GATE CS question library

Which one of the following combinations is incorrect?

Based on the given statements, select the most appropriate option to solve the given question. If two floors in a certain building are $9$ feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? Statements: Each step is $3/4$ foot high. Each step is $1$ foot wide.

Given Set $A= {2, 3, 4, 5}$ and Set $B= { 11, 12, 13, 14, 15}$, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals $16$?

Which of the following options is the closest in meaning of the sentence below? She enjoyed herself immensely at the party.

Didn't you buy ____ when you went shopping?

Which one of the following well-formed formulae is a tautology?

Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is ______.

The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.

$\text{Host A}$ sends a $\text{UDP}$ datagram containing $8880\text{ bytes}$ of user data to $\text{host B}$ over an $\text{Ethernet LAN}.$ Ethernet frames may carry data up to $1500\text{ bytes (i.e. MTU = 1500 bytes)}.$ Size of $\text{UDP}$ header is $8\text{ bytes}$ and size of $\text{IP}$ header is $20\text{ bytes}.$ There is no …

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: …