## Engineering Mathematics, Question Paper of MCA Semester 1, Download Question Paper 2

• Thursday, November 26, 2015
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Roll No………
Total No. of Questions: 9

Paper ID [B0104]
MCA (Sem.-1st)
COMPUTER MATHEMATICAL FOUNDATION
(MCA-104)

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.
(a) Show that set of real numbers in [0,1] is uncountable set.
(b) Prove that A x (B =(A x B) (A x C)
Q2.    Let R=[(1,2),(2,3),(3,1)] and A={1,2,3}. Find reflexive, symmetric and transitive closure of R using.
(a) Graphical Representation of R.
(b) Composition of matrix relation R.
SECTION –B
Q3.    Show that using mathematical induction.
Q4.    Prove that the following propositions are tautology
(a) ~ (P ^q)v q
(b) p=( P v q)
SECTION –C
Q5.    Solve the following system of equations using matrix inversion method.
2x-y+3z=8, -x+2y+z=4, 3x+y-4z=0
Q6.    Find the rank of matrix. A= SECTION –D
Q7.    A planar graph G is 5-colorable. Prove.
Q8.    Using adjacency matrix represent the following graphs. SECTION –E
Q9.
(a) Draw the truth table for-(p=1)= P ^ ~q.
(b) Negate the statement for all real numbers x, if x>3, then x2>9.
(c) Prove that A-(B (d) Distinguish between (e) If A=[0,i], where i the set of integers, find
(i) A1 A2
­                (ii) Ai