Indira Gandhi National Open University (IGNOU) 2005 Diploma Computer Applications CS08 (S) Numerical and Statistical Computing - - Question Paper

ADCA / MCA (II Yr)
Term-End exam

December, 2005

CS08 (S): Numerical & Statistical Computing

Time: three hours
Maximum Marks: 75

Note : ques. No. one is compulsory. Attempt any 3 ques. from Q2 to Q5. Use of calculators is not allowed.
1. (a) discuss what is wrong in the subsequent 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 subsequent mathematical expressions: (3)
(i) 5P - 4QR + loge6
(ii) ?P3/2 - Q-1/2?
(iii)ez2/2s/v2p

(c) lndicate the fault in the subsequent : (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.
obtain the value of W in the subsequent (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) learn N numbers(N = 100) in an array A. Write a program part to obtain the smallest number and print it. N is already stored in the computer memory. (3)

(f) Write a program part to multiply 2 matrices A (p x q) and B (q x r) to form a matrix C. You can presume that A, B and C are already declared in the program. (3)

(g) obtain the standard deviation for the subsequent data : (3)

xi one two three four five
fi one three two three one

(h) A die is thrown five times and the number three or four on the top is counted as a success. What is the probability of getting 2 successes only ? (3)

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

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

2. (a) A company decides to provide an increment to its employees according to the subsequent formula (percentage of salary) : (7)
for salary = 5000, increment 10%
5000 < salary = 8000, increment 9%
8000 < salary, increment 8%
Write a program to learn the salary of an employee, calculate the increment and the increased salary. Print them. Use ELSEIF.

(b) learn N pairs of values (Xi, Yi), i = 1, 2, ... N in 2 arrays X and Y. Write a program part to calculate the coefficient of correlation. You can presume N is already stored in the computer memory. (8)

3. (a) learn 3 real numbes A, B and C, which form 3 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 outcome should also be printed. The program should also include finding its area using the formula vs(s-A) (s-B) (s-C) and printing the outcome. (8)

(b) obtain the first and third Quartiles and Mode for the subsequent data :

Marks No. of Students
0-5 four
5-10 10
10-15 20
15-20 eight
20-25 five
25-30 three

4. (a) Write a program part to learn N followed by N numbers, 1 by 1 (not array). obtain the smallest number and print it.

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

Scores in Maths (X) Scores in English (Y)
Mean 80 50
S.D. 15 10

The coefficient of correlation ranging from X and Y = 0.4. Estimate the marks found in Mathematics by a learner who has secured 60 marks in English. Also calculate the marks found in English when she secures 85 marks in Mathematics.

5. (a) 2 coins are tossed 6 times. What is the probability that heads appear on both the coins at lowest price ? (7)

(b) define the 4 tests as criteria for a good Index Number. From the subsequent data compute the price index number for 2002 with 2001 as base year, by Fisher's method : (8)

2001 2002
Commodity Price volume Price volume
A 20 eight 40 six
B 50 10 60 five
C 40 15 50 15
D 20 20 20 25

Earning:   Approval pending.