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

RN—9002 Seat No._______
First Year M.Sc. (CA & IT) exam
August -- 2002
Advance Mathematics : Paper --- 102

Time : three Hours] [Total Marks :70


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


1 (a) If A,B and C are any 3 non-empty 3
sets then prove that
A U ( B n C ) = (A U B ) n ( A U C)
(b) If A = {1,2,3}, B = {2,4} and C = {3,4} then 3
prove that A × ( B ? C ) = ( A× B ) ? ( A × C )
(c) (i) If f : Z ? Z, x ? Z = 3x + 2. Is it three
one-one ? Is it even ?
(ii) If f : R-> R f(x) = 2x + K, g : R->R, 3
g(x) = 3x + four and fog = gof then obtain
K and fog(-2).

OR

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














(b) IF n(U) = 100, n(A) = 62,n(B) = 52 and 3
n( A U B) =88 then obtain n( A n B), n( A' U B’ )
and n(A n B' ).
(c) (i) If f : R->R , x ? R,f(x)=2x + three then 3
prove that f its inverse function
and find it
(ii) A company sells its product for Rs.4 3
per unit. Fixed cost for the company
are Rs. 2800 and variable costs are
estimated to run 30% of the total
revenue. Determine :
(i) The total revenue function
(ii) The total cost function
(iii) The break-even point.


2 (a) Evaluate : four

Earning:   Approval pending.