GATE CS question library

In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true?

Which of the following is/are regular languages? $L_1: \left\{ wxw^R \mid w, x \in \{a, b\} ^* \text{ and } |w|, |x| > 0\right\}, w^R \text{ is the reverse of string } w$ $L_2: \left\{ a^nb^m \mid m \neq n \text{ and } m, n \geq 0 \right\}$ $L_3: \left\{ a^pb^qc^r \mid p, q, r \geq 0 \right\}$

Consider a typical disk that rotates at $15000$ rotations per minute (RPM) and has a transfer rate of $50 \times 10^6$ bytes/sec. If the average seek time of the disk is twice the average rotational delay and the controller's transfer time is $10$ times the disk transfer time, the average time (in milliseconds) to read or write a $512$-byte sector of …

A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate. The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is $1.2$ microseconds. A $4$-bit-ripple-carry binary adder is implemented by using four full adders. The total propagation time …

A computer system implements $8\;\text{kilobyte}$ pages and a $32\text{-bit}$ physical address space. Each page table entry contains a valid bit, a dirty bit, three permission bits, and the translation. If the maximum size of the page table of a process is $24\;\text{megabytes}$, the length of the virtual address supported by the system is _______ …

Consider a simple checkpointing protocol and the following set of operations in the log. (start, T4); (write, T4, y, 2, 3); (start, T1); (commit, T4); (write, T1, z, 5, 7); (checkpoint); (start, T2); (write, T2, x, 1, 9); (commit, T2); (start, T3); (write, T3, z, 7, 2); If a crash happens now and the system tries to recover using both undo and redo …

Suppose you are provided with the following function declaration in the C programming language. int partition(int a[], int n); The function treats the first element of $a[\:]$ as a pivot and rearranges the array so that all elements less than or equal to the pivot is in the left part of the array, and all elements greater than the pivot is in the right …

Consider the sequence of machine instruction given below: $$\begin{array}{ll} \text{MUL} & \text{R5, R0, R1} \\ \text{DIV} & \text{R6, R2, R3} \\ \text{ADD} & \text{R7, R5, R6} \\ \text{SUB} & \text{R8, R7, R4} \\ \end{array}$$ In the above sequence, $R0$ to $R8$ are general purpose registers. In the instructions shown, the first register …

Which one of the following assertions concerning code inspection and code walkthrough is true?

Consider a processor with byte-addressable memory. Assume that all registers, including program counter (PC) and Program Status Word (PSW), are size of two bytes. A stack in the main memory is implemented from memory location $(0100)_{16}$ and it grows upward. The stack pointer (SP) points to the top element of the stack. The current value of SP is …

Consider the following routing table at an IP router: …

The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.

The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is the solution. The procedure is given below. Observe that there is an …

Consider the C program below #include <stdio.h> int *A, stkTop; int stkFunc (int opcode, int val) { static int size=0, stkTop=0; switch (opcode) { case -1: size = val; break; case 0: if (stkTop < size ) A[stkTop++]=val; break; default: if (stkTop) return A[--stkTop]; } return -1; } int main() { int B[20]; A=B; stkTop = -1; stkFunc (-1, 10); stkFunc …

Given below are some algorithms, and some algorithm design paradigms. …

The number of min-terms after minimizing the following Boolean expression is _______. $[D'+AB'+A'C+AC'D+A'C'D]'$

Consider the alphabet $\Sigma = \{0, 1\}$, the null/empty string $\lambda$ and the set of strings $X_0, X_1, \text{ and } X_2$ generated by the corresponding non-terminals of a regular grammar. $X_0, X_1, \text{ and } X_2$ are related as follows. $X_0 = 1 X_1$ $X_1 = 0 X_1 + 1 X_2$ $X_2 = 0 X_1 + \{ \lambda \}$ Which one of the following …

Assume that the bandwidth for a $\text{TCP}$ connection is $1048560$ bits/sec. Let $\alpha$ be the value of RTT in milliseconds (rounded off to the nearest integer) after which the $\text{TCP}$ window scale option is needed. Let $\beta$ be the maximum possible window size with window scale option. Then the values of $\alpha$ and $\beta$ are

Which one of the following hash functions on integers will distribute keys most uniformly over $10$ buckets numbered $0$ to $9$ for $i$ ranging from $0$ to $2020$?

Consider two relations $R_1(A,B)$ with the tuples $(1,5), (3,7)$ and $R_2(A,C) = (1,7),(4,9)$. Assume that $R(A,B,C)$ is the full natural outer join of $R_1$ and $R_2$. Consider the following tuples of the form $(A,B,C):$ $a = (1,5,null), b=(1,null,7), c=(3,null,9), d=(4,7,null), e=(1,5,7),$ $f=(3,7,null), g=(4,null,9).$ Which one of the …