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Roll No. .............................. Total No. of Questions : 13

Total No. of Pages : 03

COMPUTER MATHEMATICAL FOUNDATION

Subject Code : MCA-104 [A0504] Time : 3 Hrs.

INSTRUCTION TO CANDIDATES : 1. All questions of SECTION-A are compulsory. Each question carry TWO marks. 2. Attempt any NINE questions from SECTION-B. Each question carry FIVE marks.

Max. Marks : 75

SECTION–A

(15 × 2 = 30 Marks)

1. (a) If n(A) = 24, n(B) = 69, and n(A  B) = 81, what is n(A  B) ? (i) 6 (iii) 6 (ii) 12 (iv) 14

(b) Shade the Venn diagram to represent the set. (A  B  C)

A C

B

(c) Let R={ (3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6) } be a relation on a set A={3,6,9,12}.The relation is (i) reflexive and transitive (iii) an equivalence relation (ii) reflexive only (iv) eflexive and symmetric only

(d) Matrices A & B inverse of each other only if (i) AB = BA (iii) B = 0, BA = 1 (ii) AB – BA = l (iv) AB = BA = 1

(e) If A is a square matrix such that | A | = 2, then for any positive integer n, | An | is equal to (i) 0 (iii) 2 n (ii) 2n (iv) n2

(f) Number of relations defined on set (1, 2, 3, 4) is (g) When A = , then no. of elements in P(A) is (i) l (ii) 2 (iii) 0 (iv) none of these

(h) Find all possible partition of S={a,b,c} (i) Statement P(n) : (n + 3)2 > 2n + (i) for all n (iii) for all n >= 3

3

is true (ii) for all n >= 2 (iv) no n  N

(j) The maximum degree of any vertex in a simple graph with n vertices is (k) If p : He is very tall and q : He is very smart, then ~(~p ^ q) is

cos ,  sin   (l) If A=   then A + A’=I, then value of  is ______ sin , cos  

(i) /6

(ii) /3

(iii) 

(iv) 3/2

(m) If A is of order m × n and B is of order p × q, then AB is defined only if (i) m = q (ii) m = p (iii) n = p (iv) n = q

(n) The number of simple digraphs with V = 3 (i) 29 (ii) 28 (iii) 27 (iv) 26

(o) The number of simple digraphs with V = 3 and exactly 3 edges are

SECTION–B

2. State and prove...