West Bengal Institute of Technology (WBIT) 2008-3rd Sem B.Tech Electronics and Communications Engineering Electronics & Comm ( - ) Numerical Methods - Question Paper
C8/B.TECH (BCK/IT/EE (0)/KEE/ICE)/8EM-3/M(CS)-312/08/(08) 3
ENGINEERING & MANAGEMENT EXAMINATIONS, DECEMBER - 2008
NUMERICAL METHODS AND PROGRAMMING
SEMESTER - 3
Time : 3 Hours ] I Full Marks : 70'
GROUP-A ( Multiple Choice Type Questions)
' .
1. 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 --5 by a numerical integration method, we can obtain an
J 1 + X
0
approximate value of
a) loge 2 b) n
c) e d) log102.
iii) If a be the actual value and e be its estimated value, the formula for relative error is
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.
CS/B.TECH (ECE/IT/EE >)/EEE/ICE)/SEM-3/M(CS)-312/08/(09) 4
v) The error Involved In 4111 order R-k method is given by
a) O (h2) b) 0(h4)
c) O (h3) d) 0(h5).
vi) An nxn matrix A is said to be diagonally dominant if
a)
J= 1
n
b) | a | < X| ay |
fl
C) | a(t | > X| a ij |
J= i
1i
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 ) ;
}
b) b
d) none of these.
a) a
c) garbage value
IWHll
CS/B.TECH (ECE/IT/EE (0)/EEE/ICE)/SEM-3/M(CS)-312/08/(09) 5
vtU) Lagranges interpolation formula is used for a) equispaced arguments only 'b) unequispaced arguments only
c) both equispaced and unequispaced arguments
d) none of these.
txO If /( 3 ) = 5 and /( 5 ) = 3, then the linear interpolation function f ( x) is
f(x) = 8 + x /(x)=x + x2 + 8.
b)
d)
a) /(x) = 8- x c) /(x)=x2 If / ( x) = , the divided difference [ a, b, c ] is
1
b)
d)
a)
c)
abc
a + b + c 1
a2+b2
a + b-c'
xi)
If = x + y and y ( 1 ) = 0, then y ( 1.1) according to Eulers method is | h = 0-1 ]
a) 01 c) 0-5
b) 0-3 d) 0-9.
xii) Which one of the following results is correct ?
b) Ax1 n * = nx n 1
a) Axn - rxx
d)
c) Anex = ex
A cos x = - sin x.
xiii) In the method of iteration the function ( x) must satisfy
a) | <t>' ( x) | < 1 c) | <t> '( x) | = 1
b) [ <t>'(x) | > 1 d) | <)>' ( x ) | = 2.
CS/B.TECH (ECE/IT/EB (0)/EEE/ICE)/SEM.3/W(CS)-312/08/(09) 6
xiv} The inherent error for Simpson's ~ rd rule of integration is as {the notations have their usual meanings )
l80W(xo) bJ TiO ( *o )
_ nf*i _
c) - ~22~ /" { *0) d) none of these. [
xv) ( A - V ) x2 is equal to (the notations have their usual meanings )
a) h2 b) -2 h2
c) 2 h2 d) none of these.
GROUP -B ( Short Answer Type Questions )
Answer any three of the following. 3x5=15
|
2. From the following table find the values of / ( 12 ) by Newton's divided difference Interpolation formula: | ||||||||||||||
|
, 3. Solve the following system by Matrix Inversion Method :
2 x + y + z = 10
*
3x + 2y + 3z - 18 x + 4y + 9z = 16.
b)
f 5. a) b)
|
4. a) Evaluate the missing terms in the following table : | ||||||||||||||
| ||||||||||||||
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What is ternary operator ? Give an example. |
Solve by Taylors series method - 2x + 3y 2 given y = 0 when x = 0 at x = 0-2.
Using Eulers method obtain the solution of = x ~ y. with y ( 0 ) = 1 and h = 0-2 at x - 0-4.
CS/B.TECH (ECE/IT/EB (0)/EEE/ICE)/BEM-3/lC8)-312/08/100) 7 .
, 6. Find the first approximation of the root lying between 0 and 1 of the equation jc3 + 3x - 1 = Oby Newton1 Raphson formula.
|
x : |
0 |
1 |
2 |
3 |
4 |
|
f(x): |
1 |
1 |
15 |
40 |
85 |
GROUP -C ( Long Answer Type Questions )
Answer any three of the following questions. 3 x 15 = 45
From the following table, estimate the number of students who obtained marks
8. a) b)
9. a) b) c)
10. a) b)
|
between 40 and 45 : | ||||||||||||
|
|
Using Newton divided difference formula, evaluate f{ 8 } and /( 15 ) given . | ||||||||||||||
|
7 + 8
Find the positive real root of x3 = 18 using the bisection method of 4 iterations. Find the root of the equation x3 + x2 + x+7 = 0 using Regula Falsi method.
A curve passes through the points as given in the following table. Find the area
|
X |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Y |
0-2 |
0*7 |
1 |
1-3 |
1-5 |
1-7 |
1-9 |
2-1 |
23 |
5 + 5 + 5
Write a program In C to solve the equation x3 - 3x - 5 = 0 within ( X. 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.
1
11. a) Evaluate J xe * dx by using Trapezoidal rule taking n = 6,
o
|
b) Use Lagranges interpolation formula to find the value of /( x ) for x - 0, given the following : | ||||||||||
| ||||||||||
|
c) Prove that Newton-Raphson method has a quadratic convergence. 5 + 5 + 5 |
12. a) Solve the following system of equations by L-UFactorization Method :
*1 + X2~X3 =
2x j + 3x2 + 5x3 = - 3 - -
3x l + 2x2 - 3x3 = 6.
b) Solve the following set of equations by Gauss-Seidel method correct to 2 places of decimal :
9x - 2y + z = 50
x + 5y - 3z = 18
- 2x + 2y + 7z = 19.
c) Write a C program to approximate a real root of the following equation :
4 * sin ( x) = e x by Bisection method. 5 + 5 + 5
13. a) Write a C program to interpolate a given function at a specified argument by
Lagranges interpolation formula.
1
Find the value of log 2 1/3 from g dx using Simpsons 4 fd rule with
bj
J 1 + X <3
0
n = 4.
r
c) Calculate the approximate value of J sin x dx by Composite Trapezoidal Rule
o
by using 11 ordinates. Also compare it with the actual value of the integral.
END
33S02 (10/12)
, 5+5+5
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Attachment: |
| Earning: Approval pending. |
