GATE CS question library

In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking the …

Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set of all elements in $T$ which are not in $R$. Which one of the following is true?

Consider the following statements. TCP connections are full duplex TCP has no option for selective acknowledgement TCP connections are message streams

Consider a software project with the following information domain characteristics for calculation of function point metric. Number of external inputs (I) = 30 Number of external outputs (O) = 60 Number of external inquiries (E) = 23 Number of files (F) = 08 Number of external interfaces (N) = 02 It is given that the complexity weighting factors for I, O, E, …

Consider the relation $X(P,Q,R,S,T,U)$ with the following set of functional dependencies $F = \{ \\ \; \; \{P, R\} \rightarrow \{S, T\}, \\ \; \; \{P, S, U\} \rightarrow \{Q, R\} \\ \; \}$ Which of the following is the trivial functional dependency in $F^+$, where $F^+$ is closure to F?

Consider the following array of elements. $\langle 89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100 \rangle$ The minimum number of interchanges needed to convert it into a max-heap is

Let $L$ be the language represented by the regular expression $\Sigma^*0011\Sigma^*$ where $\Sigma = \{0, 1\}$. What is the minimum number of states in a DFA that recognizes $\bar{L}$ (complement of $L$)?

Given that hash table $T$ with $25$ slots that stores $2000$ elements, the load factor $a$ for $T$ is _________.

Among simple LR (SLR), canonical LR, and look-ahead LR (LALR), which of the following pairs identify the method that is very easy to implement and the method that is the most powerful, in that order?

In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ are

Consider a machine with a byte addressable main memory of $2^{20}$ bytes, block size of $16$ bytes and a direct mapped cache having $2^{12}$ cache lines. Let the addresses of two consecutive bytes in main memory be $\textsf{(E201F)}_{16}$ and $\textsf{(E2020)}_{16}$. What are the tag and cache line addresses ( in hex) for main memory address …

While inserting the elements $71, 65, 84, 69, 67, 83$ in an empty binary search tree (BST) in the sequence shown, the element in the lowest level is

The result evaluating the postfix expression $10 \ 5 + 60 \ 6 / * 8 -$ is

Consider a software program that is artificially seeded with 100 faults. While testing this program, 159 faults are detected, out of which 75 faults are from those artificially seeded faults. Assuming that both real and seeded faults are of same nature and have same distribution, the estimated number of undetected real faults is _______.

Two processes $X$ and $Y$ need to access a critical section. Consider the following synchronization construct used by both the processes …

The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is

In a web server, ten WebPages are stored with the URLs of the form http://www.yourname.com/var.html; where var is a different number from 1 to 10 for each Webpage. Suppose the client stores the Webpage with var = 1 (say W1) in the local machine, edits and then tests. Rest of the Webpages remains on the web server. W1 contains several relative URLs of the …

Consider the following C program segment. # include <stdio.h> int main() { char s1[7] = "1234", *p; p = s1 + 2; *p = '0'; printf("%s", s1); } What will be printed by the program?

Consider a CSMA/CD network that transmits data at a rate of $100\;\textsf{Mbps}\; (10^8\;\text{bits}$ per second) over a $1\;\textsf{km}$ (kilometre) cable with no repeaters. If the minimum frame size required for this network is $1250\;\text{bytes},$ What is the signal speed $\textsf{(km/sec)}$ in the cable?

The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.