Saurastra University 2006 B.C.A Computer Application Foundation in Mathematics & Statistics - Question Paper

SP-9416] one [Contd...
*SP-9416*
SP-9416 Seat No.__________
B. C. A. (Sem. II) exam
April / May – 2006
Foundation in Mathematics & Statistics
(New Course)
Time : three Hours] [Total Marks : 100
1 Any 2 : 20
(a) Solve the subsequent L.P. issue by simplex method :
Max. Z x x = + three four one 2
Subject to
2 three 16 one two x x + £
2 three eight one two x + £
(b) From the subsequent transportation issue. obtain
solution using lowest cost method :
X Y Z W V S Supply
A nine 12 nine six nine 10 5
B seven three seven 7 five 5 6
C six five nine 11 three 11 2
D six eight 11 two 2 10 9
Demand four 4 six two four two 22
(c) Solve the subsequent L.P. issue by graph method :
5 10 50 x y + £
x y + ³ 1
y £ four and
z x y = + is minimum.
2 Attempt any 4 : 20
(a) find the regression line y on x using subsequent data :
x
y
:
:
146 152 158 164 170 176 182
75 78 77 79 82 85 89
(b) Estimate Y when X  70 and X when Y  90 from
the subsequent outcomes :
x y r
mean .
S.D.
18 100 0 8
14 20
(c) obtain correlation co-efficient from the subsequent outcomes
n = 10, Sx = 140, Sy = 150, S ( ) , x - 10 two S ( ) , y - = 15 215 2
S ( ) ( ) x y - - = 10 15 60.
(d) Fit a 2nd degree parabola to the subsequent data :
Year : one two three four 5
Population : 11 12 14 18 16
(e) explain properties of correlation co-efficient.
3 Attempt any 4 : 20
(a) Fit a straight line y a bx = + to the subsequent data :
x
y
:
:
1 two three four 5
14 27 40 55 68
(b) Solve y
y x
y
y ' , ( ) =
-
=
2 2
0 one in the range 0 0 two £ £ x .
using Euler's method h = 0 one . .
(c) Solve y y y ' , ( ) = - = 0 one by Euler replace method for
y h ( . ), . 0 six 0 two = .
SP-9416] two [Contd...
(d) provided y x y y ' , ( ) = - = two 0 1, obtain y( . ) 0 one and y( . ) 0 two using
R-K second order method.
(e) Draw less than cumulative frequency polygon for the
subsequent distribution :
Class :
no. of
Students
10 20 20 30 30 40 40 50 50 60 60 70
8 12 20 25 30 22
- - - - - -
4 Attempt any 4 : 20
(a) Use Lagrange's interpolation formula to obtain the
value of y when x = 10.
x
y
:
:
5 six nine 11
12 13 14 16
(2) Derive Newton's forward difference formula for
interpolation.
(3) The Amount A of a substance remaining in a reacting
system after an interval of time t in a certain chemical
experiment is tabulated beneath :
t
A gm
(min. ) :
( . ) : . . . .
2 five eight 11
94 eight 87 nine 81 three 75 1
find the value of A where t = nine using Newton's
Backward formula.
(4) Using N-R method obtain a root of the formula
f x e x x ( ) = - - = two one 0 accurate to 3 decimal places
initial root x0 one two = . .
(5) discuss Bi-section method.
SP-9416] three [Contd...
5 (a) Attempt any 1 : 7
(1) Solve :
10 12 x y z + + =
x y z + - = 10 10
x y z - + = two 10 9
by Gauss Jordan method.
(2) Solve :
2 three one x y z   
x y z + + = four five 25
3 four two x y z - + =
by Gauss elimination method.
(b) Attempt any 2 : 8
(1) If ABt = LNM OQP one 3
4 7
and B = LNM OQP two 5
3 1
obtain matrix B.
(2) obtain adjoint of the subsequent matrix :
1 0 7
2 two 5
0 three 6
L
N
MMM
O
Q PPP
(3) describe the subsequent :
– Skew symmetric matrix
– Square matrix
– Column matrix
– Transpose of a matrix.
(c) Evaluate sin x dx
0
2 pz by trapezoidal rule. By taking
8 no. of intervals.
SP-9416] four [ 1200/31-27 ]

Earning:   Approval pending.