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

ADCA / MCA (II Yr)
Term-End exam

December, 2005

CS08 : Numerical and 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) (a) discuss why the subsequent are wrong :
(i) 6.0 E - 30 (a const.)
(ii) 2ABC (a variable name)
(iii) A * B = A + B (assignment statement)

(b) Write down the FORTRAN equivalent for the subsequent mathematical expressions : (3)
(i) p - 3q-1+loge4
(ii) l p3+v3 l
(iii) e-x2/2/v2p

(c) Indicate the fault in the subsequent : (3)
(i) IF (A = B) THEN
(ii) x= SIN(45º)
(iii) Y = ALOG (2/3)

(d) Let P, Q, R and W be logical variables and P = .TRUE., Q = .FALSE., R =.TRUE. obtain the value of W in the subsequent : (3)
(i) W = P .AND. R .OR. .NOT. Q
(ii) W = .NOT. P .AND. .NOT. Q .OR. .NOT. R
(iii) W = P .AND. .NOT. Q .AND. .NOT. R

(e) learn an integer array of N(= 100) numbers Write a program segment to calculate the avg. in whole number (no fraction) and print the avg. value as avg. = < value >.
You can presume N is already stored in the computer memory. (3)

(f) Write a program segment to multiply 2 matrices A (l x m) and B (m x n) and form a new matrix C. You can presume that A, B and C are already declared in the Program. (3)

(g) A card is drawn from a pack of cards. What is the probability that it is either red or a king ? (3)

(h) obtain the s.d. of a series X for which SXr = 50, SXr2 = 1000 and r = 1(1)5. (3)

(i) obtain the mean values of the variables X and Y from the subsequent regression equations :
4X - 5Y = 33
20X - 9Y = 107

(j) Fit a straight line y = a + bx by the method of lowest squares on the points (2, 10), (4, 20), (6, 25). (3)

2. (a) We want to classify the people in 3 groups according to their ages in the subsequent manner : (7)
group1 = age = 30; group2 = 30 < age = 60 group3 = 60 < age .
Write a program which reads the ages of 1000 people, 1 by one, and puts it in the improper group. Print the number of people in every group. Use ELSEIF.

(b) Wriie a program for Computing nCk = n!/k!(n-k)!. Print its value. learn N and K. (8)

3. (a) Write a program segment to learn N (= 1000) and N values in an array and obtain the maximum value. Print the value and its location in the array. (7)

(b) calculate the regression coefficients byx and bxy, and the coefficient of correlation for the subsequent data : (8)

X two four six eight 10
Y five seven nine eight 11

Also write down the regression formula of Y on X.

4. (a) learn 100 pairs of values (Xi, Fi), i = 1, 2, ... 100 as 2 arrays where Xi denotes the value of the variate X and Fi its frequency. Write a program to calculate Arithmetic Mean (AM) and Standard Deviation (SD). Print AM and SD. (8)

(b) compute the median and mode for the subsequent data : (7)

Marks No. of Students
0 - 10 four
10 - 20 six
20 - 30 20
30 - 40 10
40 - 50 seven
50 - 60 three

5. (a) Box1 contains three white and seven black balls and Box2 contains 1 white and nine black balls. A box is opted at random and a ball is drawn. (7)
(i) What is the probability that the ball drawn is white ?
(ii) If the ball drawn is white, what is the Probability that it was drawn from Box1 ?

(b) Let p0j be the price of volume q0j of commodity j in the base year. Let the corresponding figures for the current year be p1j and q1j, respectively. Write down the 4 formulae for calculating the Price Index Number P01. (8)
The subsequent data is colllected for the years 2001 and 2002 for family expenditure :

Items % Expenditure 2001 Rs. 2002 Rs.
Food 35% 150 145
Fuel 10% 25 23.
Clothing 20% 75 65
Rent 15% 30 30
Misc. 20% 40 45

compute the Cost of residing Index Number in 2002 as compared to 2001.

Earning:   Approval pending.