Test Papers / Previous Question Papers of IGNOU CS08 Numerical and Statistical Computing December 2005

ADCA / MCA (II Yr)
Term-End Examination

December, 2005

CS08 (S): Numerical & Statistical Computing

Time: 3 hours
Maximum Marks: 75

1. (a) Explain what is wrong in the following assignment statements : (3)
(i) A/B = A*B
(ii) C= 123E-05
(iii) K = ALOG (3/4)

(b) Write down the FORTRAN equivalent for the following mathematical expressions: (3)
(i) 5P - 4Q^R + log_e6
(ii) ⌈P^3/2 - Q^-1/2⌉
(iii)e^z2/2σ/√2π

(c) lndicate the error in the following : (3)
(i) IF (SPEED=50)THEN
(ii) X = cos (30°)
(iii) D = A - B * - C + 7.0

(d) Let P, Q and R be logical variables such that,
P = .TRUE., Q = .FALSE. and R = .TRUE.
Find the value of W in the following (show the working) :
(i) W = P .AND. R .OR. Q
(ii) W = .NOT. P.EQV. Q.AND. R
(iii) W = P .OR. Q .AND. .NOT. R

(e) Read N numbers(N ≤ 100) in an array A. Write a program section to find the smallest number and print it. N is already stored in the computer memory. (3)

(f) Write a program section to multiply two matrices A (p x q) and B (q x r) to form a matrix C. You can assume that A, B and C are already declared in the program. (3)

(g) Find the standard deviation for the following data : (3)

(h) A die is thrown 5 times and the number 3 or 4 on the top is counted as a success. What is the probability of getting two successes only ? (3)

(i) In a class of 60 students, 10 have failed. The average of failed students is 25 while that of the whole class is 50. What is the average of the students who have passed ? (3)

(j) Fit a straight line y = a + bx by the method of least squares to the points (2, 3), (3, 5) and (4, 8). (3)

2. (a) A company decides to give an increment to its employees according to the following formula (percentage of salary) : (7)
for salary ≤ 5000, increment 10%
5000 < salary ≤ 8000, increment 9%
8000 < salary, increment 8%
Write a program to read the salary of an employee, compute the increment and the increased salary. Print them. Use ELSEIF.

(b) Read N pairs of values (X_i, Y_i), i = 1, 2, ... N in two arrays X and Y. Write a program section to compute the coefficient of correlation. You can assume N is already stored in the computer memory. (8)

3. (a) Read three real numbes A, B and C, which form three sides of a triangle. Write a program to test whether the triangle is (i) equilateral (all sides equal), (ii) isosceles(two sides equal) or (iii) scalene( all sides unequal). The result should also be printed. The program should also include finding its area using the formula √s(s-A) (s-B) (s-C) and printing the result. (8)

(b) Find the 1st and 3rd Quartiles and Mode for the following data :

4. (a) Write a program section to read N followed by N numbers, one by one (not array). Find the smallest number and print it.

(b) The following resuits were worked out from the scores in Mathemaiics and English in certain examinations : (8)

The coefficient of correlation between X and Y = 0.4. Estimate the marks obtained in Mathematics by a student who has secured 60 marks in English. Also compute the marks obtained in English when she secures 85 marks in Mathematics.

5. (a) Two coins are tossed six times. What is the probability that heads appear on both the coins at least price ? (7)

(b) Describe the four tests as criteria for a good Index Number. From the following data calculate the price index number for 2002 with 2001 as base year, by Fisher's method : (8)