GATE CS question library

Let $\mathrm{S}$ be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one of the following $\mathrm{ER}$ diagrams CORRECTLY represents $\mathrm{S}$?

In a $\mathrm{B}^+$ tree, the requirement of at least half-full $(50 \%)$ node occupancy is relaxed for which one of the following cases?

Which of the following statements about a relation $\mathbf{R}$ in first normal form $\text{(1NF)}$ is/are TRUE?

​Let $L_1, L_2$ be two regular languages and $L_3$ a language which is not regular. Which of the following statements is/are always TRUE?

Which of the following statements about threads is/are TRUE?

Which of the following process state transitions is/are NOT possible?

Which of the following is/are Bottom-Up Parser(s)?

Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE?

​​Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

​$\mathrm{TCP}$ client $\mathrm{P}$ successfully establishes a connection to $\text{TCP}$ server $\mathrm{Q}$. Let $\text{N}_{P}$ denote the sequence number in the $\text{SYN}$ sent from $\mathrm{P}$ to $\mathrm{Q}$. Let $\text{N}_{Q}$ denote the acknowledgement number in the SYN ACK from $\text{Q}$ to $\text{P}$. Which of the following …

Consider a $5$-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Register Writeback (WB) stages. Which of the following statements about forwarding is/are CORRECT?

Which of the following fields is/are modified in the $\text{IP}$ header of a packet going out of a network address translation $\text{(NAT)}$ device from an internal network to an external network?

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.

Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. …

The number of spanning trees in a complete graph of $4$ vertices labelled $\text{A, B, C,}$ and $\text{D}$ is _________.

Consider the following two relations, $R(A, B)$ and $S(A, C)$: …

Consider a network path $\mathrm{P}-\mathrm{Q}-\mathrm{R}$ between nodes $\mathrm{P}$ and $\mathrm{R}$ via router $\mathrm{Q}$. Node $\mathrm{P}$ sends a file of size $10^6$ bytes to $\text{R}$ via this path by splitting the file into chunks of $10^3$ bytes each. Node $\text{P}$ sends these chunks one after the other without any wait time …

​Consider the following syntax-directed definition $\text{(SDD)}$. …

Consider the following pseudo-code. L 1: t1 = -1 L 2: t2 = 0 L 3: t3 = 0 L 4: t4 = 4 * t3 L 5: t5 = 4 * t2 L 6: t6 = t5 * M L 7: t7 = t4 + t6 L 8: t8 = a[t7] L 9: if t8 <= max goto L11 L 10: t1 = t8 L 11: t3 = t3 + 1 L 12: if t3 < M goto L4 L 13: t2 = t2 + 1 L 14: if t2 < N goto L3 L 15: max = t1 Which one of the following options CORRECTLY …

​​​Consider the following two threads $\mathrm{T} 1$ and $\mathrm{T} 2$ that update two shared variables $\mathrm{a}$ and $\mathrm{b}$. Assume that initially $\mathrm{a}=\mathrm{b}=1$. Though context switching between threads can happen at any time, each statement of $\mathrm{T} 1$ or $\mathrm{T} 2$ is executed atomically without interruption. …