GATE CS question library

Consider the following statements about the cyclomatic complexity of the control flow graph of a program module. Which of these are TRUE? The cyclomatic complexity of a module is equal to the maximum number of linearly independent circuits in the graph. The cyclomatic complexity of a module is the number of decisions in the module plus one, where a decision …

A hard disk has $63$ sectors per track, $10$ platters each with $2$ recording surfaces and $1000$ cylinders. The address of a sector is given as a triple $\langle c, h, s \rangle$, where $c$ is the cylinder number, $h$ is the surface number and $s$ is the sector number. Thus, the 0$^{th}$ sector is addresses as $\langle 0, 0, 0 \rangle$, …

Let $G(x)$ be the generator polynomial used for CRC checking. What is the condition that should be satisfied by $G(x)$ to detect odd number of bits in error?

In the RSA public key cryptosystem, the private and public keys are $(e, n)$ and $(d, n)$ respectively, where $n=p \times q$ and $p$ and $q$ are large primes. Besides, $n$ is public and $p$ and $q$ are private. Let $M$ be an integer such that $0<M<n$ and $\phi(n) = (p-1)(q-1)$. Now consider the following equations. …

While opening a $TCP$ connection, the initial sequence number is to be derived using a time-of-day (ToD) clock that keeps running even when the host is down. The low order $32$ bits of the counter of the ToD clock is to be used for the initial sequence numbers. The clock counter increments once per milliseconds. The maximum packet lifetime is given to be …

Consider two transactions $T_1$ and $T_2$, and four schedules $S_1, S_2, S_3, S_4$, of $T_1$ and $T_2$ as given below: $T_1: R_1[x]W_1[x]W_1[y]$ $T_2: R_2[x]R_2[y]W_2[y]$ $S_1: R_1[x]R_2[x]R_2[y] W_1[x] W_1[y] W_2[y]$ $S_2: R_1[x]R_2[x]R_2[y] W_1[x] W_2[y] W_1[y]$ $S_3: R_1[x]W_1[x]R_2[x] W_1[y] R_2[y] W_2[y]$ …

The following key values are inserted into a $B^+$ - tree in which order of the internal nodes is $3$, and that of the leaf nodes is $2$, in the sequence given below. The order of internal nodes is the maximum number of tree pointers in each node, and the order of leaf nodes is the maximum number of data items that can be stored in it. The $B^+$ - …

Let $R$ and $S$ be relational schemes such that $R=\{a,b,c\}$ and $S=\{c\}.$ Now consider the following queries on the database: $\pi_{R-S}(r) - \pi_{R-S} \left (\pi_{R-S} (r) \times s - \pi_{R-S,S}(r)\right )$ …

Which of the following statements are TRUE? There exist parsing algorithms for some programming languages whose complexities are less than $\Theta(n^3)$ A programming language which allows recursion can be implemented with static storage allocation. No L-attributed definition can be evaluated in the framework of bottom-up parsing. Code improving …

The above DFA accepts the set of all strings over $\{0,1\}$ that

Let $L = L_1 \cap L_2$, where $L_1$ and $L_2$ are languages as defined below: $L_1= \left \{ a^m b^mca^nb^n \mid m,n \geq 0 \right \}$ $L_2=\left \{ a^i b^j c^k \mid i,j,k \geq 0 \right \}$ Then $L$ is

In quick-sort, for sorting $n$ elements, the $\left(n/4\right)^{th}$ smallest element is selected as pivot using an $O(n)$ time algorithm. What is the worst case time complexity of the quick sort?

What is the maximum height of any AVL-tree with $7$ nodes? Assume that the height of a tree with a single node is $0$.

Consider the following graph: Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal’s algorithm?

The keys $12, 18, 13, 2, 3, 23, 5$ and $15$ are inserted into an initially empty hash table of length $10$ using open addressing with hash function $h(k) = k \mod 10$ and linear probing. What is the resultant hash table?

The running time of an algorithm is represented by the following recurrence relation: $T(n) = \begin{cases} n & n \leq 3 \\ T(\frac{n}{3})+cn & \text{ otherwise } \end{cases}$ Which one of the following represents the time complexity of the algorithm?

A multilevel page table is preferred in comparison to a single level page table for translating virtual address to physical address because

The enter_CS() and leave_CS() functions to implement critical section of a process are realized using test-and-set instruction as follows: void enter_CS(X) { while(test-and-set(X)); } void leave_CS(X) { X = 0; } In the above solution, $X$ is a memory location associated with the $CS$ and is initialized to $0$. Now consider the following statements: The …

In the following process state transition diagram for a uniprocessor system, assume that there are always some processes in the ready state: Now consider the following statements: If a process makes a transition $D$, it would result in another process making transition $A$ immediately. A process $P_2$ in blocked state can make transition E while …

Consider a disk system with $100$ cylinders. The requests to access the cylinders occur in following sequence: $4, 34, 10, 7, 19, 73, 2, 15, 6, 20$ Assuming that the head is currently at cylinder $50$, what is the time taken to satisfy all requests if it takes $1\;\text{ms}$ to move from one cylinder to adjacent one and shortest seek time first …