  Preparing for Exams BCA & MCA (CS-17 & CS-76) FINAL YEAR PROJECTS TMA & PROJECTS Preparing A Synopsis

## CS - 08 Numerical & Statistical Computing Dec. 2003

Q. 1. (a) Write a Fortran 90 statement for each of the following formulae:

i) r = (p+q)/(p-q) + st/21
ii) d = ((a)b)c
iii) x2 = -b - (b2 - 4ac)/2a

b) Which of the following variables names are invalid in FORTRAN and why?
i) x + y
ii) RAM -1
iii) END

c) Write which of the following FORTRAN constants are invalid:
i) 30,456
ii) 1.2E156
iii) 1.2E5.6

d) Write assignment statements in FORTRAN to interchange the value of two variables x and y having values 10.0 and 15.0 respectively.

e) Suppose L and M contain 16 and 20 respectively. Find the final values of L and M after thye execution of the following program segment:
IF (L.GE.M)
L= L + 5
IF (L.EQ.M+1) GOTO 30
L= L + 5
30 L = L + M

f) the income of 80 families are given below:

 Income No. of families 400-600 10 600-800 15 800-1000 35 1000-1200 20

Calculate the mode.

g) Fit a straight line of the data given by the following table:

 Income No. of families 2 4 3 7 5 3 6 5 7 2 8 1

h) Compute the mean deviation for the following set of data where mean is 46.70:

 Marks No. of students 20-30 5 30-40 14 40-50 10 50-60 8 60-70 6 70-80 4

i) there are 10 identical balls, 6 of blue and 4 of red colour. One ball is drawn at random. Find the probability that ball drawn is red.

Q. 2. Write a program in FORTRAN to sum up the following series using DO loop:
i) 1,3,5,7,9,....,101
ii) 2,5,10,17,26,37,50,65,82,101
iii) 3,10,29,66,127,218,345,514,731,1002

Q. 3. a) You are given the following five numbers:
10,5,7,20,9
Write a program in FORTRAN to find out the largest number out of these numbers.

b) Draw (less-than type) cumulative frequency polygon for the following frequency class distribution:

 Class Frequency Class Frequency 1-4 6 16-19 12 4-7 4 19-22 8 7-10 5 22-25 4 10-13 3 25-28 1 13-16 2 28-31 3

Q. 4 a) The probability that a regular scheduled flight departs on time is 0.83, the probability that it arrives on time is 0.82, and the probability that it departs and srrives on time is 0.78.
Find the probability that a plane
i) arrives on time given that is departed on time
ii) departed on time given that it has arrived on time.

b) The probability that a student passes statistics is 2/3 and the probability that he passes mathematics is 4/9. if the probability of passing both courses is 1/4, what is the probability that the student will pass at least one of these courses.

Q. 5. a) Calculate correlation coefficients for the following data:

 X Y 5 21 15 14 10 28 20 7 25 35 40 42

b) After analysing the wage pattern of the workers of two firms A and B, following results were obtained:

 Firm A Firm B No. of workers 400 500 Average monthly income 350 225 Standard devaition 8 9

Find which of these have the larger variation.

Q.6. A college principle is interested in measuring how the prices of certain commodities have changed during his past five years of expierence.

 Commodity Unit of purchase Typical annual consumption Price 1990 1995 Pen 12 pieces 4 60 75 Board pen 6 pieces 1/2 72 92 Registers 1 box 1 950 1100 Aspirin 1 pack 6 59 75 1141 1342

Calculate index numbers for 1995 by taking 1990 as base year by weighted aggregate method.

(b) From the following table of values of x and y, obtain dy/dx for x = 1.2.

x

y

1.0

2.7183

1.2

3.3201

1.4

4.0552

1.6

4.953

1.8

6.0496

2.0

7.3891

2.2

9.025

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