GATE CS question library

​​​​If $A=\left(\begin{array}{cc}1 & 2 \\ 2 & -1\end{array}\right)$, then which ONE of the following is $A^{8}$ ?

​​​​​The value of $x$ such that $x>1$, satisfying the equation $\int_1^x t \ln t \: dt = \frac{1}{4}$ is

​​​​Consider a binary tree $T$ in which every node has either zero or two children. Let $n>0$ be the number of nodes in $T$. Which ONE of the following is the number of nodes in $T$ that have exactly two children?

Let $L$, $M$, and $N$ be non-singular matrices of order $3$ satisfying the equations $L^2 = L^{-1}$, $M=L^8$ and $N=L^2$. Which ONE of the following is the value of the deteminant of $(M-N)$?

​​​Let $P(x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

​​​​​Consider the following statements: Address Resolution Protocol (ARP) provides a mapping from an IP address to the corresponding hardware (link-layer) address. A single TCP segment from a sender $S$ to a receiver $R$ cannot carry both data from $S$ to $R$ and acknowledgement for a segment from $R$ to $S$ Which one of the following is CORRECT?

Consider the routing protocols given in List I and the names given in List II: …

​​​A machine receives an $IPv4$ datagram. The protocol field of the $IPv4$ header has the protocol number of a protocol $X$. Which ONE of the following is NOT a possible candidate for $X$?

​​​​​Consider the following C program: #include <stdio.h> void stringcopy (char *, char *); int main() { char a[30] = "@#Hello World!"; stringcopy(a, a+2); printf("%s\n",a); return 0; } void stringcopy(char *s, char *t) { while (*t) *s++=*t++; } Which one of the following will be the output of the program?

​​​​Consider an unorders list of $N$ distinct integers. What is the minimum number of element comaparisons required to find an integer in the list that is NOT the largest in the list?

​​​​Consider the following statements about the use of backpatching in a compiler for intermediate code generation: Backpatching can be used to generate code for Boolean expression in one pass. Back[atching can be used to generate code for flow-of-control statements in one pass. Which ONE of the folloeing options is CORRECT?

​​Given the following syntax directed translation rules: Rule 1: $R \rightarrow A B\{B . i=R . i-1 ; A . i=B . i ; R . i=A . i+1 ;\}$ Rule 2: $P \rightarrow C D\{P . i=C . i+D . i ; D . i=C . i+2 ;\}$ Rule 3: $Q \rightarrow E F\{Q . i=E . i+F . i ;\}$ Which ONE is the CORRECT option among the following?

​​​​​Consider a network that uses Ethernet and $IPv4$. Assume that $IPv4$ headers do not use any options field. Each Ethernet frame can carry a maximum of $1500$ bytes in its data field. A UDP segment is transmitted. The payload (data) in the UDPO segment is $7488$ bytes. Which ONE of the following choices has the CORRECT total number of fragments …

​​​​Which ONE of the following languages is accepted by a deteministic pushdown automaton?

​​​​Let $G_{1}, G_{2}$ be Context Free Grammars (CFGs) and $R$ be a regular expression. For a grammar $G$, let $L(G)$ denote the language generated by $G$. Which ONE among the following questions is decidable?

​​​Processes $P 1, P 2, P 3, P 4$ arrive in that order at times $0,1,2$, and 8 milliseconds respectively, and have execution times of $10,13,6$, and 9 milliseconds respectively. Shortest Remaining Time First (SRTF) algorithm is used as the CPU scheduling policy. Ignore context switching times. Which ONE of the following correctly gives the average …

​​​​An audit of a banking transactions system has found that on an earlier occasion, two joint holders of account $A$ attempted simultaneous transfers of Rs. $10000$ each from account $A$ to account $B$. Both transactions read the same value, Rs.$11000$, as the initial balance in $A$ and were allowed to go through. $B$ was credited Rs.$10000$ …

​​​​Which of the following is/are part of an Instruction Set Architecture of a processor?

​​​​Which of the following statements regarding Breadth First Search (BFS) and Depth First Search (DFS) on an undirected simple graph $G$ is/are TRUE?

Consider the two lists List I and List II given below: …