GATE CS question library

Consider the following $B^{+}$tree with $5$ nodes, in which a node can store at most $3$ key values The value $23$ is now inserted in the $B^{+}$tree. Which of the following options(s) is/are CORRECT?

Consider the $3$-way handshaking protocol for TCP connection establishment. Let the three packets exchanged during the connection establishment be denoted as $\text{P1, P2}$, and $\text{P3}$, in order. Which of the following option(s) is/are TRUE with respect to TCP header flags that are set in the packets?

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a real-valued constant. Which of the following option(s) is/are CORRECT? $$\begin{array}{l} x+k y=1 \\ k x+y=-1 \end{array}$$

Let $X$ be a $3$-variable Boolean function that produces output as $'1'$ when at least two of the input variables are $'1'$. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

The number $-6$ can be represented as $1010$ in $4$-bit $2$'s complement representation. Which of the following is/are CORRECT $2$ 's complement representation(s) of $-6$?

Which of the following statement(s) is/are TRUE for any binary search tree (BST) having $n$ distinct integers?

A partial data path of a processor is given in the figure, where $\text{RA, RB,}$ and $\text{RZ}$ are $32$-bit registers. Which option(s) is/are CORRECT related to arithmetic operations using the data path as shown?

A regular language $L$ is accepted by a non-deterministic finite automaton (NFA) with $n$ states. Which of the following statement(s) is/are FALSE?

Let $\text{S}$ be the set of all ternary strings defined over the alphabet $\{a, b, c\}$. Consider all strings in $\text{S}$ that contain at least one occurrence of two consecutive symbols, that is, $\text{"aa"}$, $\text{"bb"}$ or $\text{"cc"}$. The number of such strings of length $5$ that are possible is __________. (Answer in integer).

Suppose in a multiprogramming environment, the following C program segment is executed. A process goes into I/O queue whenever an I/O related operation is performed. Assume that there will always be a context switch whenever a process requests for an I/O, and also whenever the process returns from an I/O. The number of times the process will enter the ready …

Consider the given function $f(x)$. $$f(x)=\left\{\begin{array}{ll} a x+b & \text{ for } x<1 \\ x^{3}+x^{2}+1 & \text{ for } x \geq 1 \end{array}\right.$$ If the function is differentiable everywhere, the value of $b$ must be ________. (rounded off to one decimal place)

A box contains $5$ coins: $4$ regular coins and $1$ fake coin. When a regular coin is tossed, the probability $P($ head $)=0.5$ and for a fake coin, $P($ head $)=1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is __________. (rounded off to two decimal places)

The pseudocode of a function $\text{fun ()}$ is given below: fun(int A[0,....,n-1]) { for i=0 to n-2 for j=0 to n-i-2 if (A[j]>A[j+1]) then swap A[j] and A[j+1] } Let $A[0, \ldots, 29]$ be an array storing $30$ distinct integers in descending order. The number of swap operations that will be performed, if the function $\text{fun ()}$ is called …

#include <stdio.h> void foo(int *p, int x) { *p=x; } int main(){ int *z; int a = 20, b = 25; z = &a; foo(z,b); printf("%d",a); return 0; } The output of the given $\text{C}$ program is __________. (Answer in integer)

The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node. Suppose a Min-Heap $\text{T}$ stores $32$ keys. The height of $\text{T}$ is ___________. (Answer in integer)

Consider a memory system with $1 \mathrm{M}$ bytes of main memory and $16 \mathrm{~K}$ bytes of cache memory. Assume that the processor generates $20$-bit memory address, and the cache block size is $16$ bytes. If the cache uses direct mapping, how many bits will be required to store all the $\operatorname{tag}$ values? [Assume memory is byte …

A processor has $64$ general-purpose registers and $50$ distinct instruction types. An instruction is encoded in $32$-bits. What is the maximum number of bits that can be used to store the immediate operand for the given instruction? $\text{ADD R1}$, $\#25$ / / $\text{R 1=R 1+25}$

A computer has two processors, $M_{1}$ and $M_{2}$. Four processes $P_{1}, P_{2}, P_{3}, P_{4}$ with CPU bursts of $20,16,25$, and $10$ milliseconds, respectively, arrive at the same time and these are the only processes in the system. The scheduler uses non-preemptive priority scheduling, with priorities decided as follows: $M_{1}$ uses priority …

Consider two relations describing teams and players in a sports league: teams(tid, tname): tid, tname are team-id and team-name, respectively players(pid,pname,tid): pid, pname, and tid denote player-id, playername and the team-id of the player, respectively Which ONE of the following tuple relational calculus queries returns the name of the players who play …

A packet with the destination $\text{IP}$ address $145.36 .109 .70$ arrives at a router whose routing table is shown. Which interface will the packet be forwarded to? …