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

of a triangle whose vertices are (1 , 2),(3 , 4) and (2 , 1).
(b) (i) If P(2,7) divides the line-segment 2
joining A (-1,1) and B in the ratio
3:2 from A. obtain the co-ordinates
of B.
(ii) obtain the formula of line passing 2
through the point (2,3) and parallel
to the line 3x-2y +1=0.
(c) obtain the formula of line passing 3
through (3,5) and makes and angle of
45o with the line 3x + y -1=0.

OR


5 (a) (i) Derive the formula of line y = mx+c 3
where m is the slope and c is the
intercept on y –axis.
(ii) If (-3,2) is the centroid of the 2
triangle whose vertices are (g , 2),
(h,1) and (2,k). obtain h and k.
(b) (i) If the area of the triangle with vertices 2
(2,3),(4,5) and (k,3) is five units .
obtain k.
(ii) find the intercepts on the axes of 2
the line 3x + 5y + two = 0
(c) obtain the formula of the line passing 3
through the point of intersection of the
lines x + y – five = 0 and x – y -1 =0 and
also through the point (2,3).

6 (a) (i) Solve the equations by Cramer ‘s rule 3
x/ four + y / three = 1, x / five + y / four = 1.

(ii) Prove that 2

one one one
x y z =(x – y) ( y – z) (z – x)
yz zx xy
(b) describe every with example : 2
(i) Column matrix
(ii) Skew-symmetrix
(c) If A = one two two 3
two one two then prove that
two two one
A two - 4A – 5I = 0.

OR
6 (a) (i) Solve the equations by Cramer’s rule . 3
x + 6y = 2xy,
3x + 2y = 2xy.



(ii) Prove that 2
x 2x-3p p
y 2y-3q q = 0.
z 2z-3r r


0 four three
(b) If A = one -3 -3 then prove that A2 = I.
-1 four four

(c) Solve using matrix method : 3

x + 2y = 21,
13x – y =3.
----------------------

Earning:   Approval pending.