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

Roll No………

Total No. of Questions: 9

Paper ID [MC104]

MCA (Sem.-1^st)

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) A∆B.

(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=