Class 12 study notes

NCERT Sections 1.1–1.2: electrostatics, the two kinds of charge and their conventions, charging by rubbing as electron transfer, and the gold-leaf electroscope.

NCERT Section 1.3: conductors and their free electrons, insulators, charge spreading on a conductor but staying put on an insulator, the comb and the spoon, and semiconductors.

NCERT Section 1.4: point charges, additivity, conservation and quantisation of charge (q = ne), the value of e, and NCERT Examples 1.1 and 1.2 worked in full.

NCERT Section 1.5: point charges, Coulomb’s torsion-balance method, F = k|q_₁q_₂|/r^², ε_₀, the vector form and Newton’s third law, and NCERT Examples 1.3 and 1.4 worked in full.

NCERT Section 1.6: the principle of superposition, Eqs. (1.4) and (1.5), and NCERT Examples 1.5 (charge at the centroid) and 1.6 (q, q, −q on a triangle) worked in full.

NCERT Section 1.7: the field of a point charge, source and test charges, the field of a system of charges, its physical significance, and NCERT Examples 1.7 and 1.8 worked in full.

NCERT Section 1.8: how field lines are drawn, density and field strength with the solid angle, the four properties of field lines, and NCERT Exercise 1.7 answered.

NCERT Section 1.9: the flow analogy, the area vector and the outward-normal convention, flux through an area element (Eq. 1.11), total flux, and NCERT Exercises 1.14 and 1.15.

NCERT Section 1.10: dipole moment p = q × 2a, the field on the axis and the equatorial plane, the 1/r^³ far field, polar molecules, NCERT Example 1.9 and Exercise 1.9.

NCERT Section 1.11: zero net force and torque τ = p × E on a dipole in a uniform field, the force in a non-uniform field, the comb and paper, and NCERT Exercise 1.10.

NCERT Section 1.12: linear, surface and volume charge densities (Eqs. 1.23–1.25), why they are macroscopic, and the field of a continuous distribution (Eqs. 1.26–1.27).

NCERT Section 1.13: flux of a point charge through a sphere, Gauss’s law ϕ = q/ε_₀, its six points, the Gaussian surface, NCERT Examples 1.10–1.11 and Exercises 1.16–1.19.

NCERT Section 1.14: fields of a long charged wire, an infinite plane sheet and a thin spherical shell by Gauss’s law, NCERT Example 1.12 and Exercises 1.20, 1.22 and 1.23.

NCERT Section 2.1: the Coulomb force as a conservative force, potential energy difference as the work of an external force (Eq. 2.2), and the zero of potential energy at infinity.

NCERT Section 2.2: potential as work done per unit positive charge, the potential difference (Eq. 2.4) and the zero at infinity; U = qV and the electron volt come from Section 2.8.1.

NCERT Section 2.3: deriving V = Q/4πε_₀r by integrating along a radial path, the sign for negative charges, V against E with distance, and NCERT Example 2.1.

NCERT Section 2.4: the dipole potential by superposition, the far-field result p cos θ/4πε_₀r^², the axis and the equatorial plane, and the 1/r^² fall-off.

NCERT Section 2.5: superposition of potentials, continuous charge, the potential of a charged shell inside and outside, NCERT Examples 2.2 and 2.3 and Exercises 2.1 and 2.2.

NCERT Section 2.6: equipotentials of a point charge and a uniform field, why the field is normal to them, the relation |E| = |δV|/δl (2.6.1), and NCERT Exercise 2.3.

NCERT Section 2.7: potential energy of two charges (Eq. 2.22) and of three charges (Eq. 2.26), its sign, independence of the order of assembly, and NCERT Example 2.4.

NCERT Section 2.8: energy of a single charge (qV), the electron volt, two charges in an external field (Eq. 2.29), a dipole (U = −pE cos θ), and NCERT Examples 2.5 and 2.6.

NCERT Section 2.9: zero field inside, normal field at the surface, charge on the surface, constant potential, E = σ/ε_₀ just outside, shielding, Example 2.7 and Exercise 2.4.

NCERT Section 2.10: dielectrics, polar and non-polar molecules, induced and aligned dipoles, polarisation P = ε_₀χ_ₑE, and bound surface charge on a polarised slab.

NCERT Section 2.11: a capacitor as two conductors with an insulator between, C = Q/V, the farad and its sub-multiples, and dielectric strength (air about 3 × 10^⁶ V/m).

NCERT Section 2.12: fields of the two plates cancel outside and add to σ/ε_₀ between them, fringing, V = Ed, C = ε_₀A/d, and Exercise 2.8.

NCERT Section 2.13: σ − σp = σ/K, C = ε_₀KA/d, permittivity ε = ε_₀K, K = C/C_₀, Example 2.8 and Exercises 2.5 and 2.9.

NCERT Section 2.14: series (same Q, 1/C = Σ1/C_ᵢ) and parallel (same V, C = ΣC_ᵢ), Example 2.9, and Exercises 2.6 and 2.7.

NCERT Section 2.15: work done in charging, U = Q^²/2C = ½CV^² = ½QV, energy density ½ε_₀E^², Example 2.10 and Exercises 2.10 and 2.11.

NCERT Sections 3.1–3.2: charges in motion, I = q/t with q = q_₊ − q_₋, the current at an instant as lim ΔQ/Δt, and the ampere, now fixed by e.

NCERT Section 3.3: free electrons in metals, fixed ions, random thermal motion with no net current, and why a steady current needs a steady field from a cell.

NCERT Section 3.4: V = RI, R ∝ l and R ∝ 1/A from the slab argument, R = ρl/A, current density j = I/A, E = ρj and j = σE.

NCERT Section 3.5: relaxation time, drift velocity v_d = −eEτ/m, I = neA|v_d|, σ = ne^²τ/m, mobility μ = eτ/m, and Examples 3.1–3.2.

NCERT Section 3.6: the three kinds of departure from Ohm’s law, with a curving V–I graph, a diode and GaAs (Figures 3.5–3.7).

NCERT Section 3.7: conductors, semiconductors and insulators by resistivity; metals 10^⁻⁸ to 10^⁻⁶ Ω m, insulators 10^¹⁸ times more, semiconductors in between.

NCERT Section 3.8: ρ(T) = ρ_₀[1 + α(T − T_₀)], metals, nichrome and semiconductors, ρ = m/(ne^²τ), Examples 3.3–3.4 and Exercises 3.3, 3.5 and 3.6.

NCERT Section 3.9: energy lost by charges as heat, P = IV = I^²R = V^²/R, the cell as the source, and transmission losses P^²R/V^² cut by high voltage.

NCERT Section 3.10: emf as the open-circuit potential difference, internal resistance, V = ε − Ir, I = ε/(R + r), and Exercises 3.1, 3.2 and 3.8.

NCERT Section 3.11: the equivalent cell; series ε_eq = ε₁ + ε₂, r_eq = r₁ + r₂; parallel 1/r_eq = 1/r₁ + 1/r₂ and ε_eq/r_eq = ε₁/r₁ + ε₂/r₂.

NCERT Section 3.12: labelling currents, the junction and loop rules and why they hold, Examples 3.5 (cube) and 3.6, and Exercise 3.7.

NCERT Section 3.13: the battery and galvanometer arms, the balance condition R2/R1 = R4/R3 from Kirchhoff’s rules, finding an unknown resistance, and Example 3.7.

NCERT Section 4.2: sources and fields, the Lorentz force, the tesla, and the force on a current-carrying conductor, with Examples 4.1–4.2.

NCERT Section 4.3: circular motion at right angles to B, the radius r = mv/qB, the angular frequency qB/m, helical motion and pitch, and Example 4.3.

NCERT Section 4.4: the field of a current element, its size and direction, comparison with Coulomb’s law, μ_₀ and ε_₀μ_₀ = 1/c^², and Example 4.4.

NCERT Section 4.5: the field on the axis of a circular loop from the Biot–Savart law, the field at the centre, the right-hand thumb rule, Examples 4.5–4.6.

NCERT Section 4.6: the statement of Ampere’s law, amperian loops, the field of a long straight wire, the right-hand rule, and Example 4.7 on a thick wire.

NCERT Section 4.7: the field of a long solenoid, uniform inside and nearly zero outside, B = μ_₀nI from Ampere’s law, and Example 4.8.

NCERT Section 4.8: the force between two parallel currents, attraction and repulsion, Newton’s third law, the 1946 ampere, and Example 4.9.

NCERT Section 4.9: torque on a rectangular loop, magnetic moment m = NIA, τ = m × B, stable and unstable equilibrium, and the loop as a magnetic dipole.

NCERT Section 4.10: the coil in a radial field, kφ = NIAB, conversion to an ammeter and a voltmeter, current and voltage sensitivity, Example 4.12.

NCERT Section 5.2: field lines, the bar magnet as an equivalent solenoid, torque and energy in a uniform field, the electrostatic analog, Examples 5.1–5.2.

NCERT Section 5.3: zero net magnetic flux through any closed surface, no isolated poles, and Examples 5.3–5.4 on drawing field lines correctly.

NCERT Section 5.4: magnetisation M, magnetic intensity H, B = μ_₀(H + M), susceptibility χ, relative permeability μr = 1 + χ, and Example 5.5.

NCERT Section 5.5: diamagnetism, paramagnetism and ferromagnetism, Table 5.2, superconductors and the Meissner effect, domains, and hard and soft ferromagnets.

NCERT Section 6.2: Experiments 6.1–6.3 with a magnet, a moving current-carrying coil and a key, why a changing flux explains all three, and Example 6.1.

NCERT Section 6.3: magnetic flux Φ = B·A = BA cos θ, the area vector, curved surfaces and non-uniform fields (Eq. 6.2), and the weber.

NCERT Section 6.4: Faraday’s law ε = −dΦ/dt, the coil of N turns, ways of changing the flux, and Examples 6.2–6.3 on average emf and current.

NCERT Section 6.5: Lenz’s law for the direction of induced currents, the magnet-and-coil cases, open circuits, energy conservation, and Examples 6.4–6.5.

NCERT Section 6.6: motional emf Blv from Faraday’s law and from the Lorentz force, induced electric fields, and Examples 6.6–6.7 on rotating rods and wheels.

NCERT Section 6.7: mutual inductance of coaxial solenoids, M12 = M21, self-inductance of a solenoid, back emf, energy ½LI^² and energy density B^²/(2μ_₀).

NCERT Section 6.8: a coil turning in a uniform field, flux BA cos ωt, emf NBAω sin ωt, peak emf and frequency, and Example 6.10.

NCERT Section 7.2: current in phase with the voltage, average power ½i_ₘ^²R, rms current and voltage, and Example 7.1 on a 100 W bulb.

NCERT Section 7.3: phasors as rotating vectors, vertical projections as instantaneous values, and the resistor’s phasor diagram with zero phase angle.

NCERT Section 7.4: current lags the voltage by π/2, inductive reactance XL = ωL, zero average power, and Examples 7.2 and 7.5.

NCERT Section 7.5: current leads the voltage by π/2, capacitive reactance XC = 1/ωC, zero average power, and Examples 7.3–7.4.

NCERT Section 7.6: phasor solution of the series LCR circuit, impedance Z, phase angle, resonance ω0 = 1/√LC, tuning a radio, and Example 7.6.

NCERT Section 7.7: average power VI cos φ, the power factor, the four cases including wattless current and resonance, and Examples 7.7–7.9.

NCERT Section 7.8: the transformer’s principle of mutual induction, voltage and current ratios, step-up and step-down, energy losses, and transmission.

NCERT Section 8.2: Ampere’s law for a charging capacitor, the displacement current ε_₀ dΦE/dt, the Ampere–Maxwell law and Maxwell’s equations in vacuum, with Exercises 8.1–8.2.

NCERT Section 8.3: sources of electromagnetic waves, their transverse nature, Eq. 8.7, c = 1/√(μ_₀ε_₀), B_₀ = E_₀/c, the speed in a medium and energy, with Examples 8.1–8.2.

NCERT Section 8.4: radio waves, microwaves, infrared, visible, ultraviolet, X-rays and gamma rays, with Table 8.1’s ranges, sources and detectors, and their uses.

NCERT Section 9.2: laws of reflection, the Cartesian sign convention, f = R/2, the mirror equation and magnification, with Examples 9.1–9.4 and Exercises 9.1–9.2.

NCERT Section 9.3: Snell’s law, refractive index and optical density, n_₁₂ = 1/n_₂₁, the lateral shift through a slab, and real and apparent depth.

NCERT Section 9.4: the critical angle and sin ic = n_₂₁, Table 9.1, the laser demonstration, totally reflecting prisms and optical fibres, with Exercises 9.5 and 9.17.

NCERT Section 9.5: refraction at one spherical surface, the lens maker’s formula, the thin lens formula and magnification, power, and lenses in contact, with Examples 9.5–9.8.

NCERT Section 9.6: r_₁ + r_₂ = A, the deviation δ = i + e − A, the δ–i curve, minimum deviation, n = sin[(A + Dm)/2]/sin(A/2) and the thin prism.

NCERT Section 9.7: the simple and compound microscope, the refracting telescope and the Cassegrain reflector, with their magnifying powers and Exercises 9.11–9.14 and 9.22–9.24.

NCERT Section 10.2: wavefronts as surfaces of constant phase, spherical and plane wavefronts, secondary wavelets and their envelope, and the backwave problem.

NCERT Section 10.3: Snell’s law and the law of reflection from Huygens’ construction, wavelength in two media, the critical angle, and wavefronts through prisms and lenses.

NCERT Section 10.4: coherent sources, path and phase difference, I = 4I0 cos^²(φ/2), constructive and destructive interference, and I = 2I0 for incoherent sources.

NCERT Section 10.5: why two lamps give no fringes, Young’s arrangement, bright fringes at nλD/d and dark ones at (n + 1/2)λD/d, equally spaced; Exercises 10.4 and 10.6.

NCERT Section 10.6: diffraction at a single slit, the central maximum and minima at θ ≈ nλ/a, interference and diffraction compared, and seeing the pattern with two razor blades.

NCERT Section 10.7: plane-polarised and unpolarised waves, polaroids and the pass axis, Malus’ law I = I0 cos^²θ, Example 10.2 and the uses of polaroids.

NCERT Section 11.2: the work function, the electron volt (1 eV = 1.602 × 10^⁻¹⁹ J), and thermionic, field and photoelectric emission, with Thomson’s e/m and Millikan’s e.

NCERT Section 11.3: Hertz’s discovery of photoelectric emission in 1887, Hallwachs’ electroscope and Lenard’s tube, the threshold frequency, and which metals respond to visible light.

NCERT Section 11.4: the set-up, photocurrent against intensity and collector potential, saturation current, stopping potential (Kmax = eV0), and the threshold frequency.

NCERT Section 11.5: why the wave picture of light, with energy absorbed continuously, cannot explain the threshold frequency, the intensity-independent Kmax or instant emission.

NCERT Section 11.6: light quanta of energy hν, Kmax = hν − φ0, the threshold frequency ν0 = φ0/h, V0 against ν with slope h/e, and Millikan’s confirmation; Exercises 11.2 and 11.5–11.9.

NCERT Section 11.7: the photon, its energy hν and momentum hν/c, the five properties of photons, and Example 11.1 and Exercises 11.1 and 11.4 on photon numbers.

NCERT Section 11.8: dual nature of radiation, de Broglie’s hypothesis and λ = h/p, the photon’s wavelength c/ν, and why a ball shows no wave nature; Example 11.3 and Exercise 11.10.

NCERT Section 12.2: the Geiger–Marsden experiment, the alpha-particle trajectory and impact parameter, distance of closest approach, and electron orbits; Examples 12.1–12.3.

NCERT Section 12.3: emission line spectra as a fingerprint of the gas and absorption spectra with dark lines at the same wavelengths; Exercise 12.3.

NCERT Section 12.4: why a classical orbiting electron spirals in, Bohr’s three postulates, the radius and energy of the orbits, and energy levels; Example 12.4, Exercises 12.6, 12.7, 12.9.

NCERT Section 12.5: a photon hν = Ei − Ef for each jump between levels, discrete emission lines, and absorption as an upward jump; Exercises 12.5 and 12.8.

NCERT Section 12.6: the electron as a standing wave on its orbit, 2πr_ₙ = nλ, how this gives Bohr’s condition mvr = nh/2π, and the limits of the Bohr model.

NCERT Section 13.2: the atomic mass unit, the proton and neutron and their masses, Chadwick’s discovery of the neutron, and isotopes, isobars and isotones.

NCERT Section 13.3: sizes from alpha and electron scattering, R = R_₀A^1/3 with R_₀ = 1.2 fm, and the constant nuclear density; Example 13.1, Exercises 13.4 and 13.10.

NCERT Section 13.4: E = mc^², 1 u = 931.5 MeV, mass defect and binding energy, and the binding energy per nucleon curve; Examples 13.2–13.3, Exercises 13.1–13.3.

NCERT Section 13.5: why a new force is needed, its strength, short range and saturation, charge independence, and the potential energy of a pair of nucleons.

NCERT Section 13.6: Becquerel’s discovery of radioactivity in 1896, and the three kinds of decay found in nature: alpha, beta and gamma.

NCERT Section 13.7: energy from the binding energy curve, fission of uranium-235, fusion and the proton–proton cycle in stars, and controlled fusion; Example 13.4, Exercises 13.5–13.9.

NCERT Section 14.2: classifying solids by resistivity, energy bands, the valence and conduction bands, and the band gap of metals, insulators and semiconductors.

NCERT Section 14.3: covalent bonds in Si and Ge, holes, ne = nh = ni, hole motion and the current I = Ie + Ih, and thermal generation and recombination of carriers.

NCERT Section 14.4: doping, n-type with pentavalent donors, p-type with trivalent acceptors, donor and acceptor levels, and ne nh = ni^²; Example 14.2, Exercises 14.1–14.2.

NCERT Section 14.5: how a p-n junction forms, diffusion and drift currents, the depletion region and the barrier potential; Example 14.3 and Exercise 14.4.

NCERT Section 14.6: forward and reverse bias, minority carrier injection, the V-I characteristic and its circuit, threshold and breakdown voltages and dynamic resistance; Example 14.4.

NCERT Section 14.7: the half-wave rectifier, the full-wave rectifier with a centre-tap transformer and the capacitor filter; Exercise 14.6 on output frequency.

NCERT Section 1.1: solutions as homogeneous mixtures, solvent and solute, binary solutions and the nine types of NCERT Table 1.1, with examples.

NCERT Section 1.2: mass, volume and mass by volume percentage, ppm, mole fraction, molarity and molality, with Examples 1.1–1.3 and Intext Questions 1.1–1.5.

NCERT Section 1.3: solubility of solids and gases in liquids, saturated solutions, effects of temperature and pressure, Henry’s law and its uses; Example 1.4, Intext 1.6–1.7.

NCERT Section 1.4: Raoult’s law for volatile liquids, vapour pressure–composition plots, vapour composition, Raoult’s law as Henry’s law, and solids in liquids; Example 1.5.

NCERT Section 1.5: ideal solutions, positive and negative deviations from Raoult’s law with their causes and examples, and minimum and maximum boiling azeotropes.

NCERT Section 1.6: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure, with molar masses; Examples 1.6–1.11.

NCERT Section 1.7: abnormal molar masses from dissociation and association, the van ’t Hoff factor i and its use in colligative formulas; Table 1.4, Examples 1.12–1.13.

NCERT Section 2.1: the Daniell cell and its 1.1 V, and how an opposing external voltage turns the galvanic cell into an electrolytic cell.

NCERT Section 2.2: half-cells, electrode potential, emf and cell notation, the standard hydrogen electrode and the table of standard electrode potentials.

NCERT Section 2.3: the Nernst equation for an electrode and a cell, the equilibrium constant from the emf, and ΔrG⊖ = −nFE⊖(cell), with NCERT’s examples.

NCERT Section 2.4: resistivity, conductivity and the cell constant, molar conductivity and its change with concentration, and Kohlrausch’s law with its uses.

NCERT Section 2.5: electrolytic cells, copper refining and metal extraction, Faraday’s two laws, the faraday, and the products of electrolysis with overpotential.

NCERT Section 2.6: primary batteries (dry cell, mercury cell) and secondary batteries (lead storage, nickel-cadmium), with their cell reactions.

NCERT Section 2.7 and the Hydrogen Economy box (page 58): fuel cells against thermal plants, the hydrogen–oxygen cell and its reactions, efficiency, and hydrogen as a fuel.

NCERT Section 2.8: corrosion and its cost, the rusting of iron as a tiny galvanic cell with its electrode reactions, and how corrosion is prevented.

NCERT Section 3.1: average and instantaneous rate, units of rate, rate and the balanced equation, and rates from partial pressures.

NCERT Section 3.2: rate law and rate constant, order and its units, elementary and complex reactions, molecularity and the rate determining step.

NCERT Section 3.3: integrated rate laws for zero and first order reactions, their straight-line plots, first order gas phase reactions, half-life and pseudo first order.

NCERT Section 3.4: the Arrhenius equation, activation energy and the activated complex, the Maxwell–Boltzmann energy distribution, and the effect of a catalyst.

NCERT Section 3.5: collision frequency, effective collisions and threshold energy, the orientation of colliding molecules and the steric factor, and the limits of collision theory.

NCERT Section 4.1 with the chapter opening: the d-block between the s- and p-blocks, the 3d, 4d, 5d and 6d series, and the f-block panel.

NCERT Section 4.2: the general outer configuration, Table 4.1, chromium and copper, and why zinc, cadmium and mercury are not transition elements.

NCERT Section 4.3, all 14 subsections: physical properties, sizes, ionisation enthalpies, oxidation states, E⊖ trends, magnetism, colour, complexes, catalysis, interstitials and alloys.

NCERT Section 4.4: oxides and oxoanions of the 3d metals, then potassium dichromate and potassium permanganate: preparation, structures, oxidising reactions and uses.

NCERT Section 4.5: configurations, atomic and ionic sizes, the lanthanoid contraction, oxidation states and general characteristics, with Table 4.9.

NCERT Section 4.6: configurations, ionic sizes, the actinoid contraction, oxidation states (Table 4.11) and a comparison with the lanthanoids.

NCERT Section 4.7: iron and steels, special compounds (TiO_₂ pigment, MnO_₂ cells, coinage metals, AgBr) and catalysts V_₂O_₅, Fe, Ni, PdCl_₂ and the Ziegler catalyst.

NCERT Section 5.1: the cobalt–ammonia chlorides and the AgCl test, primary and secondary valences, Werner’s postulates, and double salts against complexes.

NCERT Section 5.2: coordination entity, central atom, ligands and denticity, chelates, ambidentate ligands, coordination number, sphere, polyhedron, oxidation number.

NCERT Section 5.3: rules for writing formulas of mononuclear coordination entities and for naming coordination compounds, with Intext Questions 5.1 and 5.2.

NCERT Section 5.4: stereoisomerism (geometrical, optical) and structural isomerism (linkage, coordination, ionisation, solvate), with Examples 5.4–5.6.

NCERT Section 5.5: valence bond theory, inner and outer orbital complexes, magnetic properties, crystal field theory, the spectrochemical series and colour.

NCERT Section 5.6: homoleptic metal carbonyls and their shapes, and synergic bonding through σ donation and π back donation between the metal and CO.

NCERT Section 5.7: coordination compounds in analysis, water hardness, metal extraction and purification, biological systems, industry and medicine.

NCERT Section 6.1: haloalkanes and haloarenes classified by the number of halogens and by the sp^³ or sp^² carbon that carries the halogen.

NCERT Section 6.2: common and IUPAC names of haloalkanes and haloarenes, gem- and vic-dihalides, and the eight isomers of C_₅H_₁₁Br.

NCERT Section 6.3: the polar C–X bond, and the bond lengths, bond enthalpies and dipole moments of the methyl halides in Table 6.2.

NCERT Section 6.4: haloalkanes from alcohols (HX, PX_₃, PCl_₅, SOCl_₂), from alkanes and alkenes, and by the Finkelstein and Swarts halogen exchanges.

NCERT Section 6.5: aryl chlorides and bromides by electrophilic substitution with a Lewis acid, and aryl halides from amines by Sandmeyer’s reaction.

NCERT Section 6.6: boiling points (RI > RBr > RCl > RF, branching), the high-melting para dihalobenzenes, Table 6.3 densities and solubility in water.

NCERT Section 6.7: nucleophilic substitution (SN1, SN2, stereochemistry), elimination, Grignard and Wurtz, and the reactions of haloarenes.

NCERT Section 6.8: uses and effects of dichloromethane, chloroform, iodoform, carbon tetrachloride, freons and DDT, with NCERT’s two DDT dates checked.

NCERT Section 7.1: alcohols and phenols by the number of –OH groups and the carbon bearing –OH (1°, 2°, 3°, allylic, benzylic, vinylic); ethers.

NCERT Section 7.2: common and IUPAC names of alcohols (Table 7.1), phenols, cresols and benzenediols, and ethers (Table 7.2).

NCERT Section 7.3: the C–O bond and angle at oxygen in methanol, phenol and methoxymethane (Fig. 7.1), and why phenol’s C–O bond is shorter.

NCERT Section 7.4: preparing alcohols and phenols, their physical properties, acidity, the Lucas test, dehydration, oxidation, and phenol’s ring reactions.

NCERT Section 7.5: methanol from carbon monoxide and hydrogen, ethanol by fermentation (invertase and zymase), their properties and uses, and denaturation.

NCERT Section 7.6: ethers by dehydration and Williamson synthesis, their boiling points and solubility, cleavage by HI, and electrophilic substitution in anisole.

NCERT Section 8.1: common and IUPAC names of aldehydes and ketones, Table 8.1, and the sp^² planar, polar structure of the carbonyl group.

NCERT Section 8.2: aldehydes and ketones from alcohols, alkenes and alkynes; Rosenmund, Stephen, Etard and Gattermann–Koch; ketones from R_₂Cd, nitriles and acylation.

NCERT Section 8.3: physical state, boiling points against hydrocarbons, ethers and alcohols, solubility in water and odour of aldehydes and ketones.

NCERT Section 8.4: nucleophilic addition, reduction, Tollens’ and Fehling’s tests, haloform, aldol, Cannizzaro and ring substitution in aldehydes and ketones.

NCERT Section 8.5: formalin and bakelite, acetaldehyde as a starting material, acetone and butanone as solvents, and aldehydes and ketones in perfumes and flavours.

NCERT Section 8.6: common and IUPAC names of carboxylic acids, Table 8.3, and the planar structure of the carboxyl group with its resonance.

NCERT Section 8.7: carboxylic acids from primary alcohols, aldehydes, alkylbenzenes, nitriles and amides, Grignard reagents, and acyl halides, anhydrides and esters.

NCERT Section 8.8: physical state and odour, high boiling points from hydrogen bonding, dimers in the vapour and aprotic solvents, and solubility of carboxylic acids.

NCERT Section 8.9: acidity and the effect of substituents, anhydrides, esterification, acyl chlorides, amides, reduction, decarboxylation, Kolbe electrolysis, HVZ and ring substitution.

NCERT Section 8.10: uses of methanoic, ethanoic and hexanedioic acids, benzoic esters and sodium benzoate, and fatty acids in soaps and detergents.

NCERT Section 9.1: amines as derivatives of ammonia, the sp^³ hybridised nitrogen with its unshared pair, and the pyramidal shape, with NCERT’s trimethylamine angle.

NCERT Section 9.2: primary, secondary and tertiary amines by the number of hydrogens of ammonia replaced, and simple and mixed amines.

NCERT Section 9.3: common names (alkylamines, aniline), IUPAC alkanamines, diamines, the locant N for secondary and tertiary amines, and NCERT Table 9.1.

NCERT Section 9.4: reduction of nitro compounds, ammonolysis of alkyl halides, reduction of nitriles and amides, Gabriel phthalimide synthesis and Hofmann bromamide degradation.

NCERT Section 9.5: physical state and odour, solubility in water, and hydrogen bonding in primary and secondary amines, with NCERT Table 9.2’s boiling points.

NCERT Section 9.6: basic character and pKb, alkylation and acylation, carbylamine test, nitrous acid, Hinsberg’s reagent, and bromination, nitration and sulphonation of aniline.

NCERT Section 9.7: diazonium salts, their naming and stability, and the diazotisation of aniline with sodium nitrite and hydrochloric acid at 273–278 K.

NCERT Section 9.8: benzenediazonium chloride as a colourless, water-soluble solid that is unstable when warm or dry, and the stable, insoluble fluoroborate.

NCERT Section 9.9: replacement of the diazonium group by halogens, cyanide, H, OH and NO_₂ (Sandmeyer and Gattermann reactions), and coupling to azo dyes.

NCERT Section 9.10: groups that direct substitution cannot introduce (F, I, CN) and NCERT Example 9.5, 4-nitrotoluene to 2-bromobenzoic acid.

NCERT Section 10.1: classification, glucose and fructose (open-chain and cyclic structures), sucrose, maltose and lactose, starch, cellulose and glycogen.

NCERT Section 10.2: amino acids, their classification and zwitter ions, the peptide bond, the four levels of protein structure and denaturation.

NCERT Section 10.3: enzymes as biocatalysts, naming, activation energy; the mechanism, which the Chemistry book does not discuss, from NCERT Class 11 Biology.

NCERT Section 10.4: what vitamins are, fat-soluble and water-soluble vitamins, and Table 10.3 of sources and deficiency diseases.

NCERT Section 10.5: composition of DNA and RNA, nucleosides and nucleotides, the double helix, biological functions and DNA fingerprinting.

NCERT Section 10.6: hormones as intercellular messengers, steroid, polypeptide and amino acid derivative hormones, and their functions.

NCERT Sections 1.1–1.2: empty and universal relations, the reflexive, symmetric and transitive tests, equivalence relations and classes, with Exercise 1.1 worked in full.

NCERT Section 1.3: one-one, many-one, onto and bijective functions, the finite-set rule, with Exercise 1.2 and the function items of the Miscellaneous Exercise worked.

NCERT Section 1.4: the composite gof, why gof and fog differ, invertible functions and the inverse, with NCERT Examples 15–17 worked and the one-one and onto test explained.

NCERT Sections 2.1–2.2: restricting the six trigonometric functions, the table of domains and ranges, graphs as mirror images, and principal values, with Exercise 2.1 worked.

NCERT Section 2.3: when sin(sin^⁻¹ x) and sin^⁻¹(sin x) give back x, values outside the principal branch and substitutions, with Exercise 2.2 and the Miscellaneous Exercise worked.

NCERT Sections 3.1–3.2: rows, columns and elements, the order m × n, possible orders, and building a matrix from a rule for a_ᵢⱼ, with Exercise 3.1 Q1–Q5 and Q10 worked.

NCERT Section 3.3: row, column and square matrices, the diagonal, diagonal, scalar, identity and zero matrices, and equality of matrices, with NCERT Examples 4–5 worked.

NCERT Section 3.4: addition, scalar multiples, negative and difference, their properties, matrix multiplication and its properties, with NCERT examples and much of Exercise 3.2.

NCERT Section 3.5: the transpose A′, its order, and the properties (A′)′ = A, (kA)′ = kA′, (A + B)′ = A′ + B′ and (AB)′ = B′A′, with NCERT Examples 20–21 and Exercise 3.3 Q1–Q6.

NCERT Section 3.6: symmetric and skew symmetric matrices, the zero diagonal, A + A′ and A − A′, and the split A = ½(A + A′) + ½(A − A′), with NCERT Example 22 and Exercise 3.3 Q7–Q12.

NCERT Section 3.7: the inverse A^⁻¹ with AB = BA = I, why it is unique and (AB)^⁻¹ = B^⁻¹A^⁻¹, with the Miscellaneous Exercise items on inverses; finding an inverse from AB = I goes beyond the text.

NCERT Sections 4.1–4.2: determinants of order 1, 2 and 3, expansion along any row or column, and |kA| = k^ⁿ|A|, with NCERT Examples 1–5 and Exercise 4.1 worked.

NCERT Section 4.3: the area of a triangle as half the absolute value of a determinant, collinear points and the line through two points, with NCERT Examples 6–7 and Exercise 4.2 worked.

NCERT Section 4.4: the minor M_ᵢⱼ and cofactor A_ᵢⱼ of an element, expansion by cofactors, and why a row times another row’s cofactors gives 0, with NCERT Examples 8–11 and Exercise 4.3.

NCERT Section 4.5: the adjoint, A(adj A) = |A| I, singular matrices, |AB| = |A||B|, |adj A| = |A|^ⁿ⁻¹ and A^⁻¹ = (1/|A|) adj A, with NCERT Examples 12–15 and Exercise 4.4.

NCERT Section 4.6: consistent and inconsistent systems, AX = B, the matrix method X = A^⁻¹B, and the (adj A)B test when |A| = 0, with NCERT Examples 16–18 and most of Exercise 4.5.

NCERT Section 5.2: continuity at a point, continuous functions, points of discontinuity, |x| and [x], the algebra of continuous functions and composites, with NCERT examples and Exercise 5.1.

NCERT Section 5.3: one-sided derivatives, differentiable implies continuous, |x| at 0, the chain rule, implicit functions and inverse trigonometric derivatives, with Exercises 5.2 and 5.3.

NCERT Section 5.4: exponential and logarithmic functions, their graphs as mirror images, the laws of logarithms and change of base, and the derivatives of e^ˣ and log x, with Exercise 5.4.

NCERT Section 5.5: taking logarithms before differentiating, functions [u(x)]^v(x), the derivative of a^ˣ, and sums of variable powers, with NCERT Examples 27–30 and Exercise 5.5.

NCERT Section 5.6: curves given by x = f(t), y = g(t), and dy/dx = (dy/dt)/(dx/dt), with NCERT Examples 31–34 and Exercise 5.6.

NCERT Section 5.7: the second order derivative, its notations, and proving relations between y, y_₁ and y_₂, with NCERT Examples 35–38 and Exercise 5.7.

NCERT Section 6.2: dy/dx as a rate of change, related rates through the chain rule, and marginal cost and revenue, with NCERT Examples 1–6 and Exercise 6.1.

NCERT Section 6.3: increasing, decreasing, strictly increasing and constant functions, the first derivative test, and finding intervals of increase and decrease, with Exercise 6.2.

NCERT Section 6.4: maximum and minimum values, local extrema and critical points, the first and second derivative tests, applied problems and absolute extrema on closed intervals.

NCERT Section 7.2: anti derivatives, the indefinite integral and constant of integration, the standard integrals, properties, and integration by inspection, with Exercise 7.1.

NCERT Section 7.3: integration by substitution, the integrals of tan x, cot x, sec x and cosec x, and integration using trigonometric identities, with questions from Exercises 7.2 and 7.3.

NCERT Section 7.4: the six particular integrals and their proofs, quadratic denominators by completing the square, and linear numerators, with questions from Exercise 7.4.

NCERT Section 7.5: proper and improper rational functions and the partial fractions of Table 7.2 for linear, repeated and quadratic factors, with questions from Exercise 7.5.

NCERT Section 7.6: integration by parts, choosing the first function, ∫e^ˣ[f(x) + f′(x)] dx and the square-root integrals, with questions from Exercises 7.6 and 7.7.

NCERT Section 7.7: the definite integral, its lower and upper limits and its value F(b) − F(a), with the area meaning of Section 7.8.1 and questions from Exercise 7.8.

NCERT Section 7.8: the area function, the first and second fundamental theorems of integral calculus, the steps for evaluating, Example 25 and Exercise 7.8 questions.

NCERT Section 7.9: evaluating definite integrals by substitution, changing the limits to the new variable, NCERT Examples 26 and 27 and questions from Exercise 7.9.

NCERT Section 7.10: the properties P_₀ to P_₇ with the proof of P_₃, NCERT Examples 28–34 and questions from Exercise 7.10, including modulus, even and odd integrands.

Area under the curve for Class 12 Maths and JEE: vertical and horizontal strips, parts below the x-axis, circle and ellipse areas, solved NCERT questions.

NCERT Section 9.2: ordinary differential equations, notation, the order and the degree, and when the degree is not defined, with Exercise 9.1.

NCERT Section 9.3: what a solution is, general and particular solutions, checking a given function by substitution, with Exercise 9.2.

NCERT Section 9.4: variables separable, homogeneous equations with y = vx, linear equations with the integrating factor, and linear equations in x, with Exercises 9.3–9.5.

NCERT Sections 10.1–10.2: scalars and vectors, directed line segments, magnitude, the position vector, direction cosines and direction ratios, with Exercise 10.1 Q2 and Q3.

NCERT Section 10.3: zero and unit vectors, coinitial, collinear, equal and negative vectors, free vectors, with Exercise 10.1 Q1, Q4 and Q5.

NCERT Section 10.4: the triangle law, the difference of two vectors, the parallelogram law, and the commutative and associative properties of vector addition.

NCERT Section 10.5: λa and the unit vector, components with î, ĵ, k̂, collinear vectors, the vector joining two points and the section formula, with Exercise 10.2 questions.

NCERT Section 10.6: the scalar product, angles and projections, the two inequalities, the vector product and its determinant form, and areas, with Exercise 10.3 and 10.4 questions.

NCERT Section 11.2: direction cosines and direction ratios of a line, the line through two points, and collinear points, with Exercise 11.1.

NCERT Section 11.3: the line through a point parallel to a vector, r = a + λb, and its parametric and Cartesian forms, with Exercise 11.2 Q4–Q7.

NCERT Section 11.4: the angle between two lines from direction ratios or cosines, perpendicular and parallel lines, and the vector and Cartesian forms, with Exercise 11.2 Q1–Q3 and Q8–Q11.

NCERT Section 11.5: intersecting, parallel and skew lines, the shortest distance between skew lines in vector and Cartesian form, and between parallel lines, with Exercise 11.2 Q12–Q15.

Linear programming (LPP) for Class 12 Maths: objective function, constraints, feasible region, corner point method, unbounded regions, solved examples.

NCERT Section 13.2: conditional probability P(E|F) = P(E ∩ F)/P(F), the reduced sample space, its three properties, and all 17 questions of Exercise 13.1.

NCERT Section 13.3: the multiplication rule P(E ∩ F) = P(E) P(F|E) for two and three events, with NCERT Examples 8–9 on draws without replacement.

NCERT Section 13.4: independent events, P(E ∩ F) = P(E) P(F), independent versus mutually exclusive, three events and complements, with Exercise 13.2.

NCERT Section 13.5: partition of a sample space, theorem of total probability, Bayes’ theorem on a tree, NCERT’s random variable remark, and all 14 questions of Exercise 13.3.

NCERT Section 1.1: flowers in human culture and as the sites of sexual reproduction, and the parts of a typical flower from NCERT Figure 1.1.

NCERT Section 1.2: stamen, microsporangium and pollen grain; the ovule and the embryo sac; pollination, outbreeding devices, pollen–pistil interaction, emasculation and bagging.

NCERT Section 1.3: the two male gametes in the embryo sac, syngamy giving the diploid zygote, and triple fusion giving the triploid primary endosperm nucleus.

NCERT Section 1.4: endosperm, embryo (dicot and grass), albuminous and non-albuminous seeds, perisperm, dormancy, true, false and parthenocarpic fruits, and seeds’ advantages.

NCERT Section 1.5: apomixis as seed formation without fertilisation, its two routes, polyembryony in citrus and mango, and why apomixis matters for hybrid seed.

NCERT Section 2.1: testes and scrotum, seminiferous tubules with Sertoli and Leydig cells, the accessory ducts and glands, seminal plasma and the penis.

NCERT Section 2.2: the ovaries (cortex and medulla), fallopian tubes, uterus and its three layers, cervix and vagina, external genitalia and mammary glands.

NCERT Section 2.3: spermatogenesis and its hormonal control, spermiogenesis, the structure of a sperm, oogenesis, the follicle stages and ovulation.

NCERT Section 2.4: menarche and menopause, the menstrual, follicular and luteal phases, the LH surge and ovulation, the corpus luteum, and menstrual hygiene.

NCERT Section 2.5: insemination, fertilisation in the ampulla and the zona pellucida, the sperm deciding the sex of the baby, cleavage to morula and blastocyst, and implantation.

NCERT Section 2.6: chorionic villi and the placenta, placental and pregnancy hormones, the three germ layers and stem cells, and foetal development month by month.

NCERT Section 2.7: the gestation period, parturition by the foetal ejection reflex and oxytocin, and lactation with colostrum.

NCERT Section 3.1 with the chapter Introduction: WHO’s definition, family planning and RCH programmes, sex education, amniocentesis and its ban, and signs of improvement.

NCERT Section 3.2: population growth and its causes, measures to check it, the ideal contraceptive, and natural, barrier, IUD, hormonal and surgical methods.

NCERT Section 3.3: what MTP is, why it is done, the law (the 2021 Amendment Act, which NCERT prints as 2017), first-trimester safety and female foeticide.

NCERT Section 3.4: the common STIs, other routes of hepatitis-B and HIV, which STIs are curable, complications such as PID and infertility, and prevention.

NCERT Section 3.5: infertility and its causes, and assisted reproductive technologies: IVF with ZIFT and IUT, GIFT, ICSI, artificial insemination, IUI and adoption.

NCERT Section 4.1 with the chapter Introduction: inheritance and variation, Mendel’s hybridisation experiments on pea, true-breeding lines and the seven pairs of traits.

NCERT Section 4.2: the monohybrid cross, alleles, genotype and phenotype, the Punnett square, test cross, the laws of dominance and segregation, incomplete dominance and co-dominance.

NCERT Section 4.3: the dihybrid cross and 9 : 3 : 3 : 1, independent assortment, the chromosomal theory of inheritance, Morgan’s linkage and recombination, and gene maps.

NCERT Section 4.4: traits on a gradient such as human height, polygenic traits, the influence of the environment, and NCERT’s three-gene model of skin colour.

NCERT Section 4.5: pleiotropic genes, the metabolic-pathway mechanism and phenylketonuria, with the disorder’s account in Section 4.8.2 and the pea starch gene of Section 4.2.

NCERT Section 4.6: Henking’s X body, the XO, XY and ZW types, male and female heterogamety, sex determination in humans and in the honey bee.

NCERT Section 4.7: mutation as a source of variation, chromosomal aberrations, the sickle-cell point mutation, frame-shift mutations (with Section 5.6.1) and mutagens.

NCERT Section 4.8: pedigree analysis; Mendelian disorders (colour blindness, haemophilia, sickle-cell anaemia, phenylketonuria, thalassemia); chromosomal disorders.

NCERT Section 5.1: length of DNA, the polynucleotide chain, RNA versus DNA, the double helix and Chargaff’s rules, the central dogma, nucleosomes and chromatin.

NCERT Section 5.2: Griffith’s transforming principle, Avery, MacLeod and McCarty, the Hershey–Chase experiment, the criteria for a genetic material and DNA versus RNA.

NCERT Section 5.3: RNA as the first genetic material, RNA as a catalyst (with the ribozyme of Section 5.7) and the evolution of the more stable DNA from RNA.

NCERT Section 5.4: semiconservative replication, the Meselson–Stahl and Taylor experiments, DNA polymerase, the replication fork, DNA ligase, the origin and S-phase.

NCERT Section 5.5: why one strand is copied, the transcription unit, template and coding strands, split genes, RNA types, σ and ρ, RNA polymerases I–III and mRNA processing.

NCERT Section 5.6: Gamow’s triplet code, Khorana, Nirenberg and Ochoa, the codon table, features of the code, point and frameshift mutations, and tRNA.

NCERT Section 5.7: charging of tRNA, the ribosome and its ribozyme, the translational unit and UTRs, and initiation, elongation and termination.

NCERT Section 5.8: levels of regulation in eukaryotes, activators, repressors and operators, and the lac operon with its i, z, y and a genes and induction by lactose.

NCERT Section 5.9: why the HGP was a mega project, its goals, ESTs and sequence annotation, BAC and YAC, Sanger sequencing, the genome’s features and SNPs.

NCERT Section 5.10: repetitive and satellite DNA, DNA polymorphism, Alec Jeffreys’ VNTR probe, the steps of the technique and its uses in forensics and paternity.

NCERT Section 6.1: the Big Bang and the early earth, panspermia, spontaneous generation and Pasteur, Oparin and Haldane’s chemical evolution, and Miller’s experiment.

NCERT Section 6.2: the theory of special creation, Darwin’s voyage on H.M.S. Beagle, variation, reproductive fitness, natural selection and Alfred Wallace.

NCERT Section 6.3: fossils, embryology and von Baer, homologous and analogous organs, proteins and genes, artificial selection, industrial melanism and resistance.

NCERT Section 6.4: adaptive radiation defined, Darwin’s finches of the Galapagos, Australian marsupials, and convergent evolution of placental mammals and marsupials.

NCERT Section 6.5: natural selection and fitness, the bacterial example, branching descent, Lamarck’s use and disuse, Malthus and Darwin’s observations.

NCERT Section 6.6: the origin of variation, Hugo de Vries’ mutations in the evening primrose, Darwinian variation compared with mutation, and saltation.

NCERT Section 6.7: allele frequencies and genetic equilibrium, p^² + 2pq + q^² = 1, the five factors, gene flow, drift, the founder effect and the three kinds of selection.

NCERT Section 6.8: first cells and oxygen, invertebrates, jawless fish, land plants, lobefins and amphibians, reptiles and dinosaurs, mammals, and the geological periods.

NCERT Section 6.9: the early primates, man-like primates, australopithecines, the first human-like hominids, Neanderthal man, modern humans, cave art and agriculture.

NCERT Section 7.1: pathogens; typhoid, pneumonia, common cold, malaria and its parasite’s life cycle, amoebiasis, ascariasis, filariasis, ringworm; hygiene and vector control.

NCERT Section 7.2: innate and acquired immunity, antibodies (H_₂L_₂), humoral and cell-mediated responses, active and passive immunity, vaccines, allergy, lymphoid organs.

NCERT Section 7.3: HIV as a retrovirus, its four routes of spread, reverse transcriptase, macrophages and helper T-cells, ELISA and the prevention of AIDS.

NCERT Section 7.4: contact inhibition, benign and malignant tumors, metastasis, carcinogens and oncogenes, detection and the four approaches to treatment.

NCERT Section 7.5: opioids, cannabinoids, coca alkaloids, tobacco and nicotine, adolescence, addiction and dependence, effects, misuse in sports and prevention.

NCERT Section 8.1: lactic acid bacteria and curd, fermented dough for idli, dosa and bread, toddy and other fermented foods, and the microbes in cheese.

NCERT Section 8.2: fermentors, fermented beverages, antibiotics and the discovery of penicillin, organic acids, enzymes, streptokinase, cyclosporin A and statins.

NCERT Section 8.3: primary and secondary treatment of sewage, flocs, BOD, activated sludge, anaerobic sludge digesters and the Ganga and Yamuna Action Plans.

NCERT Section 8.4: biogas, methanogens and their anaerobic life, cattle dung (gobar) as raw material, and how a biogas plant works.

NCERT Section 8.5: biocontrol in organic farming, ladybirds and dragonflies, Bt and Bt-cotton, the fungal biocontrol agent, baculoviruses and IPM.

NCERT Section 8.6: biofertilisers from bacteria, fungi and cyanobacteria, covering symbiotic and free-living nitrogen fixers, mycorrhiza and phosphorus, and cyanobacteria in paddy fields.

NCERT Section 9.1, with the chapter opening: biotechnology and the EFB definition, genetic and bioprocess engineering, the origin of replication, the first recombinant DNA.

NCERT Section 9.2: restriction enzymes and their names, palindromes and sticky ends, gel electrophoresis, cloning vectors, pBR322, insertional inactivation, competent hosts.

NCERT Section 9.3: isolating DNA, cutting it, PCR and its three steps, insertion into the host, obtaining the product, bioreactors and downstream processing.

NCERT Section 10.1, with the chapter opening: options for food production, tissue culture and micropropagation, virus-free meristems, somatic hybrids, GM crops, Bt cotton, RNAi.

NCERT Section 10.2: recombinant therapeutics, genetically engineered insulin and the C peptide, gene therapy for ADA deficiency, and molecular diagnosis by PCR, probes and ELISA.

NCERT Section 10.3: what transgenic animals are, which animals have been made, NCERT’s five reasons for making them, alpha-1-antitrypsin and Rosie the transgenic cow.

NCERT Section 10.4: why biotechnology needs regulation, GEAC, patents on biological resources, the Basmati rice patent, biopiracy and the Indian Patents Bill.

Organisms and populations for Class 12 Biology and NEET: birth and death rates, age pyramids, exponential and logistic growth and the six interactions.

NCERT Section 12.1 with the chapter opening: what an ecosystem is, its types, abiotic and biotic components, species composition, stratification, the four functions and the pond.

NCERT Section 12.2: primary production and productivity, GPP and NPP, secondary productivity, the factors that set productivity, and why oceans produce less than land.

NCERT Section 12.3: detritus and detritivores, fragmentation, leaching, catabolism, humification and mineralisation, the decomposition cycle, and what speeds or slows decay.

NCERT Section 12.4: PAR, producers and consumers, grazing and detritus food chains, food webs, trophic levels, standing crop and the 10 per cent law.

NCERT Section 12.5: pyramids of number, biomass and energy with NCERT Figure 12.4’s values, upright and inverted pyramids, trophic levels as functional levels, and limitations.

NCERT Section 13.1 with the chapter opening: levels of biodiversity, species counts, India as a mega diversity country, latitudinal and species–area patterns, importance and loss.

NCERT Section 13.2: why we conserve biodiversity, in situ and ex situ conservation, hotspots, protected areas, sacred groves and the two world summits.