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Posted By: Lenin Member Level: Diamond Posted Date: 30 May 2008
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2005 Indira Gandhi National Open University (IGNOU) Diploma Computer Applications CS08 Numerical and Statistical Computing - December 2005 Question paper
ADCA / MCA (II Yr)
Term-End Examination
December, 2005
CS08 : Numerical and Statistical Computing
Time: 3 hours
Maximum Marks: 75
Note : Question No. 1 is compulsory. Attempt any three questions from Q2 to Q5. Use of calculators is not allowed.
1. (a) (a) Explain why the following 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 following mathematical expressions : (3)
(i) p - 3q-1+loge4
(ii) l p3+v3 l
(iii) e-x2/2/v2p
(c) Indicate the error in the following : (3)
(i) IF (A = B) THEN
(ii) x= SIN(45ยบ)
(iii) Y = ALOG (2/3)
(d) Let P, Q, R and W be logical variables and P = .TRUE., Q = .FALSE., R =.TRUE. Find the value of W in the following : (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) Read an integer array of N(= 100) numbers Write a program segment to compute the average in whole number (no fraction) and print the average value as AVERAGE = < value >.
You can assume N is already stored in the computer memory. (3)
(f) Write a program segment to multiply two matrices A (l x m) and B (m x n) and form a new matrix C. You can assume 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) Find the s.d. of a series X for which SXr = 50, SXr2 = 1000 and r = 1(1)5. (3)
(i) Find the mean values of the variables X and Y from the following regression equations :
4X - 5Y = 33
20X - 9Y = 107
(j) Fit a straight line y = a + bx by the method of least squares on the points (2, 10), (4, 20), (6, 25). (3)
2. (a) We want to classify the people in three groups according to their ages in the following manner : (7)
group1 = age = 30; group2 = 30 < age = 60 group3 = 60 < age .
Write a program which reads the ages of 1000 people, one by one, and puts it in the appropriate group. Print the number of people in each group. Use ELSEIF.
(b) Wriie a program for Computing nCk = n!/k!(n-k)!. Print its value. Read N and K. (8)
3. (a) Write a program segment to read N (= 1000) and N values in an array and find the maximum value. Print the value and its location in the array. (7)
(b) Compute the regression coefficients byx and bxy, and the coefficient of correlation for the following data : (8)
X 2 4 6 8 10
Y 5 7 9 8 11
Also write down the regression equation of Y on X.
4. (a) Read 100 pairs of values (Xi, Fi), i = 1, 2, ... 100 as two arrays where Xi denotes the value of the variate X and Fi its frequency. Write a program to compute Arithmetic Mean (AM) and Standard Deviation (SD). Print AM and SD. (8)
(b) Calculate the median and mode for the following data : (7)
Marks No. of Students
0 - 10 4
10 - 20 6
20 - 30 20
30 - 40 10
40 - 50 7
50 - 60 3
5. (a) Box1 contains 3 white and 7 black balls and Box2 contains one white and 9 black balls. A box is selected 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 quantity q0j of commodity j in the base year. Let the corresponding figures for the current year be p1j and q1j, respectively. Write down the four formulae for calculating the Price Index Number P01. (8)
The following 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
Calculate the Cost of Living Index Number in 2002 as compared to 2001.
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