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

Roll No………

Total No. of Questions: 9

Paper ID [B0104]

MCA (Sem.-1^st)

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)  A_i