Engineering Mathematics, Question Paper of MCA Semester 1, Download Question Paper 5

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Roll No………
Total No. of Questions: 9

Paper ID [MC104]
MCA (Sem.-1st)
COMPUTER MATHEMATICAL FOUNDATION
SUBJECT CODE: (MCA-104)(N2)

Time: 3 Hrs.                                                                           Max. Marks: 60
Instruction to Candidates:
1. Attempt any One question from each Section-A, B, C, & D.
2. Section-E is Compulsory.
SECTION-A
Q1.    Let R={(1,2),(2,3),(3,1)} and A={1,2,3}, find the reflexive, symmetric and transitive closure of R, using.
(a) Composition of relation R
(b) Composition of matrix relation R
Q2.    (a) Prove that A (b) Prove that (A SECTION-B
Q3.    Show that p=q=(p v q)= (p v q) using
(a) Truth Table (b) Algebra of propositions
Q4.    Prove by mathematical induction that 6n+2+72n+1 is divisible by 43 for each positive integer ‘n’.
SECTION-C
Q5.    Find the rank of matrix A= Q6.    Solve the equations using matrix inversion method
X+y+z=9, 2x+5+7z=52, 2x+y-z=0
SECTION-D
Q7.    Find the shortest path from vertex s to t and its length from the graph given below.

Q8.    A non empty connected graph G is Eulerianif and only if its vertices are all of even degree.
SECTION-E
Q9.    (a) Write the negation of each of the following conjuctions.
(i) Paris is in France and London is in England.
(ii) 2+4=6 and 7<12.
(b) Draw the truth table for ~(p-q)= p- ~ q = ~ p-q.
(c) Draw the venn diagram for the following (i) A-B (ii) AB.
(d) Prove that (A (e) Distinguish between {0} and 0.
(f) Define Transpose of a matrix.
(g) Find the rank of a matrix, A= (h) Define Biparite Graph with example.
(i) Give an example of a graph which is Hamiltonian but not Eulerian.
(j) Draw the graph G corresponding to adjacency matrix. A= 