Code: AE07 Subject: NUMERICAL ANALYSIS &
Time: 3 Hours COMPUTER PROGRAMMING
Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.
· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.
· Any required data not explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or best alternative in the following: (2x10)
a. What does the following declarations means
(i) int *ptr[10];
(ii) int (*ptr) [10];
(A) (i) Array of 10 pointers
(ii) Same as (i)
(B) (i) Pointers to the array of 10 elements
(ii) Array of 10 integer pointers
(C) (i) Array of 10 integer pointers
(ii) Pointers to the array of 10 elements
(D) (i) Pointers to the array of 10 elements
(ii) Same as (i)
b. What is the output of the following program.
#include<stdio.h>
void main( )
{
int i=0;
for(i=0; i<=4; i++);
printf("Welcome");
}
(A) Welcome will be printed only once
(B) Welcome will be printed 5 times
(C) Error as there should not be ; at the end of for loop
(D) None of these
c. The convergence of Bisection Method is
(A) linear (B) quadratic
(C) cubic (D) None of the above
d.
If 
is
the Forward Difference operator then the value of 
equals
to
(A) 
(B) 
(C)
(D) None of the above
e.
The value of 
is
(A) 
(B)
(C) 
(D) 
f. After Rounding off 865250 to four significant figures, the absolute error will be
(A) 50 (B) 86
(C) 6.71 x 10–5 (D) None of the above
g. For Trapezoidal Rule, the interpolating polynomial is a
(A) straight line (B) parabola
(C) hyperbola (D) None of the above
h. Which interpolation method is used for unequal intervals
(A) Langrange's interpolation formulae
(B) Bessel's formulae
(C) Taylor's formulae
(D) None of the above
i. The approximate value of
by using Two-Point open type
rule is
(A) 0.7325 (B) 0.9546
(C) 0.6537 (D) None of the above
j. Which of the method is not used for finding a solution for differential equation
(A) Runge-Kutta method (B) Euler's method
(C) Trapezoidal method (D) Taylor's series method
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Find a root of
the equation 
, by using Newton-Raphson method.
Correct to three decimal
places
(8)
b. Find a real root of the equation 
by
Regula-Falsi Method correct to 3 decimal
places.
(8)
Q.3 a. Consider the system of equations
where a is a real
constant. Find the values of a for which, the Jacobi and Gauss Seidal
Methods
converge.
(8)
b. Show that LU Decomposition method fails to solve the system of equations
(8)
Q.4 a. Given the data (8)
|
x |
0 |
1 |
2 |
3 |
|
f(x) |
1 |
2 |
33 |
244 |
Fit Quadratic Splines with 
Hence find
f(2.5).
b. Write a program in C to implement Lagrange's Interpolation formula. (8)
Q.5 a. The velocity v (km / min) of a vehicle which starts from rest, is given at fined intervals of time t (min) as follows:
|
t: |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
|
v: |
10 |
18 |
25 |
29 |
32 |
20 |
11 |
5 |
2 |
0 |
Estimate approximately the distance covered in 20 minutes. (8)
b.
Evaluate the integral 
using Gauss-Laguerre two point
formulae.
(8)
Q.6 a. Evaluate the integral
using Gauss-Legendre three
point
formulae.
(8)
b. Find the values of y at x = 0.1 and x = 0.2 to five places of
decimals from 
by Taylor's
series.
(8)
Q.7 a. Prove with the usual notations, that
(i) 
(ii) 
Where E = Shift operator
= Forward difference
operator
=
Central difference operator (8)
b.
Using Runge-Kutta method of 4th order, Solve 
with y(0) = 1 at x = 0.2. (8)
Q.8 a. Write a C program to solve a system of equations using Gauss-Seidel iteration method. (10)
b. Evaluate 
by using Trapezoidal
Rule.
(6)
Q.9 a. Compute the middle value of the numbers a = 4.568, b = 6.762 using the four digit arithmetic. (6)
b. Write notes of the following
(i) Storage classes in C programming.
(ii) Preprocessor in C programming. (10)