GATE CS question library

Consider the following segment of C-code: int j, n; j = 1; while (j <= n) j = j * 2; The number of comparisons made in the execution of the loop for any $n > 0$ is:

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

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

Suppose the letters $a, \,b, \,c, \,d, \,e, \,f$ have probabilities $\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}, \dfrac{1}{16}, \dfrac{1}{32}, \dfrac{1}{32}$, respectively. What is the average length of the Huffman code for the letters $a, \,b, \,c, \,d, \,e, \,f$?

Consider the following Finite State Automaton: The minimum state automaton equivalent to the above FSA has the following number of states:

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: $S \rightarrow aB$ $S \rightarrow bA$ $B \rightarrow b$ $A \rightarrow a$ $B \rightarrow bS$ $A \rightarrow aS$ $B \rightarrow aBB$ $A \rightarrow bAA$ For …

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, …