GATE CS question library

Consider the three-way handshake mechanism followed during $\text{TCP}$ connection establishment between hosts $P$ and $Q$. Let $X$ and $Y$ be two random $32$-bit starting sequence numbers chosen by $P$ and $Q$ respectively. Suppose $P$ sends a $\text{TCP}$ connection request message to $Q$ with a $\text{TCP}$ segment having …

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$?

Let $L \subseteq \{0,1\}^*$ be an arbitrary regular language accepted by a minimal $\text{DFA}$ with $k$ states. Which one of the following languages must necessarily be accepted by a minimal $\text{DFA}$ with $k$ states?

Consider the following $\text{ANSI C}$ program. #include <stdio.h> int main() { int arr[4][5]; int i, j; for (i=0; i<4; i++) ​​​​​​{ for (j=0; j<5; j++) { arr[i][j] = 10 * i + j; } } printf(“%d”, *(arr[1]+9)); return 0; } What is the output of the above program?

Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ to the set $\{0, 1, 2\}$ Which of the following choice(s) is/are correct?

Let $L_1$ be a regular language and $L_2$ be a context-free language. Which of the following languages is/are context-free?

In the context of compilers, which of the following is/are $\text{NOT}$ an intermediate representation of the source program?

Which of the following statement(s) is/are correct in the context of $\text{CPU}$ scheduling?

Choose the correct choice(s) regarding the following proportional logic assertion $S$: $$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$$

Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid$ is …

Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________

If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________

Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________

Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ processor. If $0.5 \%$ processor cycles are used for $\text{DMA}$, the data transfer rate of the device is …

A data file consisting of $1,50,000$ student-records is stored on a hard disk with block size of $4096$ bytes. The data file is sorted on the primary key $\textrm{RollNo}$. The size of a record pointer for this disk is $7$ bytes. Each student-record has a candidate key attribute called $\textrm{ANum}$ of size $12$ bytes. Suppose an index file …

For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________

Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________

Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________

Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________

​​​​​​Assume a two-level inclusive cache hierarchy, $L1$ and $L2$, where $L2$ is the larger of the two. Consider the following statements. $S_1$: Read misses in a write through $L1$ cache do not result in writebacks of dirty lines to the $L2$ $S_2$: Write allocate policy must be used in conjunction with write through caches and no-write …