MATHEMATICS
a. COMPLEX NUMBER
Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a
complex number. cube roots of unity, triangle inequality.
b. MATRICES AND DETERMINANTS
Determinants and matrices of order two and three- properties of determinants, evaluation of
determinants, addition and multiplication of matrices, adjoint and inverse of a matrix. Solution of
simultaneous linear equations using determinants.
c. QUADRATIC EQUATIONS
Quadratic equations and their solutions, relation between roots and coefficients, nature of roots,
formation of quadratic equations with given roots.
d. PERMUTATIONS AND COMBINATIONS
Fundamental principle of counting; permutation as an arrangement and combination as a selection,
meaning of P(n, r) and C(n, r), simple applications.
e. SEQUENCES AND SERIES
Arithmetic, Geometric and Harmonic progressions. Relation between A.M., G.M. and H.M.. Special series’
∑n, ∑ n2, ∑n3, Arithmetico-Geometric series, exponential and logarithmic series.
f. VECTOR ALGEBRA
Vectors and scalars, addition of two vectors, components of a vector in two and three dimensional space,
scalar and vector products, scalar and vector triple products. Application of vectors to plane geometry.
g. TRIGONOMETRY
Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties
of triangles including centroid, incentre, circumcentre and orthocentre. Solution of triangles. Heights and
distances.
h. MEASURES OF CENTRAL TENDENCY AND DISPERSION
Calculation of mean, median and mode, standard deviation, variance and mean deviation for grouped and
ungrouped data.
i. PROBABILITY
Probability of an event, addition and multiplication theorems of probability and their applications.
Conditional probability; Bayes’ theorem. Probability distribution of a random variate- Binomial and Poisson
distributions and their properties.
j. DIFFERENTIAL CALCULUS
Polynomial, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions.
Limits, continuity and differentiation of the sum, difference, product and quotient of two functions.
Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit
functions; derivatives of order up to two. Applications of derivatives-maxima and minima of functions of
one variable, tangents and normals, Rolle’s and Lagrange’s mean value theorems.
k. INTEGRAL CALCULUS
Integral as an anti derivative, fundamental integrals involving algebraic, trigonometric, exponential and
logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using
trigonometric identities. Integral as a limit of sum. Properties of definite integrals. Evaluation of definite
integral, determining areas of the regions bounded by simple curves.
l. DIFFERENTIAL EQUATIONS
Formation of differential equations. Solutions of first order differential equations- the method of
separation of variables, homogeneous and linear differential equations.
m. TWO DIMENSIONAL GEOMETRY
Review of cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle,
condition for the collinearity of three points, slope of a line, parallel and perpendicular lines, intercepts
of a line on the coordinate axes.
n. THE STRAIGHT LINE AND PAIR OF STRAIGHT LINES
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for
concurrence of three lines, distance of a point from a line. Equations of internal and external bisectors of
angles between two lines, equation of a family of lines passing through the point of intersection of two
lines, point of intersections and angles between two lines. Pair of straight lines- condition for the general
second degree equation to represent a pair of lines, point of intersection and angle between pair of lines
through the origin, combined equation of the bisectors of the angles between a pair of lines,
o. CIRCLES AND FAMILY OF CIRCLES
Equation of a circle- standard form, general form, parametric form, equation of a circle when the end
points of a diameter are given. Radius and centre of a circle, points of intersection of a line and a circle.
Condition for a line to be tangent, equation of a family of circles through the intersection of two circles,
condition for two intersecting circles to be orthogonal.
p. CONIC SECTIONS
Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms,
conditions for a line to be a tangent and point(s) of tangency.
PHYSICS
a. UNITS AND DIMENSIONS
Units for measurement, system of units, SI, fundamental and derived units, dimensions and their
applications
b. MECHANICS
Motion in straight line, uniform and non-uniform motion, uniformly accelerated motion and its applications
Scalars and Vectors, and their properties; resolution of vectors, scalar and vector products; uniform circular
motion and its applications, projectile motion
Newton’s Laws of motion; conservation of linear momentum and its applications, laws of friction, Concept
of work, energy and power; energy-kinetic and potential; conservation of energy; different forms of energy.
Elastic collisions in one and two dimensions.
Center of mass of a many particle system; center of mass of a rigid body, rotational motion and torque.
Angular momentum and its conservation. Moments of inertia, parallel and perpendicular axes theorem,
moment of inertia for a thin rod, ring, disc and sphere.
Gravitation: Acceleration due to gravity and its properties. One and two dimensional motion under gravity.
Universal law of gravitation, planetary motion, Kepler’s laws, artificial satellite-geostationary satellite,
gravitational potential energy near the surface of earth, gravitational potential and escape velocity.
c. SOLIDS AND FLUIDS
Solids: Elastic properties, Hooke’s law, Young’s modulus, bulk modulus, modulus of rigidity.Liquids:
Cohesion and adhesion; surface energy and surface tension; flow of fluids, Bernoulli’s theorem and its
applications; viscosity, Stoke’s Law, terminal velocity
d. OSCILLATIONS AND WAVES
Periodic motion, simple harmonic motion and its equation, oscillations of a spring and simple pendulum.
Wave motion, properties of waves, longitudinal and transverse waves, superposition of waves, Progressive
and standing waves. Free and forced oscillations, resonance, vibration of strings and air columns, beats,
Doppler effect
e. HEAT AND THERMODYNAMICS
Thermal expansion of solids, liquids and gases and their specific heats, relationship between Cp and Cv for
gases, first and second laws of thermodynamics , Carnot cycle, efficiency of heat engines. Transference of
heat; thermal conductivity; black body radiations, Kirchoff’s law, Wein’s Law, Stefan’s law of radiation and
Newton’s law of cooling.
f.ELECTROSTATICS,CURRENT ELECTRICITY AND MAGNETOSTATICS
Coloumb’s law, dielectric constant, electric field, lines of force, field due to dipole , electric flux, Gauss’s
theorem and its applications; electric potential, potential due to a point charge; conductors and insulators,
distribution of charge on conductors; capacitance, parallel plate capacitor, combination of capacitors,
energy stored in a capacitor
Electric current : Cells -primary and secondary, grouping of cells; resistance and specific resistivity and its
temperature dependence. Ohm’s law, Kirchoff’s Law. Series and parallel circuits; Wheatstone’s Bridge and
potentiometer with their applications.
Heating effects of current, electric power, concept of thermoelectricity-Seebeck effect and thermocouple;
chemical effect of current- Faraday’s laws of electrolysis.
Magnetic effects: Oersted’s experiment, Biot Savert’s law, magnetic field due to straight wire, circular loop
and solenoid, force on a moving charge in a uniform magnetic
field(Lorentz force),forces and torques on a current carrying conductor in a magnetic field, force between
current carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter
Magnetostatics: Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field,
earth’s magnetic field; para, dia and ferro magnetism, magnetic induction, magnetic susceptibility
g. ELECTROMAGNETIC INDUCTION AND ELECTROMAGNETIC WAVES
Induced e.m.f., Faraday’s law, Lenz’s law, self and mutual inductance; alternating currents, impedance and
reactance, power in ac; circuits with L C and R series combination, resonant circuits, transformer and AC
generator. Electromagnetic waves and their characteristics; electromagnetic spectrum from gamma to
radio waves.
h. RAY AND WAVE OPTICS
Reflection and refraction of light at plane and curved surfaces, total internal reflection; optical fiber;
deviation and dispersion of light by a prism; lens formula, magnification and resolving power; microscope
and telescope Wave nature of light, interference, Young’s double experiment; thin films, Newton’s rings.
Diffraction: diffraction due to a single slit; diffraction grating, polarization and applications.
i. MODERN PHYSICS
Charge on an electron, photoelectric effect, Alpha particle scattering experiment, atomic masses, size of
the nucleus; radioactivity, alpha, beta and gamma particles/rays. Radioactive decay law, half life and mean
life of radio active nuclei; Nuclear binding energy, mass energy relationship, nuclear fission and nuclear
fusion. Energy bands in solids, conductors, insulators and semiconductors, pn junction, diode, diode as a
rectifier, transistor action, transistor as an amplifier.
CHEMISTRY
a. BASIC CONCEPTS
Atomic and molecular masses; Chemical Equation and stoichiometry.
b. STATES OF MATTER
Gaseous State: Gas laws, Avogadro’s hypothesis and gas equations; Kinetic Theory of Gases;
Liquefaction, Critical Phenomena; Liquid State and Solid state.
c. ATOMIC STRUCTURE
Bohr’s Model; de Broglie equation; Quantum Mechanical Model; Aufbau’s Principle, Pauli’s Exclusion
Principles, Hund’s Rule, Electronic Configuration; Bonding: Lewis structure, SEPR theory, hybridization,
ionic, covalent and coordinate covalent bonds, bonding in solid state, MO theory, bond order and
magnetic properties of H2, O2, N2, F2.
d. SOLUTIONS
Types, Units of concentration, Raoult’s Law, colligative properties, abnormal molecular weights.
e. CHEMICAL ENERGETICS AND THERMODYNAMICS
internal Energy, Enthalpy, Hess’s Law, First & Second Laws of thermodynamics & applications; entropy,
free energy; spontaneity of a chemical reaction.
f. CHEMICAL KINETICS & CHEMICAL EQUILIBRIUM
Rate and orders of a reaction; activation energy; catalyst; Rate law; physical & chemical equilibria;
Le Chateliers’s principle; acid base equilibrium; acids and bases; pH; buffers; solubility product.
g. REDOX REACTIONS, ELECTROCHEMISTRY & SURFACE CHEMISTRY
Electron Transfer Concepts of Oxidation and reduction; Electrochemical cells; emf; Nernst Equation;
Molar conductivity; Kohlrausch’s Law; Fuel Cells; Corrosion. Physical & Chemical adsorbtion isotherms;
Colloids: Preparation & properties; Homogenous and Hetrogenous Catalysis; Enzymes.
h. PERIODIC PROPERTIES, CHEMICAL FAMILIES, CHEMISTRY OF NON METALS & METALS
Modern Periodic Law; Ionization Energy, Electron Affinity, Atomic Radii, Valency, Trends in Groups and
periods. Chemistry of s and p block elements; Alkali metals, Alakaline Earth metals, Boron, Carbon,
Nitrogen, Oxygen Halogen and Noble gases families; Hydrogen: Position, Ortho para, Isotopes, hybrids;
Oxygen, Water, Hydrogen peroxide, Hard & Soft water; Ammonia, Nitrogen oxides, Nitric acid; Boron,
Boric Acid, Borax; Carbides, Allotropy of Carbon; Sodium, Magnesium, Copper, Silver, Zinc, Transition
Metals, and Lanthanides: Extraction, properties and uses.
i. CO-ORDINATION CHEMISTRY
Nomenclature, isomerism and bonding in coordination compounds; Werner’s Theory.
j. NUCLEAR CHEMISTRY
Radioactivity, Nuclear reactions, Radiocarbon dating, Radioactive series, Artificial Transmutation.
k. ORGANIC CHEMISTRY FUNDAMENTALS
Purification; detection and estimation of elements; Empirical and Molecular formulae,
Classification, Functional Groups, IUPAC Nomenclature, Hemolytic and Heterolytic Bond
Fissions, Structural and Stereoisomerisms, Free radicals, Carbocations and carbanions; Substitution,
addition, elimination and rearrangement reactions.
l. HYDROCARBONS & HALO ALKANES & HALO ALKENES
Alkanes, Alkenes and Alkynes, Halo alkanes & Halo alkenes: Preparation, properties and uses; Aromatic
Hydrocarbons: Benzene, Structure, Resonance, Substitution in Benzene.
Petroleum: Cracking, reforming, Octane number.
m. ORGANIC COMPOUNDS CONTAINING OXYGEN, NITROGEN
Preparation properties and uses of Aromatic and aliphatic alcohols, Polyhydric alcohols, ethers,
aldehydes, ketones, carboxylilc acids and their derivatives; Cyanides, isocyanides, nitro compounds and
amines.
n. SYNTHEIC AND NATURAL POLYMERS & BIOMOLECULES
Natural and Synthetic polymers; Teflon, PVC, Polystyrene, Nylon 66 Terylene, and Bakelite;
carbohydrates, amino acids and peptides, Nucleic Acids, lipds etc.
o. CHEMISTRY IN ACTION & ENVIRONMENTAL CHEMISTRY
Dyes, Medicines (Antipyretics, Analgesics and Antibiotics), Rocket Propellants; Acid Rain, Ozone Hole,
Green House Effect, Global Warming Industrial Pollution.