GATE CS question library

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

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

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 $P$ …

An index is clustered, if

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.

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

The transport layer protocols used for real time multimedia, file transfer, $\textsf{DNS}$ and email, respectively are

A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with 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

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?

Consider the languages $L_1 = \phi$ and $L_2 = \{a\}$. Which one of the following represents $L_1 {L_2}^* \cup {L_1}^*$ ?

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?

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

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

The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is

Which one of the following does NOT equal $$\begin{vmatrix} 1 & x & x^{2}\\ 1& y & y^{2}\\ 1 & z & z^{2} \end{vmatrix} \quad ?$$

Consider an instruction pipeline with five stages without any branch prediction: Fetch Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction (EI) and Write Operand (WO). The stage delays for FI, DI, FO, EI and WO are $\text{5 ns, 7 ns, 10 ns, 8 ns and 6 ns},$ respectively. There are intermediate storage buffers after each stage …

Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ?

A computer uses $46\text{-bit}$ virtual address, $32\text{-bit}$ physical address, and a three–level paged page table organization. The page table base register stores the base address of the first-level table $\text{(T1)}$, which occupies exactly one page. Each entry of $\text{T1}$ stores the base address of a page of the second-level table …

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?