GATE CS question library

A process, has been allocated $3$ page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): $1, 2, 1, 3, 7, 4, 5, 6, 3, 1$ Least Recently Used (LRU) page replacement policy is a practical approximation to optimal page replacement. For …

Consider a machine with a byte addressable main memory of $2^{16}$ bytes. Assume that a direct mapped data cache consisting of $32$ lines of $64$ bytes each is used in the system. A $50$ x $50$ two-dimensional array of bytes is stored in the main memory starting from memory location $1100H$. Assume that the data cache is initially empty. The …

Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the line segment from $(4,4)$ to $(5,4)$. With this constraint, how many distinct paths …

Consider the DAG with $V = \{1,2,3,4,5,6\}$ shown below. Which of the following is not a topological ordering?

Information about a collection of students is given by the relation $\text{studInfo(}\underline{\text{studId}},\text{ name, sex)}$. The relation $\text{enroll(}{\text{studId}},{\text{ courseId}})$ gives which student has enrolled for (or taken) what course(s). Assume that every course is taken by at least one male and at least one female student. What …

Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the robot to reach the point $(10,10)$ starting from the initial position $(0,0)$?

A process has been allocated $3$ page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): $\mathbf{1, 2, 1, 3, 7, 4, 5, 6, 3, 1}$ If optimal page replacement policy is used, how many page faults occur for the above reference string?

Consider the CFG with $\left\{S, A, B\right\}$ as the non-terminal alphabet, $\{a, b\}$ as the terminal alphabet, $S$ as the start symbol and the following set of production rules: $S \rightarrow aB$ $S \rightarrow bA$ $B \rightarrow b$ $A \rightarrow a$ $B \rightarrow bS$ $A \rightarrow aS$ $B \rightarrow aBB$ $A \rightarrow bAA$ Which …

Suppose the letters $a, \,b, \,c, \,d, \,e, \,f$ have probabilities $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \frac{1}{32}$, respectively. Which of the following is the Huffman code for the letter $a, \,b, \,c, \,d, \,e, \,f$?

Consider a machine with a byte addressable main memory of $2^{16}$ bytes. Assume that a direct mapped data cache consisting of $32$ lines of $64$ bytes each is used in the system. A $50 \times 50$ two-dimensional array of bytes is stored in the main memory starting from memory location $1100H$. Assume that the data cache is initially empty. The …

Consider the following Finite State Automaton: The language accepted by this automaton is given by the regular expression

Consider the following program segment. Here $\text{R1, R2}$ and $\text{R3}$ are the general purpose registers. …

Match the following: …

The distance between two stations $M$ and $N$ is $L$ kilometers. All frames are $K$ bits long. The propagation delay per kilometer is $t$ seconds. Let $R$ bits/second be the channel capacity. Assuming that the processing delay is negligible, the $\text{minimum}$ number of bits for the sequence number field in a frame for maximum utilization, …

The message $11001001$ is to be transmitted using the CRC polynomial $x^3 +1$ to protect it from errors. The message that should be transmitted is:

The address of a class $\text{B}$ host is to be split into subnets with a $6\;\text{-bit}$ subnet number. What is the maximum number of subnets and the maximum number of hosts in each subnet?

In a token ring network the transmission speed is $10^7$ bps and the propagation speed is $200\;\text{meters}/\mu \text{s}.$ The $1$-bit delay in this network is equivalent to:

There are $n$ stations in slotted LAN. Each station attempts to transmit with a probability $p$ in each time slot. What is the probability that ONLY one station transmits in a given time slot?

Consider the following schedules involving two transactions. Which one of the following statements is TRUE? $S_1 :r_1(X); r_1(Y); r_2(X); r_2(Y); w_2(Y); w_1(X)$ $S_2 :r_1(X); r_2(X); r_2(Y); w_2(Y); r_1(Y); w_1(X)$

The order of a leaf node in a $B^+$ - tree is the maximum number of (value, data record pointer) pairs it can hold. Given that the block size is $1K\;\text{bytes}$, data record pointer is $7\;\text{bytes}$ long, the value field is $9\;\text{bytes}$ long and a block pointer is $6 \;\text{bytes}$ long, what is the order of the leaf node?