GATE CS question library

A certain computation generates two arrays a and b such that $a[i] = f(i)$ for $0 \leq i < n$ and $b[i] = g(a[i])$ for $0 \leq i < n$. Suppose this computation is decomposed into two concurrent processes $X$ and $Y$ such that $X$ computes the array $a$ and $Y$ computes the array $b$. The processes employ two binary semaphores $R$ …

In an IPv4 datagram, the $M$ bit is $0$, the value of $HLEN$ is $10$, the value of total length is $400$ and the fragment offset value is $300$. The position of the datagram, the sequence numbers of the first and the last bytes of the payload, respectively are:

The following figure represents access graphs of two modules M1 and M2. The filled circles represent methods and the unfilled circles represent attributes. If method $m$ is moved to module M2 keeping the attributes where they are, what can we say about the average cohesion and coupling between modules in the system of two modules?

Determine the maximum length of the cable (in km) for transmitting data at a rate of $500$ Mbps in an Ethernet LAN with frames of size $10,000$ bits. Assume the signal speed in the cable to be $2,00,000$ km/s.

Consider the following relational schema. Students(rollno: integer, sname: string) Courses(courseno: integer, cname: string) Registration(rollno: integer, courseno: integer, percent: real) Which of the following queries are equivalent to this query in English? “Find the distinct names of all students who score more than $90\%$ in the course numbered 107” …

Consider the DFA $A$ given below. Which of the following are FALSE? Complement of $L(A)$ is context-free. $L(A) = L((11^*0+0)(0 + 1)^*0^*1^*)$ For the language accepted by $A, A$ is the minimal DFA. $A$ accepts all strings over $\{0, 1\}$ of length at least $2$.

A shared variable $x$, initialized to zero, is operated on by four concurrent processes $W, X, Y, Z$ as follows. Each of the processes $W$ and $X$ reads $x$ from memory, increments by one, stores it to memory, and then terminates. Each of the processes $Y$ and $Z$ reads $x$ from memory, decrements by two, stores it to memory, and then …

Consider the following languages. $L_1 = \left \{ 0^p1^q0^r \mid p,q,r \geq 0 \right \}$ $L_2 = \left \{ 0^p1^q0^r \mid p,q,r \geq 0, p\neq r \right \}$ Which one of the following statements is FALSE?

Consider a hard disk with $16$ recording surfaces $(0-15)$ having $16384$ cylinders $(0-16383)$ and each cylinder contains $64$ sectors $(0-63)$. Data storage capacity in each sector is $512$ bytes. Data are organized cylinder-wise and the addressing format is $\langle \text{cylinder no.}, \text{surface no.}, \text{sector no.} \rangle$ . A …

Consider the following function: int unknown(int n){ int i, j, k=0; for (i=n/2; i<=n; i++) for (j=2; j<=n; j=j*2) k = k + n/2; return (k); } The return value of the function is

The number of elements that can be sorted in $\Theta(\log n)$ time using heap sort is

Consider the following sequence of micro-operations. MBR ← PC MAR ← X PC ← Y Memory ← MBR Which one of the following is a possible operation performed by this sequence?

What is the logical translation of the following statement? "None of my friends are perfect."

The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if $e$ and $e'$ are incident with the same vertex in $G$. Which of the following statements …

Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even.

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\dfrac{1}{2}.$ What is the expected number of unordered cycles of length three?

Function $f$ is known at the following points: $x$ 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is

Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$?

In a $k$-way set associative cache, the cache is divided into $v$ sets, each of which consists of $k$ lines. The lines of a set are placed in sequence one after another. The lines in set $s$ are sequenced before the lines in set $(s+1)$. The main memory blocks are numbered 0 onwards. The main memory block numbered $j$ must be mapped to any one of …

What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?