# GATE Computer Science and Information Technology Solved Paper 2013 - Part 1

Q.1 to Q.25 carry one mark each.
1.       A binary operation Å on a set of integers is defined as xÅy=x2+y2. Which one of the following statements is TRUE about Å ?
(A) Commutative but not associative
(B) Both commutative and associative
(C) Associative but not commutative
(D) Neither commutative nor associative
2.       Suppose p is number of cars per minute passing through a certain road junction between 5 PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval ?
(A) 8/(2e3)          (B) 9/(2e3)
(C) 17/(2e3)       (D) 26/(2e3)
3.       Which one of the following does NOT equal
4.       The smallest integer than can be represented by an 8-bit number in 2’s complement form is
(A) -256             (B) -128
(C) -127             (D) 0
5.       In the following truth table, V=1 if and only if the input is valid.
What function does the truth table represent?
(A) Priority encoder     (B) Decoder
(C) Multiplexer             (D) Demultiplexer

6.       Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort ?
(A) O(log n)       (B) O(n)
(C) O(n log n)   (D) O(n2)
7.       Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes ?
(A) O(1)              (B) O(log n)
(C) O(n)             (D) O(n log n)
8.       Consider the languages L1 = Φ and L2 = {a}. Which one of the following represents L1L2*UL1* ?
(A) { є }               (B) Φ
(C) a*                  (D) { є, a}
9.       What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon and unit-production (i.e., of type A→є and Aa) to parse a string with n tokens?
(A) n/2                (B) n-1
(C) 2n-1             (D) 2n