**College / University:**Acharya Nagarjuna University, Guntur

Contents

## LIFE SCIENCES

**1. Cell Biology:** Ultra structure of prokaryotic and eukaryotic cell, Structure and function of cell organelles. Cell division ‐ Mitosis and Meiosis. Chromosomes structure, Karyotype.

**2. Genetics:** Mendelian principles, Gene Interaction, Linkage and Crossing over, Sex determination, Sex linkage, Mutations ‐ Genic and chromosomal (Structural and numerical); Chromosomal aberrations in humans. Recombination in prokaryotes transformation, conjugation, transduction, sexduction. Extra genomic inheritance.

**3. Molecular Biology and Genetic Engineering:** Structure of eukaryotic gene, DNA and RNA structure, DNA replication in pro and eukaryotes, Transcription and translation in pro and eukaryotes, genetic code. Regulation of gene expression in prokaryotes, Principles of recombinant DNA technology. DNA vectors, Transgenesis. Applications of genetic engineering.

**4. Biotechnology:** Plant and animal cell culture, cloning, Fermentors types and process, Biopesticides, Biofertilizers, Bioremediation, Renewable and non ‐ renewable energy resources, Non‐conventional fuels.

**5. Biomolecules:** Carbohydrates, proteins, amino acids, lipids, vitamins and porphyrins. Enzymes classification and mode of action, enzyme assay, enzyme units, enzyme inhibition, enzyme kinetics, Factors regulating enzyme action.

**6. Immunology:** Types of immunity, cells and organelles of immune system, Antigen – antibody reaction. Immunotechniques, Hypersensitivity, Vaccines.

**7. Techniques:** Microscopy ‐ Light and Electron, Centrifugation, Chromatography, Eletrophoresis, Calorimetric and Spectrophotometric techniques, Blotting techniques, PCR, DNA finger printing.

**8. Ecology, Environment and Evolution:** Theories and evidences of organic evolution, Hardy – Weinberg law. Components of an ecosystem, Ecological pyramids, Biogeochemical cycles, Ecological adaptations. Climatic and edaphic and biotic factors. Ecological sucession ‐ Hydrosere and xerosere, Natural resources, Biodiversity, current environmental issues, Environmental pollution, Global warming and climate change.

**9. Physiology:** Structure and function of liver, kidney and heart, composition of blood, blood types, blood coagulation, Digestion and absorption, Endocrinology, Muscle and Nervous system.

**10. Metabolism:** Metabolism of carbohydrates, lipids, proteins, aminoacids and nucleic acids. Biological oxidation and bioenergetics.

**11. Animal Science:** Biology of invertebrates and chordates, Embryology of chordates, Classification of marine environment ‐ Physical and chemical parameters, Marine, estuarine, reservoir and riverine fisheries, Cultivation of fin and shell fish. Culture practices.

**12. Plant Science:** Classification of cryptogams and phanerogams. General characteristics of taxonomic groups at class and family level Water relations and mineral nutrition of plants, Plant growth regulators, Ethnobotany and medicinal plants, Biology of plant seed, Photosynthesis.

**13. Microbiology:** Microbes ‐ Types, distribution and biology. Isolation and cultivation of bacteria and virus. Staining techniques. Bacterial growth curve, Microbial diseases ‐ food and water borne, insect borne, contact diseases in humans. Microbial diseases in plants ‐ by bacteria, fungi and virus, Plant microbe ‐ interactions.

**14. Nutrition:** Biological value of proteins, protein malnutrition, disorders, Chemistry and physiological role of vitamins and minerals in living systems

## PHYSICAL SCIENCES

**Electricity, Magnetism and Electronics:**

**1. Electrostatics:** Gauss law and its applications‐Uniformly charged sphere, charged cylindrical conductor and an infinite conducting sheet of charge. Deduction of Coulmb’s law from Gauss law Mechanical force on a charged conductor Electric potential ‐ Potential due to a charged spherical conductor, electric field strength from the electric dipole and an infinite line of charge. Potential of a uniformly charged circular disc.

**2. Dielectrics:** An atomic view of dielectrics, potential energy of a dipole in an electric field. Polarization and charge density, Gauss’s law for dielectric medium‐ Relation between D,E, and P. Dielectric constant, susceptibility and relation between them. Boundary conditions at the dielectric surface. Electric fields in cavities of a dielectric‐needle shaped cavity and disc shaped cavity.

**3. Capacitance:** Capacitance of concentric spheres and cylindrical condenser, capacitance of parallel plate condenser with and without dielectric. Electric energy stored in a charged condenser – force between plates of condenser, construction and working of attracted disc electrometer, measurement of dielectric constant and potential difference.

**4. Magnetostatics:** Magnetic shell ‐ potential due to magnetic shell ‐ field due to magnetic shell ‐equivalent of electric circuit and magnetic shell ‐ Magnetic induction (B) and field (H) ‐permeability and susceptibility ‐Hysteresis loop.

**5. Moving charge in electric and magnetic field:** Hall effect, cyclotron, synchrocyclotron and synchrotron ‐ force on a current carrying conductor placed in a magnetic field, force and torque on a current loop, Biot ‐Savart’s law and calculation of B due to long straight wire, a circular current loop and solenoid.

**6. Electromagnetic induction:** Faraday’s law ‐Lenz’s law ‐ expression for induced emf ‐ time varying magnetic fields ‐Betatron ‐Ballistic galvanometer ‐ theory ‐ damping correction ‐ self and mutual inductance, coefficient of coupling, calculation of self inductance of a long solenoid ‐toroid – energy stored in magnetic field ‐ transformer ‐ Construction, working, energy losses and efficiency.

**7. Varying and alternating currents:** Growth and decay of currents in LR, CR and LCR circuits – Critical damping. Alternating current relation between current and voltage in pure R,C and L‐vector diagrams ‐Power in ac circuits. LCR series and parallel resonant circuit ‐ Q‐factor. AC & DC motors‐single phase, three phase (basics only).

**8. Maxwell’s equations and electromagnetic waves:** A review of basic laws of electricity and magnetism ‐displacement current ‐ Maxwell’s equations in differential form ‐ Maxwell’s wave equation, plane electromagnetic waves ‐Transverse nature of electromagnetic waves, Poynting theorem, production of electromagnetic waves (Hertz experiment).

**9. Basic Electronics:** Formation of electron energy bands in solids, classification of solids in terms of forbidden energy gap. Intrinsic and extrinsic semiconductors, Fermi level, continuity equation ‐ p‐n junction diode, Zener diode characteristics and its application as voltage regulator. Half wave and full wave, rectifiers and filters, ripple factor (quantitative) – p n p and n p n transistors, current components in transistors, CB.CE and CC configurations ‐ transistor hybrid parameters ‐ determination of hybrid parameters from transistor characteristics ‐transistor as an amplifier — concept of negative feed back and positive feed back ‐ Barkhausen criterion, RC coupled amplifier and phase shift oscillator (qualitative).

**10. Digital Principles:** Binary number system, converting Binary to Decimal and vice versa. Binary addition and subtraction (1’s and 2’s complement methods). Hexadecimal number system. Conversion from Binary to Hexadecimal ‐ vice versa and Decimal to Hexadecimal vice versa.

**11. Logic gates:** OR, AND, NOT gates, truth tables, realization of these gates using discrete components. NAND, NOR as universal gates, Exclusive ‐ OR gate, De Morgan’s Laws ‐ statement and proof, Half and Full adders. Parallel adder circuits.

**Thermodynamics and Optics: **

**1. Kinetic theory of gases: Introduction ‐ Deduction of Maxwell’s law of distribution of molecular speeds, Experimental verification Toothed Wheel Experiment, Transport Phenomena ‐ Viscosity of gases ‐ thermal conductivity ‐ diffusion of gases. **

**2. Thermodynamics:** Introduction ‐ Reversible and irreversible processes ‐ Carnot’s engine and its efficiency ‐ Carnot’s theorem ‐ Second law of thermodynamics, Kelvin’s and Claussius statements ‐Thermodynamic scale of temperature ‐ Entropy, physical significance ‐ Change in entropy in reversible and irreversible processes ‐ Entropy and disorder ‐ Entropy of universe ‐ Temperature‐ Entropy (T‐S) diagram ‐ Change of entropy of a perfect gas‐change of entropy when ice changes into steam.

**3. Thermodynamic potentials and Maxwell’s equations:** Thermodynamic potentials – Derivation of Maxwell’s thermodynamic relations – Clausius ‐ Clayperon’s equation ‐ Derivation for ratio of specific heats ‐ Derivation for difference of two specific heats for perfect gas. Joule Kelvin effect – expression for Joule Kelvin coefficient for perfect and Vanderwaal’s gas.

**4. Low temperature Physics:** Introduction ‐ Joule Kelvin effect ‐ liquefaction of gas using porous plug experiment. Joule expansion ‐ Distinction between adiabatic and Joule Thomson expansion – Expression for Joule Thomson cooling ‐ Liquefaction of helium, Kapitza’s method ‐ Adiabatic demagnetization ‐ Production of low temperatures‐Principle of refrigeration, vapour compression type. Working of refrigerator and Air conditioning machines. Effects of Chloro and Fluro Carbons on Ozone layer; applications of substances at low‐temperature.

**5. Quantum theory of radiation:** Black body‐Ferry’s black body ‐ distribution of energy in the spectrum of Black body ‐ Wein’s displacement law, Wein’s law, Rayleigh‐Jean’s law ‐ Quantum theory of radiation ‐ Planck’s law ‐ deduction of Wein’s law, Rayleigh‐Jeans law, from Planck’s law ‐ Measurement of radiation ‐ Types of pyrometers ‐ Disappearing filament optical pyrometer ‐ experimental determination‐ Angstrom pyroheliometer ‐ determination of solar constant, effective temperature of sun.

**6. Statistical Mechanics:** Introduction to statistical mechanics, concept of ensembles, Phase space, Maxwell‐Boltzmann’s distribution law, Molecular energies in an ideal gas, Bose‐Einstein Distribution law, Fermi‐Dirac Distribution law, comparison of three distribution laws, Black Body Radiation, Rayleigh‐Jean’s formula, Planck’s radiation law, Weins Displacement, Stefan’s Boltzmann’s law from Plancks formula. Application of Fermi‐Dirac statistics to white dwarfs and Neutron stars.

**7. The Matrix methods in paraxial optics:** Introduction, the matrix method, effect of translation, effect of refraction, imaging by a spherical refracting surface. Imaging by a co‐axial optical system. Unit planes. Nodal planes. A system of two thin lenses.

**8. Aberrations:** Introduction ‐ Monochromatic aberrations, spherical aberration, methods of minimizing spherical aberration, coma, astigmatism and curvature of field, distortion. Chromatic aberration – the achromatic doublet ‐ Removal of chromatic aberration of a separated doublet.

**9. Interference:** Principle of superposition ‐ coherence ‐ temporal coherence and spatial coherence ‐conditions for Interference of light Interference by division of wave front: Fresnel’s biprism ‐determination of wave length of light. Determination of thickness of a transparent material using Biprism ‐change of phase on reflection ‐ Lloyd’s mirror experiment. Interference by division of amplitude: Oblique incidence of a plane wave on a thin film due to reflected and transmitted light (Cosine law) ‐ Colours of thin films ‐ Non reflecting films ‐ interference by a plane parallel film illuminated by a point source ‐ Interference by a film with two non‐parallel reflecting surfaces (Wedge shaped film) ‐ Determination of diameter of wire‐Newton’s rings in reflected light with and without contact between lens and glass plate, Newton’s rings in transmitted light (Haidinger Fringes) ‐ Determination of wave length of monochromatic light ‐ Michelson Interferometer ‐ types of fringes ‐Determination of wavelength of monochromatic light, Difference in wavelength of sodium 0^2 lines and thickness of a thin transparent plate.

**10. Diffraction:** Introduction ‐ Distinction between Fresnel and Fraunhoffer diffraction Fraunhoffer diffraction:‐ Diffraction due to single slit and circular aperture ‐ Limit of resolution ‐ Fraunhoffer diffraction due to double slit ‐ Fraunhoffer diffraction pattern with N slits (diffraction grating) Resolving Power of grating – Determination of wave length of light in normal and oblique incidence methods using diffraction grating. Fresnel diffraction:‐ Fresnel’s half period zones ‐ area of the half period zones ‐ zone plate ‐ Comparison of zone plate with convex lens ‐ Phase reversal zone plate ‐diffraction at a straight edge ‐ difference between interference and diffraction.

**11. Polarization:** Polarized light: Methods of Polarization, Polarizatioin by reflection, refraction, Doublerefraction, selective absorption , scattering of light ‐ Brewsters law ‐ Malus law – Nicol prism polarizer and analyzer ‐ Refraction of plane wave incident on negative and positive crystals (Huygen’s explanation) ‐ Quarter wave plate, Half wave plate ‐ Babinet’s compensator ‐ Optical activity, analysis of light by Laurent’s half shade polarimeter.

**12. Laser, Fiber Optics and Holography:** Lasers: Introduction ‐ Spontaneous emission – Stimulated emission ‐ Population inversion. Laser principle ‐ Einstein coefficients ‐ Types of Lasers ‐ He‐Ne laser ‐Ruby laser ‐Applications of lasers. Fiber Optics: Introduction ‐ Optical fibers ‐ Types of optical fibers ‐Step and graded index fibers ‐ Rays and modes in an optical fiber ‐ Fiber material ‐ Principles of fiber communication (qualitative treatment only) and advantages of fiber communication. Holography: Basic Principle of Holography ‐ Gabor hologram and its limitations, Holography applications.

**Mechanics and Waves and Oscillations:**

**1. Vector Analysis:** Scalar and vector fields, gradient of a scalar field and its physical significance. Divergence and curl of a vector field and related problems. Vector integration, line, surface and volume integrals. Stokes, Gauss and Greens theorems‐ simple applications.

**2. Mechanics of Particles:** Laws of motion, motion of variable mass system, motion of a rocket, multistage rocket, conservation of energy and momentum. Collisions in two and three dimensions, concept of impact parameter, scattering cross‐section, Rutherford scattering

**3. Mechanics of rigid bodies:** Definition of Rigid body, rotational kinematic relations, equation of motion for a rotating body, angular momentum and inertial tensor. Eulers equation, precession of a top, Gyroscope, precession of the equinoxes

**4. Mechanics of continuous media:** Elastic constants of isotropic solids and their relation, Poisson’s ratio and expression for Poisson’s ratio in terms of y, n, k. Classification of beams, types of bending, point load, distributed load, shearing force and bending moment, sign conventions, simple supported beam carrying a concentrated load at mid span, cantilever with an end load

**5. Central forces:**Central forces ‐ definition and examples, conservative nature of central forces, conservative force as a negative gradient of potential energy, equation of motion under a central force, gravitational potential and gravitational field, motion under inverse square law, derivation of Kepler’s laws, Coriolis force and its expressions.

**6. Special theory of relativity:** Galilean relativity, absolute frames, Michelson‐Morley experiment, Postulates of special theory of relativity. Lorentz transformation, time dilation, length contraction, addition of velocities, mass‐energy relation. Concept of four vector formalism.

**7. Fundamentals of vibrations:** Simple harmonic oscillator, and solution of the differential equation‐Physical characteristics of SHM, torsion pendulum, ‐ measurements of rigidity modulus , compound pendulum, measurement of ‘g’, combination of two mutually perpendicular simple harmonic vibrations of same frequency and different frequencies, Lissajous figures

**8. Damped and forced oscillations:** Damped harmonic oscillator, solution of the differential equation of damped oscillator. Energy considerations, comparison with undamped harmonic oscillator, logarithmic decrement, relaxation time, quality factor, differential equation of forced oscillator and its solution, amplitude resonance, velocity resonance

**9. Complex vibrations:** Fourier theorem and evaluation of the Fourier coefficients, analysis of periodic wave functions‐square wave, triangular wave, saw‐tooth wave

**10. Vibrations of bars:** Longitudinal vibrations in bars‐ wave equation and its general solution. Special cases (i) bar fixed at both ends ii) bar fixed at the mid point iii) bar free at both ends iv) bar fixed at one end. Transverse vibrations in a bar‐ wave equation and its general solution. Boundary conditions, clamped free bar, free‐free bar, bar supported at both ends, Tuning fork.

**11. Vibrating Strings:** Transverse wave propagation along a stretched string, general solution of wave equation and its significance, modes of vibration of stretched string clamped at both ends, overtones, energy transport, transverse impedance

**12. Ultrasonics:** Ultrasonics, properties of ultrasonic waves, production of ultrasonics by piezoelectric and magnetostriction methods, detection of ultrasonics, determination of wavelength of ultrasonic waves. Velocity of ultrasonics in liquids by Sear’s method. Applications of ultrasonic waves.

## MATHEMATICAL SCIENCES

**LINEAR ALGEBRA AND VECTOR CALCULUS**

**Linear Algebra:** Vector spaces, General properties of vector spaces, Vector subspaces, Algebra of subspaces, linear combination of vectors. Linear span, linear sum of two subspaces, Linear independence and dependence of vectors, Basis of vector space, Finite dimensional vector spaces, Dimension of a vector space, Dimension of a subspace. Linear transformations, linear operators, Range and null space of linear transformation, Rank and nullity of linear transformations, Linear transformations as vectors, Product of linear transformations, Invertible linear transformation. The adjoint or transpose of a linear transformation, Sylvester’s law of nullity, characteristic values and characteristic vectors , Cayley‐ Hamilton theorem, Diagonalizable operators. Inner product spaces, Euclidean and unitary spaces, Norm or length of a vector, Schwartz inequality, Orthogonality, Orthonormal set, complete orthonormal set, Gram ‐ Schmidt orthogonalisation process.

**Multiple integrals and Vector Calculus:** Multiple integrals: Introduction, the concept of a plane, Curve, line integral‐ Sufficient condition for the existence of the integral. The area of a subset of R2 , Calculation of double integrals, Jordan curve , Area, Change of the order of integration, Double integral as a limit, Change of variable in a double integration. Vector differentiation. Ordinary derivatives of vectors, Space curves, Continuity, Differentiability, Gradient, Divergence, Curl operators, Formulae involving these operators. Vector integration, Theorems of Gauss and Stokes, Green’s theorem in plane and applications of these theorems

**REAL NUMBERS:** The Completeness Properties of R, Applications of the Supremum Property. Sequences and Series ‐ Sequences and their limits, limit theorems, Monotonic Sequences, Sub‐sequences and the Bolzano ‐ Weirstrass theorem, The Cauchy’s Criterion, Properly divergent sequences, Introduction to series, Absolute convergence, test for absolute convergence, test for non‐absolute convergence. Continuous Functions‐continuous functions, combinations of continuous functions, continuous functions on intervals, Uniform continuity.

**DIFFERENTIATION AND INTEGRATION:** The derivative, The mean value theorems, L’Hospital Rule, Taylor’s Theorem. Riemann integration ‐ Riemann integral, Riemann integrable functions, Fundamental theorem.

**DIFFERENTIAL EQUATIONS & SOLID GEOMETRY**

**Differential equations of first order and first degree:** Linear differential equations; Differential equations reducible to linear form; Exact differential equations; Integrating factors; Change of variables; Simultaneous differential equations; Orthogonal trajectories.

**Differential equations of the first order but not of the first degree:** Equations solvable for p; Equations solvable for y; Equations solvable for x; Equations that do not contain x (or y); Equations of the first degree in x and y ‐ Clairaut’s equation.

**Higher order linear differential equations:** Solution of homogeneous linear differential equations of order n with constant coefficients. Solution of the non‐homogeneous linear differential equations with constant coefficients by means of polynomial operators. Method of undetermined coefficients; Method of variation of parameters; Linear differential equations with non‐constant coefficients; The Cauchy‐Euler equation

**System of linear differential equations:** Solution of a system of linear equations with constant coefficients; An equivalent triangular system. Degenerate Case: p1(D) p4(D)‐p2(D) p3(D) = 0.

**SOLID GEOMETRY**

**The Plane:** Equation of plane in terms of its intercepts on the axis, Equations of the plane through the given points, Length of the perpendicular from a given point to a given plane, Bisectors of angles between two planes, Combined equation of two planes, Orthogonal projection on a plane.

**The Line:** Equations of a line, Angle between a line and a plane, The condition that a given line may lie in a given plane, The condition that two given lines are coplanar, Number of arbitrary constants in the equations of a straight line. Sets of conditions which determine a line, The shortest distance between two lines. The length and equations of the line of shortest distance between two straight lines, Length of the perpendicular from a given point to a given line, Intersection of three planes, Triangular Prism.

**The Sphere:** Definition and equation of the sphere, Equation of the sphere through four given points, Plane sections of a sphere. Intersection of two spheres; Equation of a circle. Sphere through a given circle; Intersection of a sphere and a line. Power of a point; Tangent plane. Plane of contact. Polar plane, Pole of a plane, Conjugate points, Conjugate planes; Angle of intersection of two spheres. Conditions for two spheres to be orthogonal; Radical plane. Coaxial system of spheres; Simplified from of the equation of two spheres.

## STATISTICS

**Descriptive Statistics and Probability Distributions: **

1. Descriptive Statistics: Concept of primary and secondary data. Methods of collection of primary data and secondary data. Classification and tabulation of data. Measures of central tendency (mean, median, mode, geometric mean and harmonic mean) topics are constrained to definitions merits and demerits only (but proofs are not necessary). Concepts of absolute & relative measure of dispersion (range, quartile deviation, mean deviation, and standard deviation)

2. Importance of moments, central and non‐central moments, and their interrelationships, Sheppard’s corrections for moments for grouped data. Measures of skewness based on quartiles and moments and kurtosis based on moments with suitable examples.

3. Basic concepts in Probability—deterministic and random experiments, trail, outcome, sample space, event, and operations of events, mutually exclusive and exhaustive events, and equally likely and favorable outcomes with examples. Mathematical, statistical and axiomatic definitions of probability with merits and demerits. Properties of probability based on axiomatic definition. Conditional probability and independence of events. Addition and multiplication theorems for n events. Boole’s inequality and Bayes’ theorem. Problems on probability.

4. Definition of random variable, discrete and continuous random variables, functions of random variables, probability mass function and probability density function with illustrations. Distribution function and its properties. Transformation of one‐dimensional random variable (simple 1‐1 functions only). Notion of bivariate random variable, bivariate distribution and statement of its properties. Joint, marginal and conditional distributions. Independence of random variables.

5. Mathematical Expectation: Mathematical expectation of a function of a random variable. Raw and central moments and covariance using mathematical expectation with examples. Addition and multiplication theorems of expectation. Definition of moment generating function (m.g.f), cumulant generating function (c.g.f), probability generating function (p.g.f) and characteristic function (c.f) and statements of their properties with applications. Chebyshev’s , and Cauchy‐Schwartz’s inequalities. Statement of weak law of large numbers and central limit theorem for identically and independently distributed (i.i.d) random variables with finite variance.

6. Discrete distributions: Uniform, Bernoulli, Binomial, Poisson, Negative binomial, Geometric and Hyper‐geometric (mean and variance only) distributions. Properties of these distributions such as m.g.f., c.g.f., p.g.f., c.f., & derive moments up to second order from them. Reproductive property wherever exists. Binomial approximation to Hyper‐geometric, Poisson approximation to Binomial and Negative BD.

7. Continuous distributions: Rectangular and Normal distributions. Normal distribution as a limiting case of Binomial and Poisson distributions. Exponential, Gamma, Beta of two kinds (mean and variance only) and Cauchy (definition and c.f. only) distributions. Properties of these distributions such as m.g.f., c.g.f., c.f., and moments up to fourth order, their real life applications and reproductive productive property wherever exists

**Statistical Methods and Inference: **

1. Bivariate data, scattered diagram Correlation coefficient and it’s properties. Computation of correlation coefficient for grouped data. Correlation ratio, Spearman’s rank correlation coefficient and it’s properties. Simple linear regression properties of regression coefficients, correlation verses regression. Principles of least squares, fitting of quadratic and power curves. Concepts of partial and multiple correlation coefficients (only for three variables).

2. Analysis of categorical data, independence and association and partial association of attributes, various measures of association (Yule’s)& coefficient of colligation for two way data and coefficient of contingency (pearsonss’s & Tcheprow’s)

3. Concept of population, parameter, random sample, statistic, sampling distribution and standard error. Standard error of sample mean (s) and sample proporations (s). Exact sampling distributions:‐ Statements and properties of X^2,t, &F distributions and their inter relationships.

4. Point estimation of a parameter. Concept of bias and mean square error of an estimate. Criteria of good estimator‐consistency, unbiasedness, efficiency and sufficiency with examples. Statement of Neyman’s Factorisation theorem, derivations of sufficient statistics in case of Binomial, Poisson, Normal and Exponential (one parameter only) distributions. Estimation by the method of moments, Maximum likelihood (ML), statements of asymptotic properties of MLE. Concept of interval estimation. Confidence Intervals of parameters of normal population.

5. Concepts of statistical hypothesis, null and alternative, hypothesis, critical region, two Types of errors, level of significance and power of a test. One and two tailed tests, Neyman pearson”s fundamental lemma for Randomised tests. Examples in case of Binomial, poisson, Exponential and

Normal distributions and their powers. Use of central limit theorem in testing large sample tests and confidence intervals for mean(s), proportion(s), standard deviation(s) and correlation coefficient(s).

6. Test of significance based on X^2, t, F. X^2‐test for goodness of fit and test for independence of attributes. Definition of order statistics.

7. Non‐Parametric tests their advantages and disadvantages, comparison with parametric tests. Measurement scale: nominal, ordinal, interval and ratio. One sample runs test, sign test and Wilcoxon‐signed rank tests (single and paired samples). Two independent sample tests: Median test, Wilcoxon –Mann‐Whitney U test, Wald Wolfowitz’s runs test.

## APPLIED STATISTICS:

**Design of Sample Surveys: **

Concept of population, sample, sampling unit, parameter, statistic, sampling errors, sampling distribution, sample freme and standard error. Principle steps in sampling surveys‐need for sampling, census verses samples surveys Sampling and non‐sampling errors, sources and treatment of non‐sampling errors, advantages and limitations of sampling. Types of sampling: subjective, probability and mixed sampling methods. Methods of drawing random samples with and without replacement. Estimates of population mean, total and proportion, their variances and estimates of variances in the following methods

i) SRSWRAND SRSWOR

ii) Stratified random sampling with proportional and Neyman allocation.

Comparison of relative efficiencies. Concept of Systematic sampling N=nk

**Analysis of Variance and Design of Experiments:** ANOVA‐one‐way, two way classifications with one observation percell‐concept of Gauss ‐ Markoff linear model, Statement of Cochran’s theorem, Mathematical Analysis, importance and applications of design of experiments. Principles of Experimentation, Analysis of Completely randomized Design (CRD), Randomized Block Design (RBD) and Latin Square Design (LSD)

**Time Series:** Time series and it’s components with illustrations, additive, multiplicative and mixed models, Determination of trend by least squares, moving average methods Determination of Seasonal indices by Ratio to moving average, Ratio to trend and link relative methods.

**Index Numbers:** Concept, Construction, uses and limitations of simple and weighted index numbers, lasperyer’s, Paasche’s and Fisher’s Index numbers. Fisher’s index as ideal index number. Fixed and chain base index numbers. Cost of living index numbers and wholesale price index numbers. Base shifting, Splicing and deflation of index numbers.

**Official Statistics:** Functions and organization of CSO and NSSO. Agricultural Statistics, area and yield statistics. National Income and it’s coputation, utility and difficulties in estimation of National income. Vital Statistics: Introduction, definition and uses of vital statistics. Sources of vital statistics, registration method and census method. Rates and ratios, Crude Death rate, age specific death rate, standardized death rates, crude birth rate, age specific fertility rate, general fertility rate, total fertility rate. Measurement of population Growth, crude rate in natural increase – Pearl’s vital index. Gross reproductive rate and net reproductive rate, Life tables, contruction and uses of life tables and abridged life tables.

**Demand Analysis:** Introduction, Demand and supply, price elastics of supply and demand. Methods of determining demand and supply curves, Leontief’s, Pigous’s methods of determining demand curve from time series data, limitations of these methods.

## Quick Links

http://www.nagarjunauniversity.ac.in/admissions15/ANUPGCET-2015Brochure.pdf