
Q. The equations of the sides AB and AC of a triangle
ABC are (λ + 1)x + λy = 4 and
λx + (1 - λ)y + λ = 0 respectively. Its vertex A is on the
y-axis and its orthocentre is (1, 2). The length of the
tangent from the point C to the part of the parabola
y2 = 6x in the first quadrant is
(A) √6
(B) 2√2
(C) 2
(D) 4
JEE Main 25th July 2022 S-2
Q. The tangents at the point A(1, 3) and B(1, -1) on
the parabola y2 - 2x - 2y = 1 meet at the point P.
Then the area (in unit2) of the triangle PAB is:
(A) 4
(B) 6
(C) 7
(D) 8
Tangent to parabola
JEE Main 25th June 2022 S-2
JEE Main 25th June 2022 S-1
Q. If the line y = 4 + kx, k > 0, is the tangent to
the parabola y = x - x2 at the the point P and V
is the vertex of the parabola, then the slope of
the line through P and V is:
(A) 3/2
(B) 26/9
(C) 5/2
(D) 23/6
Q. If y = m1x + c1 and y = m2x + c2, m1 ≠ m2, are two
common tangents of circle x2 + y2 = and parabola
y2 = x, then the value of 8|m1 m2| is equal to
(A) 3 + 4√2
(B) -5 + 6√2
(C) -4 + 3√2
(D) 7 + 6√2
JEE Main 28th July 2022 S-1
JEE Main 30th Jan 2023 S-2
Q. If the tangents drawn at the points P and Q
on the parabola y2 = 2x - 3 intersect at the point
R(0, 1), then the orthocentre of the triangle PQR
is:
(A) (0, 1)
(B) (2, -1) (C) (6, 3) (D) (2, 1)
JEE Main 28th July 2022 S-2
Q. Two tangent lines l1 and l2 are drawn from the
point (2, 0) to the parabola 2y2 = -x. If the lines l1
and l2 are also tangent to the circle
(x - 5)2 + y2= r, then 17r is equal to
Q. Let A be a point on the x-axis. Common tangents
are drawn from A to the curves x2 + y2 = 8 and
y2 = 16x. If one of these tangents touches the two
curves at Q and R, then (QR)2 is equal to:
(A) 64
(B) 76
(C) 81
(D) 72
JEE Main 27th July 2022 S-2
Q. If the length of the latus rectum of a
parabola, whose focus is (a, a) and the tangent
at its vertex is x + y = a, is 16, then |a| is equal to
(A) 2√2
(B) 2√3
(C) 4√2
(D) 4
Physics
Dimensions
JEE Main 29th Jan 2023 S-1
JEE Main 24th Jan 2023 S-1
Q. Match List I with List II
LIST I
LIST II
A.
Planck’s
constant(h)
I.
[M1L2T-2]
B.
Stopping
potential (Vs)
II.
[M1L1T-1]
Work
function(ф)
III.
[M1L2T-1]
IV.
[M1L2T-3A-1]
C.
D.
Momentum (p)
(A) A-III, B-I, C-II, D-IV (B) A-III, B-IV, C-I, D-II
(C) A-II, B-IV, C-III, D-I (D) A-I, B-III, C-IV, D-II
Q. Match List I with List II:
Choose the correct answer from the options
given below:
LIST I
LIST II
A.
Pressure gradient
I.
[M0L-2T-2]
B.
Energy density
II.
[M1L-1T-2]
C.
Electric Field
III.
[M1L-2T-2]
D.
Latent heat
IV.
[M1L1T-3A-1]
(A) A-III, B-I, C-II, D-IV (B) A-III, B-IV, C-I, D-II
(C) A-II, B-IV, C-III, D-I (D) A-I, B-III, C-IV, D-II
Dimensions
JEE Main 31th June 2023 S-2
JEE Main 1st Feb 2023 S-2
Q. Match List - I with List - II
Q. If the velocity of light c, universal gravitational
constant G and planck’s constant h are chosen as
fundamental quantities. The dimensions of mass
in the new system is :
LIST I
A.
LIST II
Angular
Momentum
I.
B.
Torque
II.
[ML-2 T-2]
C.
Stress
III.
[ML2 T-1]
D.
pressure gradient
IV.
[ML-1 T-2]
[ML2 T-2]
(A)
(A) A - I, B-IV, CIII, D-II (B) A - III, B-I, CIV, D-II
(C) A - II, B-III, CIV, D-I (D) A - IV, B-II, CI, D-III
(B)
(C)
JEE Main 1st Feb 2023 S-1
(D)
Q.
Represents the equation of
state of some gases. Where P is the pressure, V is
the volume. T is the temperature and a, b, R are
the constants. The physical quantity, which has
dimensional formula as that of
, will be :
(A) Bulk modulus
rigidity
(C) Compressibility
(B) Modulus of
(D) Energy density
Dimensions
JEE Main 29th June 2022 S-1
JEE Main 28th July 2022 S-2
Q. In Vander Waals equation
P is pressure, V is volume, R is universal gas constant
and T is temperature. The ratio of constants
is
dimensionally equal to:
(A)
(B)
(C)Main
PV 27th June 2022 S-2
JEE
3
Q. If L, C and(D)
R are
self inductance, capacitance and
PVthe
resistance respectively, which of the following does not
have the dimension of time ?
(A) RC
(B)
(C)
(D)
Q. Match List - I with List - II
List-I
List-II
A
Angular Momentum
I
[ML2T-2]
B
Torque
II
[ML-2T-2]
C
Stress
III
[ML2T-1]
D
Pressure gradient
IV
[ML-1T-2]
Choose the correct answer from the options
given below:
(A) A - I, B-IV, CIII, D-II (B) A - III, B-I, CIV, D-II
(C) A - II, B-III, CIV, D-I (D) A - IV, B-II, CI, D-III
Range & Velocity
JEE Main 24th Jan 2023 S-1
JEE Main 29th Jan 2023 S-2
Q. The maximum vertical height to which a man
can throw a ball is 136 m. The maximum
horizontal distance upto which he can throw the
same ball is
(A) 192 m (B) 136 m (C) 272 m (D) 68 m
Q. A particle of mass 100 is projected at time
t = 0 with a speed 20 ms-1 at an angle 45° to the
horizontal as given in the figure. The magnitude
of the angular momentum of the particle about
the starting point at time t = 2s is found to be √K
kg m2/s. The value of K is.
(Take g = 10 ms-2)
JEE Main 25th Jan 2023 S-2
Q. Two objects are projected with same velocity
‘u’ however at difference angles ⍺ and β with the
horizontal. If ⍺ + β = 90°, the ratio of horizontal
range of the first object to the 2nd object will be:
(A) 4 : 1
(B) 2 : 1
(C) 1 : 2
(D) 1 : 1
JEE Main 29th Jan 2023 S-1
Q. A stone is projected at angle 30° to the
horizontal. The ratio of kinetic energy of the stone
at point of projection to its kinetic energy at the
highest point of flight will be:
(A) 1 : 2
(B) 1 : 4
(C) 4 : 1
(D) 4 : 3
JEE Main 31th Jan 2023 S-1
Q. The initial speed of a projectile fired from
ground is u. At the highest point during its motion,
the speed of projectile is √3/2u. The time of flight
of the projectile is:
(A) u/2g
(B) u/g
(C) u/g
(D) √3u/g
Range & Velocity
JEE Main 01st Feb 2023 S-1
JEE Main 24th June 2022 S-2
Q. A child stands on the edge of the cliff 10m above
the ground and throws a stone horizontally with an
initial speed of 5 ms-1. Neglecting the air resistance,
the speed with which the stone hits the ground will
be______ ms-1 (given, g = 10 ms-2).
(A) 20
(B) 15
(C) 30
(D)
26
Q. A body is projected from the ground at an angle
of 45° with the horizontal. Its velocity after 2s is 20
ms-1. The maximum height reached by the body
during its motion is___m.
(use g = 10ms-2)
JEE Main 24th June 2022 S-1
Q. A projectile is projected with velocity of 25 m/s
at an angle θ with the horizontal. After t seconds its
inclination with horizontal becomes zero. If R
represents horizontal range of the projectile, the
value of θ will be: [use g = 10 m/s2]
(A)
(B)
(C)
(D)
JEE Main 26th June 2022 S-1
Q. A fighter jet is flying horizontally at a certain
altitude with a speed of 200 ms-1. When it passes
directly overhead an anti-aircraft gun, bullet is
fired from the gun, at an angle θ with the horizontal,
to hit the jet. If the bullet speed is 400 m/s, the
value of θ will be____°.
JEE Main 27th June 2022 S-1
Q. A projectile is launched at an angle ‘α’ with the
horizontal with a velocity 20 ms-1. After 10 s, its
inclination with horizontal is ‘β’. The value of tanβ
will be: (g = 10 ms-2)
(A) tan α + 5 sec α
(B) tan α - 5 sec α
Range & Velocity
JEE Main 25th June 2022 S-2
JEE Main 29th June 2022 S-2
Q. Given below are two statements. One is
labelled as Assertion A and the other is labelled
as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ' u ' at two different angles
with horizontal attained the same range R. If A
and B reached the maximum height h1 and h2
respectively, then R = 4√h1h2
Reason R: Product of said heights.
Q. A person can throw a ball upto a maximum
range of 100 m. How high above the ground he
can throw the same ball?
(A) 25 m
(B) 50 m
(C) 100 m (D) 200 m
JEE Main 25th July 2022 S-2
Q. A ball is projected from the ground with a
speed 15 ms-1 at an angle θ with horizontal so
that its range and maximum height are equal,
then ‘tan θ’ will be equal to
(A) ¼
(B) ½
Choose the CORRECT answer:
Q. Two projectile thrown at 30° and 45° with the
(C)2022
2reach
(D) 4
JEE Main
26th July
S-1the maximum
horizontal
respectively,
(A) Both A and R are true and R is the correct
height in same time. The ratio of their initial
explanation of A.
velocities is
(B) Both A and R are true but R is NOT the
(A) 1 : √2
(B) 2 : 1
(C) √2 : 1 (D) 1 : 2
correct explanation of A.
(C) A is true but R is false
(D) A is false but R is true
Range & Velocity
JEE Main 28th July 2022 S-1
Q. A NCC parade is going at a uniform speed of
9 km/h under a mango tree on which a monkey
is sitting at a height of 19.6 m. At any particular
instant, the monkey drops a mango. A cadet
will receive the mango whose distance from the
tree at time of drop is: (Given g = 9.8 m/s2)
(A) 5m
(B) 10 m
(C) 19.8 m (D) 24.5 m
JEE Main 27th July 2022 S-1
Q. A ball of mass m is thrown vertically upward.
Another ball of mass 2 m is thrown an angle θ
with the vertical. Both the balls stay in air for the
same period of time. The ratio of the heights
attained by the two balls respectively is 1/x. The
value of x is____.
JEE Main 28th July 2022 S-1
Q. A ball is projected with kinetic energy E, at an
angle of 60° to the horizontal. The kinetic energy
of this ball at the highest point of its flight will
become :
(A) Zero
(B) E/2
(C) E/4
(D) E
JEE Main 26th July 2022 S-1
Q. If the initial velocity in horizontal direction of
a projectile is unit vector and the equation of
trajectory is y = 5x (1 - x). The y component
vector of the initial velocity is___
(Take g = 10 m/s2)
Range & Velocity
JEE Main 31th Jan 2023 S-2
Q. Two bodies are projected from
ground with same speeds 40 ms-1 at
two different angles with respect to
horizontal. The bodies were found to
have same range. If one of the body
was projected at an angle of 60°, with
horizontal then sum of the maximum
heights, attained by the two
projectiles is___________m.
(Given g = 10 ms-2)
JEE Main 29th July 2022 S-1
Q. An object is projected in the air with initial
velocity u at an angle θ. The projectile motion is
such that the horizontal range R, is maximum.
Another object is projected in the air with a
horizontal range half of the range of first object.
The initial velocity remains same in both the
case. The value of the angle of projection, at
which the second object is projected, will
be____degree.
Moment of inertia
JEE Main 31st Jan 2023 S-2
JEE Main 25th Jan 2023 S-2
Q. ICM is moment of inertia of a circular
disc about an axis (CM) passing through
its center and perpendicular to the plane
its center and perpendicular to the plane
of disc. IAB is it’s moment of inertia about
an axis AB perpendicular to plane and
parallel to axis CM at a distance 2/3R
from center. Where R is the radius of the
disc. The ratio of IAB and ICM is x : 9. The
value of x is _____ .
Q. Two discs of same mass and different radii are
made of different materials such that their thicknesses
are 1 cm and 0.5 cm respectively. The densities of
materials are in the ratio 3 : 5. The moment of inertia of
these discs respectively about their diameters will be
in the ratio of x/6. The value of x is
JEE Main 25th June 2022 S-2
Q. Moment of Inertia (M.I.) of four bodies having same
mass ‘M’ and radius ‘2R’ are as follows:
I1 = M.I. of solid sphere about its diameter
I2 = M.I. of solid cylinder about its axis
I3 = M.I. of solid circular disc about its diameter
I4 = M.I. of thin circular ring about its diameter
If 2(I2 + I3) + I4 = x. I1 then the value of x will be
Moment of inertia
JEE Main 01st Feb 2023 S-2
JEE Main 29th June 2022 S-2
Q. Moment of inertia of a dise of mass M and radius ‘R’
about any of its diameter is
. The moment of
inertia of this disc about an axis normal to the disc
and passing through a point on its edge will be,
.
The value of x is _____ .
Q. The moment of inertia of a uniform thin rod about a
perpendicular axis passing through one end is I1.The
same rod is bent into a ring and its moment of inertia
about a diameter is I2. If
then the value of x
will be ______ .
JEE Main 27th July 2023 S-1
Q. A pulley of radius 1.5 m is rotated about its axis by a
force F = (12t - 3t2) N applied tangentially (while t is
measured in seconds). If moment of inertia of the
pulley about its axis of rotation is 4.5 kg m2, the
number of rotations made by the pulley before its
direction of motion is reversed, will be K/𝜋. The value of
K is _____ .
Variation in g
JEE Main 26th June 2022 S-1
JEE Main 25th January 2023 S-1
Q. T is the time period of simple pendulum on
the earth’s surface. Its time period becomes x T
when taken to a height R (equal to earth’s
radius) above the earth’s surface. Then, the
value of x will be:
(A) 1
(B) 2
(C) ½
(D) ¼
Q. The variation of acceleration due to gravity
(g) with distance (r) from the centre of the
earth is correctly represented by: (Given R =
radius of earth)
(A)
(B)
JEE Main 26th July 2022 S-1
Q.The percentage decrease in the weight of a
rocket, when taken to a height of 32 km above
the surface of earth will, be:
(Radius of earth = 6400 km)
(A) 1%
(B) 3%
(C) 4%
(D) 0.5%
(C)
(D)
Variation in g
JEE Main 24th January 2023 S-2
Q. A body weight W, is projected vertically
upwards from earth’s surface to reach a height
above the earth which is equal to nine time the
radius of earth. The weight of the body at that
height will be:
(A) W/91
(B) W/100 (C) W/9
(D) W/3
JEE Main 25th July 2022 S-2
Q.An object is taken to a height above the
surface of earth at a distance 5/4R form the
centre of the earth. Where radius of earth, R =
6400 km. The percentage decrease in the
weight of the object will be
(A) 36%
(B) 50%
(C) 64%
(D) 25%
JEE Main 28th July 2022 S-2
Q.Assume there are two identical simple
pendulum Clocks - 1 is placed on the earth and
Clock - 2 is placed on a space station located
at a height h above the earth surface. Clock - 1
and Clock - 2 operate at time periods 4s and 6s
respectively. Then the value of h is_
(Consider radius of earth RE = 6400 km and g
on earth 10m/s2)
(A) 1200 km
(B) 1600 km
(C) 3200 km
(D) 4800 km
JEE Main 25th June 2022 S-1
Q.The height of any point P above the surface of
earth is equal to diameter of earth. The value of
acceleration due to gravity at point P will be :
(Given g = acceleration due to gravity at the
surface of earth)
(A) g/2
(B) g/4
(C) g/3
(D) g/9
Variation in g
JEE Main 24th June 2022 S-1
Q. The approximate height from the surface of
earth at which the weight of the body becomes
of its weight on the surface of earth is: [Radius
of earth R = 6400 km and
= 1.732]
(A) 3840 km
(B) 4685
km
(C) 2133 km
(D) 4267
JEE Main 29th July 2022 S-1
Q. If the acceleration due to gravity experienced
by a point mass at a height h above the surface
of earth is same as that of the acceleration due
to gravity at depth 𝛼h (h << Re) from the earth
surface. The value of 𝛼 will be _____ .
(use Re = 6400 km)
JEE Main 24th January 2023 S-2
Q. Given below are two statements : one is labelled as
Assertion A and the other is labelled as Reason R.
Assertin A: A pendulum clock when taken to Mount
Everest becomes fast.
Reason R : The value of g (acceleration due to gravity)
is less at Mount Everest than its value on the surface of
earth.
In the light of the above statements, choose the most
appropriate answer from the options given below
(A) Both A and R are correct but T is NOT the correct
explanation of A
(B) Both A and R are correct but T is the correct
explanation of A
(C) A is not correct but R is correct
(D) A is not correct but R is not correct
Variation in g
JEE Main 24th January 2023 S-2
JEE Main 01st February 2023 S-1
Q. Given below are two statements:
Statements I : Acceleration due to earth’s gravity decreases
as you go ‘up’ or ‘down’ from earth’s surface.
Statements II : Acceleration due to earth’s gravity is same at a
height ‘h’ and depth ‘d’ from earth’s surface, if h = d.
In the light of above statements, choose the most appropriate
answer from the options given below
(A) Statement I is incorrect but Statement II is correct
(B) Both Statement I and Statement II are incorrect
(C) Statement I is correct but Statement II is incorrect
(D) Both Statement I and Statement are correct
Q. Given below are two statements:
Statement – I :Acceleration due to gravity is
different at different places on the surface of
earth.
Statement - II : Acceleration due to gravity
increases as we go down below the earth’s
surface.
In the light of the above statements, choose the
correct answer from the options given below
(A) Both Statement I and Statement II are true
(B) Both Statement I and Statement II are false
(C) Statement I is true but Statement II is false
(D) Statement I is true but Statement II is true
Young's Modulus
25 Jan -Shift 1 JEE 2023
JEE Main 31st January 2023 S-1
Q. As shown in the figure, in an experiment to
determine Young’s modulus of a wire, the
extension-load curve is plotted. The curve is a
straight line passing through the origin and
makes an angle of 45° with the load axis. The
length of wire is 62.8 cm and its diameter is 4
mm. The Young’s modulus is found to be x × 104
Nm-2. The value of x is____ .
Q. A thin rod having a length of 1 m and area of
cross-section 3 × 10-6 m2 is suspended vertically
from one end. The rod is cooled from 210°C to
160°C. After cooling, a mass M is attached at the
lower end of the rod such that the length of rod
again becomes 1 m. Young’s modulus and
coefficient of linear expansion of the rod are 2 ×
1011 Nm-2 and 2 × 10-5 K-1, respectively. The value
of M is _____ kg. (Take g = 10 m s-2)
JEE Main 26th July 2022 S-1
31 Jan -Shift 2 JEE 2023
Q. For a solid rod, the Young’s modulus of
elasticity is 3.2 × 1011 Nm-2 and density is 8 × 103 kg
m-3. The velocity of longitudinal wave in the rod
will be
(A) 145.75 × 103 ms-1
(B) 3.65 × 103 ms-1
3
-1
3
-1
Q. In an experiment of determine the Young’s
modulus of wire of a length exactly 1m, the
extension in the length of the wire is measured as
0.4 mm with an uncertainty of ± 0.01 mm. The
error in the measurement of Young’s modulus
(ΔY) is found to be x × 1010 Nm-2. The value of x
is____ [Take g = 10 m/s2]
Young's Modulus
JEE Main 28th July 2022 S-1
Q. The force required to stretch a wire of crosssection 1 cm2 to double its length will be:
(Given Young’s modulus of the wire = 2 × 1011
N/m2)
(A) 1 × 107 N
(B) 1.5 × 107 N
(C) 2 × 107 N
(D) 2022
2.5 × S-2
107 N
JEE Main 26th July
Q. A uniform heavy rod of mass 20 kg. Cross
sectional area 0.4 m2 and length 20 m is
hanging from a fixed support. Neglecting the
lateral contraction, the elongation in the rod
due to its own weight is x × 10-9 m. The value of x
is____.
Given Young’s modulus Y = 2 × 1011 Nm-2 and g
= 10 ms-2)
JEE Main 28th July 2022 S-2
Q. A string of area of cross section 4 mm and
length 0.5 is connected with a rigid body of
mass 2 kg. The body is rotated in a vertical
circular path of radius 0.5 m. The body acquires
a speed of 5 m/s at the bottom of the circular
path. Strain produced in the string when the
body is at the bottom of the circle is ………. × 10-5.
(Use Young’s modulus 1011 N/m2 and g = 10
m/s2)
JEE Main 31st January 2023 S-2
Q. Under the same load, wire A having length
5.0 m and cross section 2.5 × 10-5 m2 stretches
uniformly by the same amount as another wire
B of length 6.0 m and a cross section of 3.0 × 105 m2 stretches. The ratio of the Young’s modulus
of wire A to that of wire B will be:
(A) 1 : 4
(B) 1 : 1
(C) 1 : 10
(D) 1 : 2
Young's Modulus
01 Feb -Shift 2 JEE 2023
Q. The Young’s modulus of a steel wire of length
6 m and cross-sectional area 3 mm2, is 2 × 1111
N/m2. The wire is suspended from its support
on a given planet. A block of mass 4 kg is
attached to the free end of the wire. The
acceleration due to gravity on the planet is ¼ of
its value on the earth. The elongation of wire is
(Take g on the earth = 10 m/s2)
27 July -Shift 2 JEE 2022
Q. A steel wire of length 3.2 m (Y s = 2.0 × 1011 Nm2) and a copper wire of length 4.4 M
(YC = 1.1 × 1011 Nm-2), both of radius 1.4 mm are
connected end to end. When stretched by a
load, the net elongation is found to be 1.4 mm.
The load applied, in Newton, will be:
(Given π = 22/7)
(A) 360
(B) 180
(C) 1080
(D) 154
JEE Main 29th July 2022 S-1
Q. If the length of a wire is made double and
radius is halved of its respective values. Then, the
Young’s modulus of the material of the wire will:
(A) Remains same
(B) Biome 8 times its initial value
(C) Become 1th/4 of its initial value
(D) Become 4 times its initial value
Heat Engine
JEE Main 26th June 2022 S-2
JEE Main 30th January 2023 S-2
Q. A heat engine operates with the cold
reservoir at temperature 324 K. The minimum
temperature of the hot reservoir, if the heat
engine takes 300 J heat from the hot reservoir
and delivers 180 J heat to the cold reservoir per
cycle, is ___________K.
Q. Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R Assertion A:
Efficiency of a reversible heat engine will be highest at -273°C
temperature of cold reservoir.
Reason R: The efficiency of Carnot engine depends not only
on temperature of cold reservoir but it depends on the
temperature of hot reservoir too and is given as
In the light of the above statements, choose the correct
answer from the options given below:
(A) A is true but R is false
(B) Both A and R are true but R is NOT the correct explanation
of A
(C) A is false but R is true
(D) Both A and R are true and R is the correct explanation of A
JEE Main 1st Feb 2023 S-2
Q. A carnot engine operating between two
reservoirs has efficiency ⅓. When the
temperature of cold reservoir raised by x, its
efficiency decreases to ⅙. The value of x, if the
temperature of hot reservoir is 99°C, will be:
(A) 16.5 K (B) 33 K
(C) 66 K
(D) 62 K
Heat Engine
JEE Main 27th July 2022 S-2
Q. In 1st case, Carnot engine operates between
temperatures 300 K and 100 K. In 2nd case,
case shown in the figure, a combination of two
engines is used. The efficiency of this
combination (in 2nd case) will be:
(A) Same as the 1st case
(B) Always greater than the 1st case
(C) Always less than the 1st case
(D) May increase or decrease with
respect to the 1st case
JEE Main 26th Jun3 2022 S-1
Q. The efficiency of a Carnot engine, working
between steam point and oce point, will be :
(A) 26.81% (B) 37.81% (C) 47.81% (D) 57.81%
JEE Main 28th July 2022 S-1
Q. A carnot engine has efficiency of 50%. If the temperature of
sink is reduced by 40oC , its efficiency increases by 30%. The
temperature of the source will be :
(A) 166.7 K
(B) 255.1 K
(C) 266.7 K
(D) 367.7 K
JEE Main 24th June 2022 S-1
Q. A carnot engine whose heat sinks at 27°C, has an
efficiency of 25%. By how many degrees should the
efficiency by 100% of the original efficiency?
(A) Increases by 18° C
(B) Increases by 200°C
(C) Increases by 120°C
(D) Increases by 73°C
JEE Main 24th June 2022 S-1
Q. A carnot engine take 5000 kcal of heat from a reservoir at
727°C and gives heat to a sink at 127°C. The work done by the
engine is :
(A) 3 x 106 J
(B) Zero
(C) 12.6 x 106 J
(D) 8.4 x 106 J
Heat Engine
JEE Main 27th June 2022 S-1
Q. In a carnot engine, the temperature of reservoir is 527°C
and that os sink is 200 K. If the work done by the engine
when it transfers heat from reservoir to sink is 12000 kl, the
quality of heat absorbed by the engine from reservoir is
__________× 106 J.
JEE Main 25th January 2023 S-1
Q. A carnot engine with efficiency 50% takes
heat from a source at 600 K. In order to
increase the efficiency to 70%, keeping the
temperature of sink same, the new temperature
of the source will be:
(A) 360 K (B) 1000 K (C) 900 K (D) 300 K
Time period
JEE Main 26th July 2023 S-2
Q As per given figures, two springs
of spring constants K and 2K are
connected to mass m. If the
period of oscillation in figure (a) is
3s, then the period of oscillation
in figure (b) will be √x s. The value
of x is____
JEE Main 24th Jan 2023 S-2
Q A mass “m” attached to free end of a spring executes
SHM with a period of 1 s. If the mass is increased by 3 kg
the period of oscillation increases by one second, the
value of mass “m” is_____ kg.
JEE Main 30th Jan 2023 S-2
Q The velocity of a particle executing SHM
varies with displacement (x) as 4v2 = 50 - x2 .
The time period of oscillations is x/7 s. The
value of x is_____.
JEE Main 27th June 2023 S-2
Q The displacement of simple harmonic
oscillator after 3 seconds starting from its
mean position is equal to half of its amplitude.
The time period of harmonic motion is:
(A) 6 s
(B) 8 s
(C) 12 s (D) 36 s
Time period
JEE Main 31st Jan 2023 S-2
JEE Main 25th July 2023 S-2
Q In the figure given
below, a block of mass
M = 490 g placed on a
frictionless table
is connected with two
springs having same spring
constant (K = 2 Nm-1). If the block is
horizontally displaced through ‘X’ m then the
number of complete oscillations it will make in
14𝜋 seconds will be_____.
Q n figure (A), mass ‘2 m’ is
fixed on mass ‘m’ which is
attached to two springs of
spring constant k. In
figure (B), mass ‘m’ is
attached to two spring of spring constant ‘k’ and ‘2k’. If mass
‘m’ in (A) and (B) are displaced by distance ‘x’ horizontally
and then released, then time period T1 and T2 corresponding
to (A) and (B) respectively follow the relation.
A.
B.
C.
D.
Electric Field
JEE Main 30th Jan 2023 S-2
JEE Main 26th July 2022 S-2
Q As shown in the figure, a point charge Q is
placed at the centre of conducting spherical
shell of inner radius a and outer radius b. The
electric field due to charge Q in three different
regions I, II and III is given by :
(I : r < a, II : a < r < b, III : r > b)
(A) EI = 0, EII = 0, EIII ≠ 0
(B) EI ≠ 0, EII = 0, EIII ≠ 0
(C) EI ≠ 0, EII = 0, EIII = 0
(D) EI = 0, EII = 0, EIII = 0
Q.Two uniformly charged spherical conductors
A and B of radii 5 mm and 10 mm are separated
by a distance of 2 cm. If the spheres are
connected by a conducting wire, then in
equilibrium condition, the ratio of the
magnitudes of the electric fields at the surface
of the sphere A and B will be :
(A) 1 : 2
(B) 2 : 1
(C) 1 : 1
(D) 1 : 4
JEE Main 25th Jan 2023 S-2
Q. A point charge of 10μC is placed at the origin.
At what location on the X-axis should a point
charge of 40μC be placed so that the net
electric field is zero at x = 2 cm on the X-axis ?
(A) x = 6 cm
(B) x = 4 cm
(C) x = 8 cm
(D) x = -4 cm
JEE Main 28th June 2022 S-2
Q.Two point charges A and B of magnitude +8 ×
10-6 C and -8 × 10-6C respectively are placed
at a distance d apart. The electric field at the
middle point O between the charges is 6.4 × 104
NC-1. The distance ‘d’ between the point
charges A and B is
(A) 2.0 m (B) 3.0 m (C) 1.0 m (D) 14.0 m
Electric Field
JEE Main 25th June 2022 S-1
JEE Main 28th June 2022 S-1
Q. In the figure, a very large plane sheet of positive
charge is shown, P1 and P2 are two points at distance l
and 2l from the charge distribution. If 𝜎 is the surface
charge density then the magnitude of electric fields E1
and E2 at P1 and P2 respectively are:
(A) E1 = 𝜎/𝜀0, E2 = 𝜎/𝜀0,
(B) E1 = 2𝜎/𝜀0, E2 = 𝜎/𝜀0,
(C) E1 = E2 = 𝜎/2𝜀0,
(D) E1 = E2 = 𝜎/𝜀0,
Q. Given below are two statements:
Statement-I : A point charge is brought in an electric
field. The value of electric field at a point near to the
charge may increase if the charge is positive.
Statement-II : An electric dipole is placed in a nonuniform electric field. The net electric force on the
dipole will not be zero
Choose the correct answer from the options given
below:
(A) Both statement-I and statement-II are ture.
(B) Both statement-I and statement-II are false.
(C) Statement-I is true but statement-II if false
(D) Statement-I is false but statement-II if true.
JEE Main 27th July 2022 S-2
Q. A long cylindrical volume contains
a uniformly distributed charge of density
𝜌 Cm-3. The electric field inside the
cylindrical volume at a distance
axis is ______ Vm-1
from its
Electric Field
JEE Main 28th June 2022 S-1
JEE Main 29th July 2022 S-1
Q. The three charges q/2, q and q/2 are placed at the
corners A, B and C of a square of side ‘a’ as shown if
figure. The magnitude of electric field (E) at the
comer D of the square, is:
(A)
Q. A spherically symmetric charge distribution is
considered with charge density varying as
(B)
(C)
(D)
Where, r(r < R) is the distance from
the centre O (as shown in figure).
The electric field at point P will be:
(A)
(B)
(C)
(D)
Dielectrics
JEE Main 25th Jan 2023 S-2
JEE Main 25th Jan 2023 S-1
Q A capacitor has capacitance 5𝜇F When it’s
parallel plates are separated by air medium
of thickness d. A slab of material of dielectric
constant 1.5 having area equal to that of
plates but thickness d/2 is inserted between
the plates. Capacitance of the capacitor in
the presence of slab will be ____ 𝜇F.
Q A parallel plate capacitor has plate area 40 cm2 and
plates separation 2 mm. The space between the plates is
filled with dielectric medium of a thickness 1 mm and
dielectric constant 5. The capacitance of the system is:
A. 24 ε0 F
JEE Main 26th June 2023 S-2
Q A parallel plate capacitor with plate area A and
plate separation d = 2 m has a capacitance of 4 𝜇F.
The new capacitance of the system if half of the
space between them is filled with a dielectric
material of dielectric constant K = 3 (as shown
in figure) will be:
A. 2𝜇F B. 32𝜇F C. 6𝜇F D. 8𝜇F
B.
C.
D. 10 ε0 F
Dielectrics
JEE Main 31st Jan 2023 S-2
JEE Main 24th June 2023 S-1
Q Two parallel plate capacitors C1 and C2 each
having capacitance of 10 μF are individually
charged by a 100 V D. C. source. Capacitor C1 is
kept connected to the source and a dielectric
slab is inserted between it plates. Capacitor C2
is disconnected from the source and then a
dielectric slab is inserted in it. Afterwards the
capacitor C1 is also disconnected from the
source and the two capacitors are finally
connected in parallel combination. The
common potential of the combination will
be______ V. (Assuming Dielectric
Constant = 10)
Q A parallel plate capacitor is formed by two plates each of
area 30𝜋 cm2 separated by 1 mm. A material of dielectric
strength 3.6 × 107 Vm-1 is filled between the plates. If the
maximum charge that can be stored on the capacitor
without causing any dielectric breakdown is 7 × 10-6 C, The
value of dielectric constant of the materials is:
(A) 1.66 (B) 1.75
(C) 2.25 (D) 2.33
JEE Main 29th June 2023 S-1
Q A parallel plate capacitor filled with a medium of dielectric
constant 10, is connected across a battery and is charged.
The dielectric slab is replaced by another slab of dielectric
constant 15. Then the energy of capacitor will :
A. Increased by 50% B. Decrease by 15%
C. Increased by 25% D. Increase by 33%
Dielectrics
JEE Main 29th June 2023 S-2
JEE Main 25th June 2023 S-2
Q The displacement current of 4.425 𝜇A is
developed in the space between the plates of
parallel plate capacitor when voltage is
changing at a rate of 106 Vs-1. The area of
each plate of the capacitor is 40 cm2. The
distance between each plate of the
capacitor is x × 10-3m. The value of x is
(Permittivity of free space, E0 = 8.85 x 1012C2N-1m-2)
Q Two metallic plates form a parallel plate capacitor.
The distance between the plates is ‘d’. A metal sheet of
thickness d/2 and of a area equal to area of each plate
is introduced between the plates. What will be the ratio
of the new capacitance to the original capacitance of
the capacitor?
JEE Main 27th June 2023 S-2
Q A parallel plate capacitor is made up of
stair like structure with a plate area A of
each stair and that is connected with a
wire of length b, as shown in the figure.
The capacitance of the arrangement is
The value of x is _____
A. 2 : 1
B. 1 : 2
C.
1:4
D.
4:1
JEE Main 25th Jan 2023 S-2
Q Two parallel plate capacitors of capacity C
and 3C are connected in parallel
combination and charged to a potential
difference 18V. The battery is then
disconnected and the space between the
plates of the capacitor of capacity C is
completely filled with a material of dielectric
constant 9. The final potential difference
across the combination of capacitors will be
Dielectrics
JEE Main 26th July 2023 S-1
JEE Main 27th July 2023 S-2
Q A composite parallel plate capacitor is made
up of two different dielectric materials with
different thickness (t1 and t2) as shown in
figure. The two different dielectric material are
separated by a conducting foil F. The voltage of
the conducting foil is _____ V.
Q A parallel plate capacitor with width 4 cm, length 8 cm
and separation between the plates of 4mm is connected to
a battery of 20 V. A dielectric slab of dielectric constant 5
having length 1 cm, width 4 cm and thickness 4 mm is
inserted between the plates of parallel plate capacitor. The
electrostatic energy of this system will be _____∈0 J.
(Where ∈0 is the permittivity of free space)
JEE Main 28th July 2023 S-2
Q Sectional area as the plates of a parallel
plate capacitor and thickness ¾ d, where d is
the separation of the plates. The capacitance of
the capacitor when the slab is inserted between
the plates will be:
(Given Co = capacitance of capacitor with air
as medium between plates.)
A.
B.
C.
D.
Straight Wire & Circular Coil
JEE Main 24th Jan 2023 S-2
Q A long solenoid is formed by winding 70 turns
cm-1. If 2.0 A current flows, then the magnetic
field produced inside the solenoid is _____
(μ0 = 4π × 10-7 TmA-1)
A. 1232 × 10-4 T
B. 176 × 104T
C. 352 × 10-4 T
D. 88 × 10-4 T
JEE Main 29th July 2022 S-1
Q A closely wound circular coil of radius 5cm
produces a magnetic field of 37.68 × 10-4 T at its
center. The current through the coil is______
A. [Given, number of turns in the coil is 100 and
π = 3.14]
JEE Main 24th Jan 2023 S-1
Q A circular loop of radius r is carrying current I
A. The ratio of magnetic field at the centre of
circular loop and at a distance r from the centre
of the loop on its axis is:
A.
B.
C.
D.
Straight Wire & Circular Coil
JEE Main 01st Feb 2023 S-2
JEE Main 29th Jan 2023 S-2
Q As shown in the figure, along straight
conductor with semicircular arc of radius 𝜋/10
m is carrying current I = 3A. The magnitude of
the magnetic field at the centre O of the arc is:
(The permeability of the vacuum = 4π × 10-7 NA2)
(A) 6 μT
(B) 1 μT
(C) 4 μT
(D) 3 μT
Q. The electric current in a circular coil of four turns produces
a magnetic induction 32 T at its centre. The coil is unwound
and is rewound into a circular coil of single turn, the magnetic
induction at the centre of the coil by the same current will be :
(A) 8T
(B) 4T
(C) 2T
(D) 16T
JEE Main 29th Jan 2023 S-2
Q. The electric current in a circular coil of 2 turns produces a
magnetic induction B1 at its centre. The coil is unwound and is
rewound into a circular coil of 5 turns and the same current
produces a magnetic induction B2 at its centre. The ratio of
(A)
(B)
(C)
(D)
Straight Wire & Circular Coil
JEE Main 31st Jan 2023 S-2
JEE Main 29th June 2022 S-2
Q A long conducting wire having a current I
flowing through it, is bent into a circular coil of N
turns. Then it is bent into a circular coil of n
turns. The magnetic field is calculated at the
centre of coils in both the cases. The ratio of the
magnetic field in first case to that of second
case is:
Q An infinitely long hollow conducting cylinder
with radius R carries a uniform current along its
surface. Choose the correct representation of
magnetic field (B) as a function of radial
distance (r) from the axis of cylinder.
(A)
(A)
(C)
(B)
(D)
(C)
(B)
(D)
Straight Wire & Circular Coil
JEE Main 24th June 2022 S-1
JEE Main 29th June 2022 S-2
Q Two long current carrying conductors are
placed parallel to each other at a distance of 8
cm between them. The magnitude of magnetic
field produced at mid-point between the two
conductors due to current flowing in them is
300 µT. The equal current flowing in the two
conductors is:
(A) 30A in the same direction
(B) 30A in the opposite direction
(C) 60A in the opposite direction
(D) 300A in the opposite direction
Q. The magnetic field at the centre of a
circular coil of radius r, due to current I flowing
through it, is B. The magnetic field at a point
along
the axis at a distance r/2 from the centre is
(A)
JEE Main 25th June 2022 S-1
Q. A long straight wire with a circular cross-section having
radius R, is carrying a steady current I. The current I is uniformly
distributed across this cross-section. Then the variation of
magnetic field due to current I with distance r (f < R) from its
centre will be:
(A) B ∝ r2
(B)
B∝r
(C)
(D)
(B) 2B
(C)
(D)
JEE Main 26th July 2022 S-1
Q. Bx and BY are the magnetic field at the
centre of two coils X and Y respectively, each
carrying equal current. If coil X has 200 turns
and 20 cm radius and coil Y has 400 turns
and 20 cm radius, the ratio of Bx and BY
(A) 1:1
(B) 1:2
(C)
2:1
(D)
4:1
Series RLC Circuit
JEE Main 25th Jan 2023 S-2
Q A series LCR circuit is connected to an AC
source of 220 V, 50 Hz. The circuit contains a
resistance R = 80Ω, an inductor of inductive
reactance XL = 70Ω, and a capacitor of
capacitive reactance XC = 130Ω. The power
factor of circuit is x/10. The value of x is:
JEE Main 25th Jan 2023 S-2
Q A series LCR circuit is connected to an ac
source of 220V, 50Hz. The circuit contain a
resistance R = 100Ω and an inductor of
inductive reactance XL = 79.6Ω. The
capacitance of the capacitor needed to
maximize the average rate at which energy is
supplied will be_____μF.
JEE Main 25th Jan 2023 S-2
Q For the given figures, choose the correct options:
(A) The rms current in circuit (b) can never be larger than
that in (a)
(B) The rms current in figure (a) is always equal to that in
figure (b)
(C) The rms current in circuit (b) can be larger than that
in (a)
(D) At resonance, current in (b) is less than that in (a)
Series RLC Circuit
JEE Main 25th July 2022 S-1
Q To increase the resonant frequency in series
LCR circuit,
(A) Source frequency should be increased
(B) Another resistance should be added in
series with the first resistance.
(C) Another capacitor should be added in
series with the first capacitor
(D) The source frequency should be decreased.
JEE Main 25th July 2022 S-1
Q An inductor of inductance 2 μH is connected
in series with a resistance, a variable capacitor
and an AC source of frequency 7 kHz. The value
of capacitance for which maximum current is
drawn into the circuit is 1/x F, where the value of
x is______. (take 𝜋 = 22/7)
JEE Main 26th July 2022 S-1
Q The effective current I in the given circuit at
very high frequencies will be _____ A
JEE Main 28th June 2022 S-1
Q An AC source is connected to an inductance
of 100 mH, a capacitance 100 𝜇F and a
resistance of 120 𝛺 as shown in figure. The time
in which the resistance having a thermal
capacity 2 Jo/C will
get heated by 16 oC
is __ s.
Series RLC Circuit
JEE Main 29th June 2022 S-2
JEE Main 29th June 2022 S-1
Q An inductor of 0.5 mH, a capacitor of 200 𝜇F
and a resistor of 2 𝛺 are connected in series
with a 220 V ac source. If the current is in phase
with the emf, the frequency of ac source will be
______× 102 Hz.
Q For a series LCR circuit, I vs 𝜔 curve is shown:
(a) To the left of 𝜔t, the circuit is mainly
capacitive.
(b) To the left of 𝜔t, the circuit is mainly
inductive.
(c) At 𝜔t, impedance of the circuit is equal to
the resistance of the circuit.
(d) At 𝜔t, impedance of the circuit is 0.
Choose the most appropriate answer from the
options given below:
(A) (a) and (d) only
(B) (b) and (d) only
(C) (a) and (c) only
(D) (b) and (c) only
JEE Main 29th June 2022 S-2
Q In the given circuit, the
magnitude of VL and VC are
twice that of VR. Given that
f = 50 Hz, the inductance of
the coil is 1/K𝜋 The value of
K is __
EM Waves : E / B = C
JEE Main 25th July 2022 S-2
JEE Main 29th January 2023 S-2
Q. Given below are two statements:
Statement I: Electromagnetic waves are not
deflected by electric and magnetic field
Statement II: The amplitude of electric field and the
magnetic field in electromagnetic waves are
related to each other as
In the light of the above statements, choose the
correct answer from the option given below:
(A) Statement I is true but Statement II is false
(B) Both Statement I and Statement II are true
(C) Statement I is false but Statement II is true
(D) Both Statement I and Statement II are false
JEE Main 25th July 2022 S-1
Q. Light wave traveling in air along x-direction is
given by Ey = 540 sin π × 104 (x - ct) Vm-1. Then, the
peak value of magnetic field of wave will be (Given
c = 3 × 108 ms-1)
(A) 18 × 10-7 T
(B) 54 × 10-7 T
-8
-8
Q. The electromagnetic wave travel in a medium at
a speed of 2.0 × 108 m/s. The relative permeability
of the medium is 1.0. The relative permittivity of the
medium will be:
(A) 2.25
(B) 4.25
(C) 6.25
(D) 8.25
JEE Main 24th June 2020 S-1
Q. A plane electromagnetic wave travels in a
medium of relative permeability 1.61 and relative
permittivity 6.44. If magnitude of magnetic intensity
is 4.5 × 10-2 Am-1 at a point, what will be the
approximate magnitude of electric field intensity at
that point?
(Given : Permeability of free space 𝜇0 = 4𝜋 × 10-7 NA-2,
speed of light in vacuum c = 3 × 108 ms-1)
(A) 16.96 Vm-1
2.25 × 10-2 Vm-1
(C) 8.48 Vm-1
6.75 × 106 Vm-1
(B)
(D)
EM Waves : E / B = C
JEE Main 24th June 2022 S-1
Q. The oscillating magnetic field in a plane
electromagnetic wave is given by By = 5 × 10-6 sin
1000π (5x - 4 × 108 t) T. The amplitude of electric field
will be:
(A) 15 × 102 Vm-1
(B) 5 × 10-6 Vm-1
(C) 16 × 1012 Vm-1
(D) 4 × 102 Vm-1
JEE Main 24th June 2022 S-1
Q. If electric field intensity of a uniform plane
electromagnetic wave is given as
Then, magnetic intensity H of this wave in Am-1 will be:
[Given: Speed of light in vacuum c = 3 × 108 ms-1,
permeability of vacuum 𝜇0 = 4𝜋 × 10-7 NA-2]
(A)
(B)
(C)
(D)
JEE Main 27th June 2022 S-2
Q. Given below are two statements:
Statement I: A time varying electric field is a source
of changing magnetic field and vice-versa. Thus a
disturbance in electric or magnetic field creates EM
wave
Statement II: In a material medium. The EM wave
travels with speed
In the light of the above statements, choose the
correct answer from the options given below:
(A) Both statement I and statement II are true
(B) Both statement I and statement II are false
(C) Statement I is correct but statement II is false
(D) Statement I is incorrect but statement II is true
EM Waves : E / B = C
JEE Main 28th June 2022 S-2
Q. An EM wave propagating in x-direction has a
wavelength of 8 mm. The electric field vibrating ydirection has maximum magnitude of 60 Vm-1.
Choose the correct equations for electric and
magnetic field if the EM wave is propagating in
vacuum:
JEE Main 26th July 2022 S-1
Q. The magnetic field of a plane electromagnetic
wave is given by
The amplitude of the electric field would be
A
6Vm-1 along x-axis
B
3Vm-1 along z-axis
C
6Vm-1 along z-axis
D
2 × 10-8 Vm-1 along z-axis
(A)
(B)
(C)
(D)
Young's Double Slit Experiment
JEE Main 26th July 2023 S-1
Q. In young’s double slit experiment, the fringe
width is 12mm. If the entire arrangement is
placed in water of refractive index 4/3, then the
fringe width becomes (in mm)
(A) 16
(B) 9
(C) 4.8
(D) 12
JEE Main 27th June 2022 S-1
Q. In Young’s double slit experiment the two
slits are 0.6 mm distance apart. Interference
pattern is observed on a screen at a distance
80 cm from the slits. The first dark fringe is
observed on the screen directly opposite to
one of the slits. The wavelength of light will
be___nm.
JEE Main 28th June 2022 S-2
Q. In Young’s double slit experiment performed
using a monochromatic light of wavelength 𝜆,
when a glass plate (𝜇 = 1.5) of thickness x𝜆 is
introduced in the path of the one of the
interfering beams, the intensity at the position
where the central maximum occurred
previously remains unchanged. The value of x
will be:
(A) 3
(B) 2
(C) 1.5
(D) 0.5
JEE Main 25th Jan 2023 S-1
Q. In Young’s double slits experiment, the
position of 5th bright fringe from the central
maximum is 5 cm. The distance between slits
and screen is 1 m and wavelength of used
monochromatic light is 600 nm. The separation
between the slits is :
(A) 60 𝞵m (B) 48 𝞵m (C) 12 𝞵m (D) 36 𝞵m
Young's Double Slit Experiment
JEE Main 30th Jan 2023 S-1
Q.In Young’s double slit experiment, two slits S 1
and S2 are ’d’ distance apart and the
separation from slits to screen is D (as shown in
figure). Now if two transparent slabs of equal
thickness 0.1 mm but refractive index 1.51 and
1.55 are introduced in the
path of beam (𝞴 = 4000 𝞴)
from S1 and S2 respectively.
The central bright fringe
spot will shift by______.
number of fringes.
JEE Main 28th June 2022 S-2
Q. In a Young’s double slit experiment, an
angular width of the fringe is 0.35° on a screen
placed at 2 m away for particular wavelength
of 450 nm. The angular width of the fringe,
when whole system is immersed in a medium
of refractive index 7/5, is 1/⍺. The value of α is_
JEE Main 29th June 2022 S-2
Q. In a double slit experiment with
monochromatic light, fringes are obtained on a
screen placed at some distance from the plane
of slits. If the screen is moved by 5 × 10-2 m
towards the slits, the change in fringe width is
3 × 10-3 cm. If the distance between the slits is 1
mm, then the wavelength of the light will be_nm.
JEE Main 31st Jan 2023 S-2
Q. Two light waves of wavelengths 800 and 600
nm are used in Young’s double slit experiment to
obtain interference fringes on a screen placed 7
m away from plane of slits. If the two slits are
separated by 0.35 mm, then shortest distance
from the central bright maximum to the point
where the bright fringes of the two wavelength
coincide will be ________mm.
MODERN PHYSICS
Half Life
JEE Main 29th Jan 2023 S-1
JEE Main 29th Jan 2023 S-2
Q. If a radioactive element having half-life of
30 min is undergoing beta decay, the fraction
of radioactive element remains undecayed
after 90 min will be:
(A) ⅛
(B) 1/16
(C) ¼
(D) ½
Q. Substance A has atomic mass number 16
and half life of 1 day. Another substance B has
atomic mass number 32 and half life of ½ day.
If both A and B simultaneously start undergo
radioactivity at the same time initial mass 320
g each, how many total atoms of A and B
combined would be left after 2 days.
(A) 3.38 × 1024
(B) 6.76 × 1024
(C) 6.76 × 1023
(D) 1.69 × 1024
JEE Main 24th June 2022 S-2
Q. A sample contains 10-2 kg each of to
substances A and B with half lives 4 s and 8s
respectively. The ratio of then atomic weights is
1 : 2. The ratio of the amounts of A and B after 16
s is x/100, the value of x is__.
JEE Main 29th June 2022 S-2
Q. The half life of a radioactive substance is 5
years. After x years a given sample of the
radioactive substance gets reduced to 6.25% of
its initial value of x is_____.
JEE Main 26th June 2022 S-2
Q. A radioactive nucleus can decay by two
different processes. Half-life for the first
process is 3.0 hours while it is 4.5 hours for the
second process. The effective half-life of the
nucleus will be:
(A) 3.75 hours
(B) 0.56 hours
(C) 0.26 hours
(D) 1.80 hours
JEE Main 29th Jan 2023 S-1
JEE Main 27th July 2022 S-1
Q. The activity of a radioactive material is
6.4 × 10-4 curies. Its half life is 5 days. The
activity will become 5 × 10-6 curies after:
(A) 7 days
(B) 15 days
(C) 25 days
(D) 35 days
Q. What is the half-life period of a radioactive
material if its activity drops to 1/16th of its initial
value of 30 years ?
(A) 9.5 tears
(B) 8.5
years
(C) 7.5 years
(C) 10.5
JEE Main 26th July 2022 S-1
years
JEE Main 30th Jan 2023 S-2
Q. A radioactive nucleus decays by two
different process. The half life of the first
process is 5 minutes and that of the second
process is 30s. The effective half-life of the
nucleus is calculated to be ⍺/11. The value of α
is____.
JEE Main 29th June 2022 S-1
Q. The activity of a radioactive material is
2.56 × 10-3 Ci. If the half life of the material is 5
days, after how many days the activity will
becomes 2 × 10-5 Ci?
(A) 30 days
(B) 35 days
(C) 40 days
(D) 25 days
Q. The disintegration rate of a certain
radioactive sample at any instant is 4250
disintegrations per minute. 10 minutes later,
the rate becomes 2250 disintegrations per
minutes. The approximate decay constant is:
(Take log101.88 = 0.274)
(A) 0.02 min-1
(B) 2.7 min-1
(C) 0.063 min-1
(D) 6.3 min-1
JEE Main 28th July 2022 S-1
JEE Main 29th July 2022 S-2
Q. The half life period of a radioactive
substance is 60 days. The time taken for ⅞ th of
its original mass to disintegrate will be:
(A) 120 days
(B) 130 days
(C) 180 days
(D) 20 days
Q. Two radioactive materials A and B have
decay constants 25λ and 16λ respectively. If
initially they have the same number of nuclei,
then the ratio of the number of nuclei of B to
that of A will be “e” after a time 1/⍺λ. The value
of a is _______ .
JEE Main 28th July 2022 S-1
Q. A freshly prepared radioactive source of half
life 2 hours 30 minutes emits radiation which is
64 times the permissible safe level. The
minimum time, after which it would be possible
to work safely with source, will be ______
hours.
JEE Main 28th July 2022 S-1
Q. A radioactive sample decays 7/4 times its
original quantity in 15 minutes. The half-life of
the sample is
(A) 5 min (B) 7.5 min (C) 15 min (D) 30 min
MODERN PHYSICS
Photoelectric effect
24 Jan - Shift 1 JEE 2023
25 Jan - Shift 2 JEE 2023
From the photoelectric effect experiment,
following observations are made. Identify
which of these are correct
A. The stopping potential depends only
on the work function of the metal.
B. The saturation current increases as the
intensity of incident light increases.
C. The maximum kinetic energy of a
photo electron depends on the intensity
of the incident light.
D. Photoelectric effect can be explained
using wave theory of light.
Choose the correct answer from the
options given below:
Given below are two statements :
Statement I : Stopping potential in
photoelectric effect does not depend on
the power of the light source.
Statement II : For a given metal, the
maximum kinetic energy of the
photoelectron depends on the
wavelength of the incident light.
(A) B, C Only
(D) A, B, D
(B) 1A, C, D
(C) B Only
In the light of above statements, choose
the most appropriate answer from the
options given below.
(A) I is incorrect but II is correct
(B) Both I & II are incorrect
(C) I Correct but II Incorrect
(D) Both I & II are correct
29 Jan - Shift 1 JEE 2023
31 Jan - Shift 2 JEE 2023
The threshold wavelength
for photoelectric emission
from a material is 5500 Å.
Photoelectrons will be
emitted, when this
material is illuminated with
monochromatic radiation
from a
If the two metals A and B are exposed to
radiation of wavelength 350 nm. The work
functions of metals A and B are 4.8 eV and 2.2
eV. Then choose the correct option.
(A) B will not emit photoelectron
(B) Both A & B will emit photo electron
(C)
neither A nor B will emit photo
electron
(D)
A will not emit photoelectron
A. 75 W infrared lamp
B. 10 W infrared lamp
C. 75 W ultra-violet lamp
D. 10 W ultra-violet lamp
Choose the correct answer
from the options given
below :
(1)
(2)
(3)
(4)
B & C Only
A & D Only
C Only
C & D Only
24 June - shift 12022
When light of frequency twice the threshold
frequency is incident on the metal plate, the
maximum velocity of emitted electron is v1.
When the frequency of incident radiation is
increased to five times the threshold value,
the maximum velocity of emitted electron
becomes v2. If v2 = x v1, the value of x will
be_____.
26 June - shift 2 2022
The stopping potential for
photoelectrons emitted from a
surface illuminated by light of
wavelength 6630 Å is 0.42 V. if
the threshold frequency is x ×
1013/s, where x
is______(nearest integer).
(Give, speed light = 3 × 108 m/s,
Planck’s constant = 6.63 × 10-34
Js)
24 June - shift 2 2022
The light of two different frequencies
whose photons have energies 3.8 eV and
1.4 eV respectively, illuminate a metallic
surface whose work function is 0.6 eV
successively. The ratio of maximum
speeds of emitted electrons for the two
frequencies respectively will be:
(A) 1:1 (B) 2:1 (C) 4:1 (D) 1:4
25 July - shift 1 2022
A metal exposed to light of
wavelength 800 nm and emits
photoelectrons with a certain
kinetic energy. The maximum
kinetic energy of photoelectron
doubles when light of wavelength
500 nm is used. The work function
of the metal (Take hc = 1230 eVnm).
(A) 1.537 eV (B) 2.46 eV
28 June - shift 2 2022
Let K1 and K2 be the maximum kinetic energies of
photoelectrons emitted when two monochromatic
beams of wavelength 𝜆1 and 𝜆2, respectively are
incident on a metallic surface. If 𝜆1 = 3𝜆2 then:
(A)
(B)
(D)
(C)
29 June - shift 1 2022
Given below are two statements: one is labelled as
Assertion A and the other is Reason R.
Assertion A: The photoelectric effect does not take place, if the
energy of the incident radiation is less than the work function of a
metal.
Reason R: Kinetic energy of the photoelectrons is zero, if the energy
of the incident radiation is equal to the work function of a metal.
In the light of the above statements, choose the most appropriate
answer from the options, given below,
(A)
(B)
(C)
(D)
A & R are correct & R is correct explanation of A
A & R are correct but R is not correct explanation of A
A is correct but R is not correct
A is not correct but R is correct
29 July - shift 1 2022
The kinetic energy of emitted electron is E when the light
incident on the metal has wavelength 𝜆. To double the
kinetic energy, the incident light must have wavelength
(A)
(B)
(D)
(C)
28 July - shift 2 2022
Two streams of photons, possessing energies to five and
ten times the work function of metal are incident on the
metal surface successively. The ratio of the maximum
velocities of the photoelectron emitted, in the two cases
respectively, will be
(A)
1:2
2:3
(B)
(D)
3:2
1:3
(C)
MODERN PHYSICS
De broglie
JEE Main 24th Jan 2023 S-2
JEE Main 26th June 2022 S-1
Q. An α-particle, a proton and an electron have
the same kinetic energy. Which one of the
following is correct in case of their De-Broglie
wavelength:
(A) 𝜆α > 𝜆p > 𝜆e
(B) 𝜆α < 𝜆p <
𝜆e
(C) 𝜆α ≡ 𝜆p = 𝜆e
(D) 𝜆α > 𝜆p <
JEE Main 24th Jan 2023 S-2
𝜆e
Q. An electron with speed v and a photon with
speed c have the same de-Broglie wavelength.
If the kinetic energy and momentum of
electron are Ee and pe and that of photon are
Eph and pph respectively. Which of the following
is correct?
Q. The ratio of de-Broglie wavelength of an αparticle and a proton accelerated from rest by
the same potential is 1/√m, the value of m is
(A) 4
(B) 16
(C) 8
(D) 2
JEE Main 01st Feb 2023 S-1
Q. A proton moving with one tenth of velocity of
light has a certain de-Broglie wavelength of 𝜆.
An alpha particle having certain kinetic energy
has the same de-Brogle wavelength 𝜆. The
ratio of kinetic energy of proton and that of
alpha particle is:
(A) 2 : 1
(B) 4 : 1
(C) 1 : 2
(D) 1 : 4
(A)
(B)
(C)
JEE Main 25th Jan
(D)2023 S-1
Q. Electron beam used in an electron
microscope, when accelerated by a voltage of
20 kV. Has a de-Broglie wavelength of 𝜆0. If the
voltage is increased to 40 kV. then the deBroglie wavelength associated with the
electron beam would be:
(A) 3λ0
(B) 9λ0
(C) λ0/2
(D) λ0/√2
JEE Main 27th June 2022 S-1
Q. An α particle and a carbon 12 atom has
same kinetic energy K. The ratio of their deBroglie wavelength (𝜆a : 𝜆C12) is:
(A) 1 : √3 (B) √3 : 1
(C) 3 : 1
(D) 2 : √3
JEE Main 25th July 2022 S-2
Q. The ratio of wavelengths of proton and
deuteron accelerated by potential Vp and Vd is
1 : √2. Then, the ratio of Vp to Vd will be
(A) 1 : 1
(B) √2 : 1
(C) 2 : 1
(D) 4 : 1
JEE Main 27th June 2022 S-1
Q. The equation
can be used to
find the de-Brogli wavelength of an electron. In
this equation x stands for:
Where
m = mass of electron
P = momentum of electron
K = Kinetic energy of electron
V = Accelerating potential in volts for electron
(A)
(C)
(B)
(D)
JEE Main 30th Jan 2023 S-2
JEE Main 28th June 2022 S-1
Q. An electron accelerated through a potential
difference V1 has a de-Broglie wavelength of 𝜆.
When the potential is changed to V2, its deBroglie wavelength increases by 50%. The
value of (V1/V2)is equal to:
(A) 3
(B) 9/4
(C) 3/2
(D) 4
Q. The de-Brogue wavelength for an electron
and a photon are 𝜆e and 𝜆p respectively. For the
same kinetic energy of electron and photon
which of the following presents the correct
relation between the de-Brogue wavelengths
of two?
(A) 𝜆p ∝ 𝜆e2
(B) 𝜆p ∝ 𝜆e
(c)
(D)
MODERN PHYSICS
Electronic transition
JEE Main 24th Jan 2023 S-2
JEE Main 01st Feb 2023 S-2
Q. A photon is emitted in transition from n = 4 to
n = 1 level in hydrogen atom. The corresponding
wavelength for this transition is
(given, h = 4 × 10-15 eVs):
(A) 94.1 nm (B) 941 nm (C) 97.4 nm (D) 99.3 nm
Q. An electron of a hydrogen like atom, having
Z = 4, jumps from 4th energy state to 2nd energy
state, the energy released in this process, will be:
(Where Rch = 13.6 eV)
Where R = Rydberg constant
c = Speed of light in vacuum
h = Planck’s constant
(A) 13.6 eV (B) 10.5 eV (C) 3.4 eV (D) 40.8 eV
JEE Main 01st Feb 2023 S-1
Q. A light of energy 12.75 eV is incident on a
hydrogen atom in its ground state. The atom
absorbs the radiation and reaches to one of its
excited states.The angular momentum of the
atom in the excited state is x/π × 10-17 eVs. The
value of x is ____
(use h = 4.14 × 10-15 eVs, c = 3 × 108 ms-1)
JEE Main 27th June 2022 S-1
Q. A beam of monochromatic light is used to
excite the electron in Li++ from the first orbit to
the third orbit. The wavelength of
monochromatic light is found to be x × 10-10 m.
The value of x is ____ .
[Given he = 1242 eV nm]
JEE Main 26th July 2022 S-1
JEE Main 31st Jan 2023 S-1
Q. In a hydrogen spectrum, 𝜆 be the wavelength
of first transition line of Lyman series. The
wavelength difference will be “a𝜆” between the
wavelength of 3rd transition line of Paschen
series and that of 2nd transition line of Balmer
Series where a = ___
Q. For hydrogen atom 𝜆1 and 𝜆2 are the
wavelengths corresponding to the transitions 1
and 2 respectively as shown in figure. The ratio
of 𝜆1 and 𝜆2 is x/32. The value of x is____.
JEE Main 25th Jan 2023 S-2
Q. The energy levels of an atom is shown is
figure. Which one of these transitions will result
in the emission of a photon of wavelength 124.1
nm? Given
(h = 6.62 × 10-34 Js)
(A) B
(B) A
(C) C
(D) D
JEE Main 25th July 2022 S-2
Q. Hydrogen atom from excited state comes to
the ground by emitting a photon of wavelength
𝜆. The value of principal quantum number ‘n’ of
the excited state will be: (R : Rydberg constant)
(A)
(C)
(B)
(D)
Diode & Logic Gates
JEE Main 24th Jan 2023 S-2
JEE Main 29th Jan 2023 S-2
Q The logic gate equivalent to the given circuit
diagram is:
(A) OR
(B) NAND
(C) NOR
(D) AND
Q For he given logic gates combination, the
correct truth table will be
JEE Main 28th June 2022 S-1
Q In the following circuit, the correct relation
between output (Y) and inputs A and B will be:
(A) Y = AB
(B) Y = A + B
(C)
(D)
(A)
(B)
(C)
(D)
Diode & Logic Gates
JEE Main 30th Jan 2023 S-1
JEE Main 30th Jan 2023 S-1
Q The output waveform of the given logical
circuit for the following inputs A and B as shown
below, is:
(A)
Q The output Y for the inputs A and B of circuit is
given by Truth table of the shown circuit is:
(B)
(B)
(A)
(C)
(D)
(C)
(D)
JEE Main 25th June 2022 S-2
Q Identify the logic operation performed by the
given circuit
(A) ADA gate
(B) OR gate
(C) NOR Gate
(D) NAND gate
Diode & Logic Gates
JEE Main 27th July 2022 S-1
JEE Main 27th July 2022 S-1
Q A logic gate circuit has two inputs A and B
and output Y. The voltage waveforms of A, B
and Y are shown below The logic gate circuit is
(A) AND gate
(B) OR gate
(C) NOR gate
(D) NAND gate
Q Identify the correct Logic Gate for the following output
(Y) of two inputs A and B.
(A)
(B)
(C)
(D)
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