GATE CSE 2013

Question 1
A binary operation \oplus on a set of integers is defined as x \oplus y= x^{2}+y^{2}. Which one of the following statements is TRUE about \oplus ?
A
Commutative but not associative
B
Both commutative and associative
C
Associative but not commutative
D
Neither commutative nor associative
Discrete Mathematics   Set Theory
Question 2
Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, 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/(2e^{3})
B
9/(2e^{3})
C
17/(2e^{3})
D
26/(2e^{3})
Discrete Mathematics   Probability Theory
Question 3
Which one of the following does NOT equal
\begin{bmatrix} 1 & x&x^{2} \\ 1& y & y^{2}\\ 1&z & z^{2} \end{bmatrix}?
A
\begin{bmatrix} 1 & x(x+1)&x+1 \\ 1& y(y+1) & y+1\\ 1&z(z+1) & z+1 \end{bmatrix}
B
\begin{bmatrix} 1 & x(x+1)&x^{2}+1 \\ 1& y(y+1) & y^{2}+1\\ 1&z(z+1) & z^{2}+1 \end{bmatrix}
C
\begin{bmatrix} 0& x(x+1)&x^{2}+1 \\ 0& y(y+1) & y^{2}+1\\ 1&z & z^{2} \end{bmatrix}
D
\begin{bmatrix} 2& x(x+1)&x^{2}+1 \\ 2& y(y+1) & y^{2}+1\\ 1&z & z^{2} \end{bmatrix}
Engineering Mathematics   Linear Algebra
Question 4
The smallest integer that can be represented by an 8-bit number in 2's complement form is
A
-256
B
-128
C
-127
D
0
Digital Logic   Number System
Question 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
Digital Logic   Combinational Circuit
Question 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(n^{2})
Algorithm   Sorting
Question 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)
Data Structure   Binary Search Tree
Question 8
Consider the languages L_{1}=\phi abd L_{2}=\{a\}. Which one of the following represents L_{1} L_{2}^{*} \cup L_{1}^{*}?
A
\{ \epsilon \}
B
\phi
C
a^{*}
D
\{ \epsilon ,a \}
Theory of Computation   Regular Language
Question 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\rightarrow \epsilon and A \rightarrow a ) to parse a string with n tokens?
A
n/2
B
n-1
C
2n-1
D
2^{n}
Compiler Design   Parsing
Question 10
A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero?
A
This algorithm is equivalent to the first-come-first-serve algorithm.
B
This algorithm is equivalent to the round-robin algorithm.
C
This algorithm is equivalent to the shortest-job-first algorithm.
D
This algorithm is equivalent to the shortest-remaining-time-first algorithm.
Operating System   CPU Scheduling
There are 10 questions to complete.

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