Question 1.

(a) Write FORTRAN 77 and FORTRAN 90 expressions for the following

Ans.

EQUIVALENT FORTRAN EXPRESSION

= ((a * X + b ) / c) + (( 1. - EXP(-ALPHA * SQRT(X))) /(1. + X * EXP(-ABS(X)))) + (ALPHA * COS(OMEGA * T +PHI) / SQRT (ALPHA**2 + OMEGA**2))
(b) Evaluate the following FORTRAN 77 expressions:

(i) 2 * * 3 * * 2 * 2 + 4/3 * 2,

(ii) (a/2) (a+2.5)/b,
a = 2.5 and b = 3.5,

(iii) 4 + 7 .LT. 9 .OR. 8 .GT. 4 + 7

Ans.

Solution 1(b)(i).

2**3**2*2+4/3*2
=2^3^2*2+4/3*2
=2^9*2+8/3
=2^10+2.6667
=1024+2.6667
=1026.6667 =1026.7

solution 1(b)(ii).

(a/2)(a+2.5)/b
=(2.5/2)(2.5+2.5)/3.5
=(1.25)(5)/3.5
=(1.25)(1.4286)
=2.6786

solution 1(b)(iii).

(4 + 7 .LT. 9 .OR. 8 .GT. 4 + 7)
PERFORMING THE RELATIONAL COMARISIONS (.LT. , .GT. )LEFT TO RIGHT
(false .OR. 8 .GT. 4 + 7)
From the hierarchy table , when both inputs are false, OR operator is false
(false .OR. false ) gives false

Question 2.

(a) The mean annual salary paid to all employees of a company was Rs. 5000/-. The mean annual salaries paid to male and female employees were Rs. 5200/- and Rs. 4200/- respectively. Determine the percentage of males and females employed by the company.

x1=5200, x2=4200, x=5000

x = n1x1 + n2x2
n1+n2

5000 = 5200n1 + 4200n2
n1+n2

5000(n1 + n2) = 5200n1 + 4200n2

5000n2 - 4200n2 = 5200n1 - 5000n1

8000n2=2000n1

8n2=2n1

n1/n2 = 8/2 =4/1

Therefore ,

percentage of male employee in the company =4/4+1*100=400/5=80%

percentage of female employee in the company =1/4+1*100=100/5=20%
(b) Three urns of the same appearance have the following proportion of balls

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

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

Ans.

r = (n åxy - åx åy)

( {n åx² -(åx)²} {n*åy²-(åy)²} )

= 192
318.396

= 0.603023

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