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

Roll No……

Total No. of Questions: 13

 Paper ID [A0504]

MCA (Sem.-1^st)

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 A∆B= (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.