West Bengal Institute of Technology (WBIT) 2009-3rd Sem B.Tech Electronics and Communications Engineering Electronics & Comm ( - ) Numerical Methods - Question Paper
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CS/B.Tcch (IT, ECE, EEE, ICE)/SEM-3 / M(CS}-312/2009-10
2009 NUMERICAL METHODS AND PROGRAMMING
Time Allotted : 3 Hours Full Marks : 70
The figures in the margin Indicate full marks.
Candidates are required to give their answers in their own words
as far as practicable.
GROUP-A ( Multiple Choice Type Questions )
1. Choose the correct alternatives for any ten of the following : 10 x 1 = 10
i) If the interval of differencing is unity and f(x) - ax2 ( a is a constant) which of the following choices is wrong ? a) Af (x) = a(2x +1) b) A2/(x)~2a *
c) A3/(x) = 2 d) A4/(*) = 0.
ii) The number of significant figures in 6,00,000 is
a) 1 b) 7
c) 0 d) 6.
iii) Which of the following is true ?
a) A" x" = (n +1)! b) A" x" = n ! /
c) A" xn = 0 d) A"x"=n.
iv) When Gauss elimination method is used to solve AX = B, A is transformed to a
a) unit matrix
b)lertfer ttfangulif matrix
c) diagonally dominant matrix
d) upper triangular matrix.
v) The method of iteration formula <t> ( x ) must satisfy a) |<t>'(x)|<l b* |VW|>1
c) (x)|-l | V (*) | 2.
vi) Regula-Falsi method is
a) conditionally convergent
b) linearly convergent
c) divergent
d) none of these.
vii) Which of the following is true ?
a) E = 1 - A b) E = 1 + A
c) A = 1 + E d) E = 1/A.
viii) The order of h in the error expression of Trapezoidal rule is
a) 6 b) 3
c) 5 d) 2.
ix) The degree of precision of Simpsons one third rule is
a) 1 b) 2
c) 3 d) 5.
CS/B.Tech (IT, ECE, EEE, ICE)/SEM-3/M(CS)-3l2/2009-10
x) Which of the following methods is an iterative method ?
a) Gauss Elimination method
b) Gauss-Jordan method
c) Gauss-Seidel method
d) Crouts method.
xi) main ()
{
print("%x",-l4);
}
a) 0 b) FO
c) FFFF d) FFFO.
xii) main ()
{
char s[] = {'a','b','c','\n','c','\0'}; char *p, *str,*strl; p=&s[3]; str=p;
strl=s; ,
printfT%d",++*p + ++*strl-32);
}
a) 177
b) 122
xiii) main ()
{
lnta=2,*fl, *f2; fl =f2=&a;
*2+=*f2+=a+=2-5;
printfl\n%d %d %d", a, *fl, *f2);
}
a) 16 15 14 b) 16 16 16
c) 16 15 16 d) 24 24 24.
xiv) main ()
{
printfTXnab"); printf!"\bsi"); printfl"\rha");
}
What will be the output for the above code ?
a) hai_ b) ha
c) h d) ab
GROUP - B (Short Answer Type Questions )
Answer any three of the following. 3 x5 = 15
2. a) What is the difference between interpolation and extrapolation ? Give suitable examples. 2
b) If y ( 10 ) = 35-3, y ( 15 ) = 32-4, y ( 20 ) = 29-2, y ( 25 ) = 26 1, y ( 30 ) = 23-2 and y ( 35 ) = 20-5, find y ( 12 ) using Newtons forward interpolation formula. 3
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3. a) Use Newtons divided difference formula to find / f 5 ) from the following data ; 3 | ||||||||||||||
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b) What do you mean by geometrical interpretation of Simpsons rd rule ? 2
Find the values of y'(x) and y"(x) at x = 1-1 from the
4, a)
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following data, using Newtons forward interpolation formula : 3 | ||||||||||||||
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b) What is ternary operator ? Give examples.
Find the approximate value of J- J*dx/(1 +x) when the
5. a)
interval is ( 0. 1 ) and h Use trapezoidal rule. 3
2
b) Show that A log/ ( * ) = log [ 1 + A/ (;c J IJ ( jc ) ], where A is the forward difference operator. 2
GROUP -C ( Long Answer Type Questions )
Answer any three of the following. 3x15 = 45
8. a) Solve the system of linear equations by Gauss
Elimination method :
5*! - x2 - 9 -x1+5x2-x3-4
-x2 + 5x3 - - 6. 7
b) Find the Newton-Raphson iterative formula to find the pth root of positive number N and hence find the cube-root of 17. . 5
. c) Evaluate the following: 3
A2 j(5x + 12)/(x2 + 5x + 6)|, taking h = 1
9. a) Write a C program to interpolate a given function as
specified argument by divided difference formula. 7
b) Compute J*x/sin xdx, where the interval is ( 0, 1/2 ) using Simpsons rule with h =1/4. 5
c) Deduce trapezoidal rule for Newton-Cotes quadrature formula. . 3
CS/B.Tech (IT, ECE, EEE, ICE)/SEM-3/M(CS)-312/2009-10
10. a) Find the inverse of the following matrix. 5
3 -1 1
-15 6 -5
5 -2 2
' /
b) Solve the following system of equations by LU factorization method : 5
2x - 6y + 8z = 24
5x + 4y - 3z = 2
3x + y + 2z = 16
c) Evaluate Jxex dx where the interval is ( 0, -1 ) by using Trapezoidal rule taking n = 6. 5
11. a) Write a C program to solve the equation x3 - 3x - 50 within ( 1, 2 ) by Bisection method correct upto 3 places of decimal. 8
b) Write a program in C using recursive function to calculate the GCD of any two given numbers. 7
12. a) Find the root of the equation 3x - cosx -1=0 that lies
between 0 and 1, correct to four places of decimal, using bisection method. 7
b) Find the root of the equation x3 -5x-7-0, that lies between 2 and 3, correct to 4 places of decimals, using the method of false position. 7
c) State the condition of convergence of Newton-Raphson method. 1
13. a) Solve the following system of equations, correct to four
places of decimals, by Gauss-Seidel iteration method : 8
\
x + y + 54 z =110 27x + 6y - z = 85 Qx + 15y + 2z = 72
b) Find the values of y ( 01 ), y ( 0-2 ) and y ( 0-3 ) using Runge-Kutta method of the fourth order, given that
dy/dx-xy + y2,y(0)-l. ' 7
33502 8
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Attachment: |
| Earning: Approval pending. |
