Hemchandracharya North Gujarat University 2003 B.Sc Computer Science 102 : Advance Mathematics - Question Paper

-1 four four

A2 = I


(2) IF A = one two and B = four 0
three four two one

Prove that (AB)T = B2 AT
(c) describe every with example : 3
(1) Row matrix
(2) Null matrix
(3) Skew-symetrix metrix.
















4 (a) obtain : 6
__ __
(1) ? (v x + 1/ v x )2
(2) x log x dx
two
(3) ? 2x + five / x2 +5x +3 dx
1

(b) Find tht area of region bounded by 3
Y = x2 and the line y=x +2
(c) describe differential formula . Determine the 3
degree and the order of the differential
___________
formula v d2 y/d x2 +2y=dy/dx
(d) Solve tany 1 : 2
(1) dy/dx = ex-y + x2 xey
(2) dy/dx +y = ex

OR
4 (a) obtain : 6
(1) ? x ex dx
(2) ? ex (sin x+ cos x) dx

two
(3) ? logx / x dx
one

















(b) obtain the quantity of sphere of radius r 3
using the definite integral
(c) discuss the method of solving a linear three
formula dy/dx+Py = Q where P and Q are
the function of x only.

(d) Solve any 1 : 2
(1) (x+5) dy + y dx=0
(2) ( x2 + y2 ) dy/dx xy .

5 (a) (1) Derive the formula to obtain the area of 3
A triangle ?ABC whose vertices are
A(x1,y1), B(x2,y2) and C= (x3,y3)
(2) A( 0 , 0 ) ,B( four , two ), C( three , -3 ) and 3
D( k , -2 ) are provided points. obtain k if
<-----> <-----> <-----> <----->
AB || CD and AB | CD
(b) (1) Prove that points ( four , three ) ,( seven , one ) and two
( 9, three ) are the vartices of an isoseceles
triangle.
(2) If P( four , k ) divides the line segement 2
joining A( 2, 3) and B(5, -1). obtain the
ratio of division from A and value of k .





















(c) obtain the formula of a line passing through 4
The point ( two , five ) and marking an angle of
45o with line x – 3y + two = 0

OR

5 (a) (1) find the formula of line of the 3
From x/a + y/b = one where ab ? 0
(2) If the area of the triangle with 3
Varitices (k ,3) ,(4,5) and (3,1) is
six unites ,find k.
(b) (1) Show that the 3 points 2
A(1,4), B(3,-2) and C(-3,16) are
Collinear.
(2) If (-3,4) is the centroid of the triangle 2
whose certices are (6,2),(x,3) and
(0,y) then obtain x,y.
(c) obtain the formula of line parallel to 4
3x + y + five = 0 and pass through the
point of intersection of lines
x + y – three =0 and x – y -5=0.

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Earning:   Approval pending.