41.

Answer: 0.99

42. Suppose
L={p, q, r, s, t} is a lattice represented by the following Hasse diagram:

For any x,y Îµ L not necessarily distinct, x V
y and x É… y are join and meet of x, y, respectively. Let L

^{3}={(x,y,z): x,y,z Îµ L } be the set of all ordered triplets of the elements of L. Let p_{r}be the probability that an element (x,y,z) Îµ L^{3}chosen equiprobably satisfies xV(yÉ…z) = (xVy) É… (xVz). Then
(A) p

_{r}= 0 (B) p_{r}= 1
(C) 0<p

_{r}≤1/5 (D) 1/5<p_{r}<1
Answer: D

43. Consider
the operations

f(X,Y,Z) = X’YZ + XY’ + Y’Z’ and g(X,Y,Z) =
X’YZ + X’YZ’ + XY

Which one of the following is correct?

(A) Both {f} and {g} are functionally
complete

(B) Only {f} is functionally complete

(C) Only {g} is functionally complete

(D) Neither {f} nor {g} is functionally
complete

Answer: B

44. Let
G be a connected planar graph with 10 vertices. If the number of edges on each
face is three, then the number of edges in G is .................

Answer: 24

45. Let
a

_{n}represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_{n}?
(A) a

_{n-2}+a_{n-1}+2^{n-2 }(B) a_{n-2}+2a_{n-1}+2^{n-2}
(C) 2a

_{n-2}+a_{n-1}+2^{n-2 }(D) 2a_{n-2}+2a_{n-1}+2^{n-2}
Answer: A

46. A
variable x is said to be live at a statement S

_{i}in a program if the following three conditions hold simultaneously:
i. There exists a statement S

_{j}that uses x
ii. There is a path from S

_{i}to S_{j}in the flow graph corresponding to the program
iii. The path has no intervening assignment
to x including at S

_{i}and S_{j}
The variables which are live both at the
statement in basic block 2 and at the statement in basic block 3 of the above
control flow graph are

(A) p, s, u (B)
r, s, u

(C) r, u (D)
q, v

Answer: C

47. The
least number of temporary variables required to create a three-address code in
static single assignment form for the expression q + r / 3 + s – t * 5 + u * v
/w is .........................

Answer: 8

48. Consider
an Entity-Relationship (ER) model in which entity sets E

_{1}and E_{2}are connected by an m : n relationship R_{12}. E_{1}and E_{3}are connected by a 1 : n (1 on the side of E_{1}and n on the side of E_{3}) relationship R_{13}.
E

_{1}has two single-valued attributes a_{11}and a_{12}of which a_{11}is the key attribute. E_{2}has two single-valued attributes a_{21}and a_{22}of which a_{21}is the key attribute. E_{3}has two single-valued attributes a_{31}and a_{32}of which a_{31}is the key attribute. The relationships do not have any attributes.
If a relational model is derived from the
above ER model, then the minimum number of relations that would be generated if
all the relations are in 3NF is ................

Answer: 4

49. Consider
the DFAs M and N given below. The number of states in a minimal DFA that
accepts the language L(M) ∩ L(N) is ....................

Answer: 1

50. Consider
the NPDA <Q = {q

_{0},q_{1},q_{2}}, Î£ = {0,1}, Î“ = {0,1, ⊥}, Î´, q_{0}, ⊥, F = {q_{2}}> where (as per usual convention) Q is the set of states, Î£ is the input alphabet, Î“ is the stack alphabet, Î´ is the state transition function, q_{0}is the initial state, ⊥ is the initial stack symbol, and F is the set of accepting states. The state transition is as follows:
Which one of the following sequences must
follow the string 101100 so that the overall string is accepted by the
automaton?

(A) 10110 (B)
10010

(C) 01010 (D)
01001

Answer: B

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