UGC NET_CS_ Paper-II dec-13_IV

31. The dual of a Boolean expression is obtained by interchanging

 (A) Boolean sums and Boolean products

 (B) Boolean sums and Boolean products or interchanging 0’s and 1’s

 (C) Boolean sums and Boolean products and interchanging 0’s & 1’s 

 (D) Interchanging 0’s and 1’s

32. Given that (292)10 = (1204)x in some number system x. The base x of that number system is

 (A) 2

 (B) 8

 (C) 10

 (D) None of the above 

33. The sum of products expansion for the function

 F(x, y, z) = (x + y)z' is given as

 (A) x' y'z + xy'z + x'yz'

 (B) xyz + xy'z + xy' z'

 (C) x y' z' + x' y' z' + xyz'

 (D) x yz' + xy' z' + x' yz' 

34. Let P(m, n) be the statement  “m divides n” where the universe of discourse for both the variables is the set of positive integers. Determine the truth values of each of the following propositions :

 I. ∀m ∀n P(m, n),

 II. ∃m ∀n P(m, n)

 (A) Both I and II are true

 (B) Both I and II are false

 (C) I – false & II – true 

 (D) I – true & II – false

35. Big – O estimate for  f(x) = (x + 1) log(x2 + 1) + 3x2 is given as

 (A) O(x log x)

 (B) O(x2) 

 (C) O(x3)

 (D) O(x2 log x)

36. How many edges are there in a forest of t-trees containing a total of n

vertices ?

 (A) n + t

 (B) n – t 

 (C) n ∗ t

 (D) n^t

37. Let f and g be the functions from the set of integers to the set integers

defined by

 f(x) = 2x + 3 and g(x) = 3x + 2

 Then the composition of f and g and g and f is given as

 (A) 6x + 7, 6x + 11 

 (B) 6x + 11, 6x + 7

 (C) 5x + 5, 5x + 5

 (D) None of the above

38. If n and r are non-negative integers and n ≥ r, then p(n + 1, r) equals to

 (A) p(n, r) (n + 1)(n + 1 – r) 

 (B) p(n, r) (n + 1)(n – 1 + r)

 (C) p(n, r) (n – 1)(n + 1 – r)

 (D) p(n, r) (n + 1)(n + 1 + r)

39. A graph is non-planar if and only if it contains a subgraph homomorphic to

 (A) K3, 2 or K5    (B) K3, 3 and K6

 (C) K3, 3 or K5    (D) K2, 3 and K5

40. Which of the following statements are true ?

 I. A circuit that adds two bits, producing a sum bit and a carry bit is called half adder.

 II. A circuit that adds two bits, producing a sum bit and a carry bit is called full adder.

 III. A circuit that adds two bits and a carry bit producing a sum bit and a carry bit is called full adder.

 IV. A device that accepts the value of a Boolean variable as input and produces its complement is called an inverter.

 (A) I & II        (B) II & III

 (C) I, II, III     (D) I, III & IV