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M (CS) 312 NUMERICAL METHODS & PROGRAMMING
Multiple Type Choice Questions
1. i) Which of the following relations is/are true?a) . = - c) .
= +b) . = / d) all of theseii) The (n+ 1) th order forward
difference of the nth degree polynomial is
a) n ! c) 0b) ( n + 1 ) ! d) none of these
iii) To solve the ordinary differential equation 3 + 5y
2
= sin x, y(0) = 5 by Eulers method, youneed to rewrite the
equation as
a) = sin x 5y2, y(0) = 5b) = (sin x 5y2), y(0) = 5c) = (-cos x
), y(0) = 5d) = sin x, y(0) = 5iv) The condition of convergence of
Newton-Raphson method when applied to an equation f (x)
= 0 in an interval is
a) f (x) = 0b) |f (x)| < 1c) |f (x)f (x)| < [f (x)]2d) [f
(x)]2 > |f(x).f(x)|v) Output of the following programme code
main ()
{
int x, y;
y = 4;
x = y
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}
is
a) 63 c) 64b) 60 d) 65vii) Simpsons one-third rule is applicable
only if the number of subinterval is even.
a) Trueb) Falseviii) The error involved in 4th order R-K method
is given by
a) O (h2) c) O (h4)b) O (h3) d) O (h5)ix) Find the output of the
following program:
main ()
{
char a, b;
a = b;
b = a;
printf( b = %c\n, b);
}
a) a c) garbage valueb) b d) none of thesex) The no. of
significant digits in 1.00234 is
a) 4 c) 3
b) 6 d) 5
Short Answer Type Questions
2. Find the inverse of the matrix
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by Gauss elimination method.
3. a) Prove thatf(4) = f(3) + f(2) + 2 f(1) + 3 f(1).
b) Evaluate 2 cos 2x.
4. a) Solve by Taylors series method = 2x + 3y2 given y = 0 when
x = 0 at x = 0.2.b) Using Eulers method obtain the solution of = x
y, with y (0) = 1 and h = 0.2 at x = 0.4.
5. Evaluate to three decimals by Netown-Raphson method.6. a)
What do you mean by geometrical interpolation of Simpsons 1/3rd
rule?
b) Calculate the area of the function f (x) = sin x with limits
(0 900) by Simpsons 1/3rd rule using
11 ordinates.
Long Answer Type Questions
7. a) Find by Lagranges interpolation polynomial passing through
the set of points:x 0 1 2
y 4 3 6
Use it to find y at x = 1.5, at x = 0.5 and evaluate .
b) Write a C program in C for Trapezoidal Rule, taking any
function of your choice.
8. a) Solve the following equation using LU decomposition
method:3x1 + 2x2 + x3 = 10
2x1 + 3x2 + 2x3 = 14
x1 + 2x2 + 3x3 = 14
b) Solve x2 4x 10 = 0 using bisection method in the range [-1,
-2] counted up to 6th
approximation.
9. a) Given with initial condition y = 1 at x = 0, find y for x
= 0.1 by Eulers method,correct up to 4 decimal places, taking step
length h = 0.02.
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b) Calculate by Simpsons 1/3rd rule, the value of the integral
dx, correct up to three
significant figures by taking six intervals.
c) Write a C program in C using recursive function to calculate
the sum of all digits of any
number.
10.a) Find the roots of the equation x3 5x 7 = 0 that lies
between 2 and 3, correct up to 4decimal places, using the method of
false position.
b) Find the value of y (0.1), y(0.2) and y(0.3) using
Runge-Kutta method of the fourth order,
given that
11.a) Compute the value of from the formula,
using Trapezoidal rule with 10 sub-intervals.
b) Using Newton divided difference formula, evaluate f(8) and
f(15) given:
x: 4 5 7 10 11 13
f(x): 48 100 294 900 1210 2028
