# GATE Computer Science and Information Technology Solved Paper 2013 - Part 3

21.       Which one of the following expressions does NOT represent exclusive NOR of x and y?
(A) xy + x'y'        (B) xy'
(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 03f(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.
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