List of top Questions asked in GATE CS

Consider a network that uses Ethernet and IPv4. Assume that IPv4 headers do not use any options field. Each Ethernet frame can carry a maximum of 1500 bytes in its data field. A UDP segment is transmitted. The payload (data) in the UDP segment is 7488 bytes. Which ONE of the following choices has the CORRECT total number of fragments transmitted and the size of the last fragment including IPv4 header?

Let \( L, M, \) and \( N \) be non-singular matrices of order 3 satisfying the equations: \[ L^2 = L^{-1}, \quad M = L^8, \quad N = L^2. \] Which ONE of the following is the value of the determinant of \( (M - N) \)?

Consider a binary tree \( T \) in which every node has either zero or two children. Let \( n%gt;0 \) be the number of nodes in \( T \). Which ONE of the following is the number of nodes in \( T \) that have exactly two children?

The value of \( x \) such that \( x%gt;1 \) , satisfying the equation \[ \int_{1}^{x} t \ln t \, dt = 1 \] is

Consider the following C code:

int main() {
    sum = 0;
    for (n = 1; n < 3; n++) {
        n++;
        sum += g(f(n));
    }
    printf("%d", sum);
}

int g(n) {
    return 10 + n;
}

int f(n) {
    return g(2 * n);
}

What is the output?

The value printed by the given C program is __________ (Answer in integer).

Refer to the given 3-address code sequence. This code sequence is split into basic blocks. The number of basic blocks is __________. (Answer in integer)
1001: i = 1
1002: j = 1
1003: t1 = 10i
1004: t2 = t1+j
1005: t3 = 8t2
1006: t4 = t3-88
1007: a[t4] = 0.0
1008: j = j+1
1009: if j <= 10 goto 1003
1010: i = i+1
1011: if i <= 10 goto 1002
1012: i = 1
1013: t5 = i-1
1014: t6 = 88t5
1015: a[t6] = 1.0
1016: i = i+1
1017: if i <= 10 goto 1013

Suppose in a multiprogramming environment, the following C program segment is executed. A process goes into the I/O queue whenever an I/O related operation is performed. Assume that there will always be a context switch whenever a process requests an I/O, and also whenever the process returns from an I/O. The number of times the process will enter the ready queue during its lifetime (not counting the time the process enters the ready queue when it is run initially) is _________ (Answer in integer).

In a double hashing scheme, \( h_1(k) = k \mod 11 \) and \( h_2(k) = 1 + (k \mod 7) \) are the auxiliary hash functions. The size \( m \) of the hash table is 11. The hash function for the \( i \)-th probe in the open address table is \( [h_1(k) + i \cdot h_2(k)] \mod m \). The following keys are inserted in the given order: 63, 50, 25, 79, 67, 24. The slot at which key 24 gets stored is:

The maximum value of \(x\) such that the edge between the nodes B and C is included in every minimum spanning tree of the given graph is ___________ (answer in integer).

Consider the following C program

The value printed by the given C program is _________ (Answer in integer).

Let LIST be a datatype for an implementation of a linked list defined as follows:

Suppose a program has created two linked lists, L1 and L2, whose contents are given in the figure below (code for creating L1 and L2 is not provided here). L1 contains 9 nodes, and L2 contains 7 nodes. Consider the following C program segment that modifies the list L1. The number of nodes that will be there in L1 after the execution of the code segment is:

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is:

Consider a finite state machine (FSM) with one input \(X\) and one output \(f\), represented by the given state transition table. The minimum number of states required to realize this FSM is __________ (Answer in integer).

Consider a probability distribution given by the density function \( P(x) \).

\[ P(x) = \begin{cases} Cx^2, & \text{for } 1 \leq x \leq 4, \\ 0, & \text{for } x<1 \text{ or } x>4. \end{cases} \]
The probability that \( x \) lies between 2 and 3, i.e., \( P(2 \leq x \leq 3) \), is ______. (rounded off to three decimal places)

Suppose a message of size 15000 bytes is transmitted from a source to a destination using IPv4 protocol via two routers as shown in the figure. Each router has a defined maximum transmission unit (MTU) as shown in the figure, including IP header. The number of fragments that will be delivered to the destination is ___________. (Answer in integer)

Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is ___________. (rounded off to three decimal places)

Consider the following database tables of a sports league. player (\( pid \), \( pname \), \( age \)) coach (\( cid \), \( cname \)) team (\( tid \), \( tname \), \( city \), \( cid \)) members (\( pid \), \( tid \)) An instance of the table and an SQL query are given.
Player table

coach table:

team table:

members table:

SQL query: \[ {SELECT MIN(P.age)} \] \[ {FROM player P} \] \[ {WHERE P.pid IN (} \] \[ { SELECT M.pid} \] \[ { FROM team T, coach C, members M} \] \[ { WHERE C.cname = 'Mark'} \] \[ { AND T.cid = C.cid} \] \[ { AND M.tid = T.tid)} \] The value returned by the given SQL query is _________. (Answer in integer)

A computer has a memory hierarchy consisting of two-level cache (L1 and L2) and a main memory. If the processor needs to access data from memory, it first looks into L1 cache. If the data is not found in L1 cache, it goes to L2 cache. If it fails to get the data from L2 cache, it goes to main memory, where the data is definitely available. Hit rates and access times of various memory units are shown in the figure. The average memory access time in nanoseconds (ns) is __________. (rounded off to two decimal places)

Consider the following deterministic finite automaton (DFA) defined over the alphabet, \( \Sigma = \{a, b\} \). Identify which of the following language(s) is/are accepted by the given DFA.

Let \( A = \{0, 1, 2, 3, \dots\} \) be the set of non-negative integers. Let \( F \) be the set of functions from \( A \) to itself. For any two functions, \( f_1, f_2 \in F \), we define \[ (f_1 \circ f_2)(n) = f_1(n) + f_2(n) \] for every number \( n \in A \). Which of the following is/are CORRECT about the mathematical structure \( (F, \circ) \)?

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used are: \( {mother}(y, x) \): \( y \) is the mother of \( x \) \( {noteq}(x, y) \): \( x \) and \( y \) are not equal

Consider a relational schema team(name, city, owner), with functional dependencies \( \{ {name} \rightarrow {city}, {name} \rightarrow {owner} \} \). The relation team is decomposed into two relations, \( t_1({name}, {city}) \) and \( t_2({name}, {owner}) \). Which of the following statement(s) is/are TRUE?

Which of the following statement(s) is/are TRUE while computing First and Follow during top-down parsing by a compiler?