# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.

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1. Q13 Option D – Correction (decryption part of the option has X and Y interchangef)