Gauhati University Question Papers for Mathematics 6th Semester

Gauhati University Question Papers for Mathematics 6th Semester

Question Paper from 2010 available 

          

More than 50 question papers every semester

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 More than 50 question papers every semester

6th Semester

Revised Syllabus of Mathematics

For

Three year Degree Course ( Major Course) Paper-M601

Hydrostatics

Unit1: Pressure equation, condition of equilibrium, lines of force, homogeneous and heterogeneous fluids, elastic fluids, surface of equal pressure, fluid at rest under action of gravity, rotating fluids.                                                                                         
 Unit2:Fluid pressure on plane surfaces, centre of pressure, resultant pressure on curved surfaces.                                                                                                                15 marks. Unit3: Equilibrium of a floating body, curves of buoyancy, surface of buoyancy, stability of equilibrium of floating bodies, meta centre, work done in producing a displacement, vessel containing a liquid.                                                                                  

Unit4: Gas law, mixture of gases, internal energy, adiabatic expansion, work done in compressing a gas, isothermal atmosphere, connective equilibrium.                 1

6th Semester

Revised Syllabus of Mathematics

For

Three year Degree Course ( Major Course) Paper-M602

Numerical Analysis Marks 

Unit1: Normalized floating point representation of real numbers and operations using it, normalization and its consequence, errors in arithmetic operations, absolute and relative error, truncation and round off errors, approximation and significant figures.       

Unit2:Calculus of finite difference: different interpolation formulae with remainder

terms, finite difference operators and their operations on function of a single variable, interpolation with equal and unequal intervals,Newton;s formulae, Lagrange’s formula,

Gauss, Bessel and sterling’s formula,Hermite interpolation.    
                           
 Unit3: Numerical differentiation and integration: Numerical differentiation with the help of different interpolation formulae, general quadrature formula, trapezoidal rule, Simpson’s one third and three eighth rule, Weddel’s rule, Newton-Cote’s formula, Gauss quadrature formula,Chebycheve’s formula.                                                           

Unit4: Solution of polynomial and transcendental equations: Bisection method, secant method, regula falsi method, Newton-Raphson method, rate of convergence and comparison of methods.                                                                                          

6th Semester

Revised Syllabus of Mathematics

For

Three year Degree Course ( Major Course) Paper-M603

Computer Programming in C

Unit1:Brief introduction of central processing, main memory, secondary memory, input/output devices, operating system and its need, representation of numbers and characters in computer, machine level language and high level language, compiler,interpreter,assembler,linker, loader, editor, debugger, algorithm, flowchart and computer programmes, decision table and trees, efficiency and analysis of algorithm. Introduction to C-requirement of programming language to solve problems.        
Unit2:Elementary data types/variables, constants and identifiers, integer, character, floating point and string constants, variable declaration,initializationof variables during declaration, constant data types),Syntax and semantics, reserved words, expression in C(operator precedence and associatively, unary, binary and ternary operators, C

arithmetic operators, assignment operators, relational operators, logical and bitwise operators, L-value and R-value, expression statement, cast and size of operator, automatic type conversion.                                                                                                      
Unit3:Conditional Statement:if,if-else,switch.Iterative statement: while, do while. For. Arrays and pointers(preliminary ideas).

Other statements: break, continue, go to,   return, null statement, block statement

 Unit4:Function (function declaration, calling a function by value, call by reference and its absence in C),storage class(automatic register,static,external);recursion and how it works( use of machine stack for storing return address, parameters and local

variables),conversion of recursive programmes to non-recursive version.           

 To evaluate an arithmetic expression, to find gcd,factorial, Fibonacci number, prime number generation, reversing digits of an integer, finding square root of a number, roots

of a quadratic equation, sum of different algebraic and trigonometric series, base conversion, towers of Hanoi, test for Palindrome, addition subtraction and multiplication of matrices, to find the greatest and smallest of a finite number of numbers, interpolation and solution of transcendental equation.

6th Semester

Revised Syllabus of Mathematics

For

Three year Degree Course ( Major Course) Paper-M604

Discrete Mathematics

Unit1:Divisibility theory: Peano’s axiom, well ordered principle, mathematical induction, division algorithm, the basis representation theorem, prime numbers, unique factorization theorem.                                                                                    

Unit2: ( Congruence’s): Basic properties of congruence’s, residual systems, linear congruence’s and their solutions, special divisibility tests, the Chinese remainder theorem

and its applications, Fermat’s Little theorem and Wilson’s theorem. Polynomial

congruence’s.                                                                                               

Unit3: Diophantine equation: linear Diophantine equation, the equation

x2+y2=z2 and x4+y4=z4. Fermat’s last theorem, representation of a number by two or four squares.

                                                                                                 

Unit4: Number theoretic function: Euler’s phi function, Euler’s theorem, combinatorial study of the Euler’s phi function, the function τ and σ, basic theorems on τ(n) and σ(n), the Mobious function, multiplicative arithmetic function, inversion formula, greatest integer function.                                                                                           

Unit5:Propositional Calculus: operation on statements, truth function, laws of propositional logic, Boolean algebra of statement bundles, adequate system of connectives, binary connectives ‘Nor’ and ‘and’.                                          

Unit6: Boolean Algebra: disjunctive normal form(DNF), Complement of Boolean expression in DNF, construction of a Boolean function  corresponding to a Boolean expression, conjunctive normal form(CNF), Complement of Boolean expression in CNF, transformation of normal form to the other form, applications.                    

6th Semester

Revised Syllabus of Mathematics

For

Three year Degree Course ( Major Course) Paper-M605

Graph and Combinatorics Marks 

Unit: 1 : Elementary combinatorics, Rules of sum and product, two models of counting, sample and distribution model of counting. Examples and solution. Integer solution of an equilateral problem.                                       

Unit 2: Varities of Graphs, Walks and connectedness, degrees, problem of Ramsey, intersection graphs, operations on graphs.                                                    

Unit 3 : Block, Cut points. Bridges, Block graphs, Cut point graphs, Trees, Characterization of trees.                                                                            

Unit 4: Connectivity and Line connectivity, Graphical variation of Menger’s theorem.

Unit 5: Travessavility : Eulerian graphs, Hamiltonian graphs and their characterizations