Leta 0.345 x b 0.245 x and c 0·432 x . Using 3-digit decimal arithmetic with rounding, prove that

c a c).

Obtain the positive root of the equation x^2 1 0 by Regula-Falsi method, correct up to 2 decimal places.

Solve the following linear system of equations using Gauss Elimination method:

X1 x2 x3 3

4x1 3x2 4x3 8

9x1 3x2 4x3 7

From the following data, estimate the value of f(2.25) using Backward Difference Formula:

<img src='./qimages/10169-1d.jpg'>

Calculate the value of the integral

<img src='./qimages/10169-1e.jpg'>

using

Trapezoidal rule

Simpson's rule 1/3

Assume h 0·2. Compare the numerical solutions with the exact solution.

Explain the concept of Exponential Random Variable with a suitable example.

Find a polynomial of degree 2 with the properties P(1.5) 0. 4

Given the following system of linear equations, determine the value of each variable using LU decomposition method:
6x1 2x2 14
9x1 x2 x3 21
3x1 7x2 5x3 9

Evaluate

<img src='./qimages/10169-2b.jpg'>

using Simpson's rule with 11 points.

If a bank receives on an average 6 bad cheques per day, what is the probability that it receives 4 bad cheques on any given day?

Evaluate the integral

<img src='./qimages/10169-3a.jpg'>

using the Gauss-Legendre 1-point, and 2-point quadrature rules. Compare with the exact solution.

Calculate the correlation coefficient for the following heights (in inches) of fathers and their sons

X 65 66 67 67 68 69 70 72
Y 67 68 65 68 72 72 69 71

A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at random. Find the probability that among the balls drawn there is at least one ball of each colour.

Solve the initial value problem -2t u^2 with 1 and h 0·2 on the interval Use the fourth order classical Runge-Kutta method.

Estimate the missing term in the following data which represents a polynomial of degree

<img src='./qimages/10169-4b.jpg'>

Evaluate the integral

<img src='./qimages/10169-4c.jpg'>

using Trapezoidal rule, with h 1·0.

Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys, and 1 girl and 3 boys. One child is selected at random from each group. Show that the chance that the three selected children consist of 1 girl and 2 boys is 13/32

Find the most likely price in Bombay corresponding to the price of RS 70 at Kolkata from the following data:

<img src='./qimages/10169-5b.jpg'>

Correlation coefficient between the prices of commodities in the two cities is 0·8.

Fit a straight line to the following data with x as the independent variable:

<img src='./qimages/10169-5c.jpg'>

Hence find the difference between the actual value of y and the value of y obtained from the fitted curve when x 3.