Hemchandracharya North Gujarat University 2002 B.Sc Computer Science 102 : Advance Mathematics - exam paper

upward and concave downward.

4 (a) describe differential formula . Determine 2
the degree and order of the differential

formula ___________________
v d two y / dx two + 5y = dy/dx
(b) Solve : 4
(i) ( 3x + five ) dy + ydx = 0
(ii) dy / dx + 2y = e -x .
(c) (i) obtain the area of the region bounded 3
by y = three x two - nine ,x-axix and lines x = 0
x = 1.
(ii) Draw the graph of the linear equalities 3
x = 0 ; y = 0 ; x = four ;
x + y = one ; x + 2y = 10 .

OR
4 (a) discuss the method of solving a linear 2
formula dy/dx + Py = Q where P and Q
are function of x only.
(b) Solve : 4
(i) xydx – (x two + y 2) dy = 0
(ii) dy / dx + y / x =xy 2.
(c) (i) Determine the cost of producing 300 3
pens if the marginal cost (in ruppes
per unit) is Mc = x / 200 + 3.5.
(ii) Draw the graph of the linear 3
equalities .
x = 0 ; y = 0 ; x + 3y = 9,
x + y = 2, x = 3


5 (a) (i) Derive the formula to obtain the area 3
of a triangle ? ABC whose vertices
are A(x1,y1) , B(x2,y2)and C(x3 ,y3).
(ii) obtain the co-ordinates of the circumcentre 2

Earning:   Approval pending.