# ST 4202 - Loyola College

```14.04.2004
9.00 - 12.00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.Sc., DEGREE EXAMINATION - STATISTICS
FOURTH SEMESTER – APRIL 2004
ST-4202/STA202 - NUMERICAL METHODS USING 'C'
Max:100 marks
SECTION -A
(10  2 = 20 marks)
1. What is an assignment statement? What is the relationship between an assignment
statement and an expression statement?
2. Mention the difference between pre-increment and post-increment operator.
3. Give the syntax of ternary operator.
4. What is the output of the following program segment?
for (i = 0, j = 0; i &lt; = 5; i ++, j ++)
print f (&quot; %d\ n&quot;, i+j);
5. Mention the difference between break and continue statement.
6. What is an array?
7. Comment on the following statement:
&quot; scanf () and get char() functions are equivalent&quot;.
8. Find the value of f (10) using Lagrange's linear interpolation for the following function:
x: 7 19
f: 15 35.
1. 2
9. Evaluate
 f ( x) dx using Trapezoidal rule where f(x) is defined as
0 .8
x:
0.8
0.9
1.0
1.1
1.2
f:
0.71736
0.78333
0.84147
0.92314
0.96356
10. Give the steps to find the root of an equation by Newton-Raphson method.
SECTION - B
(5  8 = 40 marks)
11. a) Explain the data types available in C.
b) What are type qualifiers?
(6+2)
12. Explain the concept of branching and looping with examples.
13. Explain the syntax of the following:
a) printf()
b) toupper() c) pow()
d) floor()
1
14. Give the output of the following program segments:
a) i = x = 0;
b) x = 0;
do
for (i = 0; i&lt;5; i++)
{
{
if (i% 5 = =0)
for (j = 0; j&lt;i;j++)
{
{
x++;
switch (i+j-1)
printf(&quot;%d \n”, x);
{
}
case -1:
i++;
case 0: x = x+1;
}while (i&lt;20);
break;
printf (&quot;%d'1' x);
case 1:
case 2:
case 3: x = x+2;
break;
default: x = x+3;
break;
}
printf (&quot;%d\n&quot;, x);
}
}
(3+5)
15. a) Write a program to accept an integer and display it in reverse order.
b) Write a program using function to find the factorial of a given positive integer.
(4+4)
16. Find the determinant of the following matrix by pivotal condensation method.
1
1
A
 3

1
1 0.5 1
2 0 1
1 2 1

0 0 2
17. Write a program to solve the equation x2+3x-5=0 using bisection method.
18. Write a program to find the largest eigen vector by the method of iteration.
SECTION - C
19. a) Explain the structure of a C program.
b) Write a program to find the maximum among 'n' given integers.
c) Explain the concept of arrays with an example.
(2  20 = 40 marks)
(6+6+8)
20. a) Write a program to find the roots of a quadratic equation of the form ax2+bx+c=0.
b) Write a program to find the sum of 2 square matrices of order mxm.
c) What are user defined functions? Explain the method of declining and defining a user
defined function.
(6+6+8)
2
21. a) Explain the Gauss-elimination method to solve a given set of simultaneous equation
and write a program for the same.
0. 8
b) Evaluate
 (log ( x  1)  sin 2 x)dx using simpson's 1/3 rule by taking h as 0.1.
(12+8)
0
22. a) Write a program using Lagrange's interpolation method to evaluate f(y) where 'f' is a
function defined as
x : x1 x2 ........xn
f(x): f1 f2 ........fn
Assume that x1, x2.....xn, f1, f2,......fn are known values.
b) Find the inverse of the following matrix by Gauss-Jordon elimination method.
4 3  1
A = 1 1 1 
3 5 3 
(12+8)

3
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