GATE CS question library

The minimum number of comparisons required to find the minimum and the maximum of $100$ numbers is ________

Consider a hash table with $9$ slots. The hash function is $h(k)= k \mod 9$. The collisions are resolved by chaining. The following $9$ keys are inserted in the order: $5, 28, 19, 15, 20, 33, 12, 17, 10$. The maximum, minimum, and average chain lengths in the hash table, respectively, are

Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?

There are $5$ bags labeled $1$ to $5$. All the coins in a given bag have the same weight. Some bags have coins of weight $10$ gm, others have coins of weight $11$ gm. I pick $1, 2, 4, 8, 16$ coins respectively from bags $1$ to $5$ Their total weight comes out to $323$ gm. Then the product of the labels of the bags having $11$ gm coins is …

Which of the regular expressions given below represent the following DFA? $0^*1(1+00^*1)^*$ $0^*1^*1+11^*0^*1$ $(0+1)^*1$

Let $L$ be a language and $\bar{L}$ be its complement. Which one of the following is NOT a viable possibility?

A canonical set of items is given below $S \to L .> R$ $Q \to R.$ On input symbol $<$ the set has

Assume that there are $3$ page frames which are initially empty. If the page reference string is $\text{1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6}$ the number of page faults using the optimal replacement policy is__________.

Consider the following set of processes that need to be scheduled on a single CPU. All the times are given in milliseconds. …

An operating system uses the Banker's algorithm for deadlock avoidance when managing the allocation of three resource types $X, Y,$ and $Z$ to three processes $P0, P1,$ and $P2.$ The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max …

Given the following two statements: S1: Every table with two single-valued attributes is in $\text{1NF, 2NF, 3NF}$ and $\text{BCNF}.$ S2: $AB \to C, D \to E, E \to C$ is a minimal cover for the set of functional dependencies $AB \to C, D \to E, AB \to E, E \to C$. Which one of the following is CORRECT?

Consider the following four schedules due to three transactions (indicated by the subscript) using read and write on a data item x, denoted by $r(x)$ and $w(x)$ respectively. Which one of them is conflict serializable?

Consider a selective repeat sliding window protocol that uses a frame size of $1$ $\text{KB}$ to send data on a $1.5$ $\text{Mbps}$ link with a one-way latency of $50$ $\text{msec}$. To achieve a link utilization of $60\%$, the minimum number of bits required to represent the sequence number field is ________.

Let the size of congestion window of a TCP connection be $32$ KB when a timeout occurs. The round trip time of the connection is $100$ msec and the maximum segment size used is $2$ KB. The time taken (in msec) by the TCP connection to get back to $32$ KB congestion window is _________.

Consider a token ring network with a length of 2 km having 10 stations including a monitoring station. The propagation speed of the signal is $2 \times10^8m/s$ and the token transmission time is ignored. If each station is allowed to hold the token for $2 µsec$, the minimum time for which the monitoring station should wait (in $µsec$) before assuming …

Identify the correct order in which the following actions take place in an interaction between a web browser and a web server. The web browser requests a webpage using HTTP. The web browser establishes a TCP connection with the web server. The web server sends the requested webpage using HTTP. The web browser resolves the domain name using DNS.

Which of the following are used to generate a message digest by the network security protocols? RSA SHA-$1$ DES MD5

Given the following statements: S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL. S2: Given the table $R(a,b,c)$ where $a$ and $b$ together form the primary key, the following is a valid table definition. CREATE TABLE S ( a INTEGER, d INTEGER, e INTEGER, PRIMARY KEY (d), FOREIGN KEY (a) references R) Which …

Consider the following three statements about link state and distance vector routing protocols, for a large network with $500$ network nodes and $4000$ links. [S1]: The computational overhead in link state protocols is higher than in distance vector protocols. [S2]: A distance vector protocol (with split horizon) avoids persistent routing loops, but not …

Consider the relation scheme $R = (E, F, G, H, I, J, K, L, M, N)$ and the set of functional dependencies $$\left\{ \{E, F \} \to \{G\}, \{F\} \to \{I, J\}, \{E, H\} \to \{K, L\}, \\ \{K\} \to \{M\}, \{L\} \to \{N\}\right\}$$ on $R$. What is the key for $R$?