# Computer Science and Information Technology - GATE 2013 Paper Solution

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 $\oplus$?

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 ?

Which one of the following does NOT equal $\left|\begin{array}{ccc}1& x& {x}^{2}\\ 1& y& {y}^{2}\\ 1& z& {z}^{2}\end{array}\right|$?

The smallest integer that can be represented by an 8-bit number in 2’s complement form is

In the following truth table, V = 1 if and only if the input is valid.

 Inputs Outputs D0 D1 D2 D3 X0 X1 V 0 0 0 0 X X 0 1 0 0 0 0 0 1 X 1 0 0 0 1 1 X X 1 0 1 0 1 X X X 1 1 1 1

What function does the truth table represent?

Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort?

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?

Consider the languages ${L}_{1}=\mathrm{\Phi }$ and ${L}_{2}=\left\{a\right\}$. Which one of the following represents ${L}_{1}{L}_{2}^{\ast }\cup {L}_{1}^{\ast }$?

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 $\mathrm{A}\to \mathrm{ϵ}$ and $\mathrm{A}\to \mathrm{a}$) to parse a string with n tokens?

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?

Match the problem domains in GROUP I with the solution technologies in GROUP II.

 GROUP I GROUP II (P) Service oriented computing (1) Interoperability (Q) Heterogeneous communicating systems (2) BPMN (R) Information representation (3) Publish-find-bind (S) Process description (4) XML

The transport layer protocols used for real time multimedia, file transfer, DNS and email,respectively are

Using public key cryptography, X adds a digital signature σ to message M, encrypts <M, σ>, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations?

Assume that source S and destination D are connected through two intermediate routers labeled R. Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D. An index is clustered, if

Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes?

Which of the following statements is/are FALSE?
1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine.
2. Turing recognizable languages are closed under union and complementation.
3. Turing decidable languages are closed under intersection and complementation.
4. Turing recognizable languages are closed under union and intersection.

Which of the following statements are TRUE?
1. The problem of determining whether there exists a cycle in an undirected graph is in P.
2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.