Kerala KEAM Mathematics Syllabus

MATHEMATICS

UNIT I: ALGEBRA

SETS, RELATIONS AND FUNCTIONS

Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams; Complement of a set; Operations on Sets (Union, Intersection and (Difference of Set); Applications of sets: Ordered Pairs, Cartesian Product of Two sets; Relations: Domain,Co-domain and Range: Functions: into, on to, one – one in to, one-one on to Functions; Constant Function;Identity Function; composition of Functions; Invertible Functions; Binary Operations.

Complex Numbers

Complex Numbers in the form a + i b; Real and Imaginary Parts of a complex Number; Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane; Modulus and Argument of a Complex Number; Algebra of Complex Numbers; Triangle Inequality; Polar Representation of a Complex Number.

Quadratic Equations

Solution of a Quadratic Equation in the Complex Number System by (i) Factorization (ii) Using Formula; Relation between Roots and Coefficients; Nature of Roots; Formation of Quadratic Equations with given Roots; Equations Reducible to Quadratic Forms.

Sequences and Series

Sequence and Examples of Finite and Infinite Sequences; Arithmetic Progression (A.P): First Term,Common Difference, nthTerm and sum of n terms of an A.P.; Arithmetic Mean (A.M); Insertion of Arithmetic Means between any Two given Numbers; Geometric Progression (G.P): first Term, Common Ratio and nth term, Sum to n Terms, Geometric Mean (G.M); Insertion of Geometric Means between any two given Numbers.

Permutations, Combinations, Binomial Theorem and Mathematical Induction

Fundamental Principle of Counting; The Factorial Notation; Permutation as an Arrangement; Meaning of P(n, r); Combination: Meaning of C(n,r); Applications of Permutations and Combinations. Statement of Binomial Theorem; Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method; General and Middle Terms in Binomial Expansions; Properties of Binomial Coefficients; Binomial Theorem for any Index (without proof); Application of Binomial Theorem. The Principle of Mathematical Induction, simple Applications.

Matrices and Determinants

Concept of a Matrix; Types of Matrices; Equality of Matrices (only real entries may be considered): Operations of Addition, Scalar Multiplication and Multiplication of Matrices; Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only; Determinant of a Square Matrix; Minors and Cofactors; singular and non-singular Matrices; Applications of Determinants in (i) finding the Area of aTriangle (ii) solving a system of Linear Equations (Cramer’s Rule); Transpose, Adjoint and Inverse of a Matrix; Consistency and Inconsistency of a system of Linear Equations; Solving System of Linear Equations in Two or Three variables using Inverseof a Matrix (only up to 3X3 Determinants and Matrices should be considered).

Linear Inequations

Solutions of Linear Inequation in one variable and its Graphical Representation; solution of system of Linear Inequations in one variable; Graphical solutions of Linear inequations in two variables; solutions of system of Linear Inequations in two variables.

Mathematical Logic and Boolean Algebra

Statements; use of Venn Diagram in Logic; Negation Operation; Basic Logical Connectives and Compound Statements including their Negations.

Trigonometric functions and Inverse Trigonometric functions

Degree measures and Radian measure of positive and negative angles; relation between degree measure and radian measure, definition of trigonometric functions with the help of a unit circle, periodic functions, concept of periodicity of trigonometric functions, value of trigonometric functions of x, trigonometric functions of sum and difference of numbers, Trigonometric functions of multiple and submultiples of numbers. Conditional identities for the angles of a triangle, solution of trigonometric equations of the type Sin x = Sin a ; Cos x = Cos a; Tan x = Tan a and equations reducible to these forms. Inverse Trigonometric functions.

Simple problems

Graph of the following trigonometric functions;

y = Sin x ; y = Cos x ; y = Tan x ; y = a Sin x ;y = a Cos x, y = a Sin bx ; y = a Cos bx;

UNIT III: GEOMETRY

Cartesian System of Rectangular Co ordinates

Cartesian system of co ordinates in a plane, Distance formula, Centroid and incentre, Area of a triangle, condition for the collinearity of three points in a plane, Slope of line, parallel and perpendicular lines,intercepts of a line on the co ordinate axes, Locus and its equation.

Lines and Family of lines

Various forms of equations of a line parallel to axes, slope-intercept form, The Slope point form, Intercept form, Normal form, General form, Intersection of lines. Equation of bisectors of angle between two lines, Angles between two lines, condition for concurrency of three lines, Distance of a point from a line, Equations of family of lines through the intersection of two lines.

Circles and Family of circles

Standard form of the equation of a circle General form of the equation of a circle, its radius and center, Equation of the circle in the parametric form.

Conic sections

Sections of a cone. Equations of conic sections [ Parabola, Ellipse and Hyperbola] in standard form.

Vectors

Vectors and scalars, Magnitude and Direction of a vector, Types of vectors (Equal vectors, unit vector,

Zero vector). Position vector of a point, Localized and free vectors, parallel and collinear vectors,

Negative of a vector, components of a vector, Addition of vectors, multiplication of a vector by a scalar,position vector of point dividing a line segment in a given ratio, Application of vectors in geometry. Scalar product of two vectors, projection of a vector on a line, vector product of two vectors.

Three Dimensional Geometry

Coordinate axes and coordinate planes in three dimensional space, coordinate of a point in space,

distance between two points, section formula, direction cosines, and direction ratios of a line joining two points, projection of the join of two points on a given line, Angle between two lines whose direction ratios are given, Cartesian and vector equation of a line through (i) a point and parallel to a given vector (ii) through two points, Collinearity of three points, coplanar and skew lines, Shortest distance between two lines, Condition for the intersection of two lines, Carterian and vector equation of a plane (i) When the normal vector and the distance of the plane from the origin is given (ii) passing though a point and perpendicular to a given vector (iii) Passing through a point and parallel to two given lines through the intersection of two other planes (iv) containing two lines (v) passing through three points, Angle between (i) two lines (ii) two planes (iii) a line and a plane, Condition of coplanarity of two lines in vector and Cartesian form, length of perpendicular of a point from a plane by both vector and Cartesian methods.

UNIT IV: STATISTICS

Statistics and probability

Mean deviation for ungrouped data, variance for grouped an ungrouped data, standard deviation. Random experiments and sample space, Events as subset of a sample space, occurrence of an event, sure and impossible events, Exhaustive events, Algebra of events, Meaning of equality likely outcomes, mutually exclusive events. Probability of an event; Theorems on probability; Addition rule, Multiplication rule, Independent experiments and events. Finding P (A or B), P (A and B), random variables, Probability distribution of a random variable.

UNIT V : CALCULUS

Functions, Limits and continuity

Concept of a real function; its domain and range; Modulus Function, Greatest integer function: Signum functions; Trigonometric functions and inverse trigonometric functions and their graphs; composite functions, Inverse of a function.Limit of a function; meaning and related notations; Left and right hand limits; Fundamental theorems on limits. Limits at Infinity and infinity limits; continuity of a function at a point, over an open/ closed interval; Sum, Product and quotient of continuous functions; Continuity of special functions- Polynomial, Trigonometric, exponential, Logarithmic and Inverse trigonometric functions.

Differentiation

Derivative of a function; its geometrical and physical significance; Relationship between continuity and  differentiability; Derivatives of polynomial, basic trigonometric, exponential, logarithmic and inverse trigonometric functions from first principles; derivatives of sum, difference, product and quotient of functions; derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric and implicit functions; Logarithmic differentiation; derivatives of functions expressed in parametric for;chain rule and differentiation by substitution; Derivatives of Second order.

Application of Derivatives

Rate of change of quantities; Tangents and Normals; increasing and decreasing functions and sign of the derivatives; maxima and minima; Greatest and least values; Rolle’s theorem and Mean value theorem;Approximation by  differentials.

Indefinite Integrals

Integration as inverse of differentiation; properties of integrals; Integrals involving algebraic, trigonometric, exponential and logarithmic functions; Integration by substitution; Integration by parts;Integrals of the type: Integration of rational functions; Partial fractions and their use in integration; Integrals of the type

Definite Integrals

Definite integral as limit of a sum; Fundamental theorems of integral calculus without proof); Evaluation of definite integrals by substitution and by using the following properties.  Application of definite integrals in finding areas bounded by a curve, circle, parabola and ellipse in standard form between two ordinates and x-axis; Area between two curves, line and circle; line and parabola: line and ellipse.

Differential Equations

Definition; order and degree; general and particular solutions of a differential equation; formation of differential equations whose general solution is given; solution of differential equations by method of Separation of variables; Homogeneous differential equations of first order and their solutions; Solution of linear differential equations

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admin All India Entrance KEAM Mathematics Syllabus

Jamia Hamdard University MCA Entrance Exam Syllabus

The admission to MCA programme will be on the basis of the merit determined by the performance of the candidates in the written Entrance Test only. The Entrance Test Paper will be based on questions from subjects of BCA of Jamia Hamdard.Syllabus of BCA is given below:

• Mathematics

Differentiation and partial differentiation, derivative of sum, dot product and cross product of two vectors, gradient, divergence and curl;. System of circles, standard equations and properties of parabola and Ellipse; General equation of second degree in two variables, tracing of conic sections, sphere; Successive differentiation, Libneitz theorem, partial differentiation, curvature, asymptotes, singular points, concavity, points of inflexion and tracing of Cartesian curves; Differential equation of first order; Matrix Algebra including rank, inverse, linear system of equations, Eigen value & Caley Hamilton Theorem; team working and management.Sets and related operations, Relations and their properties, matrix of relations, functions and its properties, Introduction to graph theory, Significance of graph theory for computer science, matrix representation of graphs, Path Matrix, Shortest path algorithm, Introduction to recurrence relation, Formulation of recurrence relations, Characteristic equation and Characteristic roots of recurrence relation, Solution of recurrence relations, Introduction to prepositional calculus, logical operations, Truth tables of logical identities, Equivalence of logical identities, Introduction to Boolean Algebra.Numerical methods versus numerical analysis, Errors and Measure of Errors.Non-linear Equations, Iterative solutions, multiple rocks and other difficulties, interpolation methods of BI-section, false position methods, Newton Raphson-Methods. Simultaneous Solutions of Equations, Gases Elimination Methods Gaues Jordan methods Gaues seedily methods. Interpolation and curve fitting, Lagrangian polynomials, Newton’s methods: Forward Difference methods, Backward Difference methods Divided difference methods. Numerical Integration and Different Trapezoidal Rule, Simpson 1/3 Rule Simpson’s 3/8 Rule. Numerical differentiation by polynomial Fit.

• Statistical Techniques

Measure of Central Tendency, Preparing frequency distribution table, Mean Arithmetic mean harmonic, mean medial mode. Measure of dispersion, skewness and kurtosis Ranges, Mean deviation. Standard deviation, co-efficiency of variation, Moments skew ness kurtosis. Correlation. Regression linear; Regression. Least square fit liner trend, Non-linear trend.

• Introduction to Computer and IT

Computer Organisation: Block Diagram, Basic Architecture etc. Evolution and Different Types of Computer and then Characterizing features; Functional unit of computers, primary and secondary memory. Number System: Decimal, octal, binary and hexadecimal.Representation of Integers, fixed and floating point, character representation schemeIntroduction to operating system: DOS & Windows Elements of IT: Introduction to Range of Info Technologies; Audio, video, multimedia, Internet and Intranets.Introduction to Intelligent systems. Expert systems, Virtual Reality System Development life cycles : Waterfall methods, prototyping, JAD, RAD, etc.

• Programming in C

Programming Fundamentals, algorithm development, techniques of problem solving, flowcharting, stepwise refinement; Programming in C including features of ‘C’, C tokens, data type, operators, expressions, Branching Constructs: if-else, switch, conditional operator & goto statements; Looping Constructs: while, do-while, for and Jumping statements; Arrays, string processing, Functions: categories of functions, recursion; Pointers: operations on pointers, pointers & structures; Structures and Unions; File Management: Defining & opening a file, closing a file, input/output operations. Development of efficient programs; Debugging, verification and testing of programs.

• Organizational Behavior

Psychological dimensions and relevance in the emerging society; Learning : styles and principles; Skinner, Thorndike and Piaget theories; Conditions of learning; Organizational behavior: essential attributes; Memory: short term and long term; Efficient and effective ways in respect of thinking, problem solving and decision making ; Stress management; models of personality, factors and desirable features of a healthy personality; Basic Needs and their hierarchy: Mallow model and self actualizing personalities.

• Communication Skills

Review of English Grammar; Written and Spoken Language; Common Errors in language; Punctuation (purpose, role, importance and use); Effective use of dictionary, thesaurus, encyclopedia, OED; Figures of speech; Language Skills (Listening, Speaking, Reading, Writing); Meaning what you mean; Listening: Effective and efficient listening in various situations (discussions, lectures, news, seminars, speech, telephone calls etc.);Speaking: Phonetics, intonation, accent, usage; strategies for a good rhetoric; Reading: Purpose; Comprehension; Tactics and strategies for good reading; Writing: Guidelines for good writing; various writing styles (General and Technical writing styles);Communication (purpose, role, importance, elements); Effective and efficient communication; Role of content, context and language; Spoken and written communication; Presentation and delivery; Role of speaker and audience; Style and body language; Planning, organization, presentation, participation, conduction and feedback of discussions, meetings, seminars etc; Effective and efficient presentation and discussion skills; Discussion and Presentation skills of conferences, meetings, seminars etc; General and Technical documents (correspondence (applications, letters, resumes, CV), drafts, essays, memos; minutes; notes, proposals, precis, reports, summary, synopsis,), appendices, references, table of contents, acknowledgements, prologue, epilogue, revision; Use of Audio-Visual Aids: OHP, Slides, Charts, Computers etc.

• Introduction to Data Structures

Representation of data , Data Types, ADT and Data Structures, Arrays : single and multidimensional arrays , Structures , Static and Dynamic implementations of data structures, Stacks and it’s applications ,infix, prefix and postfix notations and conversions ,Recursion, queues other general lists and applications; Linked Lists: dynamic memory allocation & pointers, linked stacks & queues. Trees : Binary Trees, Tree search ,tree traversals , threaded binary tree, Height Balancing- AVL trees; graphs – BFS and DFS ; B-trees, b+ trees , searching and sorting techniques and their analysis of algorithms , searching : linear search, binary search, tree search. Sorting : bubble sort, quick sort, insertion sort, heap sort, shell sort , merge sort and radix sort .

• Computer Organization

Number System, complements, binary arithmetic, and logic gates. Boolean functions. Dual of a Boolean function. Inverse of a Boolean function. Boolean function representation: canonical form, standard form. Boolean function Simplification: Algebraic method, Karnaugh Map method. Boolean function implementation: NAND implementation, NOR implementation. Binary codes: BCD, EBCDIC, ASCII, Excess-3, gray code. Combinational circuits: adder, subtractor, decoder, and encoder, MUX/DEMUX etc. Sequential circuits: Flip-flops, registers and Counters.

• Business Data Processing and File Systems

Data Processing: Concept, relevance and cycle; Organisation and attributes of business data processing; Computing environments; Programming methodologies: structured, object oriented etc.; Programming Principles: style, coding, testing and refinements; Input and output devices: an overview; Business Systems; Business computing: characteristics, significance and distinguishing features; Physical storage devise and their characteristics, File : fields, records, fixed and variable length records, primary and secondary keys; File operations, Basic file system operations; File organisations: Sequential, indexed Sequential, Direct, relative etc; Data processing using COBOL/FoxPro , Introduction to database design.

• Computer Based Financial Accounting and Management

Conceptual Framework, Nature and Scope of accounting information; Identifying and recording accounting transactions using traditional and accounting equations approach; Generally accepted accounting principles; Accounting standards in India; Bases of accounting-cash and accrual; Capital and revenue items. Fundamentals of computerized accounting system: concept of grouping the accounting heads; Schemes of assigning the codes to accounting heads, maintaining the hierarchy of ledger accounts for preparing control accounts; Case Study and use of a software tool.

• Fundamental Concepts of Operating Systems

Operating systems overview: Computer System Structure, operating systems structure, OS functions, facilities; Processes: introduction, concurrency, inter process communication, classical problems, process scheduling, Memory management: swapping, virtual memory, segmentation. File systems: files, directories, file system implementation, security, and protection mechanism. Input / output: principles of input / output hardware and software, disks, clocks, terminals. Deadlocks: introduction, detection, recovery, and prevention; Coordinated Case Study of Unix and Windows.

• Introduction to Object Oriented Programming using C++

OOP : Programming methodologies: concepts of structured and object oriented programming; advantage of OOP methodologies, characteristics of OOP languages: objects, classes, Data Abstraction , Encapsulation ,inheritance, reusability, polymorphism and operator overloading, function overloading;Programming in C++ :data types, constants, expressions and statements, Arrays Strings, function overloading, functions, friend functions , in line functions constructors and destructors, derived classes, friend classes , operator overloading , support for data abstraction, derived class, base class, pointers and arrays, pointers and functions, support for OOP.

• System Programming concepts & Compiler Design

Mathematical preliminaries, sets, relations and functions, graphs and trees, strings, theory of automata, DFA, NFA, acceptability of a string by finite automata, minimization of finite automata, applications of finite automata –lexical analysis, text editors etc. Introduction to formal languages- regular grammars , context free grammar, context sensitive grammar. Evolution of the Components of a Programming System,compilers, Assemblers, Loaders Absolute loader, relocating loader,Direct linkage loader, Linkers,Macros, Variety of software tools, Text editors, Interpreters and program generators Debug Monitor. Compilers : Basic concepts, compilers and interpreters, pass of a compilers, phases-lexical phase, syntax phase, semantic analysis phase, parser, top down, bottom up parsing, translation schemes, type analysis and type checking, code generation phase and optimization. Symbol table management, error handling.

• Systems Analysis and Design

System : definition and concept; Real time and distributed systems; Data information and related attributes; System analysis and analyst; System development life cycle: study, analysis, design, development and implementation; System planning; data & fact finding techniques; System design and modeling: logical and physical design representation, data flow diagram, ERD, structure charts; forms design : classification, user interface; standards; control and validation checks; user interface guidelines modular and structured design; System implementation & maintenance; Project management techniques; use of an available tool to implement a case study.

• Software Engineering , testing and Quality Assurance

Introduction to S/W engineering; software product and process: Generic Phases, software development models; Project Scheduling and Tracking; Software architecture and design: prominent design methodologies; Verification, validation and performance evaluation;; SW Configuration Management and maintenance; SW measurement-Size, Process and Project Metrics; LOC , FP metrics; Testing and the related concepts : Testability and features of Test Cases; Software Testing techniques: WBT,BBT, Software Testing Strategies: Approach, Issues; integration, System, alpha , Beta testing etc; Quality Factors, framework , Quality assurance: concepts, Activities ect. . SW Reliability, SQA Plan, Quality models: ISO 9000 and SEI-CMM and their relevance. Functions of CASE tools and their use with practical examples of special CASE tools, such as Turbo Analyst.

• Introduction to DBMS and Oracle

Concept of Database and its evaluation, Data abstraction and data integration; the three level architecture of a DBMS, components of a DBMS; Data models and their implementations : relational. Network, Hierarchical; Relational data manipulations : relational algebra, relational calculus, SQL; Relational database design: functional dependencies, finding keys, 1st to 3rd Normal Forms, BCNF, lossless join and Dependency preserving decomposition, computing closures of set FD’s, finding keys. Introduction to Oracle – Data types, SQL *PLUS, PL/SQL: Function, Procedure, Cursor, Exceptions, Triggers etc.

• Management Information System

Introduction to the concept of Decision Support system: Component of DSS ialogue management; data management and Model management for DSS ;example of different types of DSS ;system Analysis & Design for DSS ;Model in the context of DSS ;Algorithm & Heuristics; DSS application in different functions ;Design for interfaces in DSS, An overview of DSS generators, Group discussion in Support system ( GDSS) . And decision conferencing. Introduction of Expert System . Expert system in management; case study on expert system. introduction to GIS ;MIS based on GIS; case studies ;Executive Information system( EIS).

• Introduction to Unix and Windows NT

Introduction to UNIX, UNIX files and directories Commonly used commands in UNIX pipes and processes editor, basic shell programming awk utility UNIX file system. WIN NT: The windows NT environment installing window NT file system disk partitions and fault tolerance setting up and administering user and group accounts, securing resources running applications configuring the windows NT environment, Windows NT services, printing from Windows NT, trouble shooting Windows NT.

• Data Communication & Computers Networks

Data Communication System: Purpose, Components : Source, transmitter, transmission System, receiver, and destination. Data transmission: Frequency, Spectrum and Bandwidth. Time-domain and frequency dominion Concepts. Relationship between data-rate and Bandwidth. Analog and digital data transmission. Data and signal. Analog and digital Signaling of analog and digital data. Modem, Modulation techniques,CODEC, Digital Transmitter etc. Transmission impairments : Attenuation and attenuation distortion, delay distortion, noise. Introduction to Network, OSI reference model, TCP/IP reference model. Transmission Media: Magnetic Media, Twisted-Pair cables, Baseband & Broadband Coaxial cables, Fiber Optics.Wireless Transmission: Radio Transmission, Microwave Transmission.ISDN; ATM; Data Link Layer: Services, Framing, Error Control, Error-detecting & Correcting Codes.Data Link Protocols: Stop-and-Wait Protocol, Sliding Window Protocol.HDLC; Static & Dynamic Channel allocation in LANs & MANs.Multiple Access Protocols: ALOHA, CSMA/CD; IEEE standards 802.3 and Ethernet, 802.4: Token Bus; 802.5: TokenRing. Bridges, Routers, Gateways, Routing Algos, Congestion control Algos, Internetworking, The TCP/IP Protocol, IP Addressing, Subnets.

• Computer Graphics

Basics of Graphics Systems Applications, Display Devices : Video Displays, Raster-Scan Displays, Rondom Scan Displays, DVST, Flat-panel Displays. Input devices : Keyboards, Mouse, Trackball and Spaceball, Joysticks, Digitizers, Image Scanner, Touch panel, light pens, Voice Systems etc. Line drawing algorithms: DDA Algorithm, Bresenham’s line Algorithm.Bresenham’s Circle drawing algorithm, Mid-Point Circle Algorithm, Scan-line Polygen Fill Algorithm, Inside-Outside test, Boundery Fill algorithm, Flood-Fill algorithm. Pixel, Pixel addressing, Antialiasing.Clipping : Cehen-Sutharland line clipping algorithm, Line clipping using nonrectangular clip windows, Polygon clipping. Text clipping. Two-dimensional geometric transformation : Translation, Rotation, Scaling, Reflection, Shear, Matrix representation and Homogeneous coordinates.Composite transformation: Translations, Rotations, Scalings.General Pivot-Point Rotation and Scaling

• Visual Language Programming

Generic Concept of procedure & event oriented languages; Low and high level visual languages; Visual architecture: methods, statements and properties; Basic concepts of visual program design and comparison with non-visuals; Visual programming environment and development of visual programs: project window, forms, code, properties & event procedures; Program design including case solution, run time properties; Programming using Visual Basic/VC++; implementation of a case study.

• Internet Technology and Applications & e-commerce

Introduction of Internet, understanding the Internet, A tower of the Internet Hardware requirement to connect to the Internet, S/W requirement and Internet service products Internet Addressing Mall using mail from shell account understanding the web, using the web, Introduction to usenet file types used on the Internet Mailing list Telnet Talk facts: using talk from a shell a/c IRC Basics of TCP/IP, Introduction to Internet Programming with JAVA/Perl: creating applets, applications, security.Introduction to E-Business, Electronic Fund Transfer (EFT), Value-chain, internet Business strategy, Functional Architecture, implementation Strategies; Building Blocks of E-commerce, System design, creating and managing content etc; Cryptography and security management; Payment systems; Auxiliary system; transaction Processing; Building e-commerce system, system architecture, secure links etc;Present and future Trend; Impact of e-commerce; A case Study on development of e-commerce system.

• Object Oriented Methodology and UML

Object modelling bject and classes ;links and association, generalisation and inheritance; Grouping construct, Aggregation, generalisation as extension and restriction .Multiple inheritance; Meta data, candidate Keys .Dynamic Modelling :Events and states nesting Concurrency .Functional modelling : Analysis bject modelling ,functional modelling adding operations, Iteration; System design : Subsystem , concurrency .Allocation to Processors and tasks. Management of data stores. Control implementation. Boundary condition. Architectural Framework . object design ptimization , Implementation of control . Adjustment of inheritance. Design of associations, Documentation ,Comparison of methodologies.; Implementation : Using a programming language , a data base system . Programming styles , reusability , extensibility , robustness . programming –in – the- large , case study; Overview of UML: Terminology, Methology; Application of UML with a system example.

• Network Programming

Inter Process Communication: Pipes, FIFOs, message queues, Semaphores. Communication protocols: TCP/IP, XNS, SNA, NetBIOS, UUCP. Berkley Sockets. System V Transport Layer Interface. Security. Winsock programming using the Windows sockets and blocking I/O. Other Windows Extensions. Network dependent DLLs. Sending and receiving data over connections. Terminations; Novel IPX/SPX: Novel’s windows driver. Network interface for windows. IPX/SPX procedure. Datagram Communication. Connection oriented communication with SPX. IPX/SPX implementation of DLLs. Programming application: Time and Date routines. Ping, Trivial File Transfer Protocol, Remote Login, RPC.

• Advance DBMS

Review of database management systems; Design and knowledge database; Review of different database models; Concept of data bases and storage structures ;Query Optimization , Integrity of databases : need for concurrency control, locking, deadlock avoidance etc. database recovery; Coding: representation of knowledge, classification and compression; Object relational databases, Object oriented databases, Distributed databases: advantages, techniques and related concepts ; Management of Distributed transactions, Heterogeneous Database, Client server Databases technologies ,temporal and spatial databases , Internet databases . Case Study – ORACLE as RDBMS, ORDBMS, OODBMS capabilities.

• Parallel Processing

Concept of parallelism, Mechanism for uniprocessor systems; Parallel computer architecture; Pipelining and vector processing; Instruction and arithmetic pipelining; parallel algorithms for array processors; SIMD computers and performance enhancements; Microprocessor Architecture and Programming: Functional Structure, interconnection networks, multiprocessors; Parallel Algorithms for multiprocessors; Data driven computing and languages.

• Artificial Intelligence

Scope of AI : Games ,the ROM proving ,natural language processing , vision and speech processing , robotics expert system, AI technique search knowledge, abstraction ;Problem Solving : State space search : production system. Search space control: depth first ,breadth first search, heuristic search –hill climbing ,best first search , branch and bound . Minimax search , Alpha –Beta cut offs. Solemnizing queries , Unification .Modus pones . Resolution , dependency directed backtracking, forward reasoning : Conflict resolution, Logic Programming in PROLOG.

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admin All India Entrance Jamia Hamdard University MCA Entrance Exam Syllabus.

West Bengal JEE Exam Syllabus for Biology

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM – 2009

BIOLOGICAL SCIENCES

Unit of Life : Definition of life, Cell as the basic unit of life. Cell theory, Prokaryotic and Eukaryotic cell –

structure and differences.

Ultrastructure and functions of cellular components : Cell wall, Plasma membrane, Plastid, Endoplasmic

reticulum, Golgi bodies, Mitochondria, Ribosomes, Lysosomes, Nucleus, Centrosomes, Cilia, Flagella.

Microscopy : Components and principles of Simple and Compound Microscope;

Electron Microscope : Basic functional principles.

Physical and chemical principles involved in maintenance of life processes :Diffusion, Osmosis,

Absorption, Osmoregulation.

Biomolecules : Classification and structural properties of carbohydrates, lipids, aminoacids, proteins and

nucleic acids.

Carbohydrates : Monosaccharides, digosaccharides, and polysaccharides (starch, glycogen, cellulose).

Proteins :Simple (albumins, globulins, collagen) and conjugated proteins (only examples).

Nucleic acids : Structure of DNA, RNA, types of RNA.

Enzymes : Definition & properties, Examples; Mechanism of Action, Allosterism and Regulation.

Chromosomes and Cell Division : Morphology of chromosomes; Euchromatin and Heterochromatin.

Nucleic acid as genetic material (Examples: Bacterial Transformation and Viral Transduction).

Brief idea of Polytene chromosomes:Cell cycle and phases (excluding control mechanism). Characters of

malignant cell; Process & significance of Meiosis.

Genetics : Laws of Heredity : (Monohybrid and dihybrid crosses; Mendel’s laws). Back cross, Test cross,

Linkage, Crossing over, Sex linked inheritance – Colour blindness, Haemophilia.

Mutation – Definition and Types; Replication of DNA, Transcription and Translation (Brief idea).

Origin, Evolution and Diversity of Life :Haldane and Oparin’s concept on origin of life. Modern concept

of Natural selection, Biological Species concept.

Human evolution – an outline.

Taxonomy and Classification : Definition; Importance of Taxonomy, Binomial Nomenclature, Law of

Priority (Homonym & Synonym).

Concept of Biodiversity : Definition of Biodiversity ; Genetic diversity; Species diversity and Ecosystem

diversity. Five kingdom classification (only distinct characters).Salient features of major animal phyla with

common examples, classification of Chordates (up to Sub Class) with distinctive characters only.

Population Biology :Concept of population growth (logistic and exponential) and population control.

Ecosystem : Concept of ecosystem and Biosphere, Wetland..

Brief idea of Ecological pyramids, Energy flow, Biogeochemical cycle (concept only).

Environmental pollution : Air, water and noise pollution – sources effects and probable control strategies;

Biomagnification and Bioaccumulation. Cause of Dyslexia, Minamata and Etai etai diseases. Green house

effect, BOD, COD, Acid rain and Ozone hole.

Virus and Bacteria :Morphological characteristics of Bacteriophage (T2),Plant virus (TMV);Animal virus

(influenza),Bacterial cell (E. coli).

Staining : Gram staining for bacteria.

Biotechnological application of microbes : (a)Agricultural – Rhizobium and other Nitrogen fixing

bacteria, Biofertilizers and Bio- pesticides ; (b) Industrial – Production of curd; tanning and brewery;

synthesis of antibiotics, vitamin. (c)Cloning of microbial genes.

Tissue and tissue system :(a)Plant Tissues–Meristematic and permanent (types with characterization and

function).(b)Animal Tissue – outline classification and examples.

Functions of life :

Photosynthesis :

Major photosynthetic pigments, outline concept of light and dark reaction phases, basic idea of bacterial

photosynthesis, C2, C3, C4 pathways, CAM (in brief), photorespiration.

Respiratory system :

(a) Definition of respiration, Mechanisms of glycolysis, Kreb’s cycle (Flow chart only; calculation for

ATP, CO2 & H2O) ; Outline idea of Electron Transport system, Relationships of photosynthesis and

respiration. (b)Respiratory system in human : Respiratory tract, Mechanism of breathing, Role of

intercostals muscles and diaphragm;

Significance of physiological and anatomical dead space.

Tidal volume, inspiratory and expiratory reserve volumes, residual volume, vital capacity. Composition

of inspired, expired and alveolar air. Common respiratory diseases – definition and causes – Asthma,

Tuberculosis, Hypoxia, Anoxia, Apnoea, Dyspnoea.

Cardiovascular system & Blood :

Anatomy of Heart – junctional tissues of the heart; origin and propagation of cardiac impulse. Histological

structures of arteries, veins and capillaries.

Cardiac cycle – Atrial and ventricular events only; cardiac cycle time, Heart sound.

Cardiac output – definition, Stroke and Minutes volume.

Blood pressure : factors controlling & measurement.

Blood – Composition and functions of blood.

Blood coagulation and anticoagulants, Blood group and Rh factor, Blood Transfusion, Lymph and tissue

fluid formation and functions, Portal circulation.

Nutrition and Digestive system :Basic constituents of food and their nutritional significance. Vitamins –

dietary sources, functions and deficiency symptoms of water and fat soluble vitamins. Structure and

functions of the alimentary canal and the digestive glands. Functions of the digestive juices (saliva, gastric

juice, pancreatic juice, intestinal juice), Biles.

Digestion and absorption of carbohydrates, lipids and proteins. Diseases – Peptic and Gastric ulcers,

Gastritis; fasting and obesity.

Metabolism : Definition; B.M.R. – Controlling factors; elementary idea of metabolic pathways;

glycogenesis, glycogenolysis, gluconeogenesis, Oxidation of fatty acids, Ketone body formation and its

significance.

Deamination, Transamination and Decarboxylation of aminoacids (definition only).

Excretory system : Histology and function of the nephron (brief idea)

Normal and abnormal constituents of urine.

Nervous and Muscular system : Brief outline of human brain structure.

Cranial nerves : Distribution and Function.Spinal cord – Structure and major functions, Reflex arc (types)

and reflex action : Conditional and unconditional reflexes.

Autonomic : sympathetic and parasympathetic (definition only) nervous system.

Synapse : Structure and mechanism of synaptic transmission.

Different types of muscles and their structure, properties of muscles

(i)Excitability (ii)Contractility (iii)All or none law (iv)Refractory period (v)Summation of stimuli

(vi)Tetanus (vii)Rigor mortis; Machanism of muscle contraction.

Endocrine system and animal hormones :

Definition of endocrine glands and hormones, functions of hormones released from (i)pituitary (ii)thyroid

(iii)pancreas (iv)adrenal (v)gastrointestinal gland, An outline mechanism of action of protein & steroid

hormones.

Causes and symptoms of Acromegaly,Diabetis insipidus, Diabetis mellitus, Goiter, Cushing’s disease.

Growth, Reproduction, and Ageing :

A. In Plants :

Different parts of a typical flower (China rose). Types of flower : regular and irregular, actinomorphic,

zygomorphic.Aestivation in Musaceae & Malvaceae.Floral formula : Definition, symbols used in floral

formulae in Musaceae (e.g. Banana) and Malvaceae (eg. China rose) ; Pollination – Definition, self and

cross pollination; Merits and demerits of self and cross pollination. Fertilization – Process of double

fertilization. Dispersal of fruits and seeds – Types with examples. Phases and factors of Growth, Differences

between growth and development, Abscission senescence, ageing and growth of seeding and the role of

gibberellic acid.

B. In Animals :

Primary and secondary sex organs and secondary sex characters – Testis – Histology, Functions of

Testosterone. Spermatogenesis (outline). Ovary – Histology : Functions of estrogen and progesterone;

Oogenesis (outline); structure of mature Graafian follicle .

Menstrual cycle (brief idea). Fertilization and Implantation.

Immunology : A brief idea of antigen and antibody. Elementary knowledge of inherited, acquired, humoral,

cell mediated immunity. Active and passive immunity. Prevention of AIDS and Hepatitis B.

Medical, Agricultural and Economic zoology:

A.Outline idea of diseases, their causative organism, mode of infection, symptoms and preventive measures

of :

(i) Malaria

(ii) Filariasis

(iii) Ascariaisis

Distinguishing features of Culex, Anopheles and Aedes

Life cycle and comparative study of Culex and Anopheles;

Causative agents of encephalitis and kalaazar and control of their vectors.

B. Characteristic features of major and minor carps and examples of exotic carps. Mechanism of induced

breeding – hypophysation.

Composite culture of carps, common diseases of carp – Gillrot, fin rot and Dropsy.

Definition of pest, Damage symptoms and control of Scirpophaga incertulus and Leptocorisa acuta.

C.Poultry – Types of poultry birds ; high yielding varieties of poultry birds. Species of honey bees in India

and different castes in a colony. Composition and uses of honey.

Chemical composition of silk, types of silk and silk worms.

Life cycles of mulberry silk worm. Structure of silk gland.

Symptoms of Flacherie, Muscardine, Grassarie and Pebrine.

Application of Biology :

Pesticides and Biological Pest Control – Benefit and hazards, Basic principles of ex situ and in situ

conservation. Red Data Book, Green Data Book.

Role of phytohormones in horticulture and agriculture.

Hybridization in plants – Definition and techniques.

Idea about plant cell and tissue culture – Micropropagation.

Principles and application of transgenic plants and animal, Test tube baby.

Biomedical engineering :

Application – ECG & EEG

Imaging – USG, CT Scan, X-ray,MRI

Therapeutic – Pacemaker, Dialyzer.

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West Bengal JEE Syllabus for Chemistry

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM – 2009

CHEMISTRY

Atoms, Molecules and Chemical Arithmetic :

Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s Hypothesis and its applications.

Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight;

Gram equivalent weight and mole concept; Chemical formulae; Balanced chemical equations; Calculations

(based on mole concept) involving common oxidation-reduction, neutralization, and displacement reactions;

Concentration in terms of mole fraction, molarity, molality and normality.

Percentage composition, empirical formula and molecular formula; Numerical problems.

Atomic Structure

Concept of Nuclear Atom – electron, proton and neutron (charge and mass), atomic number; Rutherford’s

model and its limitations; Extra nuclear structure; Line spectra of hydrogen atom.

Quantization of energy (Planck’s equation E = hv); Bohr’s model of hydrogen atom and its limitations,

Sommerfelds modifications (elementary idea); The four quantum numbers, ground state electronic

configurations of many electron atoms and mono-atomic ions; The Aufbau Principle; Pauli’s Exclusion

Principle and Hund’s Rule.

Uncertainty principle; The concept of atomic orbitals, shapes of s, p and d orbitals (pictorial approach)

Radioactivity and Nuclear Chemistry

Radioactivity – α-, β-, γ-rays and their properties; Artificial transmutation; Rate of radioactive decay, decay

constant, half-life and average life period of radio-elements; Units of radioactivity; Numerical problems.

Stability of the atomic nucleus – effect of neutron–proton (n/p) ratio on the modes of decay, group

displacement law, radioisotopes and their uses (C, P, Co and I as examples) isobars and isotones (definition

and examples), elementary idea of nuclear fission and fusion reactions.

The Periodic Table and Chemical Families

Modern periodic law (based on atomic number); Modern periodic table based on electronic configurations,

groups (Gr. 1–18) and periods. Types of elements-representative (s-block and p-block), transition (d-block)

elements and inner transition (f-block / lanthanides and actinides) and their general characteristics. Periodic

trends in physical and chemical properties–atomic radii, valency, ionization energy, electron affinity,

electronegativity, metallic character, acidic and basic characters of oxides and hydrides of the representative

elements (up to Z = 36). Position of hydrogen and the noble gases in the periodic table; Diagonal

relationships.

Chemical Bonding and Molecular Structure

Valence electrons, the Octet rule, electrovalent, covalent and coordinate covalent bonds with examples;

Properties of electrovalent and covalent compounds. Limitations of Octet rule (examples); Fajan’s Rule.

Directionality of covalent bonds, shapes of poly-atomic molecules (examples); Concept of hybridization of

atomic orbitals (qualitative pictorial approach) : sp, sp2, sp3 and dsp2.

Molecular orbital energy diagrams for homonuclear diatomic species – bond order and magnetic properties.

Valence Shell Electron Pair Repulsion (VSEPR) concept (elementary idea) – shapes of molecules. Concept

of resonance (elementary idea), resonance structures (examples). Elementary idea about electronegativity,

bond polarity and dipole moment, inter- and intra- molecular hydrogen bonding and its effects on physical

properties (mp, bp and solubility); Hydrogen bridge bonds in diborane.

Double salts and complex salts, co-ordination compounds (examples only), co-ordination number (examples

of co-ordination number 4 and 6 only).

Gaseous state

Measurable properties of gases. Boyle’s Law and Charles Law, absolute scale of temperature, kinetic theory

of gases, ideal gas equation – average, root mean square and most probable velocities and their relationship

with temperature.

Dalton’s Law of partial pressure, Graham’s Law of gaseous diffusion. Deviations from ideal behavior.

Liquefaction of gases, real gases, van der Waal’s equation; Numerical problems.

Chemical Energetics and Chemical Dynamics

Chemical Energetics – conservation of energy principle, energy changes in physical and chemical

transformations. First law of thermodynamics; Internal energy, work and heat, pressure-volume work;

Enthalpy. Internal energy change (ΔE) and Enthalpy change (ΔH) in a chemical reaction. Hess’s Law and its

applications (Numerical problems). Heat of reaction, fusion and vapourization; Second law of

thermodynamics; Entropy; Free energy; Criterion of spontaneity.

Chemical Equilibria – The Law of mass action, dynamic nature of chemical equilibria. Equilibrium

constants, Le Chatelier’s Principle. Equilibrium constants of gaseous reactions (Kp and Kc) and relation

between them (examples). Significance of ΔG and ΔG°.

Chemical Dynamics – Factors affecting the rate of chemical reactions (concentration, pressure,

temperature, catalyst). Arrhenius equation and concept of activation energy.

Order and molecularity (determination excluded); First order reactions, rate constant, half-life (numerical

problems), examples of first order and second order reactions.

Physical Chemistry of Solutions

Colloidal Solutions – differences from true solutions; Hydrophobic and hydrophilic colloids (examples and

uses); Coagulation and peptization of colloids; Dialysis and its applications; Brownian motion; Tyndall

effect and its applications; Elementary idea of emulsion, surfactant and micelle.

Electrolytic Solutions – Specific conductance, equivalent conductance, ionic conductance, Kohlrausch’s

law, Faraday’s laws of electrolysis, applications. Numerical problems.

Non-electrolytic Solutions – Types of solution, vapour pressure of solutions. Raoult’s Law; Colligative

properties – lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic

pressure and their relationships with molecular mass (without derivations); Numerical problems.

Ionic and Redox Equilibria

Ionic equilibria – ionization of weak electrolytes, Ostwald’s dilution law. Ionization constants of weak

acids and bases, ionic product of water, the pH – scale, pH of aqueous solutions of acids and bases;

Buffer solutions, buffer action and Henderson equation.

Acid-base titrations, acid-base indicators (structures not required).

Solubility and Solubility Products.

Common ion effect (no numerical problems).

Redox Equilibria – Oxidation-Reduction reactions as electron transfer processes, oxidation numbers,

balancing of redox reactions by oxidation number and ion-electron methods.

Standard electrode potentials (E°), Electrochemical series, feasibility of a redox reaction.

Significance of Gibb’s equation : ΔG° = – nFΔE° (without derivation), no numerical problems.

Redox titrations with (examples); Nernst equations (Numerical problems).

Chemistry of Non-metallic Elements and their Compounds

Carbon – occurrence, isotopes, allotropes (graphite, diamond, fullerene); CO and CO2 production, properties

and uses.

Nitrogen and Phosphorus – occurrence, isotopes, allotopes, isolation from natural sources and purification,

reactivity of the free elements. Preparation, properties, reactions of NH3, PH3 , NO, NO2 , HNO2, HNO3,

P4O10, H3PO3 and H3PO4.

Oxygen and Sulfur – Occurrence, isotopes, allotropic forms, isolation from natural sources and purification,

properties and reactions of the free elements. Water, unusual properties of water, heavy water (production

and uses). Hydrogen peroxide and ozone (production, purification, properties and uses).

Halogen

Halogens – comparative study, occurrence, physical states and chemical reactivities of the free elements,

peculiarities of fluorine and iodine; Hydracids of halogens (preparation, properties, reactions and uses),

inter-halogen compounds (examples); Oxyacids of chlorine.

Chemistry of metals :

General principles of metallurgy – occurrence, concentration of ores, production and purification of metals,

mineral wealth of India.

Typical metals (Na, Ca, Al, Fe, Cu and Zn) – occurrence, extraction, purification (where applicable),

properties and reactions with air, water, acids and non-metals.

Manufacture of steels and alloy steel (Bessemer, Open-Hearth and L.D. process).

Principles of chemistry involved in electroplating, anodizing and galvanizing.

Chemistry in Industry

Large scale production (including physicochemical principles where applicable omitting technical details

and uses of individual items).

Heavy chemicals : Sulfuric acid (contact process), Ammonia (Haber’s process), Nitric acid (Ostwald’s

process), sodium bi-carbonate and sodium carbonate (Solvey process).

Polymers, Polythene, Nylon-66, rubber from natural source, vulcanization.

Electrochemicals – sodium hydroxide, chlorine, bleaching powder as by-products.

Fuel Gases – LPG, CNG.

Silicon carbide and silicones.

Environmental Chemistry

Common modes of pollution of air, water and soil. Ozone layer, ozone hole – important chemical reactions.

Green House effect; Smog; Pollution of water by domestic and industrial effluents; Pollutants–pesticides,

fertilizers and plastics.

Chemistry of carbon compounds

Hybridization of carbon – σ- and π-bonds.

Isomerism – constitutional and stereoisomerism; Geometrical and optical isomerism of compounds

containing upto two asymmetric carbon atoms. IUPAC nomenclature of simple organic compounds–

hydrocarbons, mono and bifunctional molecules only (alicyclic and heterocyclic compounds excluded).

Conformations of ethane and n-butane (Newman projection only).

Electronic effects – inductive, resonance and hyperconjugation. Stability of carbocation, carbanion

and free radicals; Rearrangement of carbocation; Electrophiles and nucleophiles, tautomerism in β-

dicarbonyl compounds, acidity and basicity of simple organic compounds.

Aliphatic Compounds

Alkanes – Preparation from alkyl halides and carboxylic acids; Reactions – halogenation and

combustion.

Alkenes and Alkynes – Preparation by elimination of alcohols, alkyl halides and quaternary ammonium

hydroxides, Saytzeff and Hofmann rules; Reactions – electrophilic addition of X2, HX, HOX, H2O (X =

halogen), ozonolysis, epoxidation and oxidation with KMnO4, OsO4 (stereochemistry of addition excluded).

Markownikoff’s and anti-Markownikoff’s additions; Hydroboration; Oxymercuration – demercuration,

reduction of alkenes and alkynes (H2/Lindler catalyst and Na in liquid NH3), metal acetylides.

Alkyl halides – Preparation from alcohols; Formation of Grignard reagents and their synthetic applications

for the preparation of alkanes, alcohols, aldehydes, ketones and acids; SN1 and SN2 reactions (preliminary

concept).

Alcohols – Preparation from carbonyl compounds and esters. Reaction – dehydration, oxidation,

esterification, reaction with sodium, ZnCl2 / HCl, phosphorous halides.

Ethers – Preparation by Williamson’s synthesis; Cleavage with HCl and HI.

Aldehydes and Ketones – Preparation from esters, acid chlorides, gem-dihalides, Ca-salt of carboxylic

acids. Reaction – Nucleophilic addition with HCN, hydrazine, hydroxyl amines, semi carbazides,

alcohols; Aldol condensation, Clemmensen and Wolff-Kishner reduction, haloform, Cannizzaro and

Wittig reactions.

Carboxylic Acids – Hydrolysis of esters (mechanism excluded) and cyanides; Hunsdicker and HVZ

reactions.

Aliphatic Amines – Preparation from nitro, cyano and amido compounds. Distinction of 1º, 2º and 3º amines

(Hinsberg method); Reaction with HNO2; Carbyl amine reaction.

Aromatic Compounds

Benzene – Kekule structure, aromaticity and Hückel rule. Electrophilic substitution – halogenation,

sulfonation, nitration, Friedel Crafts reaction, ozonolysis. Directive influence of substituents in

monosubstituted benzenes.

Amines – Preparation from reduction of nitro compounds; Formation of diazonium salts and their stability;

Replacement of diazonium group with H, OH, X (halogen), CN and NO2, diazocoupling and reduction.

Haloarenes – Nucleophilic substitution, cine substitution (excluding mechanism).

Phenols – halogenation, sulfonation, nitration, Reimer-Tiemann and Kolbe reactions.

Aromatic Aldehydes – Preparation by Gattermann, Gattermann – Koch, Rosenmund and Stephen’s

method. Reactions – Perkin, Benzoin and Cannizzaro.

Application Oriented chemistry

Main ingredients, their chemical natures (structures excluded) and their side effects, if any, of common

antiseptics, analgesics, antacids, vitamin-C.

Introduction to Bio-molecules

Carbohydrates – Pentoses and hexoses. Distinctive chemical reactions of glucose.

Aminoacids – glycine, alanine, aspartic acid, cysteine (structures). Zwitterion structures of amino acids,

peptide bond.

ADP and ATP – structures and role in bioenergetics; Nucleic acids – DNA and RNA skeleton structures.

Names of essential elements in biological system.

Principles of qualitative analysis

Detection of water soluble noninterfaring Acid and Basic Radicals by dry and wet tests from among :

(a) Acid Radicals : Cl-, S2-, SO4

2-, NO–

3, CO3

2-

(b) Basic Radicals: Cu2+, Al3+, Fe3+, Fe2+, Zn2+, Ca2+, Mg2+, Na+, NH4

+

Detection of special elements (N, Cl, Br, I and S) in organic compounds by chemical tests.

Identification of functional groups in : phenols, aromatic amines, aldehydes, ketones and carboxylic

acids.

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West Bengal JEE Syllabus for Physics

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM – 2009

PHYSICS

Mechanics & General properties of matter

(i) Units and dimensions : Units of measurement, system of units, fundamental and derived units, S I

units, dimensional analysis.

Methods of measurement: Vernier scale, screw gauge, analysis of errors, significant figures.

(ii) Scalars and vectors: Addition, subtraction, multiplication of vectors.

(iii) Kinematics in one, two and three dimensions, projectiles, uniform circular motion,centripetal

force, centrifigual force, relative velocity.

(iv) Dynamics: Newton’s laws of motion; inertial frames, uniformly accelerated frame (pseudoforces),

conservation of linear momentum, rocket motion, centre of mass, impulsive forces, friction.

(v) Work, Power and Energy , conservative and non-conservative forces, conservation of energy,

collision(elastic and inelastic)

(vi) .Rotational motion : Torque, angular momentum and conservation of angular momentum,

moment of inertia, radius of gyration, moment of inertia of objects with simple geometrical shapes,

rotational kinetic energy and rolling on horizontal surface.

Gravitation: Laws of gravitation, gravitational field and potential, acceleration due to gravity and

its variation, escape velocity, Kepler’s laws and planetary motion, motion of satellites,

Geostationary orbit.

Elasticity: Hooke’s law, elastic modulii, Poisson’s ratio, elastic energy.

Hydrostatics and fluid mechanics: Pressure in a fluid, Pascal’s law, Archimedes’ principle,

hydraulic press.

Surface energy and surface tension, capillary rise.

Viscosity, streamline and turbulent motion, critical velocity, Reynold’s number, Stoke’s law,

Bernoulli’s theorem.

Vibrations: Simple Harmonic Motion, equation of motion, damped and forced vibrations,

resonance, superposition of SHM.

Wave motion: Elastic waves, longitudinal and transverse waves. progressive waves, superposition

of waves: interference, stationary waves, beats, vibration of strings, air columns, velocity of elastic

waves in different media, Doppler effect.

Thermal Physics: Scales of temperature, thermal expansion of solids, liquids and gases,

calorimetry, change of state of matter, latent heat, transition temperature, Transmission of heat:

conduction, convection, radiation, Black body radiation, absorptive and emissive powers: Kirchoffs

law, Wien’s law, Stefan’s law, Newton’s law of cooling, Kinetic theory : mean free path, pressure of

an ideal gas, mean and rms velocity of molecules of a gas, kinetic interpretation of temperature,

degrees of freedom, equipartition of energy(statement only) — application to monoatomic and

diatomic gases.

Thermodynamics: first law of thermodynamics, equivalence of heat and work, intensive and

extensive thermodynamic variables, reversible and irreversible processes, specific heats of gases,

relation between Cp and Cv.

Optics : reflection and refraction at plane and spherical surfaces, total internal reflection, thin

lenses, power of a lens, combination of lenses and mirrors, deviation and dispersion by prisms.

Simple and compound microscopes, astronomical telescope, human eye: defects and remedies.

Coherent sources, interference of light, Young’s double slit.

Electrostatics : Coulomb’s law, electric field and potential,flux of electric field, Gauss’ law,

electric field and potential due to an infinite line charge, charged infinite sheet, solid spheres and

spherical shells.Electric dipole and field due to dipole.

Capacitance, spherical and parallel plate capacitors, energy stored in a capacitor, series and parallel

combination of capacitors,

Current electricity : Electric current, drift velocity and mobility, Ohm’s law, resistivity,

combination of resistances in series and parallel, combination of cells.

Kirchoffs laws, Wheatstone bridge, Metre bridge, potentiometer.

Heating effect of current, thermoelectricity, Seebeck and Peltier effect.

Chemical effect of current, Faraday’s law of electrolysis,:primary and secondary cells.

Electromagnatism : Magnetic effects of Current, Biot Savart’s law, magnetic field due to an

infinite line charge, circular coil and solenoid, Ampere’s circuital law, Lorentz force, Fleming’s left

hand rule, force between two current carrying conductors, magnetic moment of a current loop,

magnetic dipole, torque experienced by a current carrying coil in a uniform magnetic field,

galvanometer, current sensitivity, conversion of galvanometer to voltmeter and ammeter.

Magnetic field of earth, tangent galvanometer, magnetic properties of materials : Dia, para and

ferromagnet , permeability, susceptibility.

Electromagnetic induction : Magnetic flux, Faraday’s laws of electromagnetic induction, Lenz’s

law, self and mutual induction, , Flemings right hand rule, Alternating current, peak and rms

value of alternating current; generator, D.C. motor and transformer

Qualitative idea of electromagnetic wave and its spectrum .

Modern Physics: Bohr’s atomic model for hydrogen like atom, hydrogen spectrum,

x-ray emission, Moseley’s law, wave particle duality, de Broglie’s hypothesis, photo electric effect .

Constituents of atoms, isotopes, mass defect, mass-energy equivalence, binding energy.

radioactivity – α, β, γ radiation, half life, mean life, fission, fusion.

Energy bands in solids, intrinsic and doped semiconductors, p-n junction diode, rectifier, pnp and

npn transistors, common emitter characteristics.

Binary number, AND, OR, NOT, NAND and NOR gates .

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West Bengal JEE Syllabus for Mathematics

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM – 2009

M A T H E M A T I C S

Algebra

A.P., G.P., H.P. :Definitions of A. P. and G.P.; General term; Summation of first n-terms; A.M.and

G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric series.

A.P., G.P., H.P. :Definition; General properties; Change of base.

Complex Numbers: Definition and properties of complex numbers; Complex conjugate; Triangle

inequality; Square root of complex numbers; Cube roots of unity; D’Moivre’s theorem (statement only)

and its elementary applications.

Quadratic Equations : Quadratic equations with real coefficients; Relations between roots and

coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic

expression ax2+bx+c (a,b,c are rational numbers and a≠0).

Permutation and combination : Permutation of n different things taken r at a time (r ≤ n). Permutation of n

things not all different. Permutation with repetitions (circular permutation excluded).

Combinations of n different things taken r at a time (r ≤ n). Combination of n things not all different.

Basic properties.

Problems involving both permutations and combinations.

Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of

squares, sum of cubes of first n natural numbers, divisibility properties like 2 2n – 1 is divisible by 3 (n ≥

1), 7 divides 32n+1+2 n+2(n ≥ 1).

Binomial theorem (positive integral index) :Statement of the theorem, general term, middle term,

equidistant terms, properties of binomial co-efficients.

Infinite series :Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and

Logarithmic series with range of validity (statement only), simple applications.

Matrices : Concepts of m× n (m ≤ 3, n ≤ 3) real matrices, operations of addition, scalar multiplication and

multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of

determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a

matrix. Finding area of a triangle. Solutions of system of linear equations. (Not more than 3 variables).

Sets, Relations and Mappings : Idea of sets, subsets, power set, complement, union, intersection and

difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three

finite sets, Cartesian product of sets.

Relation and its properties. Equivalence relation – definition and elementary examples, mappings, range

and domain, injective, surjective and bijective mappings, composition of mappings, inverse of a

mapping.

Probability : Classical definition, addition rule, conditional probability and Bayes’ theorem,

independence, multiplication rule.

Trigonometry

Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric

equations. Properties of triangles, inverse trigonometric functions.

Co-ordinate geometry of two dimensions

Basic Ideas : Distance formula, section formula, area of a triangle, condition of collinearity of three

points in a plane.

Polar coordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel

transformation of axes, concept of locus, elementary locus problems.

Straight line : Slope of a line. Equation of lines in different forms, angle between two lines. Condition

of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two

parallel lines. Lines through the point of intersection of two lines.

Circle : Equation of a circle with a given center and radius. Condition that a general equation of second

degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter .

Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of two

intersecting circles.

Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.

Parabola :Standard equation. Reduction of the form x = ay²+by+c or y = ax²+bx+c to the standard form

y² = 4ax or x² = 4ay respectively. Elementary properties and parametric equation of a parabola.

Ellipse and Hyperbola : Reduction to standard form of general equation of second degree when xy

term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with

respect to a conic.

Differential calculus : Functions, composition of two functions and inverse of a function, limit,

continuity, derivative, chain rule, derivatives of implicit functions and of functions defined

parametrically.

Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only). Their geometric interpretation

and elementary application. L’Hospital’s rule (statement only) and applications.

Second order derivative.

Integral calculus : Integration as a reverse process of differentiation, indefinite integral of

standard functions. Integration by parts. Integration by substitution and partial fraction.

Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus

and its applications. Properties of definite integrals.

Differential Equations : Formulation and solution of differential equations of the forms.

1) dy / dx = ƒ(x).g(y)

2) dy / dx = ƒ(y/x)

3) dy / dx = (ax+by) / (cx+dy)

4) dy / dx = (a1x+b1y+c1 )/ (a2x+b2y+c2 ) /(a1/a2 = b1/b2)

5) dy / dx + p(x)y = Q(x)

6) d²y / dx² + p1 dy/dx + p2y = 0 with p1 and p2constants.

7) d²y/dx² = ƒ(x)

Application of Calculus : Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate.Motion in a straight line with constant acceleration.Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and straight lines. Area of the region included between two elementary curves.

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VITEEE PHYSICS SYLLABUS

ELECTROSTATICS
Frictional electricity, charges and their conservation; Coulomb’s law-forces between two point electric charges – Forces between multiple electric charges-superposition principle. Electric field – Electric field due to a point charge, electric field lines; Electric dipole, electric field intensity due to a dipole – behaviour of dipole in a uniform electric field-application of electric dipole in microwave oven. Electric potential – potential difference-electric potential due to a point charge and due to a dipole-Equipotential surfaces – Electrical potential energy of a system of two point charges. Electric flux-Gauss’s theorem and its applications to find field due to (i) infinitely long straight wire (ii) uniformly charged infinite plane sheet (iii) two parallel sheets and (iv) uniformly charged thin spherical shell (inside and outside)
Electrostatic induction-capacitor and capacitance – Dielectric and electric polarisation – parallel plate capacitor with and without dielectric medium – applications of capacitor – energy stored in a capacitor – Capacitors in series and in parallel – action of points –Lightning arrester – Van de Graaff generator.
CURRENT ELECTRICITY
Electric Current – flow of charges in a metallic conductor – Drift velocity and mobility and their relation with electric current. Ohm’s law, electrical resistance – V-I characteristics – Electrical resistivity and conductivity-Classification of materials in terms of conductivity – Superconductivity (elementary ideas) – Carbon resistors – colour code for carbon resistors- Combination of resistors – series and parallel – Temperature dependence of resistance – Internal resistance of a cell – Potential difference and emf of a cell. Kirchoff’s law – illustration by simple circuits – Wheatstone’s Bridge and its application for temperature coefficient of resistance measurement – Meterbridge – Special case of Wheatstone bridge – Potentiometer- principle – comparing the emf of two cells. Electric Power – Chemical effect of current – Electro chemical cells – Primary (Voltaic, Lechlanche, Daniel)-Secondary – rechargeable cell – lead acid accumulator.
EFFECTS OF ELECTRIC CURRENT
Heating effect – Joule’s law – Experimental verification-Thermoelectric effects – Seebeck effect – Peltier effect – Thomson effect – Thermocouple, thermoemf, neutral and inversion temperature-Measurement of thermo emf using potentiometer – Thermopile. Magnetic effect of electric current – Concept of magnetic field, Oersted’s experiment – Biot-Savart law – Magnetic field due to an infinitely long current carrying straight wire and circular coil – Tangent galvanometer – Construction and working – Bar magnet as an equivalent solenoid – magnetic field lines. Ampere’s circuital law and its application to straight and Toroidal solenoids. Force on a moving charge in uniform magnetic field and electric field – cyclotron – Force on current carrying conductor in a uniform magnetic field – forces between two parallel current carrying conductors – definition of ampere. Torque experienced by a current loop in a uniform magnetic field – moving coil galvanometer – Conversion to ammeter and voltmeter – Current loop as a magnetic dipole and its magnetic dipole moment – Magnetic dipole moment of a revolving electron.
ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT
Electromagnetic induction – Faraday’s law – induced emf and current – Lenz’s law. Self induction – Mutual induction – Self inductance of a long solenoid – mutual inductance of two long solenoids. Methods of inducing emf – (i) by changing magnetic induction (ii) by changing area enclosed by the coil and (iii) by
changing the orientation of the coil (quantitative treatment). AC generator – commercial generator. (Single phase, three phase). Eddy current – Applications – Transformer – Long distance transmission.
Alternating current – measurement of AC-AC circuit with resistance – AC circuit with inductor – AC circuit with capacitor – LCR series circuit – Resonance and Q – factor – power in AC circuits.
ELECTROMAGNETIC WAVES AND WAVE OPTICS
Electromagnetic waves and their characteristics – Electromagnetic spectrum-radio, microwaves, infra-red, visible, ultraviolet, X rays, gamma rays. Emission and Absorption spectrum – Line, Band and continuous spectra – Fluorescence and phosphorescence. Theories of light – Corpuscular – Wave – Electromagnetic and Quantum theories. Scattering of light – Rayleigh’s scattering – Tyndal scattering – Raman effect – Raman spectrum – Blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Wavefront and Huygens’s principle – Reflection, total internal reflection and refraction of plane wave at a plane surface using wavefronts. Interference – Young’s double slit experiment and expression for fringe width – coherent source – interference of light- Formation of colours in thin films – analytical treatment – Newton’s rings. Diffraction – differences between interference and diffraction of light- diffraction grating. Polarisation of light waves – polarisation by reflection – Brewster’s law – double refraction – nicol prism – uses of plane polarised light and Polaroid’s – rotatory polarisation – polarimeter.
ATOMIC PHYSICS
Atomic structure – discovery of the electron- specific charge (Thomson’s method) and charge of the electron (Millikan’s oil drop method) – alpha scattering – Rutherford’s atom model. Bohr’s model – energy quantisation – energy and wave number expression – Hydrogen spectrum – energy level diagrams -
sodium and mercury spectra – excitation and ionization potentials. Sommerfeld’s atom model-X-rays – Production, properties, detection, absorption, diffraction of x-rays – Laue’s experiment
- Bragg’s law, Bragg’s X-ray spectrometer – X-ray spectra-continuous and characteristic X-ray spectrum – Mosley’s law and atomic number. Masers and Lasers – spontaneous and stimulated emission – normal population and population inversion – Ruby laser, He- Ne laser – properties and applications of laser light – holography.
DUAL NATURE OF RADIATION AND MATTER – RELATIVITY
Photoelectric effect – Light waves and photons – Einstein’s photoelectric equation – laws of photoelectric emission – particle nature of energy – experimental verification of Einstein’s photoelectric equation – work function – photo cells and their application. Matter waves – wave mechanical concept of the atom – wave nature of particles – DeBroglie relation – DeBroglie wavelength of an electron – electron microscope. Concept of space, mass, time – Frame of references – Galileon transformations, Special theory of relativity – Relativity of length, time and mass with velocity – Einstein’s mass -energy equivalence.
NUCLEAR PHYSICS
Nuclear properties – nuclear radii, masses, binding energy, density, charge- isotopes, isobars and isotones – Nuclear mass defect – binding energy – Stability of nuclei – Bainbridge mass spectrometer.
Nature of nuclear forces- Neutron – discovery – properties – artificial transmutation – particle accelerator. Radioactivity – alpha, beta and gamma radiations and their properties- α-decay, â -decay and γ -decay – Radioactive decay law – half life – mean life – Artificial radioactivity – radio isotopes – effects and uses – Geiger – Muller counter. Radio carbon dating – biological radiation hazards.
Nuclear fission – chain reaction – atom bomb – nuclear reactor – nuclear fusion – Hydrogen bomb- cosmic rays – elementary particles.
SEMICONDUCTOR DEVICES AND THEIR APPLICATIONS
Semiconductor theory – energy band in solids – difference between metals, insulators and semiconductors based on band theory- semiconductor doping – Intrinsic and Extrinsic semi conductors. Formation of P-N Junction – Barrier potential and depletion layer-P-N Junction diode – Forward and reverse bias characteristics – diode as a rectifier – Zener diode-Zener diode as a voltage regulator-LED seven segment display – LCD. Junction transistors – characteristics – transistor as a switch – transistors as an amplifier – transistor biasing – RC, LC coupled and transformer coupling in amplifiers – feed back in amplifiers – positive and negative feedback – advantages of negative feedback in amplifiers – oscillator – condition for oscillations – LC circuit – Colpitt oscillator. Logic gates – NOT, OR, AND, EXOR using discrete components – NAND and NOR gates as universal gates – difference between unipolar and bipolar devices-Integrated circuits -medium, small and very large scale integration – fabrication and
applications – TTL and CMOS, ICs. Laws and theorems of Boolean algebra – operational amplifier – parameters – pin out configuration – Basic applications- Inverting amplifier-Non-inverting amplifier – summing amplifiers. Measuring Instruments – Cathode Ray oscilloscope – Principle-Functional units-uses-Multimeter- construction and uses.
COMMUNICATION SYSTEMS
Modes of propagation, ground wave-sky wave propagation. Amplitude modulation, merits and demerits – applications – frequency modulation – advantages and applications – phase modulation. Antennas and transmission lines – current and voltage distribution – directional pattern – antenna parameters – types of
antenna – design of folded dipole. Radio transmission and reception – AM and FM – superhereterodyne receiver. TV standards, TV transmission and reception – scanning and synchronising – TV Antenna – Video signal analysis. Vidicon (camera tube) and picture tube – block diagram of a monochrome TV transmitter and receiver circuits. Radar – principle – factors influencing maximum range – applications. Digital communication -data transmission and reception – principles of fax, modem, satellite communication – wire, cable and optical fiber communication.

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VITEEE CHEMISTRY SYLLABUS

d AND f-BLOCK ELEMENTS
General Characteristics of d-block elements. Occurrence and principles of extraction: Copper, Silver and Zinc. Preparation, properties of 3 , 4 AgNO CuSO and 7 2 2 O Cr K and 4 KMnO .
Lanthanides-Introduction, oxidation state-Chemical reactivity, Lanthanide contraction, uses and brief
comparison of Lanthanides and Actinides. Nuclear energy, Nuclear fission and fusion-Radio carbon dating – Nuclear reaction in sun – Uses of radioactive Isotopes.
COORDINATION CHEMISTRY
Introduction – Terminology in coordination chemistry – IUPAC nomenclature of mononuclear coordination compounds – Isomerism in coordination compounds – structural isomerism – Geometrical isomerism in 4-coordinate, 6-coordinate complexes – Theories on coordination compounds – Werner’s theory (brief) – Valence Bond theory – Uses of coordination compounds – Biocoordination compounds (Haemoglobin and chlorophyll).

SOLID STATE
Unit cell, X-Ray crystal structure – Types of ionic crystals – Imperfections in solids – Electrical Property – Amorphous solid (elementary ideas only).

THERMODYNAMICS
I and II law of thermodynamics – Spontaneous and non spontaneous processes – entropy – Gibb’s free energy – Free energy change and chemical equilibrium – Third law of thermodynamics.

CHEMICAL EQUILIBRIUM AND CHEMICAL KINETICS
Applications of law of mass action – Le Chatlier’s principle. Rate expression and order of a reaction, zero order, first order and pseudo first order reaction – half life period, determination of rate constant/order of reaction Temperature dependence of rate constant – Arrhenius equation, activation energy.

ELECTROCHEMISTRY
Theory of electrical conductance – Theory of strong electrolytes – Faraday’s laws of electrolysis – Specific resistance, specific conductance, equivalent and molar conductance – Variation of conductance with dilution – Kohlraush’s law. Cells – Electrodes and electrode potentials – Construction of cell and EMF – Fuel cells – Corrosion and its preventions.

ALCOHOLS AND ETHERS
Nomenclature of alcohols – Classification of alcohols – General methods of preparation of primary alcohols – Properties – Methods of preparation of dihydric alcohols: Glycol – Properties – Uses – Methods of preparation of trihydric alcohols – Properties – uses – Aromatic alcohols – Preparation and properties of phenols and benzyl alcohol. Ethers – General methods of preparation of aliphatic ethers – properties – Uses – Aromatic ethers – Preparation of anisole – Reactions of anisole – Uses.

CARBONYL COMPOUNDS
Nomenclature of carbonyl compounds – Comparison of aldehydes and ketones. General methods of preparation of aldehydes – Properties – Uses. Aromatic aldehydes – Preparation of benzaldehyde – Properties and Uses. Ketones – general methods of preparation of aliphatic ketones (acetone) – Properties – Uses. Aromatic ketones – preparation of acetophenone – Properties – Uses, preparation of benzophenone – Properties.

CARBOXYLIC ACIDS
Nomenclature – Preparation of aliphatic monocarboxylic acids – formic acid – Properties – Uses. Monohydroxy mono carboxylic acids; Lactic acid – synthesis of lactic acid. Aliphatic dicarboxylic acids; Preparation of oxalic and succinic acid. Aromatic acids; Benzoic and Salicylic acid – Properties – uses. Derivatives of carboxylic acids; acetyl chloride ( COCl CH3 ) – Preparation – Properties – Uses. Preparation of acetamide, Properties – acetic anhydride – preparation, Properties. Preparation of esters – methyl acetate – Properties.

ORGANIC NITROGEN COMPOUNDS
Aliphatic nitro compounds – Preparation of aliphatic nitroalkanes – Properties – Uses. Aromatic nitro compounds – Preparation – Properties – Uses. Distinction between aliphatic and aromatic nitro compounds. Amines; aliphatic amines – General methods of preparation – Properties – Distinction between 0 0 2 , 1 , and 0 3 amines. Aromatic amines – Synthesis of benzylamine – Properties – Aniline – Preparation – Properties – Uses. Distinction between aliphatic and aromatic amines. Aliphatic nitriles – Preparation – properties – Uses. Diazonium salts – Preparation of benzene diazoniumchloride properties.

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VITEEE MATHEMATICS SYLLABUS

MATRICES AND DETERMINANTS:
Types of matrices, addition and multiplication of matrices-Properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix – Elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, Non-homogeneous equations, homogeneous linear system, rank method.

THEORY OF EQUATIONS, SEQUENCE AND SERIES
Quadratic equations – Relation between roots and coefficients – Nature of roots – Symmetric functions of roots – Diminishing and Increasing of roots – Reciprocal equations. Arithmetic, Geometric and Harmonic Progressions-Relation between A.M., G. M ., and H.M. Special series: Binomial, Exponential and Logarithmic series – Summation of Series.
VECTOR ALGEBRA
Scalar Product – Angle between two vectors, properties of scalar product, applications of dot products. Vector Product – Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines – Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points, angle between two lines. Skew lines – Shortest distance between two lines, condition for
two lines to intersect, point of intersection, collinearity of three points. Planes – Equation of a plane, passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere – Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.

COMPLEX NUMBERS & TRIGONOMETRY:
Complex number system, conjugate – properties, ordered pair representation. Modulus – properties, geometrical representation meaning, polar form principal value, conjugate, sum, difference, product quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications. Roots of a complex number – nth roots, cube roots, fourth roots. Angle measures-
Circular function-Trigonometrical ratios of related angles – Addition formula and their applications – Trigonometric equations – Inverse trigonometric functions-Properties and solutions of triangle.

ANALYTICAL GEOMETRY
Definition of a Conic – General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola – Standard equation of a parabola tracing of the parabola, other standard parabolas, the process of shifting the origin, general form of the standard equation, some practical problems. Ellipse – Standard equation of the ellipse, tracing of the ellipse (x^2/a^2 )+(y^2/a^2 ) = 1 (a> b). Other standard form of the ellipse, general forms, some practical problems Hyperbola – standard equation, tracing of the hyperbola (x^2/a^2 )-(y^2/a^2 ) = 1
, other form of the hyperbola, parametric forms of a conics, chords, tangents and normals – Cartesian
form and parametric form, equation of chord of contact of tangents from a point (x1 ,y1 ) Asymptotes, Rectangular Hyperbola –standard equation of a rectangular hyperbola.

DIFFERENTIAL CALCULUS
Derivative as a rate measure – rate of change – velocity-acceleration – related rates – Derivative as a measure of slopetangent, normal and angle between curves. Maxima and Minima. Mean value theorem- Rolle’s Theorem – Lagrange Mean Value Theorem – Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, Stationary Points – Increasing, decreasing, maxima, minima, concavity convexity points of inflexion. Errors and approximations – absolute, relative, percentage errors, curve tracing, partial derivatives – Euler’s theorem.

INTEGRAL CALCULUS AND ITS APPLICATIONS METHODS OF INTEGRATION STANDARD TYPES
Properties of definite integrals, reduction formulae for sin^n (x) and cos^n (x) , Area, length, volume and surface area.

DIFFERENTIAL EQUATIONS
Formation of differential equations, order and degree, solving differential equations (1st order) – variable separable homogeneous, linear equations. Second order linear equations with constant co-efficient f (x)=e^m(x), sin mx, cos mx,x, x^2.

DISCRETE MATHEMATICS
Mathematical Logic – Logical statements, connectives, truth tables, tautologies, sets, algebraic properties, relations, functions, permutation, combination, Induction. Binary Operations – Semi groups – monoids, groups (Problems and simple properties only), order of a group, order of an element.

PROBABILITY DISTRIBUTIONS:
Probability, axioms, theorems on probability, conditional probability, Random Variable, Probability density function, distribution function, mathematical expectation, variance, discrete distributions-Binomial , Poisson, continuous distribution – Normal

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Given Below is the Syllabus for  VITEEE Entrance Exam

VITEEE Mathematics Syllabus

VITEEE Physics Syllabus

VITEEE Chemistry Syllabus

VITEEE Biology Syllabus

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VITEEE BIOLOGY SYLLABUS

TAXONOMY OF LIVING ORGANISMS
Linnaeus and binomial nomenclature – history and types of classification – status of bacteria and viruses – botanical garden and herbaria – zoological parks and museums and economical and cultural importance – salient features of various plant groups – classification of angiosperms up to series level (Bentham and Hooker’s system) – salient features of nonchordates upto phylum level and chordates up to class level.

EVOLUTION
Darwinism, Neo-Darwinism, Lamarkism, Neo-Lamarkism – modern concepts of natural selection – theories and evidences of evolution (fossil record and biochemical evidences) – sources of variation, mutation, recombination, genetic drift, migration, natural selection – origin and concepts of species: speciation and isolation (geographical and reproductive).

CELL BIOLOGY
Cell theory (Schelieden and Schwann) – Discovery of cell and cell as a self contained unit – prokaryotic and eukaryotic cells and their ultrastructures– unicellular and multicellular organisms – tools and techniques used in cell biology – compound microscope and electron microscope – cell division: amitosis, mitosis and meiosis.

GENETICS
Heredity and variation – Mendel’s laws of inheritance – chromosomal basis of inheritance – linkage and crossing over – mutation and chromosomal aberration – sex linked inheritance – Karyotyping analysis – chromosomal mapping – DNA as a genetic material: structure, replication – RNA structure and types – genetic diversity.

MICROBIOLOGY AND IMMUNOLOGY
Introduction and history of microbiology – Leeuwenhoek, Pasteur, Robert Koch, Lister – Virology: structure, genetics, culture and diseases – bacteriology: structure, genetics and diseases – Protozoan microbiology – pathogenecity of microorganisms – antimicrobial resistance and chemotherapy – innate immunity – lymphoid organs, thymus – T-cells, Bcells ; immunoglobins structure – transplantation and types – immune system disorders.

PLANT PHYSIOLOGY
Morphology of root, leaf, stem, flowers and their modifications – tissue and tissue systems – anatomy of mono and dicot roots, leaves and stems – secondary growth – Photosynthesis: light and dark reactions, C3 and C4 plants – Photophosphorylation: cyclic and noncyclic – photorespiration – transpiration – types and modes of nutrition – mechanism of respiration – glycolysis – Kreb’s cycle – anaerobic pathway – compensation point and fermentation – respiratory quotient (RQ).

HUMAN PHYSIOLOGY
Nutrition: Digestion, Body-mass ratio, calorie value (ICMR standards), balanced diet, obesity –respiration: inspiration, expiration, exchange of gases, process of pulmonary respiration – Digestion: enzymes and its action – Muscular systems: mechanism of action – Circulation: mechanisms of blood circulation, structure of heart – Excretion: ureotelism, urea biosynthesis, nephron ultrafilteration – nervous system: physiology, coordination systems, brain function and receptor organs – reproduction: spermatogenesis, oogenesis, in vitro fertilization – endocrines: harmones and their functions.

MOLECULAR BIOLOGY AND BIOTECHNOLOGY
Concept of gene – central dogma of molecular biology – gene regulation – rDNA technology –– transgenic plants and microbes – gene cloning – genetically modified organisms – gene expression – gene bank – management of plant and animal genetic resources – genetic conservation – microbial type culture – genetic typing studies.

ECOLOGY AND ENVIRONMENT
Human population and explosion – ecosystems – ecological succession – conservation and biodiversity (Biosphere reserves) – wild life: legislation and conservation of wild life – global warming crisis and green house effect – biogeochemical cycle (O2 , C and N elements) – extinction of species – waste management – pollution (water, air, soil, noise and temperature).

APPLIED BIOLOGY AND HUMAN WELFARE
Plant tissue culture and applications – livestock and management – cattle breeding and poultry – farming methods – pisciculture – crops of economic importance: food yielding rice, oil yielding : groundnut, fibre yielding cotton, timber yielding teak – food production: breeding experiments, Biofertilizers – brief account of crop and animal diseases and their control – ethical concerns – biopatent – biopiracy – genetically modified foods – biowar – bioethics – gene therapy – recent advances in vaccine development.

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UPSC Syllabus for SCRA Exam

UPSC-SCRA-09

Paper-1

(i) English
The questions will be designed to test the candidates’ understanding and command of the language.

(ii) General Knowledge
The questions will be designed to test a candidate’s general awareness of the environment around him and its application to society. The standard of answers to questions should be as expected of students of standard 12 or equivalent.
Man and his environment
Evolution of life, plants and animals, heredity and environment-Genetics, cells, chromosomes, genes.
Knowledge of the human body-nutrition, balanced diet, substitute foods, public health and sanitation including control of epidemics and common diseases. Environmental pollution and its control. Food adulteration, proper storage and preservation of food grains and finished products, population explosion, population control. Production of food and raw materials. Breeding of animals and plants, artificial insemination, manures and fertilizers, crop protection measures, high yielding varieties and green revolution, main cereal and cash crops of India.
Solar system and the earth, Seasons, Climate, Weather, Soil-its formation, erosion. Forests and their uses. Natural calamities cyclones, floods, earthquakes, volcanic eruptions. Mountains and rivers and their role in irrigation in India. Distribution of natural resources and industries in India. Exploration of under-ground minerals including Oil Conservation of natural resources with particular reference to the flora and fauna of India.

History, Politics and Society in India
Vedic, Mahavir, Budhdha, Mauryan, Sunga, Andhra, Kushan. Gupta ages (Mauryan Pillars, Stupa Caves, Sanchi, Mathura and Gandharva Schools, Temple architecture, Ajanta and Ellora). The rise of new social forces with the coming of Islam and establishment of broader contacts. Transition from feudalism to capitalism. Opening of European contacts. Establishment of British rule in India. Rise of nationalism and national struggle for freedom culminating in Independence.
Constitution of India and its characteristic features – Democracy, Secularism, Socialism, equality of opportunity and Parliamentary form of Government. Major political ideologies-democracy, socialism, communism and Gandhian idea of non-violence. Indian political parties, pressure groups, public opinion and the press, electoral system.
India’s foreign policy and non-alignment-Arms race, balance of power. World organisation-political, social, economic and cultural. Important events (including sports and cultural activities) in India and abroad during the past two years.
Broad features of Indian social system: The caste system, hierarchy – recent changes and trends. Minority social institution – marriage, family, religion and acculturation.
Division of labour, co-operation, conflict and competition, Social control – reward and punishment, art, law, customs, propaganda, public opinion, agencies of social control – family, religion, state educational institutions; factors of social change- economic, technological, demographic, cultural; the concept of revolution.
Social disorganisation in India – Casteism, communalism, corruption in public life, youth unrest, beggary, drugs, delinquency and crime, poverty and unemployment.
Social planning and welfare in India, community development and labour welfare; welfare of Scheduled Castes and backward classes.
Money – Taxation, price, demographic trends, national income, economic growth. Private and Public Sectors; economic and non-economic factors in planning, balanced versus imbalanced growth, agricultural versus industrial development; inflation and
price stabilization, problem of resource mobilisation. India’s Five Year Plans.

(iii) Psychological Test
The questions will be designed to assess the basic intelligence and mechanical aptitude of the candidate.

Paper-II

(i) Physics
Length measurements using vernier, screw gauge, spherometer and optical lever. Measurement of time and mass.
Straight line motion and relationships among displacement, velocity and acceleration.
Newton’s laws of motion, Momentum, impulse, work, energy and power.
Coefficient of friction.
Equilibrium of bodies under action of forces. Moment of a force, couple. Newton’s law of gravitation. Escape velocity. Acceleration due to gravity.
Mass and Weight; Centre of gravity, Uniform circular motion, centripetal force, simple Harmonic motion. Simple pendulum.
Pressure in a fluid and its variation with depth. Pascal’s law. Principle of Archimedes. Floating bodies, Atmospheric pressure and its measurement.
Temperature and its measurement. Thermal expansion, Gas laws and absolute temperature. Specific heat, latent heats and their measurement. Specific heat of gases. Mechanical equivalent of heat. Internal energy and First law of thermodynamics, Isothermal and adiabatic changes. Transmission of heat; thermal conductivity.
Wave motion; Longitudinal and transverse waves. Progressive and stationary waves, Velocity of sound in gas and its dependence on various factors. Resonance phenomena (air columns and strings).
Reflection and refraction of light. Image formation by curved mirrors and lenses, Microscopes and telescopes. Defects of vision.
Prisms, deviation and dispersion, Minimum deviation. Visible spectrum.
Field due to a bar magnet, Magnetic moment, Elements of Earth’s magnetic field. Magnetometers. Dia, para and ferromagnetism.
Electric charge, electric field and potential, Coulomb’s law.
Electric current; electric cells, e.m.f. resistance, ammeters and voltmeters. Ohm’s law; resistances in series and parallel, specific resistance and conductivity. Heating effect of current.
Wheatstone’s bridge, Potentiometer.
Magnetic effect of current; straight wire, coil and solenoid electromagnet; electric bell.
Force on a current-carrying conductor in magnetic field; moving coil galvanometers; conversion to ammeter or voltmeter.
Chemical effects of current; Primary and storage cells and their functioning, Laws of electrolysis.
Electromagnetic induction; Simple A.C. and D.C. generators. Transformers, Induction coil,
Cathode rays, discovery of the electron, Bohr model of the atom. Diode and its use as a rectifier.
Production, properties and uses of X-rays.
Radioactivity; Alpha, Beta and Gamma rays.
Nuclear energy; fission and fusion, conversion of mass into energy, chain reaction.

(ii) Chemistry
Physical Chemistry
1. Atomic structure; Earlier models in brief. Atom as at three dimensional model. Orbital concept. Quantum numbers and their significance, only elementary treatment.
Pauli’s Exclusion Principle. Electronic configuration. Aufbau Principle, s.p.d. and f. block elements.
Periodic classification only long form. Periodicity and electronic configuration. Atomic radii, Electro-negativity in period and groups.
2. Chemical Bonding, electro-valent, co-valent, coordinate covalent bonds. Bond Properties, sigma and Pie bonds, Shapes of simple molecules like water, hydrogen sulphide, methane and ammonium chloride. Molecular association and hydrogen bonding.
3. Energy changes in a chemical reaction. Exothermic and Endothermic Reactions. Application of First Law of Thermodynamics, Hess’s Law of constant heat summation.
4. Chemical Equilibria and rates of reactions. Law of Mass action. Effect of Pressure, Temperature and concentration on the rates of reaction. (Qualitative treatment based on Le Chatelier’s Principle). Molecularity; First and Second order reaction. Concept of Energy of activation. Application to manufacture of Ammonia and Sulphur trioxide.
5. Solutions : True solutions, colloidal solutions and suspensions. Colligative properties of dillute solutions and determination of Molecular weights of dissolved substances. Elevation of boiling points. Depressions of freezing point, osmotic pressure. Raoult’s law (non-thermodynamic treatment only).
6. Electro-Chemistry : Solution of Electrolytes, Faraday’s Laws of Electrolysis, ionic equilibria, Solubility product.
Strong and weak electrolytes. Acids and Bases (Lewis and Bronstead concept). pH and Buffer solutions.
7. Oxidation – Reduction; Modern, electronics concept and oxidation number.
8. Natural and Artificial Radioactivity: Nuclear Fission and Fusion. Uses of Radioactive isotopes.

Inorganic Chemistry
Brief Treatment of Elements and their industrially important compounds :
1. Hydrogen : Position in the periodic table. Isotopes of hydrogen. Electronegative and electropositive character. Water, hard and soft water, use of water in industries, Heavy water and its uses.
2. Group I Elements : Manufacture of sodium hydroxide, sodium carbonate, sodium bicarbonate and sodium chloride.
3. Group II Elements : Quick and slaked lime. Gypsum, Plaster of Paris. Magnesium sulphate and Magnesia.
4. Group III Elements: Borax, Alumina and Alum.
5. Group IV Elements : Coals, Coke and solid Fuels, Silicates, Zolitis semi-conductors. Glass (Elementary treatment).
6. Group V Elements. Manufacture of ammonia and nitric acid. Rock Phosphates and safety matches.
7. Group VI Elements. Hydrogen peroxide, allotropy of sulphur, sulphuric acid. Oxides of sulphur.
8. Group VII Elements. Manufacture and uses of Fluorine, Chlorine, Bromine and Iodine, Hydrochloric acid. Bleaching powder.
9. Group O. (Noble gases) Helium and its uses.
10. Metallurgical Processes : General Methods of extraction of metals with specific reference to copper, iron, aluminium, silver, gold, zinc and lead. Common alloys of these metals; Nickel and manganese steels.

Organic Chemistry
1. Tetrahedral nature of carbon, Hybridisation and sigma pie bonds and their relative strength. Single and multiple bonds. Shapes of molecules. Geometrical and optical isomerism.
2. General methods of preparation, properties and reaction of alkanes, alkenes and alkynes, Petroleum and its refining. Its uses as fuel.
Aromatic hydrocarbons : Resonance and aromaticity. Benzene and Naphthalene and their analogues. Aromatic substitution reactions.
3. Halogen derivatives : Chloroform, Carbon Tetrachloride, Chlorobenzene, D.D.T. and Gammexane.
4. Hydroxy Compounds : Preparation, properties and uses of Primary, Secondary and Tertiary alcohols, Methanol, Ethanol, Glycerol and Phenol, Substitution reaction at aliphatic carbon atom.
5. Ethers; Diethyl ether.
6. Aldehydes and ketones : Formaldehyde, Acetaldehyde, Benzaldehyde, acetone, acetophenone.
7. Nitro compounds amines: Nitrobenzene TNT, Anlline, Diazonium Compounds, Azodyes.
8. Carboxylic acid : Formic, acetic, denezoic and salicylic acids, acetyl salicylic acid.
9. Esters : Ethylacerate, Methyl salicylates, ethylbenzoate.
10. Polymers : Polythene, Teflon, Perpex, Artificial Rubber, Nylon and polyester fibers.
11. Nonstructural treatment of Carbohydrates, Fats and Lipids, amino acids and proteins –

Paper-III

Mathematics

1. Algebra:
Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal set and Power set, Venn diagrams and simple applications. Cartesian product of two sets, relation and mapping – examples, Binary operation on a set – examples.

Representation of real numbers on a line. Complex numbers: Modulus, Argument, Algebraic operations on complex numbers. Cube roots of unity. Binary system of numbers, Conversion of a decimal number to a binary number and vice-versa. Arithmetic, Geometric and Harmonic progressions. Summation of series involving A.P., G.P., and H.P.. Quadratic equations with real co-efficients. Quadratic expressions: extreme values. Permutation and Combination, Binomial theorem and its applications.

Matrices and Determinants: Types of matrices, equality, matrix addition and scalar multiplication – properties. Matrix multiplication – non-commutative and distributive property over addition. Transpose of a matrix, Determinant of a matrix. Minors and Co-factors. Properties of determinants. Singular and non-singular matrices. Adjoint and Inverse of a square-matrix, Solution of a system of linear equations in two and three variables-elimination method, Cramers rule and Matrix inversion method (Matrices with m rows and n columns where m, n less than equal to 3 are to be considered).

Idea of a Group, Order of a Group, Abelian group. Identitiy and inverse elements-Illustration by simple examples.

2. Trigonometry:
Addition and subtraction formulae, multiple and sub-multiple angles. Products and factoring formulae. Inverse trigonometric functions – Domains, Ranges and Graphs. DeMoivre’s theorem, expansion of Sin n 0 and Cos n 0 in a series of multiples of Sines and Cosines. Solution of simple trigonometric equations. Applications: Heights and Distance.

3. Analytic Geometry (two dimensions)
Rectangular Cartesian. Coordinate system, distance between two points, equation of a straight line in various forms, angle between two lines, distance of a point from a line. Transformation of axes. Pair of straight lines, general equation of second degree in x and y – condition to represent a pair of straight lines, point of intersection, angle between two lines. Equation of a circle in standard and in general form, equations of tangent and normal at a point, orthogonality of two cricles. Standard equations of parabola, ellipse and hyperbola – parametric equations, equations of tangent and normal at a point in both cartesian and parametric forms.

4. Differential Calculus
Concept of a real valued function – domain, range and graph. Composite functions, one to one, onto and inverse functions, algebra of real functions, examples of polynomial, rational, trigonometric, exponential and logarithmic functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative – applications. Derivative of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function, chain rule. Second order derivatives. Rolle’s theorem (statement only), increasing and decreasing functions. Application of derivatives in problems of maxima, minima, greatest and least values of a function.

5. Integral Calculus and Differential equations:
Integral Calculus : Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expression, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals-determination of areas of plane regions bounded by curves- applications.

Differential equations : Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equation of various types – examples. Solution of second order homogeneous differential equation with constant co-efficients.

6. Vectors and its applications:
Magnitude and direction of a vector, equal vectors, unit vector, zero vector, vectors in two and three dimensions, position vector. Multiplication of a vector by a scalar, sum and difference of two vectors, Parallelogram law and triangle law of addition. Multiplication of vectors – scalar product or dot product of two vectors, perpendicularity, commutative and distributive properties. Vector product or cross product of two vectors – its properties, unit vector perpendicular to two given vectors. Scalar and vector triple products. Equations of a line, plane and sphere in vector form – simple problems. Area of a triangle, parallelogram and problems of plane geometry and trigonometry using vector methods. Work done by a force and moment of a force.

7. Statistics and probability:
Statistics : Frequency distribution, cumulative frequency distribution – examples. Graphical representation – Histogram, frequency polygon – examples. Measure of central tendency – mean, median and mode. Variance and standard deviation – determination and comparison. Correlation and regression.

Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability : classical and statistical – examples. Elementary theorems on probability – simple problems. Conditional probability, Bayes’ theorem – simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

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UPSC Syllabus for NDA Exam

National Defence Academy Examination (I) – NDA Syllabus 2009

Paper	Subject	Code No	Maximum Marks
I	Mathematics	01	300

1. Algebra:

Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation.

Representation of real numbers on a line. Complex numbers – basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa.

Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.

2. Matrices and Determinants:

Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

3. Trigonometry:

Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications – Height and distance, properties of triangles.

4. Analytical Geometry of two and three dimensions:

Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic.

Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

5. Differential Calculus:

Concept of a real valued function – domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpreatation of a derivative – applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

6. Integral Calculus and Differential equations:

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types – examples. Application in problems of growth and decay.

7. Vector Algebra:

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of vector, scalar product or dot product of two-vectors. Vector product and cross product of two vectors. Applications-work done by a force and moment of a force, and in geometrical problems.

8. Statistics and Probability:-

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution – examples Graphical representation – Histogram, Pie Chart, Frequency Polygon – examples. Measures of Central tendency – mean, median and mode. Variance and standard deviation – determination and comparison. Correlation and regression.

Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability – classical and statistical – examples. Elementary theorems on probability – simple problems. Conditional probability, Bayes’ theorem – simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

Paper	Subject	Code No	Maximum Marks
II	General Ability Test	02	600
Part ‘A’	English		200
Part ‘B’	Genral Knowledge		400

The question paper in English will be designed to test the candidate’s understanding of English and workman like use of words. The syllabus covers various aspects like : Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate’s proficiency in English.

The question paper on General Knowledge will broadly cover the subjects : Physics, Chemistry, General Science, Social Studies, Geography and Current Events.

The syllabus given below is designed to indicate the scope of these subjects included in this paper. The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.

Section ‘A’ (Physics)

Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.

Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion, force and Momentum, Parallelogram of forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy.

Effects of Heat, Measurement of temperature and heat, change of State and Latent Heat, Modes of transference of Heat.

Sound waves and their properties, Simple musical instruments.

Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses. Human Eye.

Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.

Static and Current Electricity, conductors and Non-conductors, Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.

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Indian Economic Service Indian Statistical Service – IES Exam Syllabus 2009

(General Economics)

Standard and Syllabi for IES/ISS Exam 2009

The standard of papers in General English and General Studies will be such as may be expected of a graduate of an Indian University.

The standard of papers in the other subjects will be that of the Master’s degree examination of an Indian University in the relevant disciplines. The candidates will be expected to illustrate theory by facts, and to analyse problems with the help of theory.

They will be expected to be particularly conversant with Indian problems in the field of Economic/Statistics.

General English

Candidates will be required to write an essay in English. Other questions will be designed to test their understanding of English and workmanlike use of words. Passages will usually be set for summary or precis.

General Studies

General Knowledge including knowledge of current events and of such matters of every day observation and experience in their scientific aspects as may be expected of an educated person who has not made a special study of any scientific subject.

The paper will also include questions on Indian Polity including the political system and the Constitution of India, History of India and Geography of a nature which the candidate should be able to answer without special study.

General Economics-I

1. Theory of Consumer’s Demand: Cardinal Utility analysis, Indifference Curve analysis – Income and Substitution Effects, the Slutsky theorem – revealed Preference approach.
2. Theory of Production – Factors of Production – Production Functions – forms of Production Function: Cobb-Douglas, CES and Fixed Co-efficient type – Laws of returns – Returns to scale and returns to a factor – Partial equilibrium versus general equilibrium approach – Equilibrium of the firm and the Industry.
3. Theory of Value: Pricing under various forms of market organisation like perfect competition, monopoly, monopolistic competition and oligopoly. Public Utility Pricing: Marginal cost pricing, Peak load pricing.
4. Theory of Distribution: Macro-distribution theories of Ricardo, Marx, Kalecki, Kaldor-Neo-classical approach: Marginal productivity theory of determination of factor prices – factor shares and the ‘adding up’ problem – Euler’s theorem – pricing of factors under imperfect competition.
5. Welfare Economics – inter-personal comparison and aggregation problem, divergence between social and private welfare, compensation principle, Pareto optimality, Social choice and other recent schools, including Coase and Sen.
6. Concept of national income and social accounting – measurement of national income – Inter-relationship between three measures of national income in the presence of the Government sector and international transactions. Measuring Economic Welfare – socio-economic indicators approach: PQLI and H.D. Index.
7. Theory of Employment, Output and Inflation – the Classicial and neo-classical approaches – Keynesian theory of Employment – Post-Keynesian developments – the Inflationary gap – Demand-Pull versus Cost-Push Inflation – the Phillip’s Curve and its policy implications.
8. Mathematical Methods in Economics: Derivatives – basic rules of differentiation and its applications to economic functions- Optimisation (concept) – Matrices and their applications in Economics, Input-Output model (concept), Linear Programming and its applications.

General Economics-II

1. Concept of economic growth and development and their measurement – Characteristics of less developed countries (LDCs) and obstacles to their development – growth, poverty and income distribution – Theories of growth: Classicial Approach: Adam Smith, Marx and Schumpeter – Neo-classical Approach: Robinson, Solow, Kaldor and Harrod-Domar – Theories of Economic Development: Rostow, Rosenstein-Rodan, Nurkse, Hirschman, Leibenstein and Arthur Lewis, Amin and Frank (Dependency school); respective role of the State and the market.
2. International Economics: Gains from International Trade, terms of trade, trade policy, international trade and economic development – Theories of International Trade: Ricardo, Haberler, Heckscher-Ohlin and Stolper-Samuelson – Theory of Tariffs – Regional Trade Arrangements.
3. Balance of Payments: Disequilibrium in Balance of Payments, Mechanism of Adjustments, Foreign Trade Multiplier, Exchange Rates, Import and Exchange Controls and Multiple Exchange Rates.
4. Global Institutions: UN agencies; World Bank, IMF and WTO, Multinational Corporations.
5. Money and Banking: its functions and value-quantity Theory of Money: Cash Transaction Approach and the Cash Balances Approach, Friedman’s Restatement of the Quantity Theory of Money – the instruments of monetary control – the neutrality of money – the money multiplier.
6. Statistical and Econometric methods: averages, dispersions, correlation and regression, time series, index numbers, sampling and survey methods, testing of hypotheses, simple non-parametric tests, drawing of curves based on various linear and non-linear functions; least square methods, other multivariate analysis (only concepts and interpretation of results); ANOVA, factor analysis, principal component analysis, discriminant analysis. Income distributions: Pareto Law of distribution – log-normal distrubution – measurement of income inequality – Lorenz Curve and Gini co-efficient.

General Economics-III

1. Environmental Economics: Club of Rome, Founex report, Stockholm and Rio Earth summit reports, Convention on Biodiversity, Montreal Protocol on CFC, global warming; externalities, public goods, economic implication of various types of environmental degradation – air, noise, water pollution and exhaustion of non-renewable resources; resource accounting, biological wealth and its depletion or accretion as a part of GDP estimates and sustainable development; remedies : regulations, taxes, market based solutions such as privatisation and pollution permits.
2. Urbanisation and migration – Lewis, Todaro; informal sector, urban labour market, urban poverty.
3. Project Appraisal: Criteria for project choices: Internal rate of return, net present value and benefit-costs ratio – social rate of discount – shadow prices of capital, unskilled labour and foreign exchange. Use of project appraisal methods in India.
4. Financial and Capital Markets: finance and economic development -financial markets – stock market, gilt market, foreign exchange market – Banking and insurance.
5. Fiscal policy and its objectives – limitations of fiscal policy – theories of taxation and expenditure – objectives and effects of public expenditure – effects and incidence of taxation – deficit financing – theory of public debt, debt management, complementarity of monetary and fiscal policy with debt.
6. State, Market and Planning: concept and types of planning – rationale of planning in a developing economy – limitations of planning, economics of regulations, decentralised planning.

Indian Economics

1. History of development and planning – alternative development strategies – goal of self reliance based on import substitution and the post-1991 globalisation strategies based on stabilisation and structural adjustment packages.
2. (a) Decentralised Planning: Panchayat experience-constitutional obligations, Balwantrai Mehta Committee, Ashok Mehta Committee and other reports, financial aspects of 73rd and 74th constitutional amendments.
   (b) Union-State financial relations: Constitutional provisions relating to fiscal and financial powers of the states, financal aspect fo Sarkaria Commission Report, Finance Commissions and their formulae for sharing taxes.
3. Poverty, Unemployment and Human Development during plan period – Appraisal of Government measures – India’s human development record in global perspective.
4. Agriculture and Rural Development: Strategies including those relating to technologies and institutions: land relations and land reforms, rural credit, modern farm inputs and marketing – price policy and subsidies; commercialisation and diversification. Rural development programmes including poverty alleviation programmes: development of economic and social infrastructure.
5. India’s experience with Urbanisation and Migration – Different types of migratory flows and their impact on the economies of their origin and destination, the process of growth of urban settlements: urban strategies.
6. Industry: Strategy of industrial development – Industrial Policy Reform; Reservation Policy relating to small scale industries. Sources of industrial finances – bank, share market, insurance companies, pension funds, non-banking sources and foreign direct investment; role of foreign capital for direct investment and portfolio investment. Public sector reform, privatisation and disinvestment.
7. Labour: Employment, unemployment and under-employment – industrial relations and labour welfare – strategies for employment generation – Urban labour market and informal sector employment; report of National Commission on labour, Social issues relating to labour e.g. Child labour, Bonded labour.
8. Foreign trade: Salient features of India’s foreign trade – composition, direction and organisation of trade: recent changes in trade policy; Balance of payments, tariff policy, exchange rate and WTO requirements.
9. Money and Banking: Organisation of India’s money market – changing roles of the Reserve Bank of India, commercial banks, development finance institutions, foreign banks and non-banking financial institutions.
10. Budgeting and Fiscal Policy: Tax, expenditure, budgetary deficits, debt and fiscal reforms. Black money and Parallel economy in India – definition, estimates, genesis, consequences and remedies.

Statistics-I

(i) Probaility

Elements of measure theory, Classical definitions and axiomatic approach. Sample space. Class of events and Probability measure. Laws of total and compound probability. Probability of m events out of n. Conditional probability, Bayes’ theorem. Random variables – discrete and continuous. Distribution function.

Standard probability distributions – Bernoulli, uniform, binomial, Poisson, geometric, rectangular, exponential, normal, Cauchy, hypergeometric, multinomial, Laplace, negative binomial, beta, gamma, lognormal and compound. Poisson distribution. Joint distributions, conditional distributions, Distributions of functions of random variables.

Convergence in distribution, in probability, with probability one and in mean square. Moments and cumulants. Mathematical expectation and conditional expectation. Characteristic function and moment and probability generating functions Inversion uniqueness and continuity theorems. Borel 0-1 law: Kolmogorov’s 0-1 law.

Tchebycheff’s and Kolmogorov’s inequalities. Laws of large numbers and central limit theorems for independent variables. Conditional expectation and Martingales.

(ii) Statistical Methods

1. Collection, compilation and presentation of data, Charts, diagrams and histogram. Frequency distribution. Measures of location, dispersion, skewness and kurtosis. Bivariate and multivariate data. Association and contingency. Curve fitting and orthogonal polynomials. Bivariate normal distribution. regression-linear, polynomial. Distribution of the correlation coefficient, Partial and multiple correlation, Intraclass correlation, Correlation ratio.
2. Standard errors and large sample test. Sampling distributions of x,s2, t, chi-squre and F; tests of significance based on them, Small sample tests.
3. Non-parametric tests-Goodness of fit, sign, median, run, Wicloxon, Mann-Whitney, Wald-Wolfowitz and Kolmogorov-Smirnov. Rank order statistics-minimum, maximum, range and median. Concept of Asymptotic relative effciency.

iii) Numerical Analysis

Interpolation formulae (with remainder terms) due to Lagrange, Newton-Gregory, Newton Divided different, Gauss and Striling. Euler-Maclaurin’s summation formula. Inverse interpolation. Numerical integration and differentiation. Difference equations of the first order. Linear difference equations with constant coefficients.

Statistics II

i) Linear Models

Theory of linear estimation. Gauss-Markoff setup. Least square estimators. Use of g-inverse. analysis of one-way and two way classified data-fixed, mixed and random effect models. Tests for regression coefficients.

ii) Estimation

Characteristics of good estimator. Estimation methods of maximum likelihood, minimum chi-square, moments and least squares. Optimal properties of maximum likelihood estimators. Minimum variance unbiased estimators. Minimum variance bound estimators. Cramer-Rao inequality. Bhattacharya bounds. Sufficient estimator. factorisation theorem. Complete statistics.

Rao-Blackwell theorem. Confidence interval estimation. Optimum confidence bounds. Resampling, Bootstrap and Jacknife.

iii) Hypotheses testing and Statistical Quality Control

1. Hypothesis testing: Simple and composite hypothesis. Two kinds of error. Critical region. Different types of critical regions and similar regions. Power function. Most powerful and uniformly most powerful tests. Neyman-Pearson fundamental lemma. Unbiased test. Randomised test. Likelihood ratio test. Wald’s SPRT, OC and ASN functions. Elements of decision and game theory.
2. Statistical Quality Control: Control Charts for variable and attributes. Acceptance Sampling by attributes-Single, double, multiple and sequential Sampling plans; Concepts of AOQL and ATI; Acceptance Sampling by variables-use of Dodge-Romig and other tables.

iv) Multivariate Analysis

Multivariate normal distribution. Estimation of mean Vector and covariance matrix. Distribution of Hotelling’s T2-statistic, Mahalanobis’s D2-statistic, and their use in testing. Partial and multiple correlation coefficients in samples from a multivariate normal population. Wishart’s distribution, its reproductive and other properties. Wilk’s criterion. Discriminant function. Principal components. Canonical variates and correlations.

Statistics III

i) Sampling Techniques

Census versus sample survey. Pilot and large scale sample surveys. Role of NSS organisation. Simple random sampling with and without replacement. Stratified sampling and sample allocations. Cos and Variance functions. Ratio and Regression methods of estimation. Sampling with probability proportional to size. Cluster, double, multiphase, multistage and systematic sampling. Interpenetrating sub-sampling. Non-sampling errors.

ii) Design and Analysis of Experiments

Principles of design of experiments. Layout and analysis of completely randomised, randomised block and Latin square designs. Factorial experiments and confounding in 2n and 3n experiments. Split-plot and strip-plot designs. Construction and analysis of balanced and partially balanced incomplete block designs. Analysis of covariance. Analysis of non-orthogonal data. analysis of missing and mixed plot data.

iii) Economic Statistics

Components of time series. Methods of their determination-variate difference method. Yule-Slutsky effect. Correlogram. Autoregressive models of first and second order. Periodogram analysis. Index numbers of prices and quantities and their relative merits. Construction of index numbers of wholesale and consumer prices. Income distribution-Pareto and Engel curves. Concentration curve.

Methods of estimating national income. Inter-sectoral flows. Inter-industry table. Role of CSO.

iv) Econometrics

Theory and analysis of consumer demand-specification and estimation of demand functions. Demand elasticities. Structure and model. Estimation of parameters in single equation model-classical least squares, generalised least-square, heteroscedasticity, serial correlation, multi-collinearity, errors in variable model. Simultaneous equation models-Identification, rank and other conditions. Indirect least squares and two stage least squares. Short-term economic forecasting.

Statistics-IV

(i) Stochastic Processes

Specifications of a Stochastic Process, Markov chains, classification of states, limiting probabilities; stationary distribution; Random walk and Gambler’s ruin problem. Poisson process, Birth and death process; applications to Queues-M/M/I and M/M/C models. Branching Process.

(ii) Operations Research

Elements of linear programming. Simplex procedure. Pirnciple of duality. Transport and assignment problems. Single and multi-period inventory control models. ABC analysis. General simulation problems. Replacemnet models for items that fail and or items that deteriorate.

(iii) Demography and Vital Statistics

The life table, its constitution and properties. Makehams and Gompertz curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations. Different birth rates. Total fertility rate. Gross and net reproduction rates. Different mortality rates. Standardised death rate. Internal and international migration: net migration.

International and postcensal estimates. Projection method including logistic curve fitting. Decennial population census in India.

(iv) Computer Application and Data Processing

(a) Computer Application

Computer system concepts: Computer system components and functions. The Central Processing unit, Main memory, Bit, Byte, Word, Input/Output Devices, Speeds and memory Capacities in computer systems.

Software concepts: Overview of Operating Systems, Types and Functions of Operating System, application Software, Software for multi-tasking, multi-programming, Batch Processign Mode, Time sharing mode, Concept of System Support Programme, Overview of Existing Software packages on Word Processing and Spreadsheets.

Overview of an application Specific Programme: Flow charts, Basics of Algorithm, Fundamental of design and analysis of Algorithm; Basics of data structure, Queue, Stack.

(b) Data Processing

Data processing: Digital Number System, Number conversions, Binary representation of integers, Binary representation of real numbers, Logical Data element like cjharacter, fields, records, files, Fundamentals of data transmission and processing incluidng error contro and error processing.

Data base management: Data Resource management. Data base and file organisation and procesing. (a) Direct, (b) Sequantial, (c) Indexed Sequential file. Concepts of Client Server architecture, Data Base Administrator. An overview of DBMS software.

>>> UPSC Syllabus Index

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Indian Civil Service Exam Syllabus (Preliminary & Mains) – Mathematics-09

Indian Civil Service Exam Syllabus (Preliminary) – Mathematics

1. Algebra :

• Elements of Set Theory; Algebra of Real and Complex numbers including Demovire’s theorem; Polynomials and Polynomial equations, relation between Coefficients and Roots, symmetric functions of roots; Elements of Group Theory; Sub-Group, Cyclic groups, Permutation, Groups and their elementary properties.
• Rings, Integral Domains and Fields and their elementary properties.

2. Vector Spaces and Matrices :

• Vector Space, Linear Dependence and Independence. Sub-spaces. Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformation of a Finite Dimensional Vector Space, Matrix Representation. Singular and Nonsingular Transformations. Rank and Nullity.
• Matrices : Addition, Multiplication, Determinants of a Matrix, Properties of Determinants of order, Inverse of a Matrix, Cramer’s rule.

3. Geometry and Vectors :

• Analytic Geometry of straight lines and conics in Cartesian and Polar coordinates; Three Dimensional geometry for planes, straight lines, sphere, cone and cylinder. Addition, Subtraction and Products of Vectors and Simple applications to Geometry.

4. Calculus :

• Functions, Sequences, Series, Limits, Continuity, Derivatives.
• Application of Derivatives : Rates of change, Tangents, Normals, Maxima, Minima, Rolle’s Theorem, Mean Value Theorems of Lagrange and Cauchy, Asymptotes, Curvature. Methods of finding indefinite integrals, Definite Integrals, Fundamental Theorem of integrals Calculus. Application of definite integrals to area, Length of a plane curve, Volume and Surfaces of revolution.

5. Ordinary Differential Equations :

• Order and Degree of a Differential Equation, First order differential Equations, Singular solution, Geometrical interpretation, Second order equations with constant coefficients.

6. Mechanics :

• Concepts of particles-Lamina; Rigid Body; Displacements; force; Mass; weight; Motion; Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of velocity, acceleration; resultant; equilibrium of coplanar forces; Moments; Couples; Friction; Centre of mass, Gravity; Laws of motion; Motion of a particle in a straight line; simple Harmonic Motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity; Motion of artificial satellites.

7. Elements of Computer Programming :

• Binary system, Octal and Hexadecimal systems. Conversion to and from Decimal systems. Codes, Bits, Bytes and Words. Memory of a computer, Arithmetic and Logical operations on numbers. Precisions. AND, OR, XOR, NOT and Shit/Rotate operators, Algorithms and Flow Charts.

Civil Service Exam Syllabus for IAS Main Exam – Mathematics – Paper – I & II

(1) Linear Algebra:

• Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation.
• Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

(2) Calculus:

• Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes;

Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian.

• Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

(3) Analytic Geometry:

• Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

(4) Ordinary Differential Equations:

• Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution.
• Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution.
• Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters.
• Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.

(5) Dynamics & Statics:

• Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler’s laws, orbits under central forces.
• Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

(6) Vector Analysis:

• Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations.
• Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae.
• Gauss and Stokes’ theorems, Green’s identities.

Paper-II

(1) Algebra:

• Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem.
• Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.

(2) Real Analysis:

• Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series.
• Continuity and uniform continuity of functions, properties of continuous functions on compact sets.
• Riemann integral, improper integrals; Fundamental theorems of integral calculus.
• Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.

(3) Complex Analysis:

• Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration.

(4) Linear Programming:

• Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality.
• Transportation and assignment problems.

(5) Partial differential equations:

• Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions.

(6) Numerical Analysis and Computer programming:

• Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation.
• Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula.
• Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods.
• Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers.
• Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms.
• Representation of unsigned integers, signed integers and reals, double precision reals and long integers.
• Algorithms and flow charts for solving numerical analysis problems.

(7) Mechanics and Fluid Dynamics:

• Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.
• Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

>>> UPSC Syllabus Index

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