21. Which one of the following
expressions does NOT represent exclusive NOR of x and y?
(A) xy + x'y' (B)
x⊕y'
(C) x'⊕y (D) x'⊕y'
Answer: D
22. Which one of the following
functions is continuous at x = 3 ?
Answer: A
23. Function f is known
at the following points:
The value of 0∫3f(x)dx computed
using the trapezoidal rule is
(A) 8.983 (B)
9.003 (C) 9.017 (D) 9.045
Answer: D
24. Consider an undirected
random graph of eight vertices. The probability that there is an edge between a
pair of vertices is ½. What is the expected number of unordered cycles of
length three ?
(A) 1/8 (B) 1
(C) 7 (D) 8
Answer: C
25. Which of the following
statements is/are TRUE for undirected graphs ?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.
(A) P only (B)
Q only
(C) Both P and Q (D)
Neither P nor Q
Answer: C
Q.26
to Q.55 carry two marks each.
26. The line graph L(G)
of a simple graph G is defined as follows:
• There is exactly one vertex v(e) in L(G)
for each edge e in G.
• For any two edges e and e’ in G, L(G)
has an edge between v(e) and v(e’), if and only if e and e’
are incident with the same vertex in G.
Which of the following statements is/are TRUE?
(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.
(A) P only (B)
P and R only
(C) R only (D)
P, Q and S only
Answer: A
27. What is the logical
translation of the following statement ?
“None of my friends are perfect.”
(A) ∃x(F(x)˄¬P(x)) (B) ∃x(¬F(x)˄P(x))
(C) ∃x(¬F(x)˄¬P(x)) (D) ¬∃x(F(x)˄P(x))
Answer: D
28. Consider the following
sequence of micro–operations.
MBR←PC
MAR←X
PC←Y
Memory←MBR
Which one of the following is a possible operation
performed by this sequence ?
(A) Instruction fetch (B) Operand fetch
(C) Conditional branch (D)
Initiation of interrupt service
Answer: D
29. Consider a hard disk with
16 recording surfaces (0−15) having 16384 cylinders (0−16383) and each cylinder
contains 64 sectors (0−63). Data storage capacity in each sector is 512 bytes.
Data are organized cylinder–wise and the addressing format is <cylinder no.,
surface no., sector no.>. A file of size 42797 KB is stored in the disk and
the starting disk location of the file is <1200, 9, 40>. What is the
cylinder number of the last sector of the file, if it is stored in a contiguous
manner?
(A) 1281 (B)
1282
(C) 1283 (D)
1284
Answer: D
30. The number of elements that
can be sorted in Θ(logn) time using heap sort is
(A) Θ(1) (B)
Θ(√logn)
(C) Θ(logn/loglogn) (D)
Θ(logn)
Answer: C
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