WBUT Question Papers CS Numerical Methods And Programming B Tech Sem 3rd Dec 2008
WBUT Question Papers CS
Numerical Methods And Programming B Tech Sem 3rd Dec 2008
Time : 3 Hours ]
Full Marks : 70′
GROUP – A ( Multiple Choice Type Questions)
 Choose the correct alternatives for any ten of the following : 10 x 1 = 10
i) Which of the following relations is true ?
a) E = 1 + A b) E = 1 – A
c) E = 1/A d) None of these.
l
f dx
ii) By evaluating 2 by a numerical integration method, we can obtain an
J I + X
0
approximate value of
a) log_{e} 2 b) n
c) e d) log_{10}2.
m) if a be the actual value and e be its estimated value, the formula for relative error is
a) a _{b}, J5L=JLL
^ e a
0 d) L^
iv) in Trapezoidal rule, the portion of curve is replaced by
a) straight line
b) circular path
c) parabolic path d) none of these.
v) The error Involved In 4^{111} order Rk method is given by
a) O (h^{2}) b) 0(h^{4})
c) O (h^{3}) d) 0(h^{5}).
vi) An n x n matrix A is said to be diagonally dominant if
a)
J= 1
b)
J= i
i^{56} J
fl
C)  a_{(t}  > X ^{a} ij 
J= 1 < *J
ij •
J= 1 i*J ■
vii) Find the output of the following program main()
{
char a, b ,
^ a = ‘b’ ;
b = a ;
printf( “b = %c\n”, b ) ;
 
 
 
 
 
 
 
 
 
 
 
 
 


 
 


 


 
xlv) The inherent error for Simpson’s ^ rd rule of integration is as (the notations have their usual meanings )
^{31} – isoHM ^{b}) ” T5o(*o)
flfl 3 _____
c) – ~j2~ f” ( x o ) d) none of these. 
xv) ( A – V ) x^{2} is equal to (the notations have their usual meanings ) a) h^{2} b) – 2h^{2}
c) 2 h^{2} d) none of these.
GROUP B ( Short Answer Type Questions )
Answer any three of the following. 3×5= 15
2. From the following table And the values of / { 12 ) by Newton’s divided difference interpolation formula :

, 3. Solve the following system by Matrix Inversion Method : 2x + y + z = 10 3x + 2y + 3z = 18 x + 4y + 9z = 16.
x :  0  1  2  3  4  5 
fix):  0  —  8  15  —  35 
4. a) Evaluate the missing terms In the following table : 
What is ternary operator ? Give an example. 
Solve by Taylor’s series method = 2x + 3y ^{2} given y = 0 when x = 0 at x = 02.
Using Euler’s method obtain the solution of ^ = x – y. with y ( 0 ) = 1 and
h = 02 at x = 04.
, 6. Find the first approximation of the root lying between 0 and 1 of the equation x^{3} + 3x – 1 = Oby Newton^{:}Raphson formula.

GROUP C ( Long Answer Type Questions )
Answer any three of the following questions. 3 x 15 = 45
8. a) From the following table, estimate the number of students who obtained marks
between 40 and 45 :

X :  4  5  7  10  11  13 
f(X):  48  100  294  900  1210  2028 
7 + 8
Find the positive real root of x^{3} = 18 using the bisection method of 4 iterations. Find the root of the equation x^{3} + x^{2} + x+ 7 = 0 using Regula Falsi method.
A curve passes through the points as given in the following table. Find the area
X  l  2  3  4  5  6  7  8  9 
y  02  07  1  13  15  17  19  21  23 
5 + 5 + 5
Write a program in C to solve the equation x^{3}3x5 = 0 within ( 1, 2 ) by Bisection method correct up to 3 places of decimal.
Write a program in C using recursive function to calculate the sum of all digits of
8 + 7
any number.
CS/B.TECH (ECE/IT/EE <0)/EEE/lCE)/SEM3/M(CS)312/08/(09) 8
1
 a) Evaluate J* xe^{x} dx by using Trapezoidal rule taking n = 6.
b) Use Lagrange’s interpolation formula to find the value of /( x ) for x – 0. given the following :

Prove that NewtonRaphson method has a quadratic convergence. 5 + 5 + 5 Solve the following system of equations by LU Factorization Method :
^{X}1^{+X}2~^{X}3 ^{=} 2
2x _{t} + 3x_{2} + 5x_{3} = – 3
3x , + 2x _{2} – 3x _{3} = 6. ’
Solve the following set of equations by GaussSeidel method correct to 2 places of decimal :
9x – 2y + z = 50
x + 5y – 3z = 18
– 2x + 2y + 7z = 19.
Write a C program to approximate a real root of the following equation :
4
sin ( x) = e ^{x} by Bisection method. 5 + 5 + 5
Write a C program to interpolate a given function at a specified argument by Lagrange’s interpolation formula.
l
Find the value of log 2 ^{1/3} from —3 dx using Simpson’s 4
j 1 + x >3
n = 4.
Calculate the approximate value of J sin x dx by Composite Trapezoidal Rule
0
by using 11 ordinates. Also compare it with the actual value of the integral.
5 + 5 + 5
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