## Computer Mathematical Foundation , Question Paper of MCA (D) Semester 1, Download Question Paper 2

• Saturday, November 28, 2015

Roll No……
Total No. of Questions: 13

Paper ID [A0504]
MCA (Sem.-1st)
COMPUTER MATHEMACIAL FOUNDATION (MCA-104)

Time: 3 Hrs.                                                                           Max. Marks: 75

Instruction to Candidates:

1.       Section-A is Compulsory.
2.       Attempt any Nine questions from Section-B.

SECTION-A
Q1.    (a) State duality principle.
(b) Define Equivalence Relation and explain with example.
(c) Define with examples Square & Anti Symmetric Matrix.
(d) Prove that AB= (A
(e) Define Reflexive relation with example.
(f) Find Determinant of: -
(g) List any 2 properties of determinants with example.
(h) Find Rank of matrix give below:-
(i) Define Binary Tree and Directed Graph.
(j) What is Bipartite graph.
(k) Define Path of a graph.
(l) Define Walk of a Graph.
(m) With Principle of Mathematical Induction Show that 2”>n for every nN.
(n) What do you mean by Tautology?
(o) What do you mean by Conditional operators?
SECTION-B
Q2.    Let R be a Relation in A={6,7,1,2,3,4,5} defined by open sentence “/x-y/ is divisible by 7”. Write R as a set of ordered pair.

Q3.    State and prove De Morgan’s Law.

Q4.    If A, B, C are any three sets, then prove by taking any example that A

Q5.     Find =
Q6.    Give an example of two square matrices of order 2 x 2 each so that (A+B) (A-B)=0.

Q7.    Using Gauss Jordan Method solve following question:
2x+2y-z=3
2x-y+3z=4
5x-3y+z=3

Q8.    Draw the Directed Graph whose adjacency matrix is given below:

Q9.

Find the Shortest Path Between “a” and “d”.
Q10. State and Prove Hand Shaking theorem in Graphs.
Q11. Prove by Principle of Mathematical Induction that for all n Sum of n Natural number is (n(n+1))/2.
Q12. By using truth table Show that (p-q) =(~p v q) is Tautology.
Q13. What do you mean by Universal and Existential Quantifiers.