Using an 8-decimal digit floating point representation digits for mantissa, 2 for exponent and one each for sign of exponent and sign for mantissa), represent the following numbers in normalised floating point form (using chopping, if required)

87426

-94·27

-0·000346

For the following two floating point numbers

x1 0·4527 x 10^4 and x2 0·5243 x find x1-x2

Find the product of xl and Q. No. above. given in

What is underflow? Explain it with an example of multiplication in which underflow occurs.

Write the following system equations in matrix form: of linear

6x+ 8y 10
-5x 3y 11

Solve the system of linear equations given by

6x+ 8y 10
-5x 3y 11

Find an interval in which the following equation has a root:

4x^2-4x-3 0

Give one example of each of

algebraic equation

transcendental equation.

Write the expressions, which are obtained by applying each of the operators to for some

V

A

E

0

Write A. and 0 in terms of E.

State the following two formulae for (equal interval) interpolation:

Newton's Backward Difference Formula

Newton's Forward Difference Formula

Construct a difference table for the following data:

x 1 2 3 4
2 9 28 65

From the Newton's Forward Difference Formula asked in Q. No. above, derive the formula for finding derivative of a function at xo.

State Simpson's rule for finding the value of the integral dx. (limits a to

Explain each of the following concepts with a suitable example:

Initial Value Problem

Degree and order of a differential equation

Let min. and max. represent respectively minimum and maximum positive real numbers representable by some floating point number system. Can every real number between max. and mm. be representable by such a number system Explain the reason for your answer.

For each of the following numbers, find the floating point representation, if possible normalized, using chopping, if required. The format is 8-digit as is mentioned in Q. No. lea) above:

3/11

74·0365

Further, find the absolute error, if any, in each case.

Find a b divided by for the floating point numbers:

a -0·4783 x b 0·5237 X 10^-5.

Find the Taylor's series for at a 1.

Solve the following system of equations, using partial pivoting Gaussian elimination method (compute upto two places of decimal only)

4x1 -5x2 6x3 24
3x1 -7x2 2x3= 17
5x1 2x2-4x3=-21

What are the advantages ofDirect methods over Iterative methods for solving a system of linear equations

For solving the following system of linear equations

a11 x1 a12 x2 a13 x3 b1,

a21 x1 a22 x2 a23 x3 b2 and

a31 x1 a32 x2 a33x3 =b3

with a11 a22 and a33 by iterative Gauss-Jacobi Method, with initial approximations as x1 1 x2 x3, find the values of next approximations of
x1,x2 and x3.

Compute the difference table and mark the forward differences for x 5.
x
1 4
2 7
3 12
4 19
5 28

For the table given above, find Newton's forward differences interpolating polynomial and find the value f(1.7) using the polynomial.

5. Attempt any two parts out of and given below:

If, in the Table of Q. No. represents the distance covered by a particle in x units of time, estimate the velocity and acceleration of the particle at 1·5.

Evaluate the integral f(2x^2 dx,(limits 0 to

using trapezoidal rule, with h =1·0.

Solve the following IVP using Euler's method: given =1.