Topic

Subtopics

Sets, Relations and Functions

Sets and their representation; Union, intersection, complement of sets and their properties; Power set; Relations, types of relations, equivalence relations, functions; one-one, into, onto functions, composition of functions

Complex Numbers and Quadratic Equations

Complex numbers as ordered pairs of reals, representation of complex numbers in the form a + ib, Argand diagram, algebra of complex numbers, modulus and argument, quadratic equations, relations between roots and coefficients, nature of roots, formation of quadratic equations with given roots

Matrices and Determinants

Matrices and their algebra, types of matrices, determinants (order 2 and 3), evaluation of determinants, area of triangles using determinants; Adjoint and inverse of matrices, test of consistency, solution of linear equations using matrices

Permutations and Combinations

Fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r), simple applications

Binomial Theorem and its Applications

Binomial theorem for positive integral index, general term, middle term, and simple applications

Sequence and Series

Arithmetic and Geometric progressions, insertion of arithmetic and geometric means, relation between A.M and G.M

Limit, Continuity and Differentiability

Real-valued functions, polynomial, rational, trigonometric, logarithmic, exponential functions; Limits, continuity, differentiability; Derivatives, applications of derivatives

Integral Calculus

Integral as anti-derivative, fundamental integrals, integration by substitution, parts, partial fractions; definite integrals, areas bounded by curves

Differential Equations

Ordinary differential equations, their order and degree, solutions by separation of variables, homogeneous and linear differential equations

Coordinate Geometry

Cartesian system of coordinates, distance formula, section formula, slope of line, parallel and perpendicular lines, intersection of lines, centroid, orthocenter, circumcenter, equation of a circle and conic sections

Three-Dimensional Geometry

Coordinates in space, distance between points, section formula, direction ratios and cosines, angle between intersecting lines, skew lines, shortest distance between lines

Vector Algebra

Vectors and scalars, vector addition, components in 2D and 3D, scalar and vector products

Statistics and Probability

Measures of dispersion (mean, median, mode), standard deviation, variance, probability (addition, multiplication theorems, Bayes’ theorem, distribution of random variable)

Topic

Subtopics

UNITS AND MEASUREMENTS

Units of measurements, System of units, SI Units, fundamental and derived units, least count, significant figures, errors in measurements. Dimensions of physical quantities, dimensional analysis and its applications.

KINEMATICS

Frame of reference, motion in a straight line, speed and velocity, uniform and non-uniform motion, average speed and instantaneous velocity, uniformly accelerated motion, velocity-time and position-time graph, relations for uniformly accelerated motion, relative velocity. Motion in a plane, projectile motion, uniform circular motion.

LAWS OF MOTION

Force and inertia, Newton’s first law of motion, momentum, Newton’s second law of motion, impulse, Newton’s third law of motion. Law of conservation of linear momentum and its applications, equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion, centripetal force and its applications: vehicle on a level circular road, vehicle on a banked road.

WORK, ENERGY AND POWER

Work done by a constant force and a variable force, kinetic and potential energies, work-energy theorem, power. The potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces, motion in a vertical circle. Elastic and inelastic collisions in one and two dimensions.

ROTATIONAL MOTION

Centre of mass of a two-particle system, centre of mass of a rigid body. Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications. The moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Equilibrium of rigid bodies, rigid body rotation, and equations of rotational motion, comparison of linear and rotational motions.

GRAVITATION

Universal law of gravitation, acceleration due to gravity and its variation with altitude and depth. Kepler’s laws of planetary motion. Gravitational potential energy, gravitational potential, escape velocity, motion of a satellite, orbital velocity, time period, and energy of satellites.

PROPERTIES OF SOLIDS AND LIQUIDS

Elastic behavior, stress-strain relationship, Hooke's Law, Young's modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column, Pascal's law and its applications, effect of gravity on fluid pressure, viscosity, Stoke’s law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's principle and its applications. Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, applications of surface tension: drops, bubbles, capillary rise. Heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, latent heat. Heat transfer: conduction, convection, and radiation.

THERMODYNAMICS

Thermal equilibrium and temperature concept, Zeroth law of thermodynamics, heat, work, and internal energy. First law of thermodynamics, isothermal and adiabatic processes. Second law of thermodynamics: reversible and irreversible processes.

KINETIC THEORY OF GASES

Equation of state of a perfect gas, work done on compressing a gas, assumptions of the kinetic theory of gases, pressure concept, kinetic interpretation of temperature, RMS speed of gas molecules, degrees of freedom, law of equipartition of energy and applications to specific heat capacities of gases, mean free path, Avogadro's number.

OSCILLATIONS AND WAVES

Oscillations and periodic motion: time period, frequency, displacement as a function of time, periodic functions. Simple harmonic motion (S.H.M.) and its equation, phase, oscillations of a spring, restoring force, and force constant, energy in S.H.M.: kinetic and potential energies, simple pendulum time period. Wave motion: longitudinal and transverse waves, speed of the travelling wave, displacement relation for a progressive wave, superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, beats.

ELECTROSTATICS

Electric charges, conservation of charge, Coulomb's law, forces between two-point charges, forces between multiple charges, superposition principle, continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, torque on a dipole in a uniform electric field. Electric flux, Gauss's law and its applications, electric potential, potential difference, equipotential surfaces, energy of system of charges, capacitors, capacitance, series and parallel combinations of capacitors, energy stored in capacitors.

CURRENT ELECTRICITY

Electric current: drift velocity, mobility, Ohm's law, electrical resistance, I-V characteristics of Ohmic and non-ohmic conductors, electrical energy and power, electrical resistivity and conductivity, series and parallel combinations of resistors, temperature dependence of resistance. Internal resistance, potential difference and emf of a cell, combination of cells, Kirchhoff’s laws, Wheatstone bridge, Metre Bridge.

MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

Biot-Savart law, Ampere's law, force on moving charges, force on current-carrying conductor, force between parallel currents, torque experienced by a current loop in a magnetic field, moving coil galvanometer, magnetic dipole moment, bar magnet equivalent solenoid, magnetic field lines, magnetic field due to a magnetic dipole, para-, dia- and ferromagnetic substances, effect of temperature on magnetic properties.

ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Faraday's law, induced emf and current, Lenz’s law, eddy currents, self and mutual inductance. Alternating currents, peak and RMS values, LCR series circuit, resonance, power in AC circuits, watt-less current, AC generator, and transformer.

ELECTROMAGNETIC WAVES

Displacement current, electromagnetic waves, their characteristics, transverse nature, electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, Gamma rays), applications of electromagnetic waves.

OPTICS

Reflection of light, spherical mirrors, mirror formula, refraction, thin lens formula, total internal reflection, magnification, power of a lens, combination of thin lenses, refraction of light through a prism, microscope and astronomical telescope, magnifying powers. Wave optics: Huygens principle, interference, Young's double-slit experiment, diffraction, polarization, Brewster's law, uses of polarized light, and Polaroid.

DUAL NATURE OF MATTER AND RADIATION

Dual nature of radiation, photoelectric effect, Einstein's photoelectric equation, matter waves, de-Broglie relation.

ATOMS AND NUCLEI

Alpha-particle scattering experiment, Rutherford's model, Bohr model, hydrogen spectrum, composition and size of nucleus, atomic masses, mass-energy relation, mass defect, binding energy per nucleon, nuclear fission and fusion.

ELECTRONIC DEVICES

Semiconductors, diode: I-V characteristics, diode as a rectifier, LED, photodiode, solar cell, Zener diode as a voltage regulator. Logic gates (OR, AND, NOT, NAND, NOR).

EXPERIMENTAL SKILLS

Familiarity with basic approach and observations of various experiments including Vernier calipers, screw gauge, simple pendulum, Young's modulus, surface tension, coefficient of viscosity, speed of sound, specific heat capacity, resistivity of wire, Ohm’s law, galvanometer, focal length, characteristic curves of p-n junction diode, Zener diode, and more.

Subject

Topic

Subtopics

Physical Chemistry 

Some Basic Concepts in Chemistry

Matter and its nature, Dalton's atomic theory, laws of chemical combination, mole concept, molar mass, empirical and molecular formulae, chemical equations, stoichiometry

Atomic Structure

Electromagnetic radiation, photoelectric effect, Bohr model, quantum mechanical model, quantum numbers, shapes of orbitals, electron configuration, Hund's rule, Pauli exclusion principle

Chemical Bonding and Molecular Structure

Ionic and covalent bonds, lattice enthalpy, electronegativity, VSEPR theory, hybridization, molecular orbital theory, metallic bonding, hydrogen bonding

Chemical Thermodynamics

First and second laws, Hess's law, spontaneity, Gibbs free energy, heat capacity, enthalpy changes

Solutions

Concentration methods, Raoult’s Law, colligative properties, molecular mass determination, abnormal molar mass, van’t Hoff factor

Equilibrium

Dynamic equilibrium, Le Chatelier’s principle, chemical equilibrium, acid-base equilibria, solubility products, buffer solutions

Redox Reactions and Electrochemistry

Oxidation-reduction, electrochemical cells, Nernst equation, Galvanic cells, dry cells, lead accumulator, fuel cells

Chemical Kinetics

Rate of reactions, factors affecting reaction rate, order and molecularity, Arrhenius theory, activation energy, collision theory

Inorganic Chemistry

Classification of Elements and Periodicity in Properties

Modern periodic law, atomic and ionic radii, ionization energy, electron gain enthalpy, chemical reactivity, trends across periods and groups

p-Block Elements

Group 13 to Group 18 elements, properties and trends, behavior of first element in each group

d- and f-Block Elements

Transition elements, lanthanoids, actinoids, properties and trends, preparation and uses of K2Cr2O7, KMnO4

Coordination Compounds

Werner's theory, ligands, coordination number, bonding theories (Valence Bond and Crystal Field), isomerism, applications of coordination compounds

Organic Chemistry

Purification and Characterisation of Organic Compounds

Crystallization, distillation, sublimation, chromatography, detection of nitrogen, sulphur, phosphorus, and halogens

Some Basic Principles of Organic Chemistry

Tetravalency of carbon, hybridization, isomerism, nomenclature, electronic displacement in covalent bonds, organic reaction types

Hydrocarbons

Classification, preparation, properties, and reactions of alkanes, alkenes, alkynes, and aromatic hydrocarbons

Organic Compounds Containing Halogens

Preparation, properties, reactions, mechanisms of halogenation, environmental effects of chloroform, iodoform, DDT

Organic Compounds Containing Oxygen

Alcohols, phenols, ethers, aldehydes, ketones, carboxylic acids, their properties and reactions

Organic Compounds Containing Nitrogen

Amines, diazonium salts, their preparation, properties, and uses

Biomolecules

Carbohydrates

Classification, aldoses and ketoses, monosaccharides, disaccharides, oligosaccharides

Proteins

α-amino acids, peptide bond, polypeptides, structure (primary, secondary, tertiary, quaternary), enzymes

Vitamins

Classification and functions

Nucleic Acids

DNA and RNA structure, biological functions

Hormones

General introduction and functions

Principles Related to Practical Chemistry

Qualitative and Quantitative Analysis

Detection of elements and functional groups, organic and inorganic analysis, empirical and molecular formulae calculations

Chemistry Involved in Preparation

Preparation of Mohr’s salt, potash alum, acetanilide, iodoform, titrimetric exercises

Qualitative Salt Analysis

Cations (Pb²⁺, Cu²⁺, Fe³⁺, etc.), anions (CO₃²⁻, SO₄²⁻, Cl⁻, etc.)

Experiments

Enthalpy of solution, neutralization, preparation of lyophilic and lyophobic sols, kinetic study of iodide reaction with hydrogen peroxide

Subject

Sub-Topics

Grammar and Language Use

Core Grammar Concepts

Tenses and verb forms, subject-verb agreement, articles and determiners, prepositions and conjunctions

Advanced Grammar Skills

Clauses, conditional sentences, types of sentences, error detection, and sentence correction

Vocabulary

Contextual Vocabulary

Synonyms and antonyms, one-word substitutions, commonly confused pairs of words, collocations, and phrasal verbs

Idiomatic Usage

Idioms

Punctuation and Usages

Punctuation Marks

Commas, semicolons, colons, dashes, capitalisation

Usage and Sentence Clarity

Identification of incorrect usage, improvement of sentences, avoiding redundancy and ambiguity, avoiding run-on sentences and fragments

Reading Comprehension

Comprehension Skills

Understanding and interpreting diverse texts, identifying main ideas and supporting details, drawing inferences and conclusions, vocabulary in context, critical reasoning, and evaluating arguments

Types of Passages

Narrative, descriptive, expository, argumentative

Particulars

Details

Test Mode 

Computer-based Test (Online)

Test Duration 

120 minutes 

Total Questions

60 

Maximum Marks 

240 

Multiple Choice Questions (MCQs)

Mathematics - 15

Physics - 10

Chemistry - 10 

English - 10 

Numerical Answer Type (NAT) 

Mathematics - 5

Physics - 5 

Chemistry - 5