Write a program in FORTRAN to read two matrices X and Y. Both X and Y matrices are square matrices. Also make a program to check whether or not.
Given four numbers C and D. Write a program in FORTRAN to arrange the values of the four numbers in an ascending order.

2.(a) Explain the following control constructs with examples: IF
GO TO

(iii) DO
COMMON Write a program in FORTRAN to calculate the area of a circle, the area of a triangle and the area of a rectangle.

3.(a) Using Newton-Raphson method, find out the real root of the equation x log10 x 1.2, correct to five decimal places.
Find the root of the equation x e^x cos x
using the Secant method, correct to four decimal places.

4.(a) Using Lagrange's interpolation formula, find the values of y when x 10, from the following table <img src='./qimages/9535-4a.jpg'> Apply Gauss elimination method to solve the following equations

x 4y-z
x y-6z 4

5.(a) Apply Crout's method to solve the following equations:

3x 2y 7z 4
2x 3y z 5
3x 4y Z 7
Use Runge-Kutta fourth order method to find an approximate value of y when x 0.2,
given that dy/dx x y 1 when x O.

6.(a) Determine the eigenvalues and corresponding eigenvectors for the matrix A.

A= -2 2 -3
2 1 -6
-1 0 Find the inverse of the matrix

A= 0 1 2
1 2 3
3 1 1 by elementary row

operations. Also find out the rank of the matrix.

7.(a) From the following table, estimate the number of students who obtained marks between 40 and 45

Marks No. of Students
30-40 31
40-50 42
50-60 51
60-70 35
70-80 31 The velocity v (km/minute) of a moped which starts from rest, is given at fixed intervals of time t (minutes) as follows:
t v
2 10
4 18
6 25
8 29
10 32
12 20
14 11
16 5
18 2
20 0

Estimate approximately the distance covered in 20 minutes.

8. Explain the following:

(a) Taylor's theorem and Intermediate value theorem Global and Local variables Additional sequential file manipulation statements Graeffe's root squaring method