GATE CS question library

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 …

Consider a system with $4$ types of resources $R1$ ($3$ units), $R2$ ($2$ units), $R3$ ($3$ units), $R4$ ($2$ units). A non-preemptive resource allocation policy is used. At any given instance, a request is not entertained if it cannot be completely satisfied. Three processes $P1$, $P2$, $P3$ request the resources as follows if …

Consider a $4$-way set associative cache (initially empty) with total $16$ cache blocks. The main memory consists of $256$ blocks and the request for memory blocks are in the following order: $0, 255, 1, 4, 3, 8, 133, 159, 216, 129, 63, 8, 48, 32, 73, 92, 155.$ Which one of the following memory block will NOT be in cache if LRU replacement policy is …

Consider a $4$ stage pipeline processor. The number of cycles needed by the four instructions $I1, I2, I3, I4$ in stages $S1, S2, S3, S4$ is shown below: …

Given the following state table of an FSM with two states $A$ and $B$,one input and one output. …

Consider a HTML table definition given below: <table border =1> <tr> <td rowspan=2> ab </td> <td colspan=2> cd </td> </tr> <tr> <td> ef </td> <td rowspan=2> gh </td> </tr> <tr> <td colspan=2> ik </td> </tr> </table> The number of rows in each column …

The coupling between different modules of a software is categorized as follows: Content coupling Common coupling Control coupling Stamp coupling Data coupling Coupling between modules can be ranked in the order of strongest (least desirable) to weakest (most desirable) as follows:

Consider the program below: #include <stdio.h> int fun(int n, int *f_p) { int t, f; if (n <= 1) { *f_p = 1; return 1; } t = fun(n-1, f_p); f = t + *f_p; *f_p = t; return f; } int main() { int x = 15; printf("%d/n", fun(5, &x)); return 0; } The value printed is:

Match all items in Group 1 with the correct options from those given in Group 2. …

Which one of the following is FALSE?

Which one of the following languages over the alphabet $\{0,1\}$ is described by the regular expression: $(0+1)^*0(0+1)^*0(0+1)^*$?