Hemchandracharya North Gujarat University 2006 B.Sc Computer Science 102 : Advance Mathematics - Question Paper

(i) lim x5/2 – one
x->1 x3/2 – one


(ii) lim 5x2 + 17x + 14
x->-2 9x2 + 5x – 26


(c) describe Null metrix , Diagonal metrix , Symmetric metrix ,
Identity metrix .






part – II

4 (a) Evaluate : 6

(i) ? 3x2 + 5x2 – 4x +7 dx
x
(ii) ? xex dx

(iii) ? (2x +3)(x2 + 3x +5 ) dx


(b) describe the subsequent terms with suitable example : 3

(i) Homogeneous formula
(ii) General solution of a differential formula
(iii) Particular solution of a differential formula

(c) Solve any 1 : 3

(i) (x+2) dy + y.dx = 0
(ii) (x2+y2) dy = xy



OR



4 (a) Evaluate : 6

(i) ? x – one three dx
x

(ii) ? ex (tan x + sec2 x) dx
(iii) ? log x dx

(b) Define differential formula. Determine the degree and the 3
Order of the differential formula.
__________
v d2y +3y +1 =2 dy
dx2 dx
(c) Solve any 1 : 3

(i) dy + y =ex
dx

(ii ) xy2 dy =(x3 + y3) dx



5 (a) Derive the formula of line y= mx + c where m is the slope 3
and c Is the intercept on y – axis.

(b) ans the subsequent :

(i) If 3 points (2,3) , (k,1) and (3,4) are collinear. obtain K . 2
(ii) obtain the co-ordinates of the circum center of a triangle
whose vertices are (1,2) , (3,4) and (2,1).


(c) obtain the formula of linew passing through the point (3,4) and 3
Parallel and perpendicular to the line 4x - 3y + two = 0.

OR

5 (a) Derive the formula of line of the form x + y = one where ab?0. 3
a b

(b) ans the subsequent :

(i) If (3,5) centroid of the triangle whose vertices (4, -1),(k ,2) 2
and (0, m) then obtain k and m.
(ii) If (4 ,k) divides the line segment joining A (2,3) and B(5,-1) 3
obtain the ratio of divison from A and value of k.
(c) obtain the formula of line passing through the point (3,2) and 4
Making an angle of 45° with the line 3x + y – five = 0.




6 (a) describe with illustrations : 6

(i) Parallel graph
(ii) Even vertex
(iii) Walk.

(b) ans the following:

(i) Draw the graph G(V,E) for which V={a,b,c} and 2
E= {( a,b ),( a,c ), ( a,a ),( b,c )} .
(ii ) Determine the degree of every vertax and all simple paths 2
from A to D for the provided graph G.


A B




C D

Graph : G

OR

6 (a) describe with illustrations : 6

(i) Simple graph
(ii) Tree
(iii) Loop

(b) Determine the subsequent for the provided graph G . 4

(i) The set V(G) of the vertices of G
(ii) The set E(G) of the edges of G
(iii) The degree of every from vertex
(iv)All simple paths from A to E.








A

B E



C D

Graph : G


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Earning:   Approval pending.