Solve the quadratic equation 4x^2 8x -21 0 using two decimal digit arithmetic with rounding, using anyone of the following methods:

Regula-Falsi

Secant

Bisection

Round off the number 4·5126 to 4 significant figures and find the relative percentage error.

Obtain the positive root of the equation x^2 0 by Newton-Raphson method, correct to two decimal places.

Explain the two pitfalls in the Gauss Elimination Method.

Solve the following system of linear equations using LU decomposition method:

6x1 -2x2 =14

9xl -x2 x3 =21

3xl 7x2 5x3 9.

What is the lowest degree polynomial which satisfies the following set of values, using forward difference polynomial Also find the polynomial.

x 0 1 2 3 4 5 6 7
0 7 26 63 124 215 342 511

Calculate the value of the integral Integral (4to5.2) log x dx by Trapezoidal Rule. Assume h 0·2. Compare the numerical solution with the exact solution.

What do you mean by the terms "Accuracy" and "Precision" How are they related to significant digits?

Show that the equation x^3 -6x 1 has a root in the interval) 0[. Obtain this root using Successive Iteration or Bisection method.

Find the Lagrange interpolating polynomial of degree 2 approximating the function y =ln x defined by the following
values mentioned in the table. Hence determine the value of ln 2·7.

x 2 2·5 3·0
y=lnx 0·69315 0.91629 1.09861

Solve the initial value problem with h =0.2 on the interval 1]. Use the fourth order classical Runge-Kutta method.

Solve the following system of equations using Gauss elimination with partial pivoting:

2x+ y Z =10
3x 2y 3z =18
x 4y 9z =16

What is the utility of residual plots? What is the disadvantage of residual plots?

If a bank receives on an average n bad cheques per day, what is the probability that it will receive 4 bad cheques on any given day, where n denotes the average arrival rate per day?

A hosiery mill wants to estimate how its monthly costs are related to its monthly output rate. For that the firm collects data regarding its cost and output for a sample of nine months as given by the following table:

Output (tons) Production Cost (thousands of dollars)
1 2
2 3
4 4
8 7
6 6
5 5
8 8
9 8
7 6

Draw the scatter diagram for the data.

Find the regression equation when the monthly output is the dependent variable and monthly cost is the independent variable

Use this regression line to predict the firm's monthly cost if they decide to produce 4 tons per month.

An individual's IQ score has a N(100, distribution. Find the probability that an individual's IQ score is between 91 and 121.

Evaluate the integral I Integral sin x dx using two-point Gauss-Legendre formulae.Compare with the exact solution and the exact value is I =1.

The following values of the function for the values of x are

and =4.

Find the value of and also the value of x in the interval for which is maximum or minimum.

Round off the number 4·5126 to four significant figures and find the relative percentage error.