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'
22. Which one of the following functions is continuous at x = 3 ?
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
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
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
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
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))
28. Consider the following sequence of micro–operations.
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
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
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)