Govt. M. M. college, Jessore
Dept. of Mathematics
4-th year (Hons.) Test Examination-2008
Sub-Discreet Mathematics Code-3748
Full Marks-50 Time-2.5 hours
[All questions are of equal value. Answer any four questions ]
- (a) Prove that is a irrational by contradiction.
(b) Use mathematical induction to prove that .
where , ,………..,are subsets of a universal set U and n is
a positive integer .
- (a) Define floor function, Ceilling function,Integer value function,
Absolute value function,logarithmic function and
(b) Let x be any real number, then the following hold :
(i) (ii) , m is any integer.
- (a) Prove that .
(b) How many integers between 1 and 300 are divisible by at least
one of 3, 5, 7? divisible by 3 and 5 but not by 7.
- (a) Let , n>1 be linear homogenous
recurrence relation with constant co-efficient . Let t be a non zero
real number , then the sequence satisfies the above relation if
and only if .
(b) Solve the linear homogenous difference equation
- (a) Define Eulerian circuit. Let G be a connected plane graph with
V vertices, E edges and R regions, then prove V-E+R=2.
(b) Show that the following two graphs and are isomorphic
- (a) Define Capacity , Value of flow and Cut. Verify the law of
conservation of flow at a , e and d
(b) Define maximum flow. Find a maximum flow in the directed
network shown in the adjacent figure and prove that it is maximum,