JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE Previous Question Paper (November/December - 2018 - R13)

What is the minimal set of connectives required for a well formed formula?

Convert the following propositional logic in to DNF pΛ(p→q).

Write the properties of semi group and abelian group.

What are the properties of Equivalence relation?

How many different outcomes are possible by tossing 20 similar coins?

How many integers between 1 and 100 have a sum of digits of integer numbers equal to 10?

What is the exponential enumerator for the permutations of 2 objects of one kind and 3 objects of another kind?

Find the generating function for the number of ways to distribute 30 balls into 5 numbered boxes where each box contains at least 3 balls and at most 7 balls.

Define spanning tree. What are its characteristics?

Write the difference between Hamiltonian graphs and Euler graphs.

Obtain the principal disjunctive normal form of p→((p→q)Λ~(~q V~p).

Simplify the given expression by using logical identities ((p→q)V(p→s))→(pVs).

Obtain the principal conjunctive normal form of (p→ (q Λ r)) Λ (~p→(~q Λ~r)).

Using the statements R: Arjun is Happy H: Arjun is rich. Write the following statement in symbolic form:

i) Arjun is neither happy nor rich

ii) Arjun is poor or he is both rich and unhappy.

If R be a relation in the set of integers z defined by R= {(x,y):x∈z,y∈z,(x-y) is divisible by 6}.

If A, B, C are three sets such that A⊆B, Show (A×B)⊆ (B×C).

Show that given any 52 integers, there exists two of them whose sum or else whose difference is divisible by 100.

Prove the identity 1×1!+2×2!+3×3!+………+n×n!=(n+1)!-1.

Using binomial identities evaluate the sum of the following: 1.2.3+2.3.4+……+ (n-2)(n- 1)n.

Compute the number of rows of 6 Americans, 7 Mexicans and 10 Canadians in which an American invariably stands between a Mexican and a Canadian and in which a Mexican and a Canadian never stand side by side.

Solve an-5an-1+6an-2=2n+n, n≥2, given a0=1, a1=1 using generating functions.

Find the number of ways in which 4 persons each rolling a single die once, can have a total of 17?

Find the particular solution for the following difference equation: an+5an-1+6an-2=42.4n

Solve an-2an-1-3an-2=5n, n≥2, given a0=-2, a1=1.

Let Cn be the cycle graph with n vertices. Prove that C5 is the only cycle graph isomorphic to its complement.

If G is non-directed graph with 12 edges. Suppose that G has 6 vertices of degree 3 and the rest have degree less than 3. Determine the minimum number of vertices, G can have.