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Basic Mathematical Concepts: Differential equations, vectors, and matrices.

Atomic Structure: Fundamental particles. Bohr's theory of hydrogen atom; Wave-particle duality; Uncertainty principles; Schrodinger's wave equation; Quantum numbers, shapes of orbitals; Hund's rule and Pauli's exclusion principle.

Theory of Gases: Kinetic theory of gases. Maxwell-Boltzmann distribution law; Equipartition of energy.

Chemical Thermodynamics: Reversible and irreversible processes; First law and its application to ideal and non-ideal gases; Thermochemistry; Second law; Entropy and free energy, Criteria for spontaneity.

Chemical and Phase Equilibria: Law of mass action; Kp , Kc, Kx and Kn; Effect of temperature on K; Ionic equilibria in solutions; pH and buffer solutions; Hydrolysis; Solubility product; Phase equilibria–Phase rule and its application to one-component and two-component systems; Colligative properties.

Electrochemistry: Conductance and its applications; Transport number; Galvanic cells; EMF and Free energy; Concentration cells with and without transport; Polarography.

Chemical Kinetics: Reactions of various order, Arrhenius equation, Collision theory; Theory of absolute reaction rate; Chain reactions – Normal and branched chain reactions; Enzyme kinetics; photochemical processes; Catalysis.

Basic Concepts in Organic Chemistry and Stereochemistry: Isomerism and nomenclature, electronic (resonance and inductive) effects. Aromaticity and Huckel's rule. Optical isomerism in compounds containing one and two asymmetric centres, designation of absolute configuration, conformations of cyclohexanes.

Organic Reaction Mechanism and Synthetic Applications: Methods of preparation and reactions of alkanes, alkenes, alkynes, arenes and their simple functional derivatives. Mechanism and synthetic applications of electrophilic aromatic substitution. Stereochemistry and mechanism of aliphatic nucleophilic substitution and elimination reactions. Diels-Alder reactions, Wittig Reactions, Mechanism of aldol condensation, Claisen condensation, esterification and ester hydrolysis, Cannizzaro reaction, benzoin condensation. Perkin reaction, Claisen rearrangement, Beckmann rearrangement and Wagner-Meerwein rearrangement. Synthesis of simple molecules using standard reactions of organic chemistry. Grignard reagents, acetoacetic and malonic ester chemistry.

Introduction to the following classes of compounds-alkaloids, terpenes, carbohydrates, amino acids, peptides and nucleic acids.

Heterocyclic Chemistry: Furans, thiophenes, pyrrols and pyridines.

Qualitative Organic Analysis: Functional group interconversions, structural problems using chemical reactions, identification of functional groups by chemical tests.

Periodic Table: Periodic classification of elements and periodicity in properties; general methods of isolation and purification of elements.

Chemical Bonding and Shapes of Compounds: Types of bonding; VSEPR theory and shapes of molecules; hybridization; dipole moment; ionic solids; structure of NaCl, CsCl, diamond and graphite; lattice energy.

Main Group Elements (s and p blocks): Chemistry with emphasis on group relationship and gradation in properties; structure of electron deficient compounds of main group elements and application of main group elements.

Transition Metals (d block): Characteristics of 3d elements; oxide, hydroxide and salts of first row metals; coordination complexes; VB and Crystal Field theoretical approaches for structure, colour and magnetic properties of metal complexes. Ligands with back bonding capabilities; molecular orbital theory approaches to explain bonding in metal-carbonyl and metal-phosphine complexes.

Analytical Chemistry: Principles of qualitative and quantitative analysis; acid-base, oxidation-reduction and EDTA and precipitation reactions; use of indicators; use of organic reagents in inorganic analysis; radioactivity; nuclear reactions; applications of isotopes. 

2) TIFR (Tata Institute of Fundamental Research)
The syllabus for the written test in Chemistry is similar to the typical standard syllabus followed in any Indian university for the B.Sc. and M.Sc. degree course. The questions are aimed at testing the basic understanding and knowledge in the areas of physical, organic, inorganic, analytical, electro and quantum chemistry, biophysics , thermodynamics, spectroscopy (NMR, fluorescence, IR, UV and X-ray), logic and statistics and mathematical methods. 

3) IISc. (Chemical Sciences)
Chemical Sciences question paper will consist of multiple choice questions for 100 marks from Chemistry, Physics and Mathematics with greater emphasis on Chemistry. These will be negative marking for wrong answer. 

Valency, Equivalent weight, periodic classification of elements, Atomic structure, Isotopes, Radioactivity, Electronegativity, Hybridisation, Oxidation states.  Compounds of Main Group elements; preparation, structures and Reactivity.
Transition metals; Electronic structure, magnetic and spectral properties of metal complexes. Stability, structure and reactivity of coordination compounds. 
Main Ores and Minerals, Principles of extraction of metals like Cu, Au, Na, Zn, Mg, and Al. Iron and Steel manufacture. Common chemical processes used in industry. 

Principles of Analytical Chemistry, Qualitative analysis and quantitative estimation of elements and groups. 

The laws of Thermodynamics, Thermodynamic functions, Kinetic theory of gases, Specific heats, Adiabatic and isothermal processes, Liquids, The solid state, x-ray Diffraction, Mixtures and solutions, colligative properties, chemical Equilibrium, phase rule. Thermochemistry, Electrochemistry, Reaction Kinetics. Surface and Colloid Chemistry. Catalysis, use of catalysis, use of catalysts in important industrial processes, Mathematics and Physics essential for Physical Chemistry. 

Geometric and optical isomerism in organic molecules. Preparation and reactions of alkanes, alkenes, alkynes, alcohols, alky halides, amines, ethers and carbonyl compounds. 
Aromatic ring systems, aromatic animes and nitro derivatives, phenols, Heterocyclinc systems, Carbohydrates Oils, Fats, Soaps and detergents, Aminoacids, Proteins, enzymes, dyes, drugs, synthetic and natural polymers. 
Basic reaction mechanism : SN1, SN2, E1 and E2 reactions, Free radical reactions, Markownikoff rule, Electrophilic aromatic substitution. 
Synthetic uses of Grignard reactions, reactions involving acetoacetic ester and malonic ester.



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