As you want to get the details of Indian Institute of Science PhD entrance exam syllabus so here it is for you:

BIOLOGICAL SCIENCES
Biological Sciences question paper will be fully of objective type. There will be negative marking for wrong answer.

SYLLABUS

General Biology

Taxonomy and physiology, Pro-and eukaryotic organisms; cell organelles and their function; multicellular organisation; energy transformations; internal transport systems of plants; respiration; regulation of body fluids and excretory mechanisms; cellular reproduction; Mendolian genetics and heredity; biology of populations and communities: evolution; genesis and diversity of organisms; animal behaviour; plant and animal diseases.

Basics of Biochemistry, Biophysics, Molecular Biology
Buffers; trace elements in biological systems; enzymes and proteins; vitamins: biological oxidations, carbohydrates and lipids and their metabolisms; digestion and absorption: detoxifying mechanisms; plant and animal hormones and their action, neuromuscular systems, nucleic acids, nature of gene and its function, Genetic code, synthesis of nucleic acids and proteins.
Structure of biomolecules; intra and intermolecular forces; thermodynamics and kinetics of biological systems, principles of x-ray diffraction, IA and UV spectroscopy and hydrodynamic techniques.

Microbiology and Cell Biology
Classes of microorganisms and their characterization, nutrient requirements for growth; laboratory techniques in microbiology, pathogenic microorganisms and disease; applied microbiology: viruses, Microbial genetics.
Cell theory : Cell architecture; methods of cell fractionation; cell division; types of chromosome structure; biochemical genetics-inborn errors of metabolisms; viruses and fungi; principles of processes of development.

CHEMICAL SCIENCES
Chemical Sciences question paper will consist of multiple choice question for 100 marks from Chemistry. Physics and Mathematics with greater emphasis on Chemistry. There will be negative marking for wrong answer.

SYLLABUS

General and Inorganic Chemistry

Valency, Equivalent weight, periodic classification of elements. Atomic structure, Isotopes, Raidoactivity, 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 exatraction of metals like Cu, Au, Na. Zn. Mg, and Al. Iron and Steel manufacture. Common chemical processes used in industry.

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

Physical Chemistry
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 catalysts in important industrial processes. Mathematics and Physics essential for Physical Chemistry.

Organic 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 animas and nitro derivatives, phenols. Heterocyclinc systems, Carbohydrates, Oils, Fats, Soaps and detergents, Aminoacids, Proteins, enzymes, dyes, drugs, synthetic and natural polymers.
Basic reaction mechanisms : SN1, SN2, El and E2 reactions, Free radical reactions, Markownikoff rule, Electrophilic aromatic substitution.
Synthetic uses of Grignard reactions, reactions involving acetoacetic ester and malonic ester.

PHYSICAL SCIENCES
Physical Sciences question paper will consist of multiple choice question for 100 marks. There will be negative marking for wrong answer.

SYLLABUS

Mechanics

Newtonian mechanics of a system of particles. Conservation of energy and momentum, collisions, simple harmonic motion, static equilibrium of a rigid body, rotational dynamics, angular momentum, gravitation, Kepler’s laws.
Properties of Matter
Stress and strain, elastic properties of solids, elastic modulii; Hydrostatics, elements of fluid mechanics, surface, tension and viscosity.

Wave Motion
Wave propagation, phase and group velocities, standing waves, Fourier analysis, sound as elastic waves, interference and diffraction of sound waves, Doppler effect.

Thermal Physics
Kinetic theory of gases, the Maxwell-Boltzmann distribution, thermal properties of ideal and real gases, liquids and solids, laws of thermodynamics, entropy, reversible and irreversible processes, Carnot cycle, heat engines, changes of phase, blackbody radiation, the Stefan-Boltzmann law. Planck’s law.

Electromagnetism, Electronics and Optics
Electric field and potential, Gauss law, Laplace and Poisson equations, electrostatic equilibrium, capacitance, dielectrics, electrostatic energy:
The magnetic field, magnetic forces on moving changes and current carrying wires, the Biot-Savart law, electromagnetic induction and Faraday’s law, magnetic susceptibility and permeability, direct and alternating current circuits, Maxwell’s equations, electromagnetic waves;
Semiconductors junctions, principles of rectification and amplification.
Reflection, refraction and polarisation of light, ray optics, thin lenses, aberrations, interference and diffraction of light, optical instruments.
Modern Physics Frames of reference, time dilation and length contraction, simultaneity, the Lorentz transformation, relativistic energy and momentum, mass-energy relation;
The photoelectric effect, the Compton effect, atomic spectra, wave-particle dualism, the wave function and its interpretation, the uncertainty principle, the Schrodingor equation.
Atomic structure, the Pauli exclusion principle, periodic classification of elements, spin of electrons, the Zeeman effect; generation and diffraction of x-rays, radioactivity, nucleus-constituents, binding, nuclear reactions, fission and fusion, nuclear reactors, particle accelerators, cosmic rays.

Experiments and Measurements
Errors in measurement, accuracy, measurements of length, mass and charge of small and large objects, fundamental constants. Basic knowledge of scientific instruments and their working.

Mathematical Physics
Theory of Systems of linear Equation. Linear algebra and matrices. Series and their convergence.
Limits and continuity, differentiation and integration, Taylor’s expansion, L’Hospital rule, maxima, minima. Analytical geometry of curves and surfaces. Ordinary (first and second order) differential equations. Complex numbers, roots of complex numbers, trigonometric identities, Argand’s diagram. Vector addition and products, gradient, divergence and curl, Gauss and Stokes theorems. Probability, basic laws of probability, mean, standard deviation.

MATHEMATICAL SCIENCES
Mathematical Sciences question paper will consist of multiple choice questions for 100 marks from mathematics. There will be negative marking for wrong answer.

SYLLABUS

Algebra

Theory of Equations Relations between roots and Coefficients. Newton’s identities. Rolle’s theorem, Reciprocal Equations, Des Cartes, Rule of Signs, Cubic and quark equations, Complex numbers and De Moivre’s Theorem. Determinants Cofactors, Properties of determinants, Solution of a Linear System, Cramer’s Rule. Inequalities AM-GM inequality, Cauchy-Schwarz inequality. Set Theory : Relations, Functions, Cardinality. Algebraic Structures Binary Operations, Groups, Rings: Definitions, Examples and Elementary Theorems. Vector Spaces Subspaces, Linear Independence, Bases, Dimension Linear Transformations, Matrices, Rank Nullity, Eigen values and Eigen vectors.

Geometry :
Two-dimensional Coordinate Geometry
Conics and their equations in Cartesian and Polar Coordinates, Ellipse, Parabola and Hyperbola.
Three-dimensional Co-ordinate Geometry
Planes, Lines, Spheres and Cones.

Vector Algebra and Vector Calculus :
Vectors, addition, Scalar multiplication. Dot Product, Cross Product, Triple Product, Equations to the Line and the Plane. Grad, Divergence and Curl, Vector Integration, Green’s Gauss’ and Stokes’ Theorems.

Calculus and Analysis
Real Number System, Sequence and Series. Continuity, Differentiability. Mean Value Theorems, Indeterminate Value Theorem, L’Hospital Rule, Tangents and Normals, Maxima and Minima. Riemann Integration, Multiple Integrals, Partial differentiations, Lengths, areas and volumes by integration.

Differential Equations
First Order ODE Method of Separation of Variables: Exact equations: Euler’s equation: Orthogonal Family of curves, Second Order Linear ODE : Variation of Parameters.