# December 2001

## Question Paper of CS 08 Numerical & Statistical Computing of Dec 2001 from IGNOU

**Time**: 3 hours

**Maximum Marks**: 75

Note: Question 1 is compulsory. Attempt any 3 from the remaining.

1. (a) Which of the variable names given below are invalid in Fortran ? Give reasons in support of your answer : – 3marks

( i ) TEMP_X

( ii ) ROLL2

( iii ) PROGRAM

(b) Which are valid real constants in exponent form: 3

( i ) 0.01540E05

( ii ) - 0.148E – 5

( iii ) 125.8E

(c) Write a Fortran statement for each of the following mathematical expressions : 3

( i ) x sup (1/3) – y sup (-2)

( ii ) a (x + y / z) sup 3.5

( iii ) | sin X | + log sqrt( 3x sup 2 + 5 y sup 2

(d) Suppose the variables A,B and C respectively contain the valuse 3,4 and 5. 3

Find the value of each of the following logical expressions :

( i ) ( A + C) . EQ . 2 * B. AND . 2 * ( C – A) . EQ . B

( ii ) . NOT . ( 3 . EQ . C – 2 . AND . A . LE . C )

( iii ) . NOT . C . GT . A . OR . B . LT . 5

(e) Write each of the following statements in Fortran : 3

( i ) If R = 2S + T, go to statement labelled 87

( ii ) If S not equal to 11, go to statement labelled 44

( iii ) if 3S > 4T, stop

(f) Draw a Pie – chart of the monthly expenses of a hostler, 3

whose expenses per month are as follows:

item Amount in ruppes

Food 2000

room rent 1000

transport 500

books/stationery 500

maintenance 1000

(g) Explain the concepts of ’skewness’ and ‘kurtosis’ along with their significance 4

in the study of distributions of mass of data.

(h) A computer while calculating correlation coefficient between 20 pairs of 5

two variables x and y obtain the following results :

n = 20, x = 100 , y = 80,

x = 520, y = 360, xy = 420

It was later discovered at the time of cheching that he had copied down two pairs as

x y

6 4

8 6

while the correct values were

x y

8 12

6 8

obtain the correct value of correlation coefficient.

( i ) Two dice are thrown. Find the probability that sum of the numbers on two 3

dice is 9 given that first dice shows 6.

2 (a). Write a fortran 90 program that reads an n-digit number (for a positive integer n ) 8

and reverses the digits of the number to obtain a new number (eg. if number 24379

is read then the new number obtained by reversing the digits is 97342).

The program then prints the result with a suitable message.

(b). Write a fortran program that goes on reading values for an integer variable N until 7

the value read is zero or negative. For each positive value of N read, the program tests

whether N is a prime number of not. Also it should print appropriate messages.

3 (a). Write a fortran program that goes on reading sets of three real values until at least one 7

of the values in any set of values is zero or negative. The three values in a set denote

lengths of the sides of a triangle. The program tests whether the triangle represented by

the values is an equilateral triangle. If te triable is equilateral then it computes the area

of the triangle. If the triangle represented is not equilateral then it finds the perimeter of

the triangle. Program prints suitable messages also.

(b). Calculate the variance for the class-frequency distribution given below : 4

Marks obtained number of students

0 – 10 15

10 – 20 20

20 – 30 25

30 – 40 17

40 – 50 12

(c). The income of 80 families are given below : 4

Income (in Rs) Number of families

4000 – 6000 8

6000 – 8000 24

8000 -10000 32

10000 – 12000 16

Find the mode.

4 (a). A five-figure number is formed by the digits 0,1,2,3,4 ( without repetition). Find the 6

probability that the number formed in divisible by 4.

(b). The average number of radioactive particles through a counter during 4

1 milli second in a laboratory experiment is 3. What is the probability that five

particles enter the counter in a given milli second ?

(c). The probability of a college student being male is 1/3 and that being female is 2/3. 5

The probability that a male student completes the course is 3/4 and that a female

student does it is 1/2. A student is selected at random and is found to have completed

course. What is the probability that the student is a male ?

5(a). Fit a straight line trend by the method of least squares to the following data: 7

Year : 1951 52 53 54 55 56

price index: 107 110 114 112 115 113

(b). The following table gives the average wholesale prices of four grains for the 8

years 1998 to 2001. Compute chain base index number.

Grain 1998 1999 2000 2001

Rice 12 18 24 12

Wheat 18 36 54 24

Gram 12 36 60 24

Barley 15 21 54 33

6(a). Compute the approximate value of the integral 7

I = ( 1 + x + x ) dx

using simpson’s rule by taking interval size h as 1.

(b). Find the value of cosh = d/dx (sinhx) at x = 1.52 from the following table : 8

x sinhx

1.5 2.129279

1.6 2.375568

1.7 2.645632

1.8 2.942174

1.9 3.268163

2.0 3.626860