# Syllabus

Syllabus

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## (Syllabus) ISAT 2012 Syllabus - Mathematics

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## PERMUTATIONS AND COMBINATIONS:

Fundamental principle of counting. Permutations and Combinations, derivation of formulae and their connections and simple applications.

## MATHEMATICAL INDUCTION:

Principle of Mathematical Induction and its simple applications.

## BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for positive integral indices, general term and middle term, properties of Binomial coefficients and simple applications.

## SEQUENCES AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series n, n2, n3. Arithmetico - Geometric sequence.

## TRIGONOMETRY:

Trigonometric functions. Trigonometrical identities and equations. Inverse Trigonometric functions, their properties and applications.

## COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals. Representation of complex numbers in a plane. Argand plane and polar representation of complex numbers. Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality. Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

## (Syllabus) ISAT 2012 Syllabus - Chemistry

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## INORGANIC CHEMISTRY:

Basic Concepts of Chemistry: particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: concept of elements, atoms and molecules. atomic and molecular masses, molecular formula, stoichiometry. Structure of Atom: atomic number, isotopes and isobars. different atomic models and limitations, shells and sub-shells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, orbitals, quantum numbers, shapes of s, p, and d orbitals, Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

Classification of Elements and Periodicity in Properties : periodic table, periodic trends in properties of elements Chemical Bonding and Molecular Structure: valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, hybridization involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules Hydrogen: Occurrence, isotopes, preparation, properties and uses of hydrogen and its compounds. s-Block Elements (Group 1 and Group 2 elements): electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties and in chemical reactivity, uses. preparation and properties of compounds of Na, Ca, Mg and their biological importance.

p-Block Elements : general Introduction to p-Block Elements Elements of Group 13, 14 15,16, 17and 18: electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group. chemical and physical properties of boron, aluminium, carbon, silicon, nitrogen, phosphorous, oxygen, sulphur, halogens and important compounds of the elements. d and f Block Elements : electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals. General Principles and Processes of Isolation of Elements : concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron. Lanthanides: electronic configuration, oxidation states, chemical reactivity and lanthanide contraction.

Actinides: electronic configuration, oxidation states. Coordination compounds: Ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding; isomerism, importance of coordination compounds.

## PHYSICAL CHEMISTRY:

States of Matter : three states of matter, intermolecular interactions, type of bonding, melting and boiling points, molecular, ionic, covalent and metallic solids, amorphous and crystalline solids, unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Boyle’s law, Charles’ law, Gay Lussac’s law, Avogadro’s law, ideal behaviour, empirical derivation of gas equation, Avogadro’s number, ideal gas equation, deviation from ideal behaviour, liquefaction of gases, critical temperature. liquid State.

Solutions : types of solutions, solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses

Thermodynamics : systems, surroundings, work, heat, energy, extensive and intensive properties, state functions. first law of thermodynamics – internal energy and enthalpy, heat capacity and specific heat, measurement of ΔU and ΔH, Hess’s law of constant heat summation, enthalpy of: bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionization, and dilution. entropy as a state function, free energy change for spontaneous and nonspontaneous process, equilibrium.

Equilibrium : equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – onization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts, buffer solutions, solubility product, common ion effect. Redox Reactions : redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

## (Syllabus) ISAT 2012 Syllabus - Physics

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## MECHANICS:

Units and Measurements: The international system of units, measurement of length, mass and time, accuracy, precision of instruments and errors in measurement, Significant figures, dimension of physical quantities, dimensional formulae and equations, dimensional analysis and its applications. Motion in a straight line: position, path length and displacement, average velocity and speed, instantaneous velocity and speed, acceleration, kinematic equations for uniformly accelerated motion, relative velocity.

Motion in a plane: scalars and vectors, multiplication of vectors by real numbers, addition and aubtraction of ectors- graphical method, resolution of vectors, vector addition – analytical method, motion in a plane, motion in a plane with constant acceleration, relative velocity in two dimensions, projectile motion, uniform circular motion.

Laws of motion: the law of inertia, Newton’s first, second and third law of motion, conservation of momentum, equilibrium of particle, common forces in mechanics,circular motion. Work, Power and Energy: the work energy theorem, kinetic and potential energy, work-energy theorem for variable force, the conservation of mechanical energy, Power, the potential energy of a spring, collisions.

System of particles and rotational motion: centre of mass, motion of centre of mass, linear momentum of a system of particles, vector product of two vectors, angular velocity and linear velocity relations, torque and angular momentum, equilibrium of a rigid body, Moment of Inertia, theorem of perpendicular and parallel axes, kinematics and dynamics of rotational motion about a fixed axis, angular momentum in case of rotation about a fixed axis, rolling motion Gravitation: Kepler’s laws, universal law of gravitation, gravitation constant, acceleration due to gravity of the earth, acceleration due to gravity below and above the surface of earth, gravitational potential energy.

## ELETROMAGNETISM:

Electric charges and Fields: Electric charges, conductors and insulators, basic properties of electric charge, Coulomb’s law, Force between multiple charges, electric field and flux, electric dipole, continuous charge distribution, Gauss’s law and its applications.

Electrostatic Potential and capacitance: electrostatic potential, potential due to a point charge and systems of charges, potential due to an electric dipole, equipotential surfaces, Potential energy in an external field, electrostatics of conductors, dielectric and polarization, capacitors and capacitance, the parallel  plate capacitor, combination of capacitors, energy stored in a capacitor. Current Electricity: electric current, electric currents in conductors, Ohm’s law, drift of electrons and origin of resistivity, resistivity and its temperature dependence, electrical energy and power, Combination of resistors (Series and Parallel) , cells, emf, internal resistance, cells in series and parallel, Kirchoff’s laws, Wheatstone bridge, meter bridge, and potentiometer.