1. Find the sum of two floating point numbers a =0·5403 x 10^3 and b =0·7182 x 10^4 .

Find the product of the two numbers a and b given above.

Define what is 'underflow'. Give an example of multiplication due to which underflow occurs.

Write the following system equations in matrix form:
8x 11y 19 and 12x 5y 17

Solve the following system of linear equations using Gauss elimination method:
5x 3y 7 and -2x 9y 5

Find an interval in which the following equation has a root:
x^2 x 2=0

Write briefly the steps of bisection method to find out the roots of an equation.

Write the expressions which are obtained by applying each of the following operators to

<img src='./qimages/8461-1h.jpg'>

Write E in separately. terms of each of and 0

Construct the difference table for the following data:

<img src='./qimages/8461-1j.jpg'>

State the following two formulae for interpolation (for equal intervals)

Newton Forward Difference Formula

Bessel's Formula

Explain the concept of 'Initial Value Problem' with an example.

2. Solve the following system of linear equations, using partial pivoting;
4x1 5x2 6X3 -24
X1 3x2 5x3 22
-2x1 8x2 x3 11

What are the relative advantages of iterative methods over direct methods for solving a system of linear equations?

3. For 3x^3 11x find V3 in terms of where h is an equally spaced interval.

Estimate the missing term in the following data using backward difference assuming that the data is a valid representation of polynomial of degree 3

<img src='./qimages/8461-3b.jpg'>

4. Attempt any two of and below:
Find at x 0·25 from the following table of values

<img src='./qimages/8461-4a.jpg'>

3 Find the approximate value of

<img src='./qimages/8461-4b.jpg'>

using Trapezoidal rule, with 5 equal parts of

Using Euler's method to find the solution of dy/dx 3x given find the solution on the interval 0.8] with h 0.2, where x is the independent variable and y is the dependent variable.

Using the 8-decimal digit floating point representation digits for mantissa, 2 digits for exponent, and one each for sign of exponent and mantissa), represent the following numbers in normalized floating point form:
-98·37
0·000893
(Use chopping, if required)

Using the 8-decimal digit format stated in above, briefly discuss how zero is represented as a floating point number.

Let a 476·9 x 10^6 b 657·2 x 10^4 and c -5·342 x 10^4 . Find out whether is associative for b and c (i.e., you are required to find out whether

c a or not).