JEE Class 12 syllabus
The Class 12 part of the JEE Main syllabus by chapter: each topic of Physics, Chemistry and Maths with its NCERT section, or marked beyond NCERT.
- 39 chapters
- 268 topics
- 264 in JEE Main
- 4 not in JEE Main
- 36 beyond NCERT
- 268 with notes
- 0 marked done
Based on the official Syllabus for JEE (Main) 2027, Paper 1 (B.E./B.Tech.) (National Testing Agency) and the NCERT Class 12 books, reprint 2026-27 and 2025-26. Checked 26 Oct 2026. Sources
- Not in JEE Main
- In the NCERT book, not in the JEE Main syllabus.
- Beyond NCERT
- In the JEE Main syllabus; the Class 12 book has no section for it.
- Linked title
- The topic has study notes.
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Physics
14 chapters 119 topics 118 in JEE Main
1.1–1.2
3 subtopics
- Positive and negative charges
- Charging by rubbing
- The gold-leaf electroscope
pp. 1–3
1.3
2 subtopics
- Free charges in conductors
- Semiconductors as a third category
pp. 3–4
1.4
3 subtopics
- 1.4.1 Additivity of charges
- 1.4.2 Charge is conserved
- 1.4.3 Quantisation of charge
pp. 4–6
1.5
4 subtopics
- Force between two point charges
- Permittivity of free space
- Coulomb’s law in vector form
- Comparison with the gravitational force
pp. 6–11
1.6
1 subtopic
- Principle of superposition
pp. 11–14
1.7
3 subtopics
- Field of a point charge
- 1.7.1 Electric field due to a system of charges
- 1.7.2 Physical significance of electric field
pp. 14–19
1.8
2 subtopics
- Field lines start on positive and end on negative charges
- Field lines never cross
pp. 19–21
1.9
2 subtopics
- Area vector
- Flux through an area element
pp. 21–23
1.10
4 subtopics
- 1.10.1 The field of an electric dipole
- Dipole moment p = q × 2a
- Field falls as 1/r at large distances
- 1.10.2 Physical significance of dipoles
pp. 23–27
1.11
Dipole in a uniform field
NCERT: Dipole in a Uniform External Field
2 subtopics
- Torque on a dipole
- Net force on a dipole in a non-uniform field
pp. 27–28
1.12
1 subtopic
- Linear, surface and volume charge densities
pp. 28–29
1.13
2 subtopics
- Statement of Gauss’s law
- Gaussian surface
pp. 29–32
1.14
3 subtopics
- 1.14.1 Field due to an infinitely long straight uniformly charged wire
- 1.14.2 Field due to a uniformly charged infinite plane sheet
- 1.14.3 Field due to a uniformly charged thin spherical shell
pp. 33–37
NCERT Physics Part I, Chapter 2
Electrostatic Potential and Capacitance
JEE Main Unit 11: Electrostatics
2.1
Electrostatic potential energy
NCERT: Introduction
3 subtopics
- The electrostatic force is conservative
- Potential energy difference as work done
- Zero of potential energy at infinity
pp. 45–47
2.2
2 subtopics
- Potential as work done per unit charge
- Potential difference
pp. 47–48
2.3
1 subtopic
- Potential falls as 1/r, the field as 1/r
pp. 48–49
2.4
Potential due to a dipole
NCERT: Potential due to an Electric Dipole
2 subtopics
- Potential on the axis and on the equatorial plane
- Potential falls as 1/r
pp. 49–51
2.5
2 subtopics
- Superposition of potentials
- Potential of a uniformly charged spherical shell
pp. 51–53
2.6
2 subtopics
- Equipotentials of a point charge and of a uniform field
- 2.6.1 Relation between field and potential
pp. 54–55
2.7
2 subtopics
- Two point charges
- Three or more charges
pp. 55–58
2.8
3 subtopics
- 2.8.1 Potential energy of a single charge
- 2.8.2 Potential energy of a system of two charges in an external field
- 2.8.3 Potential energy of a dipole in an external field
pp. 58–61
2.9
4 subtopics
- Zero field inside a conductor
- Charge resides on the surface
- Field just outside the surface
- Electrostatic shielding
pp. 61–65
2.10
2 subtopics
- Polar and non-polar molecules
- Polarisation and electric susceptibility
pp. 65–67
2.11
3 subtopics
- Capacitance C = Q/V
- Unit: the farad
- Dielectric strength
pp. 67–68
2.12
1 subtopic
- C = εA/d
pp. 68–69
2.13
2 subtopics
- Dielectric constant
- Capacitance with a dielectric between the plates
pp. 69–71
2.14
2 subtopics
- 2.14.1 Capacitors in series
- 2.14.2 Capacitors in parallel
pp. 71–73
2.15
2 subtopics
- Energy as work done in charging
- Energy density of the electric field
pp. 73–76
NCERT Physics Part I, Chapter 3
Current Electricity
JEE Main Unit 12: Current Electricity
JEE Main Unit 20: Experimental Skills
3.1–3.2
2 subtopics
- Current as the rate of flow of charge
- Unit: the ampere
pp. 81–82
3.3
3 subtopics
- Free electrons in metals
- No net current without a field
- Current under an applied field
pp. 82–83
3.4
4 subtopics
- V = RI
- Resistance and resistivity
- Current density
- Conductivity
pp. 83–85
Experiment: resistance using Ohm’s law
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (3.4) but does not describe the method.
2 subtopics
- Voltmeter-ammeter circuit with a rheostat
- Resistance from the V-I graph
3.5
4 subtopics
- Relaxation time
- Drift velocity
- Current in terms of drift velocity
- 3.5.1 Mobility
pp. 85–89
3.6
2 subtopics
- Non-ohmic conductors and devices
- V-I graphs that are not straight lines
p. 89
3.7
1 subtopic
- Conductors, semiconductors and insulators
pp. 89–90
3.8
2 subtopics
- Temperature coefficient of resistivity
- Metals, nichrome and semiconductors
pp. 90–92
3.9
Electrical energy and power
NCERT: Electrical Energy, Power
2 subtopics
- Power dissipated in a resistor
- Power loss in transmission lines
pp. 92–93
Combination of resistors
Beyond NCERT
Listed in JEE Main Unit 12; the 2026–27 NCERT book has no section on it.
3 subtopics
- Resistors in series
- Resistors in parallel
- Equivalent resistance of a network
3.10
Cells, emf and internal resistance
NCERT: Cells, emf, Internal Resistance
3 subtopics
- Emf of a cell
- Internal resistance
- Terminal potential difference
pp. 93–95
3.11
3 subtopics
- Cells in series
- Cells in parallel
- Equivalent emf and internal resistance
pp. 95–97
3.12
2 subtopics
- Junction rule
- Loop rule
pp. 97–100
3.13
2 subtopics
- Balance condition
- Finding an unknown resistance
pp. 100–102
Metre bridge
Beyond NCERT
The metre bridge is in JEE Main Unit 12 and the resistivity experiment with it in Unit 20; the NCERT book only names it, at the end of its Wheatstone bridge section.
4 subtopics
- A Wheatstone bridge with a uniform one-metre wire
- Balance length and the unknown resistance
- End corrections
- Resistivity from the resistance, length and diameter
NCERT Physics Part I, Chapter 4
Moving Charges and Magnetism
JEE Main Unit 13: Magnetic Effects of Current and Magnetism
JEE Main Unit 20: Experimental Skills
4.1–4.2
4 subtopics
- 4.2.1 Sources and fields
- 4.2.2 Magnetic field, Lorentz force
- Unit of magnetic field: the tesla
- 4.2.3 Magnetic force on a current-carrying conductor
pp. 107–111
4.3
3 subtopics
- Circular motion perpendicular to the field
- Radius and angular frequency of the path
- Helical motion
pp. 112–113
4.4
Biot–Savart law
NCERT: Magnetic Field due to a Current Element, Biot-Savart Law
2 subtopics
- Field of a current element
- Permeability of free space
pp. 113–115
4.5
Field on the axis of a loop
NCERT: Magnetic Field on the Axis of a Circular Current Loop
3 subtopics
- Field on the axis
- Field at the centre of the loop
- Right-hand thumb rule for the field
pp. 115–117
4.6
2 subtopics
- Statement of the law
- Field of an infinitely long straight wire
pp. 117–121
4.7
1 subtopic
- Field inside a long solenoid
pp. 121–122
4.8
Force between parallel currents
NCERT: Force between Two Parallel Currents, the Ampere
2 subtopics
- Parallel currents attract, antiparallel currents repel
- Definition of the ampere
pp. 122–124
4.9
3 subtopics
- 4.9.1 Torque on a rectangular current loop in a uniform magnetic field
- Magnetic moment of a current loop
- 4.9.2 Circular current loop as a magnetic dipole
pp. 124–129
4.10
4 subtopics
- Coil in a radial magnetic field
- Conversion to an ammeter with a shunt
- Conversion to a voltmeter
- Current sensitivity and voltage sensitivity
pp. 129–132
Experiment: galvanometer resistance
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (4.10) but does not describe the method.
2 subtopics
- Half-deflection method
- Figure of merit: current per division
NCERT Physics Part I, Chapter 5
Magnetism and Matter
JEE Main Unit 13: Magnetic Effects of Current and Magnetism
5.1–5.2
5 subtopics
- 5.2.1 The magnetic field lines
- 5.2.2 Bar magnet as an equivalent solenoid
- 5.2.3 The dipole in a uniform magnetic field
- 5.2.4 The electrostatic analog
- Field of a bar magnet on its axis and on its equator
pp. 136–142
5.3
Gauss’s law for magnetism
NCERT: Magnetism and Gauss’s Law
Not named in Unit 13; it states what the magnetic field lines show: with no isolated poles, the net flux through any closed surface is zero.
2 subtopics
- Net magnetic flux through a closed surface is zero
- No isolated magnetic poles
pp. 142–145
5.4
Magnetisation and magnetic intensity
Not named in Unit 13; its susceptibility sorts the para-, dia- and ferromagnetic substances.
3 subtopics
- Magnetisation M
- Magnetic intensity H
- Susceptibility and relative permeability
pp. 145–147
5.5
5 subtopics
- 5.5.1 Diamagnetism
- 5.5.2 Paramagnetism
- 5.5.3 Ferromagnetism
- Hard and soft ferromagnets
- Effect of temperature on magnetic properties
pp. 147–149
NCERT Physics Part I, Chapter 6
Electromagnetic Induction
JEE Main Unit 14: Electromagnetic Induction and Alternating Currents
6.1–6.2
2 subtopics
- A magnet moved near a coil
- A changing current in a nearby coil
pp. 154–156
6.3
2 subtopics
- Flux Φ = B·A
- Unit: the weber
pp. 156–157
6.4
2 subtopics
- Induced emf equals the rate of change of flux
- Emf of a closely wound coil
pp. 157–159
6.5
2 subtopics
- Direction of the induced current
- Lenz’s law as energy conservation
pp. 160–162
6.6
Motional emf
NCERT: Motional Electromotive Force
2 subtopics
- Emf of a rod moving in a magnetic field
- Motional emf from the Lorentz force
pp. 162–165
Eddy currents
Beyond NCERT
Listed in JEE Main Unit 14; the 2026–27 NCERT book has no section on it and names it only as a transformer loss.
3 subtopics
- Eddy currents in a moving metal plate
- Reducing them with laminated cores
- Uses: magnetic braking, damping and induction furnaces
6.7
4 subtopics
- 6.7.1 Mutual inductance
- 6.7.2 Self-inductance
- Back emf
- Energy stored in an inductor
pp. 165–170
6.8
2 subtopics
- A coil rotating in a magnetic field
- Emf ε = NBAω sin ωt
pp. 170–172
NCERT Physics Part I, Chapter 7
Alternating Current
JEE Main Unit 14: Electromagnetic Induction and Alternating Currents
7.2
3 subtopics
- Current in phase with the voltage
- Average power over a cycle
- RMS current and voltage
pp. 178–180
7.3
Phasors
NCERT: Representation of AC Current and Voltage by Rotating Vectors — Phasors
1 subtopic
- Phasor diagram
p. 181
7.4
3 subtopics
- Current lags the voltage by π/2
- Inductive reactance
- Zero average power in an inductor
pp. 181–183
7.5
3 subtopics
- Current leads the voltage by π/2
- Capacitive reactance
- Zero average power in a capacitor
pp. 184–186
7.6
Series LCR circuit
NCERT: AC Voltage Applied to a Series LCR Circuit
4 subtopics
- 7.6.1 Phasor-diagram solution
- Impedance
- 7.6.2 Resonance
- Tuning a radio
pp. 186–190
7.7
Power in ac circuits
NCERT: Power in AC Circuit: The Power Factor
3 subtopics
- Average power and the power factor
- Wattless current
- Power at resonance
pp. 190–193
7.8
3 subtopics
- Step-up and step-down transformers
- Energy losses in a transformer
- Long-distance transmission
pp. 194–196
8.1–8.2
2 subtopics
- Ampere’s law for a charging capacitor
- Ampere–Maxwell law
pp. 201–205
8.3
5 subtopics
- 8.3.1 Sources of electromagnetic waves
- 8.3.2 Nature of electromagnetic waves
- Transverse nature: E and B perpendicular to the direction of travel
- Speed c = 1/√(με) and B = E/c
- Energy carried by electromagnetic waves
pp. 205–208
8.4
7 subtopics
- 8.4.1 Radio waves
- 8.4.2 Microwaves
- 8.4.3 Infrared waves
- 8.4.4 Visible rays
- 8.4.5 Ultraviolet rays
- 8.4.6 X-rays
- 8.4.7 Gamma rays
pp. 208–211
NCERT Physics Part II, Chapter 9
Ray Optics and Optical Instruments
JEE Main Unit 16: Optics
JEE Main Unit 20: Experimental Skills
9.2
Spherical mirrors
NCERT: Reflection of Light by Spherical Mirrors
5 subtopics
- Laws of reflection
- 9.2.1 Sign convention
- 9.2.2 Focal length of spherical mirrors
- 9.2.3 The mirror equation
- Linear magnification
pp. 222–228
9.3
2 subtopics
- Snell’s law and refractive index
- Real and apparent depth
pp. 228–229
Experiment: glass slab
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (9.3) but does not describe the method.
2 subtopics
- Real and apparent thickness of the slab
- Refractive index from three microscope readings
9.4
4 subtopics
- Critical angle
- 9.4.1 Total internal reflection in nature and its technological applications
- Totally reflecting prisms
- Optical fibres
pp. 229–232
9.5
Lenses
NCERT: Refraction at Spherical Surfaces and by Lenses
6 subtopics
- 9.5.1 Refraction at a spherical surface
- 9.5.2 Refraction by a lens
- Lens maker’s formula
- Thin lens formula and magnification
- 9.5.3 Power of a lens
- 9.5.4 Combination of thin lenses in contact
pp. 232–239
Experiment: focal lengths
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (9.2 and 9.5) but does not describe the method.
4 subtopics
- Locating an image by removing parallax
- Concave mirror
- Convex mirror
- Convex lens
9.6
Prism
NCERT: Refraction through a Prism
4 subtopics
- Angle of deviation
- Angle of minimum deviation
- Refractive index from the minimum deviation
- Thin prism
pp. 239–240
Experiment: prism i–δ graph
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (9.6) but does not describe the method.
2 subtopics
- Tracing rays through a prism with pins
- The i-δ graph and the minimum deviation
9.7
7 subtopics
- 9.7.1 The microscope
- Simple microscope
- Compound microscope
- 9.7.2 Telescope
- Refracting telescope
- Reflecting telescope (Cassegrain)
- Magnifying power
pp. 240–246
10.1–10.2
2 subtopics
- Wavefronts: spherical and plane
- Secondary wavelets
pp. 255–258
10.3
Refraction and reflection by Huygens principle
NCERT: Refraction and Reflection of Plane Waves using Huygens Principle
4 subtopics
- 10.3.1 Refraction of a plane wave
- Snell’s law from Huygens principle
- 10.3.2 Refraction at a rarer medium
- 10.3.3 Reflection of a plane wave by a plane surface
pp. 258–262
10.4
4 subtopics
- Coherent sources
- Path difference and phase difference
- Constructive and destructive interference
- Incoherent sources: intensities add
pp. 262–265
10.5
Young’s double-slit experiment
NCERT: Interference of Light Waves and Young’s Experiment
JEE Main Unit 16 lists the expression for fringe width; NCERT gives the fringe positions x = nλD/d, so the fringe width is λD/d.
3 subtopics
- Young’s double-slit arrangement
- Positions of bright and dark fringes
- Bright and dark fringes are equally spaced
pp. 265–266
10.6
Diffraction
JEE Main Unit 16 lists the width of the central maximum: the gap between the first minima at θ = ±λ/a.
4 subtopics
- 10.6.1 The single slit
- Central maximum at θ = 0, minima at θ = nλ/a (n = ±1, ±2, …)
- Interference and diffraction compared
- 10.6.2 Seeing the single slit diffraction pattern
pp. 266–268
10.7
4 subtopics
- Plane-polarised and unpolarised waves
- Polaroids and the pass axis
- Malus’ law
- Uses of polaroids
pp. 269–271
3 subtopics
- Reflected light fully plane-polarised at the Brewster angle
- Brewster angle: tan iB = μ
- Reflected and refracted rays at right angles
NCERT Physics Part II, Chapter 11
Dual Nature of Radiation and Matter
JEE Main Unit 17: Dual Nature of Matter and Radiation
11.1–11.2
3 subtopics
- Work function
- The electron volt
- Thermionic, field and photoelectric emission
pp. 274–276
11.3
2 subtopics
- 11.3.1 Hertz’s observations
- 11.3.2 Hallwachs’ and Lenard’s observations
pp. 276–277
11.4
7 subtopics
- The experimental set-up
- 11.4.1 Effect of intensity of light on photocurrent
- 11.4.2 Effect of potential on photoelectric current
- Saturation current
- Stopping potential
- 11.4.3 Effect of frequency of incident radiation on stopping potential
- Threshold frequency
pp. 277–280
11.5
1 subtopic
- Why the wave picture fails
pp. 280–281
11.6
4 subtopics
- Energy quantum hν
- Kmax = hν − φ
- Threshold frequency ν = φ/h
- Stopping potential against frequency: slope h/e
pp. 281–283
11.7
Photon
NCERT: Particle Nature of Light: The Photon
2 subtopics
- Energy and momentum of a photon
- Properties of photons
pp. 283–284
11.8
3 subtopics
- De Broglie relation λ = h/p
- De Broglie wavelength of a photon
- Why everyday objects show no wave nature
pp. 284–286
12.1–12.2
Rutherford’s nuclear model
NCERT: Introduction; Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom
4 subtopics
- The Geiger-Marsden experiment
- 12.2.1 Alpha-particle trajectory
- Distance of closest approach
- 12.2.2 Electron orbits
pp. 290–296
12.3
2 subtopics
- Emission line spectra
- Absorption spectra
pp. 296–297
12.4
4 subtopics
- Why an orbiting electron should spiral in
- Bohr’s three postulates
- Radius and energy of the orbits
- 12.4.1 Energy levels
pp. 297–300
12.5
2 subtopics
- Photon emitted in a transition: hν = Ei − Ef
- Absorption as an upward transition
pp. 300–301
12.6
De Broglie and Bohr’s postulate
NCERT: De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation
2 subtopics
- Standing electron waves on an orbit
- Circumference as a whole number of wavelengths
pp. 301–302
13.2
Composition of the nucleus
NCERT: Atomic Masses and Composition of Nucleus
3 subtopics
- Atomic mass unit
- Discovery of the neutron
- Isotopes, isobars and isotones
pp. 306–309
13.3
2 subtopics
- R = RA1/3
- Nuclear density
pp. 309–310
13.4
Binding energy
NCERT: Mass-Energy and Nuclear Binding Energy
4 subtopics
- 13.4.1 Mass-energy
- 13.4.2 Nuclear binding energy
- Mass defect
- Binding energy per nucleon and mass number
pp. 310–313
13.5
Nuclear force
Not named in Unit 18; its short range explains the nearly constant binding energy per nucleon.
2 subtopics
- Short range and charge independence
- Potential energy of a pair of nucleons
pp. 313–314
13.6
Radioactivity
Not in JEE Main
2 subtopics
- Becquerel’s discovery
- Alpha, beta and gamma decay
p. 314
13.7
4 subtopics
- Energy from the binding energy curve
- 13.7.1 Fission
- 13.7.2 Nuclear fusion – energy generation in stars
- 13.7.3 Controlled thermonuclear fusion
pp. 314–318
NCERT Physics Part II, Chapter 14
Semiconductor Electronics: Materials, Devices and Simple Circuits
JEE Main Unit 19: Electronic Devices
JEE Main Unit 20: Experimental Skills
14.1–14.2
Metals, insulators and semiconductors
NCERT: Introduction; Classification of Metals, Conductors and Semiconductors
3 subtopics
- Classification by conductivity
- Valence and conduction bands
- Band gap
pp. 323–327
14.3
2 subtopics
- Electrons and holes
- Thermal generation of carriers
pp. 327–329
14.4
3 subtopics
- Doping
- n-type semiconductor and donors
- p-type semiconductor and acceptors
pp. 329–332
14.5
4 subtopics
- 14.5.1 p-n junction formation
- Diffusion and drift
- Depletion region
- Barrier potential
pp. 333–334
14.6
Semiconductor diode
The p-n junction characteristic curves are a JEE Main Unit 20 experiment; this section gives the circuit and method.
5 subtopics
- 14.6.1 p-n junction diode under forward bias
- 14.6.2 p-n junction diode under reverse bias
- Circuit for the V-I characteristics
- Threshold voltage and breakdown voltage
- Dynamic resistance
pp. 334–337
14.7
Junction diode as a rectifier
NCERT: Application of Junction Diode as a Rectifier
3 subtopics
- Half-wave rectifier
- Full-wave rectifier with a centre-tap transformer
- Capacitor filter
pp. 338–340
Zener diode
Beyond NCERT
Listed in JEE Main Unit 19, and its characteristic curve is a Unit 20 experiment; the NCERT book has no section on it.
4 subtopics
- Reverse breakdown in a heavily doped junction
- I-V characteristic and the reverse breakdown voltage
- Circuit for the characteristic curve
- Zener diode as a voltage regulator
LED, photodiode and solar cell
Beyond NCERT
Listed in JEE Main Unit 19; the NCERT book has no section on them.
3 subtopics
- Light-emitting diode and its I-V characteristic
- Photodiode in reverse bias and its I-V characteristic
- Solar cell and its I-V characteristic
Experiment: identifying components
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book does not describe the method.
2 subtopics
- Testing each component with a multimeter
- How each one responds
3 subtopics
- Truth tables
- OR, AND and NOT gates
- NAND and NOR gates
Chemistry
12 chapters 94 topics 92 in JEE Main
1.1
2 subtopics
- Binary solutions
- Gaseous, liquid and solid solutions
pp. 1–2
1.2
Concentration of solutions
NCERT: Expressing Concentration of Solutions
6 subtopics
- Mass percentage and volume percentage
- Mass by volume percentage
- Parts per million
- Mole fraction
- Molarity
- Molality
pp. 2–5
1.3
4 subtopics
- 1.3.1 Solubility of a solid in a liquid
- 1.3.2 Solubility of a gas in a liquid
- Henry’s law and its applications
- Effect of temperature on the solubility of gases
pp. 5–9
1.4
Vapour pressure of solutions
NCERT: Vapour Pressure of Liquid Solutions
5 subtopics
- 1.4.1 Vapour pressure of liquid-liquid solutions
- Raoult’s law for two volatile liquids
- Vapour pressure–composition plots
- 1.4.2 Raoult’s law as a special case of Henry’s law
- 1.4.3 Vapour pressure of solutions of solids in liquids
pp. 9–13
1.5
4 subtopics
- 1.5.1 Ideal solutions
- 1.5.2 Non-ideal solutions
- Positive and negative deviations from Raoult’s law
- Minimum and maximum boiling azeotropes
pp. 13–15
1.6
7 subtopics
- 1.6.1 Relative lowering of vapour pressure
- 1.6.2 Elevation of boiling point
- 1.6.3 Depression of freezing point
- Ebullioscopic and cryoscopic constants
- 1.6.4 Osmosis and osmotic pressure
- Isotonic, hypertonic and hypotonic solutions
- 1.6.5 Reverse osmosis and water purification
pp. 15–23
1.7
3 subtopics
- Association and dissociation of solutes
- van’t Hoff factor
- Degree of association and dissociation
pp. 23–26
NCERT Chemistry Part I, Chapter 2
Electrochemistry
JEE Main Unit 7: Redox Reactions and Electrochemistry
2.1
2 subtopics
- Daniell cell
- Galvanic and electrolytic cells
p. 32
2.2
6 subtopics
- Half-cells and the salt bridge
- Cell potential and emf
- Representing a galvanic cell
- 2.2.1 Measurement of electrode potential
- The standard hydrogen electrode
- Metal, gas and inert electrodes
pp. 33–36
2.3
4 subtopics
- Nernst equation for an electrode
- Nernst equation for a cell
- 2.3.1 Equilibrium constant from Nernst equation
- 2.3.2 Electrochemical cell and Gibbs energy of the reaction
pp. 36–41
2.4
7 subtopics
- Resistance, resistivity and conductivity
- Electronic and electrolytic conductance
- 2.4.1 Measurement of the conductivity of ionic solutions
- Cell constant and molar conductivity
- 2.4.2 Variation of conductivity and molar conductivity with concentration
- Strong and weak electrolytes
- Kohlrausch’s law and its applications
pp. 41–51
2.5
2 subtopics
- Faraday’s laws of electrolysis
- 2.5.1 Products of electrolysis
pp. 51–54
2.6
5 subtopics
- 2.6.1 Primary batteries
- Dry cell and mercury cell
- 2.6.2 Secondary batteries
- Lead storage battery
- Nickel-cadmium cell
pp. 54–56
2.7
2 subtopics
- Hydrogen–oxygen fuel cell
- Efficiency of fuel cells
pp. 56–57
2.8
Corrosion
Not in JEE Main
2 subtopics
- Rusting of iron as an electrochemical process
- Prevention of corrosion
pp. 57–58
NCERT Chemistry Part I, Chapter 3
Chemical Kinetics
JEE Main Unit 8: Chemical Kinetics
JEE Main Unit 20: Principles Related to Practical Chemistry
3.1
3 subtopics
- Average and instantaneous rate
- Units of rate
- Rate from changes in partial pressure
pp. 62–66
3.2
8 subtopics
- 3.2.1 Dependence of rate on concentration
- 3.2.2 Rate expression and rate constant
- 3.2.3 Order of a reaction
- Elementary and complex reactions
- Units of rate constant
- 3.2.4 Molecularity of a reaction
- Rate determining step
- Order and molecularity compared
pp. 66–71
Experiment: iodide and hydrogen peroxide
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 3.2) but does not describe the method.
3 subtopics
- Reaction of iodide ions with hydrogen peroxide
- Timing the blue colour with starch and thiosulphate
- Effect of iodide concentration on the rate
3.3
6 subtopics
- Differential and integrated rate equations
- 3.3.1 Zero order reactions
- 3.3.2 First order reactions
- First order gas phase reactions
- 3.3.3 Half-life of a reaction
- Pseudo first order reactions
pp. 71–78
3.4
4 subtopics
- Arrhenius equation
- Activation energy
- Maxwell–Boltzmann distribution of kinetic energies
- 3.4.1 Effect of catalyst
pp. 78–82
3.5
3 subtopics
- Collision frequency
- Effective collisions and threshold energy
- Orientation of colliding molecules
pp. 82–84
Beyond NCERT No chapter in the NCERT Class 12 books
The p-Block Elements
JEE Main Unit 10: p-Block Elements
Group 13 elements
Listed in JEE Main Unit 10, Groups 13 to 18; no 2026–27 NCERT book has a chapter on the p-block (NCERT Class 11 3.6.2 and 3.7 introduce the block and its periodic trends).
5 subtopics
- Electronic configuration ns np and oxidation states
- Atomic radius, ionization enthalpy and electronegativity down the group
- Physical properties
- Chemical properties: reactivity towards air, acids, alkalies and halogens; the inert pair effect
- Anomalous behaviour of boron
5 subtopics
- Electronic configuration ns np and oxidation states
- Atomic radius, ionization enthalpy and electronegativity down the group
- Physical properties
- Chemical properties: oxides, reactivity towards water, and halides; the inert pair effect
- Anomalous behaviour of carbon
5 subtopics
- Electronic configuration ns np and oxidation states
- Atomic radius, ionization enthalpy and electronegativity down the group
- Physical properties
- Chemical properties: hydrides, oxides and halides; the inert pair effect
- Anomalous behaviour of nitrogen
5 subtopics
- Electronic configuration ns np and oxidation states
- Atomic radius, ionization enthalpy and electronegativity down the group
- Physical properties
- Chemical properties: hydrides, oxides and halides; the inert pair effect
- Anomalous behaviour of oxygen
5 subtopics
- Electronic configuration ns np and oxidation states
- Atomic radius, ionization enthalpy and electronegativity down the group
- Physical properties
- Chemical properties: hydrides, oxides and halides
- Anomalous behaviour of fluorine
5 subtopics
- Electronic configuration ns np (helium 1s)
- Atomic radius, ionization enthalpy and electron gain enthalpy down the group
- Physical properties
- Chemical properties: low reactivity, and the xenon fluorides and oxides
- Helium, the first element
NCERT Chemistry Part I, Chapter 4
The d- and f-Block Elements
JEE Main Unit 11: d- and f-Block Elements
JEE Main Unit 20: Principles Related to Practical Chemistry
4.1
2 subtopics
- The d-block between the s- and p-blocks
- The 3d, 4d, 5d and 6d series
p. 90
4.2
3 subtopics
- General outer configuration (n–1)dns
- Configurations of chromium and copper
- Why zinc, cadmium and mercury are not transition elements
pp. 90–92
Occurrence
Beyond NCERT
Listed in JEE Main Unit 11; the 2026–27 NCERT book names it in the chapter’s opening lines but has no section on it.
2 subtopics
- Native metals and ores
- Common ores of iron, copper, chromium and manganese
4.3
14 subtopics
- 4.3.1 Physical properties
- 4.3.2 Variation in atomic and ionic sizes of transition metals
- 4.3.3 Ionisation enthalpies
- 4.3.4 Oxidation states
- 4.3.5 Trends in the M/M standard electrode potentials
- 4.3.6 Trends in the M/M standard electrode potentials
- 4.3.7 Trends in stability of higher oxidation states
- 4.3.8 Chemical reactivity and E° values
- 4.3.9 Magnetic properties
- 4.3.10 Formation of coloured ions
- 4.3.11 Formation of complex compounds
- 4.3.12 Catalytic properties
- 4.3.13 Formation of interstitial compounds
- 4.3.14 Alloy formation
pp. 92–105
4.4
Important compounds
NCERT: Some Important Compounds of Transition Elements
3 subtopics
- 4.4.1 Oxides and oxoanions of metals
- Potassium dichromate: preparation, properties and uses
- Potassium permanganate: preparation, properties and uses
pp. 105–108
Experiment: KMnO₄ titrations
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 4.4 and Class 11 NCERT 7.3.3) but does not describe the method.
3 subtopics
- KMnO as its own indicator
- Oxalic acid against KMnO at 333 K
- Mohr’s salt against KMnO
4.5
5 subtopics
- 4.5.1 Electronic configurations
- 4.5.2 Atomic and ionic sizes
- Lanthanoid contraction
- 4.5.3 Oxidation states
- 4.5.4 General characteristics
pp. 108–111
4.6
5 subtopics
- 4.6.1 Electronic configurations
- 4.6.2 Ionic sizes
- Actinoid contraction
- 4.6.3 Oxidation states
- 4.6.4 General characteristics and comparison with lanthanoids
pp. 111–113
4.7
3 subtopics
- Iron and steels
- Compounds for special purposes
- Catalysts in industry
pp. 113–114
NCERT Chemistry Part I, Chapter 5
Coordination Compounds
JEE Main Unit 12: Coordination Compounds
JEE Main Unit 20: Principles Related to Practical Chemistry
5.1
3 subtopics
- Primary and secondary valences
- Postulates of Werner’s theory
- Double salts and complexes
pp. 118–120
Experiment: double salts
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 5.1) but does not describe the method.
3 subtopics
- Double salts by crystallisation
- Mohr’s salt from iron(II) sulphate and ammonium sulphate
- Potash alum from potassium sulphate and aluminium sulphate
5.2
Ligands and other terms
NCERT: Definitions of Some Important Terms Pertaining to Coordination Compounds
7 subtopics
- Coordination entity and central atom
- Unidentate, didentate and polydentate ligands
- Ambidentate ligands, denticity and chelation
- Coordination number
- Coordination sphere and coordination polyhedron
- Oxidation number of the central atom
- Homoleptic and heteroleptic complexes
pp. 121–122
5.3
2 subtopics
- 5.3.1 Formulas of mononuclear coordination entities
- 5.3.2 Naming of mononuclear coordination compounds
pp. 122–125
5.4
7 subtopics
- Stereoisomerism and structural isomerism
- 5.4.1 Geometric isomerism
- 5.4.2 Optical isomerism
- 5.4.3 Linkage isomerism
- 5.4.4 Coordination isomerism
- 5.4.5 Ionisation isomerism
- 5.4.6 Solvate isomerism
pp. 125–128
5.5
Bonding: VBT and CFT
NCERT: Bonding in Coordination Compounds
9 subtopics
- 5.5.1 Valence bond theory
- Inner and outer orbital complexes
- 5.5.2 Magnetic properties of coordination compounds
- 5.5.3 Limitations of valence bond theory
- 5.5.4 Crystal field theory
- Splitting in octahedral and tetrahedral fields
- Spectrochemical series
- 5.5.5 Colour in coordination compounds
- 5.5.6 Limitations of crystal field theory
pp. 128–135
5.6
Metal carbonyls
NCERT: Bonding in Metal Carbonyls
Not named in JEE Main Unit 12, which lists the valence bond and crystal field approaches to bonding.
2 subtopics
- Homoleptic carbonyls
- Synergic bonding between the metal and CO
pp. 135–136
5.7
5 subtopics
- Qualitative and quantitative analysis
- Hardness of water
- Extraction of metals
- Biological systems
- Industry and medicine
pp. 136–137
NCERT Chemistry Part II, Chapter 6
Haloalkanes and Haloarenes
JEE Main Unit 16: Organic Compounds Containing Halogens
JEE Main Unit 14: Some Basic Principles of Organic Chemistry
6.1
3 subtopics
- 6.1.1 On the basis of number of halogen atoms
- 6.1.2 Compounds containing sp C–X bond (X = F, Cl, Br, I)
- 6.1.3 Compounds containing sp C–X bond
pp. 160–161
6.2
2 subtopics
- Common and IUPAC names
- Geminal and vicinal dihalides
pp. 161–163
6.3
2 subtopics
- Polarity of the carbon–halogen bond
- Bond length, bond enthalpy and dipole moment
pp. 163–164
6.4
Preparation of haloalkanes
NCERT: Methods of Preparation of Haloalkanes
6 subtopics
- 6.4.1 From alcohols
- 6.4.2 From hydrocarbons
- Free radical halogenation of alkanes
- Addition of hydrogen halides and halogens to alkenes
- 6.4.3 Halogen exchange
- Finkelstein and Swarts reactions
pp. 164–166
6.5
2 subtopics
- Electrophilic substitution in arenes
- Sandmeyer’s reaction
pp. 166–167
6.6
3 subtopics
- Melting and boiling points
- Density
- Solubility
pp. 167–169
6.7
11 subtopics
- 6.7.1 Reactions of haloalkanes
- Nucleophilic substitution
- SN2 and SN1 mechanisms
- Optical activity, chirality and enantiomers
- Inversion, retention and racemisation
- Elimination and Saytzeff’s rule
- Grignard reagents and the Wurtz reaction
- 6.7.2 Reactions of haloarenes
- Low reactivity of haloarenes in nucleophilic substitution
- Electrophilic substitution in haloarenes
- Wurtz-Fittig and Fittig reactions
pp. 169–186
6.8
7 subtopics
- 6.8.1 Dichloromethane (methylene chloride)
- 6.8.2 Trichloromethane (chloroform)
- 6.8.3 Triiodomethane (iodoform)
- 6.8.4 Tetrachloromethane (carbon tetrachloride)
- 6.8.5 Freons
- 6.8.6 p,p’-Dichlorodiphenyltrichloroethane (DDT)
- Uses and environmental effects
pp. 187–188
NCERT Chemistry Part II, Chapter 7
Alcohols, Phenols and Ethers
JEE Main Unit 17: Organic Compounds Containing Oxygen
JEE Main Unit 20: Principles Related to Practical Chemistry
7.1
5 subtopics
- 7.1.1 Alcohols—mono, di, tri or polyhydric alcohols
- Primary, secondary and tertiary alcohols
- Allylic and benzylic alcohols
- 7.1.2 Phenols—mono, di and trihydric phenols
- 7.1.3 Ethers
pp. 194–195
7.2
2 subtopics
- Common and IUPAC names of alcohols
- Names of phenols and ethers
pp. 195–198
7.3
2 subtopics
- Structures of methanol, phenol and methoxymethane
- C–O bond length in phenol
pp. 198–199
7.4
11 subtopics
- 7.4.1 Preparation of alcohols
- 7.4.2 Preparation of phenols
- Phenol from cumene
- 7.4.3 Physical properties
- 7.4.4 Chemical reactions
- Acidity of alcohols and phenols
- Lucas test for primary, secondary and tertiary alcohols
- Mechanism of dehydration of alcohols
- Oxidation of alcohols
- Nitration, sulphonation and halogenation of phenol
- Kolbe’s and Reimer-Tiemann reactions
pp. 199–213
Experiment: tests for –OH groups
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book does not describe the method.
4 subtopics
- Ceric ammonium nitrate test for alcohols
- Iodoform test for ethanol and CHCH(OH)R alcohols
- Iron(III) chloride test for phenols
- Phthalein dye test for phenols
7.5
Commercially important alcohols
NCERT: Some Commercially Important Alcohols
2 subtopics
- Methanol
- Ethanol
p. 214
7.6
6 subtopics
- 7.6.1 Preparation of ethers
- Williamson synthesis
- 7.6.2 Physical properties
- 7.6.3 Chemical reactions
- Cleavage of the C–O bond in ethers
- Electrophilic substitution in anisole
pp. 215–221
NCERT Chemistry Part II, Chapter 8
Aldehydes, Ketones and Carboxylic Acids
JEE Main Unit 17: Organic Compounds Containing Oxygen
JEE Main Unit 20: Principles Related to Practical Chemistry
8.1
Carbonyl group: names and structure
NCERT: Nomenclature and Structure of Carbonyl Group
2 subtopics
- 8.1.1 Nomenclature
- 8.1.2 Structure of the carbonyl group
pp. 228–231
8.2
5 subtopics
- 8.2.1 Preparation of aldehydes and ketones
- 8.2.2 Preparation of aldehydes
- Rosenmund reduction and Stephen reaction
- Etard and Gatterman-Koch reactions
- 8.2.3 Preparation of ketones
pp. 231–234
8.3
2 subtopics
- Boiling points
- Solubility in water
pp. 235–236
8.4
Reactions of aldehydes and ketones
NCERT: Chemical Reactions
11 subtopics
- Nucleophilic addition to the carbonyl group
- Relative reactivity of aldehydes and ketones
- Addition of HCN, sodium hydrogensulphite, Grignard reagents and alcohols
- Addition of ammonia and its derivatives
- Clemmensen and Wolff-Kishner reductions
- Tollens’ and Fehling’s tests
- Haloform reaction
- Acidity of α-hydrogens
- Aldol and cross aldol condensation
- Cannizzaro reaction
- Electrophilic substitution in aromatic aldehydes and ketones
pp. 236–243
Experiment: tests for aldehydes and ketones
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 8.4) but does not describe the method.
2 subtopics
- 2,4-DNP test for the carbonyl group
- Schiff’s, Tollens’ and Fehling’s tests for aldehydes
Experiment: preparation of iodoform
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 8.4) but does not describe the method.
3 subtopics
- Iodoform from acetone or ethanol with iodine and alkali
- Haloform reaction of the CHCO– group
- Yellow crystals of iodoform
8.5
2 subtopics
- Formalin and bakelite
- Solvents, perfumes and flavours
pp. 243–244
8.6
Carboxyl group: names and structure
NCERT: Nomenclature and Structure of Carboxyl Group
2 subtopics
- 8.6.1 Nomenclature
- 8.6.2 Structure of carboxyl group
pp. 244–245
8.7
Preparation of carboxylic acids
NCERT: Methods of Preparation of Carboxylic Acids
5 subtopics
- From primary alcohols and aldehydes
- From alkylbenzenes
- From nitriles and amides
- From Grignard reagents
- From acyl halides, anhydrides and esters
pp. 245–248
8.8
2 subtopics
- Hydrogen-bonded dimers
- Solubility in water
p. 249
8.9
7 subtopics
- 8.9.1 Reactions involving cleavage of O–H bond
- Acidity and the effect of substituents
- 8.9.2 Reactions involving cleavage of C–OH bond
- 8.9.3 Reactions involving –COOH group
- 8.9.4 Substitution reactions in the hydrocarbon part
- Hell-Volhard-Zelinsky reaction
- Ring substitution in aromatic acids
pp. 249–254
Experiment: tests for the carboxyl group
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 8.9.1 and 8.9.2) but does not describe the method.
3 subtopics
- Litmus test
- Sodium hydrogencarbonate test
- Ester test
8.10
2 subtopics
- Vinegar, nylon-6,6 and food preservatives
- Soaps and detergents from fatty acids
p. 254
NCERT Chemistry Part II, Chapter 9
Amines
JEE Main Unit 18: Organic Compounds Containing Nitrogen
JEE Main Unit 20: Principles Related to Practical Chemistry
9.1
2 subtopics
- The sp hybridised nitrogen atom
- Pyramidal shape of amines
pp. 259–260
9.2
2 subtopics
- Primary, secondary and tertiary amines
- Simple and mixed amines
p. 260
9.3
2 subtopics
- Common names
- IUPAC names
pp. 260–262
9.4
5 subtopics
- Reduction of nitro compounds
- Ammonolysis of alkyl halides
- Reduction of nitriles and amides
- Gabriel phthalimide synthesis
- Hofmann bromamide degradation
pp. 262–265
9.5
2 subtopics
- Solubility in water
- Boiling points and hydrogen bonding
pp. 265–266
9.6
8 subtopics
- Basic character of amines
- Basic strength of alkanamines and arylamines
- Alkylation, acylation and benzoylation
- Carbylamine reaction
- Reaction with nitrous acid
- Hinsberg’s reagent: benzenesulphonyl chloride
- Bromination, nitration and sulphonation of aniline
- Why aniline does not undergo Friedel-Crafts reactions
pp. 266–274
Experiment: tests for the amino group
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 9.6 and 9.9) but does not describe the method.
3 subtopics
- Solubility in dilute hydrochloric acid
- Carbylamine test
- Azo dye test
Experiment: preparation of acetanilide and p-nitroacetanilide
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 9.6) but does not describe the method.
3 subtopics
- Acetanilide by acetylation of aniline
- p-Nitroacetanilide by nitration of acetanilide
- Recrystallisation of the products
9.7
Preparation of diazonium salts
NCERT: Method of Preparation of Diazonium Salts
1 subtopic
- Diazotisation of aniline at 273–278 K
p. 274
9.8
2 subtopics
- Colourless crystalline solids
- Solubility and stability
p. 275
9.9
3 subtopics
- Displacement of nitrogen
- Sandmeyer and Gatterman reactions
- Coupling reactions
pp. 275–276
Experiment: preparation of aniline yellow
Beyond NCERT
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 9.7 and 9.9) but does not describe the method.
3 subtopics
- Diazotisation of aniline
- Coupling with aniline, or rearrangement of diazoaminobenzene
- Aniline yellow (p-aminoazobenzene)
9.10
Diazonium salts in the synthesis of aromatic compounds
NCERT: Importance of Diazonium Salts in Synthesis of Aromatic Compounds
1 subtopic
- Groups that cannot be introduced by direct substitution
pp. 276–277
10.1
9 subtopics
- 10.1.1 Classification of carbohydrates
- Aldoses and ketoses
- 10.1.2 Monosaccharides
- Glucose and fructose
- Open chain and cyclic structures of glucose
- 10.1.3 Disaccharides
- Sucrose, maltose and lactose
- 10.1.4 Polysaccharides
- 10.1.5 Importance of carbohydrates
pp. 281–290
10.2
8 subtopics
- 10.2.1 Amino acids
- 10.2.2 Classification of amino acids
- Essential and non-essential amino acids
- Zwitter ion form of amino acids
- 10.2.3 Structure of proteins
- Peptide bond
- Primary, secondary, tertiary and quaternary structure
- 10.2.4 Denaturation of proteins
pp. 290–295
10.3
1 subtopic
- 10.3.1 Mechanism of enzyme action
p. 295
10.4
3 subtopics
- 10.4.1 Classification of vitamins
- Fat soluble and water soluble vitamins
- Vitamin deficiency diseases
pp. 295–297
10.5
6 subtopics
- 10.5.1 Chemical composition of nucleic acids
- 10.5.2 Structure of nucleic acids
- Nucleosides and nucleotides
- Double helix of DNA
- 10.5.3 Biological functions of nucleic acids
- DNA fingerprinting
pp. 297–300
10.6
3 subtopics
- Hormones as intercellular messengers
- Steroid, polypeptide and amino acid derivative hormones
- Functions of hormones
pp. 300–301
Beyond NCERT No chapter in the NCERT Class 12 books
Practical Chemistry
JEE Main Unit 20: Principles Related to Practical Chemistry
Experiment: preparation of lyophilic and lyophobic sols
A JEE Main Unit 20 experiment; the NCERT book does not describe the method.
3 subtopics
- Sols and true solutions
- Lyophilic sols of starch, gum and egg albumin
- Lyophobic sols of iron(III) hydroxide and aluminium hydroxide
Experiment: salt analysis, anions
A JEE Main Unit 20 experiment; the NCERT book does not describe the method.
4 subtopics
- Dilute sulphuric acid group: CO, S and NO
- Concentrated sulphuric acid group: Cl, Br, I and NO
- Independent group: SO
- Confirmatory tests
Experiment: salt analysis, cations
A JEE Main Unit 20 experiment; the NCERT book has the theory (NCERT 5.7 and Class 11 NCERT 6.13) but does not describe the method.
7 subtopics
- Group zero: NH
- Group I: Pb
- Group II: Pb and Cu
- Group III: Al and Fe
- Group IV: Zn and Ni
- Group V: Ca and Ba
- Group VI: Mg
Mathematics
13 chapters 55 topics 54 in JEE Main
NCERT Mathematics Part I, Chapter 1
Relations and Functions (Class 12)
JEE Main Unit 1: Sets, Relations and Functions
JEE Main Unit 7: Limit, Continuity and Differentiability
1.1–1.2
4 subtopics
- Empty and universal relations
- Reflexive, symmetric and transitive relations
- Equivalence relations
- Equivalence classes
pp. 1–7
1.3
5 subtopics
- One-one (injective) and many-one functions
- Onto (surjective) functions
- Into functions (not onto)
- Bijective functions
- One-one and onto functions on a finite set
pp. 7–11
1.4
Composition and inverse
NCERT: Composition of Functions and Invertible Function
4 subtopics
- The composite function gof
- gof and fog need not be equal
- Invertible functions and the inverse f
- Invertible if and only if one-one and onto
pp. 12–13
NCERT Mathematics Part I, Chapter 2
Inverse Trigonometric Functions
JEE Main Unit 7: Limit, Continuity and Differentiability
JEE Main Unit 14: Trigonometry
2.1–2.2
Principal value branches
NCERT: Introduction; Basic Concepts
5 subtopics
- Restricting domains to make trigonometric functions one-one and onto
- Domains and ranges of sin, cos, tan, cosec, sec and cot
- Graphs as mirror images in the line y = x
- sin x is not (sin x)
- Principal values
pp. 18–27
2.3
3 subtopics
- sin(sin x) = x and sin(sin x) = x on the principal branch
- Simplifying expressions with a trigonometric substitution
- Values such as sin(sin 2π/3) outside the principal branch
pp. 27–30
3.1–3.2
3 subtopics
- Rows, columns and elements
- 3.2.1 Order of a matrix
- Constructing a matrix from a formula for its elements
pp. 34–38
3.3
5 subtopics
- Row and column matrices
- Square matrices and the diagonal
- Diagonal, scalar and identity matrices
- Zero matrix
- 3.3.1 Equality of matrices
pp. 39–43
3.4
9 subtopics
- 3.4.1 Addition of matrices
- 3.4.2 Multiplication of a matrix by a scalar
- Negative and difference of matrices
- 3.4.3 Properties of matrix addition
- 3.4.4 Properties of scalar multiplication of a matrix
- 3.4.5 Multiplication of matrices
- Matrix multiplication is not commutative
- Zero product of two non-zero matrices
- 3.4.6 Properties of multiplication of matrices
pp. 43–61
3.5
2 subtopics
- Interchanging rows and columns
- 3.5.1 Properties of transpose of the matrices
pp. 61–63
3.6
4 subtopics
- Symmetric matrices: A′ = A
- Skew symmetric matrices: A′ = −A
- A + A′ is symmetric and A − A′ is skew symmetric
- A square matrix as a sum of symmetric and skew symmetric matrices
pp. 63–68
3.7
3 subtopics
- Inverse of a square matrix: AB = BA = I
- Uniqueness of the inverse
- (AB) = BA
pp. 68–69
4.1–4.2
5 subtopics
- 4.2.1 Determinant of a matrix of order one
- 4.2.2 Determinant of a matrix of order two
- 4.2.3 Determinant of a matrix of order 3 × 3
- Expanding along any row or column
- |kA| = k|A| for a matrix of order n
pp. 76–82
4.3
3 subtopics
- Area as a determinant of the vertices
- Collinear points give zero area
- Equation of a line through two points
pp. 82–83
4.4
4 subtopics
- Minor of an element
- Cofactor A = (−1) M
- Expanding a determinant with cofactors
- Elements of one row times cofactors of another give zero
pp. 84–87
4.5
5 subtopics
- 4.5.1 Adjoint of a matrix
- A(adj A) = (adj A)A = |A|I
- Singular and non-singular matrices
- |AB| = |A||B| and |adj A| = |A|
- A = (1/|A|) adj A
pp. 87–93
4.6
Solving linear systems
NCERT: Applications of Determinants and Matrices
4 subtopics
- Consistent and inconsistent systems
- 4.6.1 Solution of system of linear equations using inverse of a matrix
- Unique solution X = AB when |A| ≠ 0
- Testing consistency when |A| = 0
pp. 93–98
NCERT Mathematics Part I, Chapter 5
Continuity and Differentiability
JEE Main Unit 7: Limit, Continuity and Differentiability
5.2
6 subtopics
- Continuity at a point
- Continuous functions on an interval
- Points of discontinuity
- Continuity of the modulus and greatest integer functions
- 5.2.1 Algebra of continuous functions
- Continuity of composite functions
pp. 104–118
5.3
6 subtopics
- Left and right hand derivatives
- Every differentiable function is continuous
- |x| is continuous but not differentiable at 0
- 5.3.1 Derivatives of composite functions
- 5.3.2 Derivatives of implicit functions
- 5.3.3 Derivatives of inverse trigonometric functions
pp. 118–125
5.4
Exponential and log functions
NCERT: Exponential and Logarithmic Functions
5 subtopics
- Exponential functions and their graphs
- The natural exponential function e
- Logarithmic functions and their graphs
- Laws of logarithms and change of base
- Derivatives of e and log x
pp. 125–130
5.5
3 subtopics
- Taking logarithms before differentiating
- Functions of the form [u(x)]
- Derivative of a
pp. 130–134
5.6
Parametric derivatives
NCERT: Derivatives of Functions in Parametric Forms
Not named in the JEE Main syllabus; NCERT finds these derivatives with the chain rule, and Unit 7 lists composite functions.
2 subtopics
- Parametric form x = f(t), y = g(t)
- dy/dx = (dy/dt)/(dx/dt)
pp. 134–137
5.7
2 subtopics
- Notation: dy/dx, f″(x), y″ and y
- Proving relations between y and its derivatives
pp. 137–140
NCERT Mathematics Part I, Chapter 6
Application of Derivatives
JEE Main Unit 7: Limit, Continuity and Differentiability
6.2
3 subtopics
- dy/dx as a rate of change
- Rates linked through the chain rule
- Marginal cost and marginal revenue
pp. 147–152
6.3
4 subtopics
- Increasing, decreasing and constant functions on an interval
- Strictly increasing and strictly decreasing functions
- The sign of f′(x) and monotonicity
- Finding intervals of increase and decrease
pp. 152–159
6.4
6 subtopics
- Maximum and minimum values in an interval
- Local maxima, local minima and critical points
- First derivative test
- Second derivative test
- Applied problems on maxima and minima
- 6.4.1 Maximum and minimum values of a function in a closed interval
pp. 159–177
7.2
Anti derivatives
NCERT: Integration as an Inverse Process of Differentiation
5 subtopics
- Anti derivatives and the constant of integration
- The indefinite integral ∫f(x) dx
- Standard integrals
- 7.2.1 Some properties of indefinite integral
- Integration by inspection
pp. 226–235
7.3
Substitution and identities
NCERT: Methods of Integration
3 subtopics
- 7.3.1 Integration by substitution
- Integrals of tan x, cot x, sec x and cosec x
- 7.3.2 Integration using trigonometric identities
pp. 235–243
7.4
Particular integrals
NCERT: Integrals of Some Particular Functions
4 subtopics
- Integrals of 1/(x ± a) and 1/(a − x)
- Integrals of 1/√(x ± a) and 1/√(a − x)
- Integrals of 1/(ax + bx + c) and 1/√(ax + bx + c)
- Integrals of (px + q)/(ax + bx + c) and (px + q)/√(ax + bx + c)
pp. 243–252
7.5
Partial fractions
NCERT: Integration by Partial Fractions
3 subtopics
- Proper and improper rational functions
- Partial fractions for distinct and repeated linear factors
- Partial fractions with a quadratic factor
pp. 252–259
7.6
5 subtopics
- The integration by parts formula
- Choosing the first and second functions
- 7.6.1 Integral of the type ∫e[f(x) + f′(x)] dx
- 7.6.2 Integrals of some more types
- Integrals of √(x ± a), √(a − x) and √(ax + bx + c)
pp. 259–266
7.7
2 subtopics
- The definite integral ∫ f(x) dx
- Lower and upper limits
p. 267
7.8
4 subtopics
- 7.8.1 Area function
- 7.8.2 First fundamental theorem of integral calculus
- 7.8.3 Second fundamental theorem of integral calculus
- Steps for evaluating a definite integral
pp. 267–271
7.9
Substitution with limits
NCERT: Evaluation of Definite Integrals by Substitution
1 subtopic
- Changing the limits with the new variable
pp. 271–273
7.10
Properties of definite integrals
NCERT: Some Properties of Definite Integrals
4 subtopics
- Reversing the limits and splitting the interval
- ∫ f(x) dx = ∫ f(a + b − x) dx
- Integrals over [0, 2a]
- Even and odd functions on [−a, a]
pp. 273–280
8.2
Area under curves
NCERT: Area under Simple Curves
4 subtopics
- Area with vertical strips: ∫ y dx
- Area with horizontal strips: ∫ x dy
- Curves below the x-axis
- Area of a circle and of an ellipse
pp. 292–296
Area between curves
Beyond NCERT
Listed in JEE Main Unit 8 (“areas of the regions bounded by simple curves”); the 2026–27 NCERT book has no section on the area between two curves.
3 subtopics
- Area as the integral of the upper curve minus the lower curve
- Limits from the points of intersection
- Regions bounded by lines, circles, parabolas and ellipses
9.2
Order and degree
NCERT: Basic Concepts
4 subtopics
- Ordinary differential equations
- 9.2.1 Order of a differential equation
- 9.2.2 Degree of a differential equation
- When the degree is not defined
pp. 300–304
9.3
4 subtopics
- Solution curves
- General solution with arbitrary constants
- Particular solution
- Verifying a solution
pp. 304–306
9.4
Solving first order equations
NCERT: Methods of Solving First Order, First Degree Differential Equations
6 subtopics
- 9.4.1 Differential equations with variables separable
- 9.4.2 Homogeneous differential equations
- Homogeneous functions and the substitution y = vx
- 9.4.3 Linear differential equations
- Integrating factor
- Linear equations in x: dx/dy + Px = Q
pp. 306–329
NCERT Mathematics Part II, Chapter 10
Vector Algebra
JEE Main Unit 11: Three Dimensional Geometry
JEE Main Unit 12: Vector Algebra
10.1–10.2
Vectors: basic concepts
NCERT: Introduction; Some Basic Concepts
5 subtopics
- Scalars and vectors
- Vectors as directed line segments
- Magnitude of a vector
- Position vector
- Direction cosines and direction ratios of a vector
pp. 338–341
10.3
4 subtopics
- Zero and unit vectors
- Coinitial and collinear vectors
- Equal vectors and the negative of a vector
- Free vectors
pp. 341–342
10.4
4 subtopics
- Triangle law
- Difference of two vectors
- Parallelogram law
- Commutative and associative properties
pp. 343–346
10.5
Scalar multiple and components
NCERT: Multiplication of a Vector by a Scalar
6 subtopics
- Magnitude and direction of λa
- Unit vector in the direction of a vector
- 10.5.1 Components of a vector
- Condition for collinear vectors
- 10.5.2 Vector joining two points
- 10.5.3 Section formula
pp. 346–355
10.6
Dot and cross products
NCERT: Product of Two Vectors
8 subtopics
- 10.6.1 Scalar (or dot) product of two vectors
- Angle between two vectors
- Scalar product in component form
- 10.6.2 Projection of a vector on a line
- Cauchy–Schwarz and triangle inequalities
- 10.6.3 Vector (or cross) product of two vectors
- Vector product as a determinant
- Areas of a triangle and a parallelogram
pp. 355–369
NCERT Mathematics Part II, Chapter 11
Three Dimensional Geometry
JEE Main Unit 11: Three Dimensional Geometry
11.2
Direction cosines and ratios
NCERT: Direction Cosines and Direction Ratios of a Line
4 subtopics
- Direction cosines and l + m + n = 1
- Direction ratios
- 11.2.1 Direction cosines of a line passing through two points
- Collinear points from direction ratios
pp. 377–381
11.3
3 subtopics
- 11.3.1 Equation of a line through a given point and parallel to a given vector
- Vector equation r = a + λb
- Parametric and Cartesian equations
pp. 381–383
11.4
3 subtopics
- Angle from direction ratios or direction cosines
- Conditions for perpendicular and parallel lines
- Angle between lines in vector and Cartesian form
pp. 383–385
11.5
Shortest distance between lines
NCERT: Shortest Distance between Two Lines
4 subtopics
- Intersecting, parallel and skew lines
- 11.5.1 Distance between two skew lines
- Shortest distance in Cartesian form
- 11.5.2 Distance between parallel lines
pp. 385–390
Line of shortest distance
Beyond NCERT
Listed in JEE Main Unit 11 (“the shortest distance between them and its equation”); the 2026–27 NCERT book finds the distance but not the equation of the line.
3 subtopics
- The common perpendicular to two skew lines
- Feet of the common perpendicular on the two lines
- Equation of the line of shortest distance
12.1–12.2
Linear programming problems
NCERT: Introduction; Linear Programming Problem and its Mathematical Formulation
6 subtopics
- 12.2.1 Mathematical formulation of the problem
- Objective function, decision variables and constraints
- 12.2.2 Graphical method of solving linear programming problems
- Feasible region and feasible solutions
- Corner point method
- Bounded and unbounded feasible regions
pp. 394–404
NCERT Mathematics Part II, Chapter 13
Probability (Class 12)
JEE Main Unit 13: Statistics and Probability
13.2
2 subtopics
- P(E|F) = P(E ∩ F)/P(F)
- 13.2.1 Properties of conditional probability
pp. 406–415
13.3
2 subtopics
- P(E ∩ F) = P(E) P(F|E)
- Multiplication rule for three or more events
pp. 415–417
13.4
4 subtopics
- P(E ∩ F) = P(E) P(F) for independent events
- Independent versus mutually exclusive events
- Independence of three events
- Complements of independent events
pp. 417–423
13.5
5 subtopics
- 13.5.1 Partition of a sample space
- 13.5.2 Theorem of total probability
- Statement and proof of Bayes’ theorem
- Hypotheses, a priori and a posteriori probabilities
- Random variable as a real valued function on the sample space
pp. 423–433
Probability distribution
Beyond NCERT
Listed in JEE Main Unit 13 (“probability distribution of a random variable”); the 2026–27 NCERT book only defines a random variable, in a remark.
2 subtopics
- Probability distribution table
- Probabilities in a distribution add up to 1
Sources
Syllabus for JEE (Main) 2027, Paper 1 (B.E./B.Tech.) (opens in a new tab), National Testing Agency.
The NCERT Class 12 books, reprint 2026-27 and 2025-26: Physics Part I, Physics Part II, Chemistry Part I, Chemistry Part II, Mathematics Part I and Mathematics Part II, from ncert.nic.in.
Chapters, units, sections, sub-sections and pages checked against these on 26 Oct 2026.