No need to worry I will provide you Indian Institute of Science paper based entrance exam syllabus, so that you can prepare hard for it.

Here is the syllabus

Mathematics:
Real Analysis:-
Real valued functions of a real variable: continuity and differentiability, uniform convergence, sequences and series of real numbers and function, Riemann integration, fundamental theorem of integral calculus. Topology of R, Compactness and Connectedness.

Complex Analysis:-
Continuity and differentiability, analytic functions. Cauchy’s theorem, Cauchy’s integral formula. Laurent’s series,Taylor and Maclaurin expansions, singularities, theory of residues and contour integration, conformal mappings.

Linear Algebra:-
Vector Space: linear independence, basis, dimension, linear transformations and matrices, Systems of linear equations, rank and nullity, characteristic values and characteristic vectors, diagonalizability, Cayley-Hamilton theorem, characteristic and minimal polynomials, Jordan canonical form.

Abstract Algebra:-
Groups: subgroups. Lagrange’s theorem, normal subgroup, quotient group, permutation groups. Cayley’s theorems, homomorphisms, Sylow theorems, Rings, Ideals Fields.

Ordinary Differential Equations: –
First order ODEs and their solutions, singular solutions, existence and uniqueness of initial value problems for first order ODE. General theory of homogeneous and non-homogeneous linear differential equations. Variation of parameters. Types of singular points in the phase plane of an autonomous system of two equations.

Chemistry:

Structure and Bonding :- Atomic orbitals: electronic configuration of atoms (Aufbau principle); periodic properties of elements, chemical bonding, the concept of hybridization, molecular orbitals, electronic configuration of diatomic molecules, shapes of molecules and physical properties, bond angles, bond order and bond energies, bond length intermolecular forces, hydrogen bond, kinetic theory of gases, Solutions-Coligivative properties, activity coefficients; solids-types of solids, crystal structure and packing.


Spectroscopy: Principles of electronic, vibrational, rotational and magnetic resonance spectroscopy and mass spectrometry and their application to simple structural problems in chemistry. Dipole moment and molecular structure.


Chemical Energetics and Chemical Dynamics: Law of conservation of energy, enthalpy, entropy and free energy of chemical reaction, relationship between free energy change and equilibrium. Rates of chemical reactions, theories of chemical reactions and Arrhenius equation, homogeneous and heterogeneous catalysis, Electro-chemistry, strong and weak electrolytes, Debye-Huckel-Onsager treatment, Electrochemical cells. Electrode-electrolyte interface.


s, p, d, f, Block Elements and Coordination Compounds: General characteristics of each block, Nuclear Chemistry: Noble gas compounds, Lanthanides and actinides: Co-ordination compounds, Crystal and ligand field theories, Spectral and magnetic properties, Stereochemistry and isomerism.


Nomenclature of Organic Compounds and Stereo Chemistry of Organic Compounds: Compounds containing not more than three rings and three hetroatoms principles of chirality and optical activity, optical and geometrical isomerism, methods of resolution, conformational analysis of cyclohexanes.


Common Organic Reactions and Mechanisms : Formation, stability and structure of carbonium ions, carbanions and radicals: nucleophilic and electrophilic substitution and addition reactions, mechanism of SN1 and SN2reactions, the concept of aromaticity and characteristic reactions of aromatic compounds; elimination reactions, rearrangements such as Beckmann, Hoffman, Claisen, pinacol-pinacolone and benzidine rearrangement. Routine functional group transformations and interconversion of simple functionalities.


Biological Sciences:

Acids, Bases and solutions: Chemical reactions, Energy, Enzymes: Viruses. Prokaryotes and eukaryotes, Cellular organisation and function, Cell cycle, Genetic material, Inheritance, Vitamins and hormones, Body defence mechanisms, Evolution.


Structure of biomolecules: Viruses, bacteriophages, prokaryotic and eukaryotic cells, Nutrition and growth of prokaryotic and cukaryotic cells, Enzymes and enzyme kinetics, Intermediary metabolism and its regulation, Structure and function of cell membranes, Photosynthesis, Gene structure, expression and regulation, Transduction, conjugation and transformation, Recombinant DNA methodology Mutation and gene mapping: Micro-organisms and diseases: Environmental and industrial microbiology; Antimicrobial agents and their mode of action; Bio-geochemical cycles: Plant and animal hormones and their mode of action: Pathogens and host parasite relationships. Antibody structure and function; Humoral and cellular immune responses and their regulation, Morphogenesis and differentiation. Mechanisms and evolution of Animal behaviour; Systematics; Population dynamics and Community Ecology of plants and animals. Population Genetics, Basic Statistical Analysis. Basic statistics and Mathematics. Basic Principles in Evolutionary Biology

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080 2293 2004