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}∫^{3}f(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 Î˜(logn) time using heap sort is

(A) Î˜(1) (B)
Î˜(√logn)

(C) Î˜(logn/loglogn) (D)
Î˜(logn)

Answer: C

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