Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 14

Roll No……..

Total No. of Questins:9]

May-2006

DISCRETE STRUCTURES

SUBJECT CODE : CS - 203

B.Tech. (Sem. – 3^{rd -} 2056)

Time : 03 Hours

Note : Section –A 9 compulsory. Attempt any Four questions form section –B. Attempt any two questions from Section-C.

Section-A

1.      

a.     State Euler’s formula for connected planar graph.

b.     Define chromatic number of a graph.

c.      State Basic counting principles.

d.     How many 4- digit telephone numbers have one or more repeated digits?

e.      Define union and intersection of two sets A &B.

f.       Define Partial order relation.

g.     Define subgroup.

h.     Define Homomorphism of Groups

i.       State De Morgan’s laws in Boolean algebra.

j.       Define Euclidean rind(domain)

Section-B

2.     State and prove Euler’s formula in connected maps.

3.     Solve the recurrence relation a_r- 2_r-1 +a_r-2 =0 given that a_n = 1 and a₁ =2

4.     Prove that intersection of two normal subgroups is again a normal subgroup.

5.     Minimize the Boolean expression f = xy⨁ x’y⨁x’y’.

6.     Prove that every cyclic group is abelian.

Section –C

7.     State and prove Lagrange’s theorem on finite groups.