BL - Biological Sciences
Biological Sciences question paper will be fully of objective type. There will be negative marking (one third) for wrong answer.
General Biology
Taxonomy and physiology, Pro-and eukaryotic organisms; cell organelles
and their function; multi cellular organisation; energy transformations;
internal transport systems of plants; respiration; regulation of body
fluids and excretory mechanisms; cellular reproduction; Mendelian
genetics and heredity; biology and populations and communities;
evolution; genesis and diversity of organisms; animal behavior, 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, nervous system, nucleic acids, nature
of gene and its function, Genetic code, synthesis of nucleic acids and
proteins. Enzyme mechanisms and kinetics, nucleic acid metabolism, photo
synthesis.
Structure of bio molecules; intra and inter molecular forces;
thermodynamics and kinetics of biological systems, principles of x-ray
diffraction, IR and UV spectroscopy and hydrodynamic techniques.
Microbiology, Cell Biology and Immunology
Classes of microorganisms and their characterization, nutrient
requirement for growth; laboratory techniques in microbiology,
pathogenic microorganisms and disease; applied microbiology; viruses,
Microbial genetics. Innate and adaptive immunity, antigen antibodies.
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.
Mathematical functions (algebraic, exponential, trigonometric), their
derivatives (derivatives and integrals of simple functions),
permutations and combinations.
BT - Biotechnology
The Biotechnology (BT) test paper comprises ofBiology (44%
weightage), Chemistry (20% weightage), Mathematics (18% weightage) and
Physics (18% weightage). The question paper will be fully of objective type. There will be negative marking (one third) for wrong answer.
BIOLOGY (10+2+3 level)
General Biology: Taxonomy; Heredity; Genetic variation; Conservation;
Principles of ecology; Evolution; Techniques in modern biology.
Biochemistry and Physiology:Carbohydrates; Proteins; Lipids; Nucleic
acids; Enzymes; Vitamins; Hormones; Metabolism-Glycolysis, TCA cycle,
Oxidative Phosphoryation; Photosynthesis. Nitrogen Fixation,
Fertilization and Osmoregulation; Vertebrates - Nervous system;
Endocrine system; Vascular system; Immune system; Digestive system and
Reproductive System. Basic Biotechnology: Tissue culture; Application of
enzymes; Antigen-antibody interaction; Antibody production; Diagnostic
aids. Molecular Biology: DNA; RNA; Replication; Transcription;
Translation; Proteins; Lipids and Membranes; Operon model; Gene
transfer. Cell Biology: Cell cycle; Cytoskeletal elements; Mitochondria;
Endoplasmic reticulum; Chloroplast; Golgi apparatus; Signaling.
Microbiology: Isolation; Cultivation; Structural features of virus;
Bacteria; Fungi; Protozoa; Pathogenic micro-organisms.
CHEMISTRY (10+2+3 level)
Atomic Structure: Bohr's theory and Schrodinger wave equation;
Periodicity in properties; Chemical bonding; Properties of s, p, d and f
block elements; Complex formation; Coordination compounds; Chemical
equilibria; Chemical thermodynamics (first and second law); Chemical
kinetics (zero, first, second and third order reactions);
Photochemistry; Electrochemistry; Acid-base concepts; Stereochemistry of
carbon compounds; Inductive, electromeric, conjugative effects and
resonance; Chemistry of Functional Groups: Hydrocarbons, alkyl halides,
alcohols, aldehydes, ketones, carboxylic acids, amines and their
derivatives; Aromatic hydrocarbons, halides, nitro and amino compounds,
phenols, diazonium salts, carboxylic and sulphonic acids; Mechanism of
organic reactions; Soaps and detergents; Synthetic polymers;
Biomolecules-amino acids, proteins, nucleic acids, lipids and
carbohydrates (polysaccharides); Instrumental techniques-chromatography
(TLC, HPLC), electrophoresis, UV-Vis, IR and NMR spectroscopy, mass
spectrometry.
MATHEMATICS (10+2 level)
Sets, Relations and Functions, Mathematical Induction, Logarithms,
Complex numbers, Linear and Quadratic equations, Sequences and Series,
Trigonometry, Cartesian System of Rectangular Coordinates, Straight
lines and Family, Circles, Conic Sections, Permutations and
Combinations, Binomial Theorem, Exponential and Logarithmic Series,
Mathematical Logic, Statistics, Three Dimensional Geometry, Vectors,
Matrices and Determinants, Boolean Algebra, Probability, Functions,
limits and Continuity, Differentiation, Application of Derivatives,
Definite and Indefinite Integrals, Differential Equations.
PHYSICS (10+2 level)
Physical World and Measurement, Elementary Statics and Dynamics,
Kinematics, Laws of Motion, Work, Energy and Power, Electrostatics,
Current electricity, Magnetic Effects of Current and Magnetism,
Electromagnetic Induction and Alternating Current, Electromagnetic
waves, Optics, Dual Nature of Matter and Radiations, Atomic Nucleus,
Solids and Semiconductor Devices, Principles of Communication, Motion of
System of Particles and Rigid Body, Gravitation, Mechanics of Solids
and Fluids, Heat and Thermodynamics, Oscillations, Waves.
CY - Chemistry
HYSICAL CHEMISTRY
Basic Mathematical Concepts: Functions, maxima and minima, integrals,
ordinary differential equations, vectors and matrices, determinants,
elementary statistics and probability theory.
Atomic and Molecular Structure: Fundamental particles, Bohr's theory of
hydrogen-like atom; wave-particle duality; Uncertainty principle;
Schrodinger's wave equation; Quantum numbers, shapes of orbitals; Hund's
rule and Pauli's exclusion principle, electronic configuration of
simple homonuclear diatomic molecules.
Theory of Gases: Equation of state of ideal and nonideal (van der Waals)
gases, Kinetic theory of gases. Maxwell-Boltzmann distribution law;
equipartition of energy. Solid state: Crystals, crystal systems, X-rays,
NaCl and Kcl structures, close packing, atomic and ionic radii, radius
ratio rules, lattice energy, Born-Haber cycle, isomorphism, heat
capacity of solids.
Chemical Thermodynamics: Reversible and irreversible processes; First
law and its application to ideal and nonideal 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; Concentration cells with and without
transport; Debey-Huckel-Onsagar theory of strong electrolytes.
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.
Adsorption: Gibbs adsorption equation, adsorption isotherm, types of
adsorption, surface area of adsorbents, surface films on liquids.
ORGANIC CHEMISTRY
Basic Concepts in Organic Chemistry and Stereochemistry: Electronic
effect (resonance, inductive, hyperconjugation) and steric effects and
its applications (acid/base property). Optical isomerism in compounds
without any stereocenters (allenes, biphenyls), conformation of acyclic
systems (substituted ethane/n-propane/n-butane) and cyclic systems (mono
and di substituted cyclohexanes).
Organic Reaction Mechanism and Synthetic Applications: Chemistry
reactive intermediates, carbine, nitrene, benzyne,
Hofmann-Curtius-Lossen rearrangement, Wolf rearrangement, Simmons-Smith
reaction, Reimer- Tiemann reaction, Michael reaction, Darzens reaction,
Witting reaction, McMurry reaction. Pinacol-pinacolone, Favorskii,
benzilic acid rearrangement, dienonc-phenol rearrangement,
Bayer-Villeger reaction). Oxidation and reduction reactions in organic
chemistry. Organometallic reagents in organic synthesis (Grignard and
organocopper). Diels-Alder reaction, Sigmatropic reactions.
Qualitative Organic Analysis: Functional group interconversions,
structural problems using chemical reactions, identification of
functional groups by chemical tests, elementary 1H NMR and IR
spectroscopy as a tool for structural elucidation.
Natural Products Chemistry : Introductory chemistry of alkaloids,
terpenes, carbohydrates, amino acids, peptides and nucleic acids.
Heterocyclic Chemistry: Monocyclic compounds with one hetero atom.
INORGANIC CHEMISTRY
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 groupelements 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. Organometallic compounds, metal
carnonyls, nitrosyls and metallocenes, ligands with back bonding
capabilities; MO theory approaches to explain bonding in metal-carbonyl,
metal-nitrosyl and metalphosphine complexes.
Bioinorganic Chemistry: Essentials and trace elements of life, basic
reactions in the biological systems and the role of metal ions
especially Fe2+, Fe3+, Cu2+ and Zn2+, function of hemoglobin and
myoglobin.
Instrumental Methods of Analysis: Basic principles, instrumentations and
simple applications of conductometry, potentiometry, UV-vis
spectro-photometry, analysis of water, air and soil samples.
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.
CA - Computer Applications
The Computer Applications (CA) test paper comprisesof Mathematics,
Computer Awareness, and Analytical Ability and General Awareness and
they will be in the ratio 4:2:1. The question paper will be fully of
objective type. There will be negative marking (one third) for wrong
answer.
MATHEMATICS
Algebra: Set theory and its simple applications. Basic concepts of groups, fields and vector spaces.
Matrices: Rank of a matrix. Existence and uniqueness of solution of a
system of linear equations. Eigenvalues and Eigenvectors. Inverse of a
matrix by elementary transformations.
Differential Calculus: Differentiation, Partial differentiation,
Taylor series and approximate calculations. Maxima and minima of
functions of one and two variables.
Integral Calculus: Single and multiple integration. Definite
integrals, Change of order and change of variables. Applications to
evaluation of area, surface and volume.
Differential Equations: First order differential equations, linear differential equations of higher order with constant coefficients.
Vector Algebra: Addition, subtraction, dot product, cross product, triple product and their applications.
Numerical Analysis: Solution of non-linear equations using iterative
methods. Interpolation (Lagrange's formula and Newton's formula for
equidistant points). Numerical differentiation and integration
(Trapezoidal and Simpson's rules).
Probability: Basic concepts of probability theory. Binomial and Poisson distributions.
Linear Programming: Formulation and its graphical solution for two variable problems.
COMPUTER AWARENESS
Elements of computers. Number systems. Basic electronic gates. Boolean
algebra. Flip-Flops. Algorithmic approach to solve problems.
Fundamentals of C language.
ANALYTICAL ABILITY AND GENERAL AWARENESS
Simple questions will be asked to test the analytical ability and general awareness of candidates.
GG - Geology
The Planet Earth: Origin of the Solar System and theEarth;
Geosphere and the composition of the Earth; Shape and size of the earth;
Earth-moon system; Formation of continents and oceans; Dating rocks and
age of the Earth; Energy in the earth system; Volcanism and volcanic
landforms; Interior of earth; Earthquakes; Earth's magnetism and
gravity, Isostasy; Elements of Plate tectonics; Orogenic cycles.
Geomorphology: Weathering and erosion; Transportation and
deposition due to wind, ice, river, sea, and resulting landforms,
Structurally controlled landforms.
Structural Geology: Concept of stratum; Contour; Outcrop
patterns; Maps and cross sections; Dip and strike; Classification and
origin of folds, faults, joints, foliation and lineation,
unconformities; shear zones.
Palaeontology: Major steps in the evolution of life forms;
Fossils; their mode of preservation and utility; Morphological
characters, major evolutionary trends and ages of important groups of
animals - Brachiopoda, Mollusca, Trilobita, Graptolitoidea, Anthozoa,
Echinodermata; Gondwana plant fossils; Elementary idea of verterbrate
fossils in India.
Stratigraphy: Principles of stratigraphy; Litho-, chronoand
biostratigraphic classification; distribution and classification of the
stratigraphic horizons of India from Archaean to Recent.
Mineralogy: Symmetry and forms in common crystal classes;
Physical properties of minerals; Isomorphism and polymorphism,
Classification of minerals; Structure of silicates; Mineralogy of common
rock-forming minerals; Mode of occurrence of minerals in rocks.
Transmitted polarised light microscopy and optical properties of
uniaxial and biaxial minerals.
Petrology: Definition and classification of rocks; Igneous rocks -
forms of igneous bodies; Crystallization from magma; classification,
association and genesis of igneous rocks; Sedimentary rocks -
classification, texture and structure; size and shape of sedimentary
bodies. Metamorphic rocks - classification, facies, texture and
properties.
Economic Geology: Properties of common economic minerals; General
processes of formation of mineral deposits; Physical characters; Mode
of occurrence and distribution in India both of metallic and
non-metallic mineral deposits; Coal and petroleum occurrences in India.
Applied Geology: Ground Water; Mineral exploration, elements of Mining Geology and Environmental Geology; Principles of Engineering Geology.
GP - Geophysics
There will be Three Sections in the Geophysics (GP)test paper, namely,
Geology, Mathematics and Physics, each with a weightage of 50%. A
candidate has to attempt any Two Sections.
The syllabi for the Geology, Mathematics and Physics Sections of the Geophysics (GP) test paper are given below:
GEOLOGY SECTION
The Planet Earth: Origin of the Solar
System and the Earth; Geosphere and the composition of the earth; Shape
and size of the Earth; Earth-moon system; Formation of continents and
oceans; dating the rocks and age of the Earth; Energy in the earth
system; Volcanism and volcanic landforms; Interior of earth;
Earthquakes. Earth's magnetism and gravity, Elements of plate tectonics.
Geomorphology: Weathering and erosion;
transportation and deposition due to wind, ice, river, sea, and
resulting landforms, structurally controlled landforms.
Structural Geology: Concept of
stratum; Contour; Outcrop patterns; Maps and cross sections; Dip and
strike; classification and origin of folds, faults, joints, foliation
and lineation, unconformities; shear zones.
Mineralogy: Symmetry and forms in
common crystal classes; physical properties of minerals; Isomorphism and
polymorphism, Classification of minerals; Structure of silicates;
Mineralogy of common rock-forming minerals; Mode of occurrence of
minerals in rock. Transmitted polarised light microscopy and optical
properties of uniaxial and biaxial minerals.
Palaeontology: Major steps in the
evolution of life forms; Fossils; their mode of preservation and
utility; Morphological characters, major evolutionary trends and ages of
important groups of animals - Brachiopoda, Mollusca, Trilobita,
Graptolitoidea, Anthozoa, Echinodermata;
Stratigraphy: Principles of Stratigraphy, Geological Time Scale and ages of major stratigraphic units of India.
Petrology: Definition and
classification of rocks; Igneous rock-forms of igneous bodies;
Crystallisation from magma; classification, association and genesis of
igneous rocks; Sedimentary rocks-classification, texture and structure;
Metamorphic rocks-Classification, facies, texture and structure.
Economic Geology: Physical properties
of common ore minerals, General processes of formation of mineral
deposits; Mode of occurrence of important metallic and nonmetallic
deposits in India; Coal, petroleum and ground water occurrences in
India.
MATHEMATICS SECTION
Sequences, Series and Differential Calculus: Sequences of real numbers,
Convergent sequences and series. Mean Value Theorem, Taylor's theorem,
Maxima and Minima, functions of several variables.
Integral Calculus: Fundamental theorem
of calculus, Integration, Double and Triple integrals, change of order
of integration, Surface Areas and Volumes.
Differential Equations: Linear and
Non-linear ODE, existence and uniqueness (without proof), Linear
Differential Equations of second order with constant coefficients.
Vector Calculus: Gradient, Divergence, Curl, Laplacian, Green's, Stokes and Gauss theorems and their Applications.
Linear Algebra: System of Linear
Equations, Matrices, Rank, Determinant, Inverse, eigenvalues and
eigenvectros. Dimension, Linear transformations.
Probability: Probability spaces,
Conditional Probability, Independence, Bayes Theorem, Univariate and
Bivariate Random Variables, Moment Generating and Characteristic
Functions, Binomial, Poisson and Normal distributions.
Statistics: Sampling Distributions of
Sample Mean and Variance, Exact Sampling Distribution (Normal
Population), Simple and Composite hypothesis, Best critical region of a
Test, Neyman-Pearson theorem, Likelihood Ratio Testing and its
Application to Normal population, comparison of normal populations,
large sample theory of test of hypothesis, approximate test on the
parameter of a binomial population, comparison of two binomial
populations.
Numerical Analysis: Difference table,
symbolic operators, differences of a factorial, representation of a
polynomial by factorials. Forward, backward and central difference
approximation formulae. Simpson's one-third rule, Newton- Raphson method
for finding the solution of f(x)=0.
PHYSICS SECTION
Mechanics and General Properties of Matter:
Newton's laws of motion and applications, Kepler's laws, Gravitational
Law and field, Conservative and non-conservative forces. System of
particles, Centre of mass (CM), equation of motion of the CM,
conservation of linear and angular momentum, conservation of energy.
Elastic and inelastic collisions. Rigid body motion, fixed axis
rotations, rotation and translation, moments of Inertia and products of
Inertia. Principal moments and axes. Elasticity, Hookeâ™s law and
elastic constants of isotropic solid, stress energy. Kinematics of
moving fluids, equation of continuity, Euler's equation, Bernoulli's
theorem, viscous fluids, surface tension and surface energy,
capillarity.
Oscillations, Waves and Optics:
Differential equation for simple harmonic oscillator and its general
solution. Superposition of two or more simple harmonic oscillators.
Lissajous figures. Damped and forced oscillators, resonance. Wave
equation, travelling and standing waves in one-dimension. Energy density
and energy transmission in waves. Group velocity and phase velocity.
Sound waves in media. Doppler Effect. Fermat's Principle. General theory
of image formation. Thick lens, thin lens and lens combinations.
Interference of light, optical path retardation. Fraunhofer diffraction.
Rayleigh criterion and resolving power. Diffraction gratings.
Polarization: linear, circular and elliptic polarization. Double
refraction and optical rotation.
Electricity and Magnetism: Coulomb's
law, Gauss's law. Concept of Potential, Field and Boundary Conditions,
Solution of Laplace's equation for simple cases. Conductors, capacitors,
dielectrics, dielectric polarization, volume and surface charges,
electrostatic energy. Magnetic susceptibility, bar magnet, Earth's
magnetic field and its elements. Biot-Savart law, Ampere's law, Lenz's
law, Faraday's law of electromagnetic induction, self and mutual
inductance. Alternating currents. Simple DC and AC circuits with R, L
and C components. Displacement current, Maxwell's equations and plane
electromagnetic waves. Lorentz Force and motion of charged particles in
electric and magnetic fields.
Kinetic theory, Thermodynamics:
Elements of Kinetic theory of gases. Velocity distribution and
Equipartition of energy. Specific heat of Mono-, di- and tri-atomic
gases. Ideal gas, Van-der-Waals gas and equation of state. Mean free
path . Laws of thermodynamics. Zeroeth law and concept of thermal
equilibrium. First law of thermodynamics and its consequences.
Isothermal and adiabatic processes. Reversible, irreversible and
quasi-static processes. Second law of thermodynamics. Carnot cycle.
Modern Physics: Inertial frames and Galilean invariance. Postulates
of special relativity. Lorentz transformations. Length contraction,
time dilation. Relativistic velocity addition theorem, mass energy
equivalence. Blackbody radiation, photoelectric effect, Bohr's atomic
model, X-rays. Wave-particle duality, Uncertainty principle, Pauli
Exclusion Principle, Structure of atomic nucleus, mass and binding
energy. Radioactivity and its applications. Laws of radioactive decay
and half life, Fission and fusion.
Solid State Physics and Electronics:
Crystal structure, Bravais lattices and basis. Miller indices. X-ray
diffraction and Bragg's law, Origin of energy bands. Concept of holes.
Intrinsic and extrinsic semiconductors. p-n junctions, transistors.
Amplifier circuits with transistors.
MA - Mathematics
SEQUENCES, SERIES AND DIFFERENTIAL CALCULUS:
Sequences and Series of real numbers: Sequences and series of
real numbers. Convergent and divergent sequences, bounded and monotone
sequences, Convergence criteria for sequences of real numbers, Cauchy
sequences, absolute and conditional convergence; Tests of convergence
for series of positive terms - comparison test, ratio test, root test,
Leibnitz test for convergence of alternating series.
Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem. Maxima and minima.
Functions of two real variable: limit, continuity, partial
derivatives, differentiability, maxima and minima. Method of Lagrange
multipliers, Homogeneous functions including Euler's theorem.
Integral Calculus: Integration as the inverse process of
differentiation, definite integrals and their properties, Fundamental
theorem of integral calculus. Double and triple integrals, change of
order of integration. Calculating surface areas and volumes using double
integrals and applications. Calculating volumes using triple integrals
and applications.
Differential Equations: Ordinary differential equations of the
first order of the form y'=f(x,y). Bernoulli's equation, exact
differential equations, integrating factor, Orthogonal trajectories,
Homogeneous differential equations-separable solutions, Linear
differential equations of second and higher order with constant
coefficients, method of variation of parameters. Cauchy- Euler equation.
Vector Calculus: Scalar and vector fields, gradient, divergence,
curl and Laplacian. Scalar line integrals and vector line integrals,
scalar surface integrals and vector surface integrals, Green's, Stokes
and Gauss theorems and their applications.
Group Theory: Groups, subgroups, Abelian groups, non-abelian
groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's
Theorem for finite groups, group homomorphisms and basic concepts of
quotient groups (only group theory).
Linear Algebra: Vector spaces, Linear dependence of vectors,
basis, dimension, linear transformations, matrix representation with
respect to an ordered basis, Range space and null space, rank-nullity
theorem; Rank and inverse of a matrix, determinant, solutions of systems
of linear equations, consistency conditions. Eigenvalues and
eigenvectors. Cayley-Hamilton theorem. Symmetric, skewsymmetric,
hermitian, skew-hermitian, orthogonal and unitary matrices.
Real Analysis: Interior points, limit points, open sets, closed
sets, bounded sets, connected sets, compact sets; completeness of R,
Power series (of real variable) including Taylor's and Maclaurin's,
domain of convergence, term-wise differentiation and integration of
power series.
MS - Mathematical Statistics
The Mathematical Statistics (MS) test paper comprisesof Mathematics (40% weightage) and Statistics (60%weightage).
Mathematics:
Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
Differential Calculus: Limits, continuity and differentiability
of functions of one and two variables. Rolle's theorem, mean value
theorems, Taylor's theorem, indeterminate forms, maxima and minima of
functions of one and two variables.
Integral Calculus: Fundamental theorems of integral calculus.
Double and triple integrals, applications of definite integrals, arc
lengths, areas and volumes. Matrices: Rank, inverse of a matrix. systems
of linear equations. Linear transformations, eigenvalues and
eigenvectors. Cayley-Hamilton theorem, symmetric, skewsymmetric and
orthogonal matrices.
Differential Equations: Ordinary differential equations of the
first order of the form y' = f(x,y). Linear differential equations of
the second order with constant coefficients.
Statistics Probability: Axiomatic definition of probability and
properties, conditional probability, multiplication rule. Theorem of
total probability. Bayes' theorem and independence of events.
Random Variables: Probability mass function, probability density
function and cumulative distribution functions, distribution of a
function of a random variable. Mathematical expectation, moments and
moment generating function. Chebyshev's inequality.
Standard Distributions: Binomial, negative binomial, geometric,
Poisson, hypergeometric, uniform, exponential, gamma, beta and normal
distributions. Poisson and normal approximations of a binomial
distribution.
Joint Distributions: Joint, marginal and conditional
distributions. Distribution of functions of random variables. Product
moments, correlation, simple linear regression. Independence of random
variables.
Sampling distributions: Chi-square, t and F distributions, and their properties.
Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).
Estimation: Unbiasedness, consistency and efficiency of
estimators, method of moments and method of maximum likelihood.
Sufficiency, factorization theorem. Completeness, Rao-Blackwell and
Lehmann-Scheffe theorems, uniformly minimum variance unbiased
estimators. Rao-Cramer inequality. Confidence intervals for the
parameters of univariate normal, two independent normal, and one
parameter exponential distributions.
Testing of Hypotheses: Basic concepts, applications of
Neyman-Pearson Lemma for testing simple and composite hypotheses.
Likelihood ratio tests for parameters of univariate normal distribution.
PH - Physics
Mathematical Methods: Calculus of single and multiplevariables,
partial derivatives, Jacobian, imperfect and perfect differentials,
Taylor expansion, Fourier series. Vector algebra, Vector Calculus,
Multiple integrals, Divergence theorem, Green’s theorem, Stokes’
theorem. First order equations and linear second order differential
equations with constant coefficients. Matrices and determinants, Algebra
of complex numbers.
Mechanics and General Properties of Matter: Newton’s laws of
motion and applications, Velocity and acceleration in Cartesian, polar
and cylindrical coordinate systems, uniformly rotating frame,
centrifugal and Coriolis forces, Motion under a central force, Kepler’s
laws, Gravitational Law and field, Conservative and non-conservative
forces. System of particles, Centre of mass, equation of motion of the
CM, conservation of linear and angular momentum, conservation of energy,
variable mass systems. Elastic and inelastic collisions. Rigid body
motion, fixed axis rotations, rotation and translation, moments of
Inertia and products of Inertia, parallel and perpendicular axes
theorem. Principal moments and axes. Kinematics of moving fluids,
equation of continuity, Euler’s equation, Bernoulli’s theorem.
Oscillations, Waves and Optics: Differential equation for simple
harmonic oscillator and its general solution. Super-position of two or
more simple harmonic oscillators. Lissajous figures. Damped and forced
oscillators, resonance. Wave equation, traveling and standing waves in
onedimension. Energy density and energy transmission in waves. Group
velocity and phase velocity. Sound waves in media. Doppler Effect.
Fermat’s Principle. General theory of image formation. Thick lens, thin
lens and lens combinations. Interference of light, optical path
retardation. Fraunhofer diffraction. Rayleigh criterion and resolving
power. Diffraction gratings. Polarization: linear, circular and elliptic
polarization. Double refraction and optical rotation.
Electricity and Magnetism: Coulomb’s law, Gauss’s law. Electric
field and potential. Electrostatic boundary conditions, Solution of
Laplace’s equation for simple cases. Conductors, capacitors,
dielectrics, dielectric polarization, volume and surface charges,
electrostatic energy. Biot- Savart law, Ampere’s law, Faraday’s law of
electromagnetic induction, Self and mutual inductance. Alternating
currents. Simple DC and AC circuits with R, L and C components.
Displacement current, Maxwell’s equations and plane electromagnetic
waves, Poynting’s theorem, reflection and refraction at a dielectric
interface, transmission and reflection coefficients (normal incidence
only). Lorentz Force and motion of charged particles in electric and
magnetic fields.
Kinetic theory, Thermodynamics: Elements of Kinetic theory of
gases. Velocity distribution and Equipartition of energy. Specific heat
of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and
equation of state. Mean free path. Laws of thermodynamics. Zeroth law
and concept of thermal equilibrium. First law and its consequences.
Isothermal and adiabatic processes. Reversible, irreversible and
quasi-static processes. Second law and entropy. Carnot cycle. Maxwell’s
thermodynamic relations and simple applications. Thermodynamic
potentials and their applications. Phase transitions and
Clausius-Clapeyron equation. Ideas of ensembles, Maxwell-Boltzmann,
Fermi- Dirac and Bose-Einstein distributions.
Modern Physics: Inertial frames and Galilean invariance.
Postulates of special relativity. Lorentz transformations. Length
contraction, time dilation. Relativistic velocity addition theorem, mass
energy equivalence. Blackbody radiation, photoelectric effect, Compton
effect, Bohr’s atomic model, X-rays. Wave-particle duality, Uncertainty
principle, the superposition principle, calculation of expectation
values, Schrödinger equation and its solution for one, two and three
dimensional boxes. Solution of Schrödinger equation for the one
dimensional harmonic oscillator. Reflection and transmission at a step
potential, Pauli exclusion principle. Structure of atomic nucleus, mass
and binding energy. Radioactivity and its applications. Laws of
radioactive decay.
Solid State Physics, Devices and Electronics: Crystal structure,
Bravais lattices and basis. Miller indices. X-ray diffraction and
Bragg’s law; Intrinsic and extrinsic semiconductors, variation of
resistivity with temperature. Fermi level. p-n junction diode, I-V
characteristics, Zener diode and its applications, BJT: characteristics
in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled
amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal
oscillators. OPAMP and applications: Inverting and non-inverting
amplifier. Boolean algebra: Binary number systems; conversion from one
system to another system; binary addition and subtraction. Logic Gates
AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; combination of
gates; de Morgan’s theorem.
