Saurastra University 2006 M.Sc Computer Science Mathematics Programming in C - Question Paper

M. Sc. (Maths) (Part - II) exam
April / May – 2006
Mathematics
Programming in C
Time : three Hours] [Total Marks : 80
Instructions : All ques. are compulsory and carry equal marks.
1 (a) describe subsequent terms :
(i) Program (ii) Compiler (iii) Higher level language (iv)
(iv) Machine Language (v) String and (vi) Operand.
(b) explain about development of C language.
(c) explain about special characters and white spaces in C
language with a few examples.
OR
1 (a) discuss about input and output statements with their
improper format and suitable examples.
(b) Determine the value of subsequent if a = 5, b = 10 and c = –6.
(i) a%b + c
(ii) (a*b)/c
(iii) a > b && a < c
(iv) a == c||b > a
(v) b  15 && c  0
(vi) a + 10 - b * c
(vii) a * b * c - 100
(viii) !cbz * ag= = bh
2 (a) discuss about for loops and also write a program which can
print 101 to 200 integers in ten lines.
(b) Write a program which can learn 2 integers and it can obtain
gcd and lcm of provided 2 integers.
OR
2 (a) explain about recursion of a function in itself by an improper
program.
(b) Write a program which can learn a matrix and it can print the
transpose of the provided matrix.
(c) explain about concatenation of strings.
3 (a) Write importance of pointers.
(b) State main function of file managements.
(c) Write a program to learn five names of students and their marks
of 3 subjects. Then declare name of those students who
have more or equal marks in all the paper than the avg.
marks of every paper.
OR
3 (a) discuss false position method.
(b) discuss addition and multiplication for normalized floating
point arithmetic system with examples.
(c) describe order of convergence for iterative method and obtain the
order of convergence for successive approximation method.
4 (a) discuss Gauss-Seidel method to solve
a x a x b 11 one 12 two one + =
a x a x b 21 one 22 two 2 + =
(b) Solve subsequent system of equations by Gauss-Elimination
method :
x x x y
x x x y
x x x y
x x x y
1 two 3
1 two 3
1 two 3
1 two 3
5
2 three four 10
4 nine 16 20
8 27 64 34
+ + + =
+ + + =
+ + + =
+ + + =
OR
4 (a) explain Lagrange interpolation polynomial and derive its
formula.
SS–7579] two [ Contd....
SS–7579] three [ 100 ]
(b) For the subsequent data of an unknown function f, obtain the
formula for f x bg, using NG backward interpolation
polynomial :
x
f x
: . .
:
2 two five three 3 five 4
9 16
5
8
28 43
7
8
65 bg
5 (a) explain trapezoidal rule for integration and obtain its formula.
(b) Write a program to obtain integration f x dx
a
bzbg by Gauss-
Legendra formula.
OR
5 (a) discuss Taylor's method to solve differential formula and
derive its formula.
(b) Show that R-K's 1st order and 2nd order methods are
numerically equivalent with Taylor's formula.
(c) Write a program for R-K's 4th order formula to solve
differential formula
dy
dx
= f x, y b g with initial condition x y o o , d i
upto X  x max.

Earning:   Approval pending.