Saurastra University 2006 B.C.A Computer Application Fundamentals in Mathematics & Statistics (New ) - Question Paper

SP-1858    Seat No._

* S P    1 8 5 8 *

B. C. A. (Sem. II) Examination April/May - 2006 Fundamentals in Mathematics & Statistics

(New Course)

[Total Marks : 100

(b) Answer any two :

(1)    Find the solution using Gauss eliminating method :

3 x + y - z = 3 2x - 8y + z = -5 x - 2 y + 9 z = 8

(2)    Solve the following equation by Gauss Jordan method :

3 x + 4 y - z = 8 -2 x + y + z = 3 x + 2 y - z = 2

[Contd.

(1)    Explain Newton's forward difference formulas.

(2)    The area A of a circle of diameter d is given for the following values :

d:	80	85	90	95	100
A:	5026	5674	6362	7088	7854

Calculate the area of circle of diameter 105.

(3) Find 10933. If 10920 = 1.3010, 10930 = 1.4771 and 10938 = 1.5798.

(b) Answer any two :    10

(1)    Explain False position method.

(2)    Find a root of the equation x¹ - x - 11 = 0 correct to four decimal using bisection method.

(3)    Using N-R method, find a root correct to three decimal places :

f (x) = xe^x - cos x

3 (a) Answer any three :    15

(1)    Apply Euler's method to solve dy

= x + y, y(0) = 0 take h = 0.2

(Carry out 5 steps)

(2)    Using R-K 4^th order. Solve

dx = y² + xy, y(0) = 1 and find y(0.1), y(0.2).

(3)    Obtain formula for R-K 2^nd order method.

(b) Find median from the following distribution :    5

Class :	5 -10	10 -15	15 -20	20 -25	25 -30	30 -35	35 -40	40 -45	45 -50
Frequency :	7	15	24	31	42	30	26	15	10

SP-1858]    2    [Contd...

(1) Calculate the lower and upper quartile from the following data :

Class:	5 I	5 -10	10 -15	15 - 20	20 - 25
Frequency :	7	18	25	30	20

(2) Calculate mean and standard deviation of the following frequency distribution of marks :

Marks:	0 10	10 -20	20 -30	30 -40	- 00 45	50 -60	60 -70
Frequency :	5	12	30	45	50	37	21

(3) You are given the following data :

	X	Y
Mean	36	85
S.D.	11	8

Correlation coefficient is 0.66.

Find :

(1)    Two regression line

(2)    Estimate the value of x when y = 75.

(b) Answer any two :    10

(1)    Write properties of correlation and regression.

(2)    Obtain two regression coefficients from the data given below :

x :	50	60	50	60	80	50	80	40	70
y:	30	60	40	50	60	30	70	50	60

Salary :	300 -400	400 -500	500 -600	600 -700	700 -800	800 -900	900 -1000	1000 -1100
No. of Employees:	20	30	60	75	45	100	60	40

(2)    A salesman is known to sell a product in 3 out of 5 attempts while another salesman in 2 out 5 attempts. Find the probability that (i) no sale will be affected when both try to sell the product and (ii) either of them will succeed in selling the product.

(3)    State and prove additional law of probability.

(4)    Find mean of variance of random variable X is :

X:	3	4	5	6
p(x):	0.2	0.4	0.3	0.1

(5) A player loses 3 fair coins. He wins Rs. 5 if 3 heads appear, Rs. 3 if 2 heads appear, Re. 1 if 1 head appears on the other hand he loses Rs. 20 if 3 tails appear. Find expected gain of the player.

SP-1858]    4    [ 200 ]

1

The coefficient of rank correlation of the marks obtained by 10 students in two subject is 0.8, It was later discovered that the difference in ranks in the two subjects obtained by one student was wrongly taken as 7 instead of 9. Find correct value of rank correlation.

Attachment: saurastra-university-2006-b-c-a-computer-application-25552-1.pdf

Earning:   Approval pending.