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

D—3502 Seat No._______
First Year M.Sc. (CA & IT) exam
October / November-2003
Paper --- 102 : Advance Mathematics

Time : three Hours] [Total Marks : 70


Instructions : (1) All ques. are compulsory.
(3) Figures to the right indicate the marks
of the corresponding ques..

1 (a) Write the De-Morgan’s lows and prove 3
any 1 of them .
(b) If A = {1,2,3}, B = {2,4} and C = {3,4} 4
then prove that
A × ( B ? C) = (A × B) ? (A × C).
(c) (i) If f : Z ->Z , x ? Z , f(x) = 4x + three 3
Is it one-one ? Is it onto? Is it even ?
(ii) If f : R -> R ,f(x) =5x + four and g : R->R, 4
g(x) = 4x + k and fog=gof then obtain k
and fog (-2).

OR
one (a) describe the subsequent terms : 3
(i) Intersection of 2 sets
(ii) Disjoint sets
(iii) Cartesian product of 2 sets



(b) If n(U)=100, n(A)=60, n(B)=50 and 4
n(A U B) = 90, then obtain n(A’ U B’),
n(A’ n B’) and n(A n B’).
(c) (1) If f : R -> R , x ? R, f(x) = 2x +3 then 3
prove that f has it’s inverse function and
find it.
(2) A company sells its product for Rs.5 4
per unit. Fixed cost for the company are
Rs.3500 and variable costs are estimates
to run 30% of the total revenue .
Determine :
(i) The total revenue functions
(ii) The total cost function
(iii) The break-even point.
two (a) (1) describe limit of a function . 2
_________
(2) Evaluate : lim v n2 + n + one – n 2
n->8

Earning:   Approval pending.