Units of physical quantities, dimensional analysis, significant figures, measurement errors, vectors and scalars, vector addition and subtraction, dot product and cross product.

Motion in a straight line, equations of motion, projectile motion, relative velocity, uniform circular motion, motion in a plane.

First, second and third laws, friction (static, kinetic, rolling), free body diagrams, equilibrium of forces, pseudo forces in non-inertial frames.

Conservation of linear momentum, impulse-momentum theorem, elastic and inelastic collisions, centre of mass, rocket propulsion.

Work-energy theorem, kinetic and potential energy, conservation of mechanical energy, power, spring force, conservative and non-conservative forces.

Torque, moment of inertia, angular momentum, angular velocity and acceleration, rotational kinetic energy, rolling without slipping, parallel and perpendicular axis theorems.

Newton’s law of gravitation, gravitational acceleration (g), Kepler’s laws, satellite motion, geostationary and polar satellites, escape velocity, gravitational potential energy.

Elasticity (stress, strain, Young’s modulus, bulk modulus, shear modulus), fluid pressure, Archimedes’ principle, viscosity, Stokes’ law, surface tension, capillarity, Bernoulli’s theorem, equation of continuity.

Simple harmonic motion (SHM), amplitude, time period and frequency, spring-mass system, simple pendulum, energy in SHM, damped oscillations, forced oscillations, resonance.

Transverse and longitudinal waves, wave speed, superposition of waves, standing waves in strings and pipes, beats, Doppler effect.

Thermal expansion, specific heat, calorimetry, heat transfer (conduction, convection, radiation), zeroth and first law of thermodynamics, second law, Carnot cycle and efficiency, kinetic theory of gases, ideal gas laws, entropy.

Coulomb’s law, electric field and field lines, Gauss’s law, electric potential and potential energy, capacitors, dielectrics, energy stored in a capacitor, Van de Graaff generator.

Ohm’s law, drift velocity, resistivity, Kirchhoff’s laws (KCL, KVL), Wheatstone bridge, metre bridge, potentiometer, EMF and internal resistance, RC circuits.

Biot-Savart law, Ampere’s law, force on a current-carrying conductor, cyclotron, solenoid and toroid, bar magnet, Earth’s magnetic field, magnetisation, diamagnetism, paramagnetism, ferromagnetism.

Faraday’s laws, Lenz’s law, self and mutual inductance, AC circuits (LCR series), impedance, resonance, transformers, electromagnetic waves and spectrum.

Reflection (plane and curved mirrors), refraction (Snell’s law, total internal reflection), lens and mirror formulae, lens maker’s formula, optical instruments; Wave optics: interference, diffraction, polarisation, Young’s double slit experiment, Brewster’s law.

Photoelectric effect, de Broglie wavelength, Bohr’s model of hydrogen atom, X-rays, nuclear physics (radioactivity, alpha/beta/gamma decay, half-life, nuclear fission and fusion), mass-energy equivalence (E=mc²).

Semiconductors (intrinsic and extrinsic, p-type and n-type), p-n junction diode, rectifiers (half-wave and full-wave), Zener diode as voltage regulator, transistors (NPN and PNP in CE configuration), logic gates (AND, OR, NOT, NAND, NOR).

Gaseous state, ideal gas equation, real gas deviations (van der Waals equation), liquefaction of gases, solid state (crystal structures, lattice energy, point defects).

Thomson’s and Rutherford’s models, Bohr’s model of the atom, quantum mechanical model, quantum numbers, electronic configuration, Aufbau principle, Hund’s rule, Pauli’s exclusion principle, Heisenberg’s uncertainty principle.

Ionic bond, covalent bond, coordinate bond, VSEPR theory, hybridisation (sp, sp2, sp3, sp3d), molecular orbital theory (bonding/anti-bonding MOs), bond parameters, hydrogen bonding, van der Waals forces, dipole moment, resonance.

First and second laws of thermodynamics, enthalpy, entropy, Gibbs free energy, Hess’s law, spontaneity, heat of reaction, Born-Haber cycle.

Law of mass action, equilibrium constants (Kp, Kc), Le Chatelier’s principle, ionic equilibrium, acids and bases (Arrhenius, Bronsted-Lowry, Lewis), pH, buffer solutions, solubility product, hydrolysis of salts.

Electrochemical cells (galvanic and electrolytic), EMF, Nernst equation, Faraday’s laws of electrolysis, conductance and molar conductivity, batteries, fuel cells, corrosion.

Rate of reaction, rate law, order and molecularity, Arrhenius equation, activation energy, half-life, first-order reactions, collision theory, catalysis.

Properties and reactions of hydrogen, hydrides, alkali metals (Group 1), alkaline earth metals (Group 2), important compounds of Na, K, Ca, Mg (NaOH, Na2CO3, NaHCO3, CaO, Ca(OH)2).

Group 13 (boron family, borax, diborane), Group 14 (allotropes of carbon, silicates), Group 15 (nitrogen family, ammonia, HNO3), Group 16 (sulphur, ozone, H2SO4), Group 17 (halogens, haloacids), Group 18 (noble gases).

Transition metals (variable oxidation states, colour, magnetic properties, catalytic behaviour), coordination chemistry (IUPAC nomenclature, Werner’s theory, VBT, crystal field theory), lanthanides and actinides.

IUPAC nomenclature, structural and stereoisomerism, electronic effects (inductive, resonance, hyperconjugation), reaction intermediates (carbocations, carbanions, free radicals), reaction mechanisms (SN1, SN2, E1, E2, electrophilic addition), alkanes, alkenes, alkynes, aromatic hydrocarbons, electrophilic aromatic substitution, aromaticity.

Geometric isomerism (cis-trans), optical isomerism, chirality, chiral centres, R-S configuration, enantiomers, diastereomers, meso compounds, optical activity.

Alcohols, phenols, ethers (preparation, properties, reactions); aldehydes and ketones (nucleophilic addition, aldol condensation, Fehling’s and Tollens’ tests); carboxylic acids, esters, acid anhydrides; amines (Hinsberg test, Gabriel synthesis), amides, nitro compounds, diazonium salts (coupling reactions).

Carbohydrates (mono/di/polysaccharides), proteins (amino acids, peptide bonds, denaturation), nucleic acids (DNA, RNA, base pairing), lipids, vitamins, polymers (addition and condensation, natural and synthetic), dyes, drug chemistry, environmental pollution (air, water, soil, greenhouse effect, ozone depletion).

Volumetric analysis (acid-base, redox, and iodometric titrations), qualitative inorganic analysis (cation and anion identification in salt analysis), determination of melting and boiling points, chromatography (paper, TLC, column).

Complex numbers (Argand plane, modulus, argument, polar form, De Moivre’s theorem, nth roots of unity), quadratic equations (nature of roots, quadratic inequalities), arithmetic and geometric progressions (sum formulas, infinite GP), permutations and combinations, binomial theorem (general term, middle term, properties of coefficients), matrices (operations, inverse, rank), determinants (up to 3×3, Cramer’s rule), mathematical induction.

Trigonometric functions and identities, compound and multiple angle formulas, sum-to-product and product-to-sum formulas, general solutions of trigonometric equations, inverse trigonometric functions (domain, range, principal values), properties of triangles (sine rule, cosine rule, area formulas), heights and distances.

Straight lines (slope-intercept, intercept, normal, parametric forms; angle between lines; distance from a point to a line; family of lines), pair of straight lines, circles (standard and general equations; tangents, normals, chords; chord of contact; power of a point; radical axis; family of circles), parabola, ellipse, hyperbola (eccentricity, foci, directrix, tangent conditions, asymptotes), conic sections.

Direction cosines and direction ratios, equations of lines and planes in 3D (vector and Cartesian forms), angle between line and plane, distance of a point from a plane, skew lines, shortest distance between two lines.

Limits (algebraic, trigonometric, L’Hopital’s rule), continuity and differentiability at a point and on an interval, first and second derivatives, chain rule, product and quotient rules, implicit and parametric differentiation, logarithmic differentiation; Applications: tangents and normals, increasing and decreasing functions, maxima and minima (first and second derivative tests), Rolle’s theorem, mean value theorem, approximate values using differentials.

Indefinite integration (standard forms, substitution method, integration by parts, partial fractions, reduction formulae), definite integration (properties, Leibniz rule, evaluation), area bounded by curves and coordinate axes, area between two curves, fundamental theorem of calculus.

Order and degree, formation of differential equations, solution methods: variable separable, homogeneous equations, linear first-order DE (integrating factor method).

Classical probability, addition and multiplication theorems, conditional probability, Bayes’ theorem, independent events, random variables, binomial distribution (mean and variance), expected value.

Vectors and scalars, position vectors, unit vectors, vector addition and subtraction, dot product (scalar product), cross product (vector product), scalar triple product (volume of parallelepiped, coplanarity), applications in geometry (area of triangle and parallelogram).

Measures of central tendency (mean, median, mode — ungrouped and grouped data), measures of dispersion (variance, standard deviation, mean deviation), Karl Pearson’s correlation coefficient, basic regression lines.

Linear inequalities in two variables, feasible region (bounded and unbounded), corner point method, maximisation and minimisation of objective function, real-world LP problems.

Formulation of real-world mathematical models, growth and decay models (population, radioactive decay), applications of differential equations in science and engineering problems.

Articles, prepositions, all 12 tenses, concord (subject-verb agreement), modifiers (dangling and misplaced), reported speech, active and passive voice, parts of speech, conjunctions, parallelism, error spotting.

Synonyms, antonyms, phrasal verbs, idioms and phrases, one-word substitution, contextual word usage, word analogies, commonly confused words (affect/effect, etc.).

Unseen passages (100–150 words, factual or literary), main idea identification, inference questions, tone and attitude of the author, title selection, specific detail questions.

Sentence completion, jumbled paragraphs (sentence ordering), paragraph coherence, cloze tests (fill-in-the-blanks in a paragraph context).

Letter analogies, number analogies, word analogies, semantic analogies, symbolic analogies; odd-one-out (classification by letters, numbers, words, or concepts).

Alphabet series, number series, mixed letter-number series, next term or missing term identification.

Statements and conclusions, syllogisms, logical arguments, assertion and reason, chart logic (reading and inferring from simple charts or data tables).

Series of figures (identify next in sequence), figure matrix (3×3 grid — find missing figure), figure analogy (A is to B as C is to ?).

Mirror images, water images, paper folding and cutting, embedded figures, figure completion, mental rotation, cube and dice problems, dot situation.