The questions for Biological Sciences (BL), Biotechnology (BT) and Computer Applications (CA) test papers will be fully objective type. There will be negative marking for wrong answers to the objective type questions in BL, BT and CA test papers. Candidates will get negative 1/3 for a wrong answer. These test papers have to be answered in an Objective Response Sheet (ORS) by

darkening appropriate bubbles using a black ink ball point pen. Since the ORS will be evaluated by electronic means, it is imperative that the instructions given on the ORS are carefully read and followed by the candidates.

All other test papers will be objective-cum-descriptive type. There will be a “question-cum-answer booklet” for each of these six test papers. Answers to various questions are to be given at appropriate places in the “question-cumanswer booklet” itself. No supplementary sheet will be provided. Each of these six test papers will have multiple choice type questions(MCQ), fill-in-blank type questions, and descriptive type questions, carrying weightages of 20%, 30% and 50%, respectively. The objective type questions in these test papers will have four choices as possible answers, of which, only one will be correct. There will be negative marking for wrong answers to the objective type questions. Each objective type question carries 02 marks for a correct answer and negative 0.50 marks for a wrong answer. There will be no negative marking for fill-in-the-blank type questions.

(a) Use of any kind of cellular phone/ electronic gadgets (other than non-programmable calculator) is NOT permitted in the examination hall.

(b) Use of calculator (non programmable) is permitted.

(c) All answers to the subjective type questions must be written in blue/ black/ blue-black ink only. Sketch pen, pencil or ink of any other colour is not permitted.

(d) The medium for all the test papers will be English only.

(e) Use of unfair means by a candidate in JAM 2013, whether detected at the time of test, evaluation or at any other stage, will lead to cancellation of his/her candidature as well as disqualification of the candidate from appearing in JAM in future.

(f) Disclosure of identity in any form, such as writing registration number or name inside the question-cumanswer booklet, or making any kind of distinguishing marks, may lead to disqualification of the candidate.

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Integrated Ph.D. in Biological Sciences

Bachelor’s degree in Biology or Chemistry or Physics or Mathematics. The candidates should have passed Biology at the Higher Secondary (10+2) level.

Integrated Ph.D.in Chemical Sciences

B.Sc. or an equivalent degree with Chemistry as one of the subjects. The candidates should have passed mathematics at the PUC or +2 level.

M.Sc.- Ph.D. Dual Degree in Biotechnology

Bachelor’s degree in any branch of Science/ Agriculture / Pharmacy / Veterinary / Engineering / Medicine (MBBS).The candidate should have passed Mathematics at the (10+2) level.

Integrated Ph.D. in Biological Sciences

Bachelor’s degree in Biology or Chemistry or Physics or Mathematics. The candidates should have passed Biology at the Higher Secondary (10+2) level.

M.Sc. Biotechnology, M.Sc.- Ph.D. Dual Degree in Biotechnology

Bachelor’s degree in any branch of Science/ Agriculture / Pharmacy / Veterinary / Engineering / Medicine (MBBS).

NOTE: For IITB only, M.Sc. Biotechnology and M.Sc.-Ph.D. Dual Degree in Biotechnology, the candidate should have passed Mathematics at the (10+2) level.

M.Sc.- Ph.D. Dual Degree in Environmental Science & Engineering

Bachelor’s degree with any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. The candidate should have passed Mathematics at (10 + 2) level.

Integrated Ph.D. in Chemical Sciences

B.Sc. or an equivalent degree with Chemistry as one of the subjects. The candidates should have passed mathematics at the PUC or +2 level.

Integrated Ph.D. in Biological Sciences

Bachelor’s degree in Biology or Chemistry or Physics or Mathematics. The candidates should have passed Biology at the Higher Secondary (10+2) level.

Joint M.Sc.-Ph.D. Programme in Chemistry, M.Sc. Chemistry, M.Sc.- Ph.D. Dual Degree Programme in Chemistry

Bachelor’s degree with Chemistry as a subject for three years/six semesters and should have passed Mathematics at (10+2) level.

M.Sc.- Ph.D. Dual Degree Programme in Energy

Bachelor’s degree with any one of Chemistry, Mathematics and Physics for two years/four semesters and any one of the remaining two subjects for at least one year/ two semesters.

M.Sc.- Ph.D. Dual Degree in Environmental Science & Engineering

Bachelor’s degree with any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. The candidate should have passed Mathematics at (10 + 2) level.

M.Sc.- Ph.D. Dual Degree in Biotechnology

Bachelor’s degree in any branch of Science/ Agriculture / Pharmacy / Veterinary / Engineering / Medicine (MBBS).The candidate should have passed Mathematics at the (10+2) level.

Computer Applications (CA)

Master of Computer Applications

Bachelor’s degree with Mathematics as a subject for at least one year for annual system candidates/ at least two papers of Mathematics for semester system candidates.

Joint M.Sc.-Ph.D. Programme in Earth Science, M.Sc. Applied Geology, Joint M.Sc.- Ph.D. Programme in Geology, M.Tech. in Geological Technology, M.Sc.- Ph.D. Dual Degree Programme in Applied Geology

Bachelor’s degree with Geology as a subject for three years/six semesters and any two

subjects among Mathematics, Physics, Chemistry, and Biological Sciences. The candidate should have passed Mathematics at

(10+2) level.

M.Sc. Applied Geophysics, M.Sc.- Ph.D. Dual Degree Programme in Applied Geophysics

Bachelor’s degree with both Mathematics and Physics as subjects for two years and at least one of them as a subject for three years.

M.Tech. in Geophysical Technology

Bachelor’s degree with Mathematics and Physics as subjects and anyone of the following subjects: Chemistry, Geology, Statistics,

Electronics and Computer Science.

Integrated Ph.D. in Mathematical Sciences

Bachelor’s degree in science or engineering with mathematics as a subject for three years/ six semesters.

Integrated Ph.D. in Biological Sciences

Bachelor’s degree in Biology or Chemistry or Physics or Mathematics with Biology at the Higher Secondary (10+2) level.

M.Sc. Mathematics

Bachelor’s degree with Mathematics as a subject for at least two years/four semesters.

Joint M.Sc.-Ph.D. Programme in Mathematics, M.Sc. Mathematics & Computing, M.Sc. Applied Mathematics, M.Sc. Industrial Mathematics and Informatics, M.Sc.- Ph.D. Dual Degree in Operations Research

Bachelor’s degree with Mathematics / Statistics as a subject for at least two years/four semesters.

M.Sc.- Ph.D. Dual Degree in Environmental Science & Engineering

Bachelor’s degree with any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. The candidate should have passed Mathematics at (10 + 2) level.

M.Sc.- Ph.D. Dual Degree Programme in Energy

Bachelor’s degree with any one of Chemistry, Mathematics and Physics for two years/four semesters and any one of the remaining two subjects for at least one year/ two semesters.

M.Sc. Applied Statistics and Informatics, M.Sc.- Ph.D. Dual Degree in Operations Research

Bachelor’s degree with either Mathematics or Statistics as a subject for at least two years or four semesters.

M.Sc. Statistics

Bachelor’s degree with Statistics as a subject for at least two years or four semesters

Integrated Ph.D. in Physical Sciences

B.Sc. or equivalent degree with Physics as one of the main subjects.

Integrated Ph.D. in Biological Sciences

Bachelor’s degree in Biology or Chemistry or Physics or Mathematics. The candidates should have passed Biology at the Higher

Secondary (10+2) level.

Integrated Ph.D. in Chemical Sciences

B.Sc. or an equivalent degree with Chemistry as one of the subjects. The candidates should have passed mathematics at the PUC or+2 level.

Joint M.Sc.-Ph.D. Programme in Physics, M.Sc. Physics, M.Sc.- Ph.D. Dual Degree Programme in Physics, M.Sc. (Physics) - M.Tech. Materials Sciences with specialization in Nano-Science & Tech.)

Bachelor’s degree with Physics as a subject for at least two years/four semesters and Mathematics for at least one year/two semesters.

M.Sc.- Ph.D. Dual Degree Programme in Energy

Bachelor’s degree with any one of Chemistry, Mathematics and Physics for two years/four semesters and any one of the remaining two subjects for at least one year/ two semesters.

M.Sc.- Ph.D. Dual Degree Programme in Environmental Science & Engineering

Bachelor’s degree with any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. The candidate should have passed Mathematics at (10 + 2) level.

M.Sc.- Ph.D. Dual Degree Programme in Biotechnology

Bachelor’s degree in any branch of Science/ Agriculture / Pharmacy / Veterinary / Engineering / Medicine (MBBS).The candidate

should have passed Mathematics at the (10+2) level.

]]>

**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; Photosynthesis. Nitrogen Fixation, Fertilization and
Osmoregulation; Nervous system; Endocrine system; Vascular system;
Immune system; Digestive system, 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; Membranes; Gene transfer. **Cell Biology: ** Cell cycle; Cytoskeletal elements; Mitochondria; Endoplasmic reticulum; chloroplast; Golgi apparatus; Signaling. **Microbiology: ** Isolation; Cultivation; Characterization and enumeration 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 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 reaction; Soaps and detergents; Synthetic
polymers; Biomolecules - aminoacids, proteins, nucleic acids, lipids
and carbohydrates (polysaccharides); Instrumental
techniques-chromatography (TLC, HPLC), electrophoresis, UV-Vis-IR and
NMR spectroscopy, mass spectrometry, etc.

**MATHEMATICS (10+2 level) **

Sets, Relations and Functions, Mathematical Induction, Logarithms, Complex numbers, Linear and Quadratic equations, Sequences and Series, Trignometry, 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, Stocks, Shares and Debentures, Average and Partition Values, Index numbers, Matrices and Determinants, Boolean Algebra, Probability, Functions, limits and Continuity, Differentiation, Application of Derivatives, Definite and Indefinite Integrals, Differential Equations, Elementary Statics and Dynamics, Partnership, Bill of Exchange, Linear Programming, Annuities, Application of Calculus in Commerce and Economics.

**PHYSICS (10+2 level) **

Physical World and Measurement, Kinematics, Laws of Motion, Work, Energy and Power Electrostatics, Current electricity, Magnetic Effects of Current and Magnetism, Electromagnetic Induction and Alternating Current, Electromagnetics 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.

]]>**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 nonideal gases; Thermochemistry ; Second law; Entropy and
free energy, Criteria for spontaneity.

**Chemical and Phase Equilibria: **
Law of mass action; K p , K c ,K x and K n ; 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; Photophysical and photochemical
processes; Catalysis.

**ORGANIC CHEMISTRY**

**Basic Concepts in Organic Chemistry and Stereochemistry: **
Isomerism and nomenclature, electronic (resonance and inductive)
effects. Optical isomerism in compounds containing one and two
asymmetric centers, designation of absolute configuration,
conformations of cyclohexanes.

**Aromaticity and Huckel's rule: ** Mono and bicyclic aromatic hydrocarbons.

**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. 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.

**Natural Products Chemistry: ** Introduction to the following classes of compounds-alkaloids, terpenes, carbohydrates, amino acids, peptides and nuclei acids.

**Heterocyclic Chemistry: ** Monocyclic compounds with one hetero atom.

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

**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 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.

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

**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
equation. 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. Application to evaluation of area, surface and
volume.

**Differential Equations: ** First order differential equations, linear differential equations of higher order with constant coefficients.

**Vector Analysis: ** Vector algebra, Gradient.

**Numerical Analysis: **
Solution of non linear equations using iterative methods. Interpolation
(Lagrange's formula and Newton 's formulae 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.

]]>**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: **
Origin and evolution of life; Fossils; their mode of preservation and
utility; Morphological characters and ages of important groups of
animals; Brachiopoda, Mollusca, Trilobita, Graptolitoidea, Anthozoa,
Echinodermata etc. Gondwana plant fossils; Elementary idea of
verterbrate fossils in India .

**Stratigraphy: **
Principles of stratigraphy; Classification, distribution and ages of
the stratigraphic formations 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 and environmental geology; Principles of engineering geology.

**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 land forms; Interior of
earth; Earthquakes and seismic waves; Earth's magnetism and gravity,
Isostasy; Elements of plate tectonics; Orogenesis.**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.**Stratigraphy: ** Principles of Stratigraphy, Geological Time Scale, ages of major stratigraphic units of India.**Petrology: **
Definition and classification of rocks; Igneous rock-forms of igneous
bodies; Crystallisation from magma; classification and association of
igneous rocks; Principles of Stratigraphy; 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 non-metallic 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, 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, Strokes and Gauss theorems and their Applications.**Linear Algebra: **
System of Linear Equations, Matrices, Rank, Determinant, Inverse,
eigen-values and eigen-vectros. Dimension, Linear transformations.**Real Analysis: ** Open and closed sets and limit points in **R ** and completeness in **R **, Uniform Continuity, Power Series, Uniform Convergence.**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.**Complex Analysis: **
Analytical functions, Harmonic functions, Cauchy's theorem, Cauchy's
Integral Formula, Taylor and Laurent Expansion, Poles and Residues.**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 and
the error in it, Gauss-Siedel method and method of elimination for
numerical solution of a system of linear equations, iteration method
and its convergence, Gradient and Newton-Raphson method and their
convergence.

**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, 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, Hooke'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,
traveling 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, Lenzes 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: **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, Devices 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.

**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, skew-symmetric 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's
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.

**Integral Calculus **: Integration, Fundamental theorem of calculus. Double and Triple, integrals, Surface areas and volumes.

**Differential Equations **:
Ordinary differential equations of the first order of the form
y'=f(x,y). Linear differential equations of second order with constant
coefficients. Euler-Cauchy equation. Method of variation of parameters.

**Vector Calculus **: Gradient, divergence, curl and Laplacian. Green's, Stokes' and Gauss' theorems and their applications.

**Algebra **:
Groups, subgroups and normal subgroups, Lagrange's Theorem for finite
groups, group homomorphisms and basic concepts of quotient groups,
rings, ideals, quotient rings and fields.

**Linear Algebra **:
Systems of linear equations. Matrices, rank, determinant, inverse.
Eigenvalues and eigenvectors. Finite Dimensional Vector Spaces over
Real and Complex Numbers, Basis, Dimension, Linear Transformations.

**Real Analysis **: Open and closed sets, limit points, completeness of R, Uniform Continuity, Uniform convergence, Power series.

**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. Principal
moments and axes. Elasticity, Hooke'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,
traveling 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. 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. Zeroeth 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.

**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,
Schrödinger equation and its solution for one, two and three
dimensional boxes. Reflection and transmission at a step potential,
tunneling through a barrier. Pauli exclusion principle.
Distinguishable and indistinguishable particles. Max-well-Boltzmann,
Fermi-Dirac and Bose-Einstein statistics. Structure of atomic nucleus,
mass and binding energy. Radioactivity and its applications. Laws of
radioactive decay. Fission and fusion.

**Solid ****State Physics, Devices and Electronics: **Crystal
structure, Bravais lattices and basis. Miller indices. X-ray
diffraction and Bragg's law, Einstein and Debye theory of specific
heat. Free electron theory of metals. Fermi energy and density of
states. Origin of energy bands. Concept of holes and effective mass.
Elementary ideas about dia-, para- and ferromagnetism, Langevin's
theory of paramagnetism, Curie's law. Intrinsic and extrinsic
semiconductors. Fermi level. p-n junctions, transistors. Transistor
circuits in CB, CE, CC modes. Amplifier circuits with transistors.
Operational amplifiers. OR, AND, NOR and NAND gates.