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'
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 03f(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.
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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