All 65 questions of GATE 2021 CS (Set 1)

The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

_____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.

Consider the following sentences:

(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

A polygon is convex if, for every pair of points, $P$ and $Q$ belonging to the polygon, the line segment $PQ$ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is __________

Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

The discount on item Q, as a percentage of its marked price, is ______

Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

A binary search tree $T$ contains $n$ distinct elements. What is the time complexity of picking an element in $T$ that is smaller than the maximum element in $T$?

Consider the following array.

Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order?

Consider the following two statements.

$S_1:$ Destination MAC address of an ARP reply is a broadcast address.
$S_2:$ Destination MAC address of an ARP request is a broadcast address.

Which one of the following choices is correct?

Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.

Which one of the following choices is correct?

Consider the following three functions:

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

Suppose that $L_1$ is a regular language and $L_2$ is a context-free language. Which one of the following languages is NOT necessarily context-free?

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

Consider the following statements.

$S_1:$ The sequence of procedure calls corresponds to a preorder traversal of the activation tree.
$S_2:$ The sequence of procedure returns corresponds to a postorder traversal of the activation tree.

Which one of the following options is correct?

Let $P$ be an array containing $n$ integers. Let $t$ be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of $n$ elements. Which one of the following choices is correct?

Consider the following statements.

$S_1:$ Every SLR(1) grammar is unambiguous but there are certain unambiguous grammars that are not SLR(1).
$S_2:$ For any context-free grammar, there is a parser that takes at most $O(n^3)$ time to parse a string of length $n$.

Which one of the following options is correct?

Which of the following standard C library functions will always invoke a system call when executed from a single-threaded process in a UNIX/Linux operating system?

Let $\langle M \rangle$ denote an encoding of an automaton $M$. Suppose that $\Sigma = \{0,1\}$. Which of the following languages is/are NOT recursive?

Consider a linear list based directory implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory foo.

Which of the following operations will necessarily require a full scan of foo for successful completion?

In the context of operating systems, which of the following statements is/are correct with respect to paging?

Suppose a database system crashes again while recovering from a previous crash. Assume checkpointing is not done by the database either during the transactions or during recovery.

Which of the following statements is/are correct?

Consider the following undirected graph with edge weights as shown:

The number of minimum-weight spanning trees of the graph is __________.

Three processes arrive at time zero with CPU bursts of 16, 20 and 10 milliseconds. If the scheduler has prior knowledge about the length of the CPU bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (rounded to nearest integer) is __________ milliseconds.

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is __________.

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

• The fastest computer gets the toughest job and the slowest computer gets the easiest job.
• Every computer gets at least one job.

The number of ways in which this can be done is __________.

Consider the following sequence of operations on an empty stack.

push(54); push(52); pop(); push(55); push(62); s = pop();

Consider the following sequence of operations on an empty queue.

enqueue(21); enqueue(24); dequeue(); enqueue(28); enqueue(32); q = dequeue();

The value of $s + q$ is __________.

In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is __________.

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

Here $S$, $E$ and $F$ denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is __________.

Consider a computer system with a byte-addressable primary memory of size $2^{32}$ bytes. Assume the computer system has a direct-mapped cache of size 32 KB $(1\text{ KB} = 2^{10}\text{ bytes})$, and each cache block is of size 64 bytes.

The size of the tag field is __________ bits.

Consider the following expression:

The value of the above expression (rounded to 2 decimal places) is __________.

A relation $r(A,B)$ in a relational database has 1200 tuples. The attribute $A$ has integer values ranging from 6 to 20, and the attribute $B$ has integer values ranging from 1 to 20. Assume that the attributes $A$ and $B$ are independently distributed.

The estimated number of tuples in the output of

is __________.

Consider the following context-free grammar where the set of terminals is $\{a,b,c,d,f\}$.

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table? “blank” denotes that the corresponding cell is empty.

The following relation records the age of 500 employees of a company, where empNo, indicating the employee number, is the key:

Consider the following relational algebra expression:

What does the above expression generate?

Consider the following recurrence relation:

Which one of the following options is correct?

Consider the following grammar that admits a series of declarations, followed by expressions, and the associated syntax directed translation (SDT) actions, given as pseudo-code:

With respect to the above grammar, which one of the following choices is correct?

For a Turing machine $M$, $\langle M \rangle$ denotes an encoding of $M$. Consider the following two languages.

Which one of the following options is correct?

Consider the relation $R(P,Q,S,T,X,Y,Z,W)$ with the following functional dependencies:

Consider the decomposition of the relation $R$ into the constituent relations according to the following two decomposition schemes.

Which one of the following options is correct?

Consider the following ANSI C program.

#include <stdio.h>
int main()
{
    int i, j, count;
    count = 0;
    i = 0;
    for (j = -3; j <= 3; j++)
    {
        if ((j >= 0) && (i++))
            count = count + j;
    }
    count = count + i;
    printf("%d", count);
    return 0;
}

Which one of the following options is correct?

Let $G$ be a group of order 6, and $H$ be a subgroup of $G$ such that $1 < |H| < 6$. Which one of the following options is correct?

Consider the following language.

Which one of the following deterministic finite automata accepts $L$?

Consider the two statements.

Which one of the following choices is correct?

Let $G=(V,E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as:

Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ on the same set of vertices with adjacency matrix $N$, where

Which one of the following statements is true?

Let $r_i(z)$ and $w_i(z)$ denote read and write operations respectively on a data item $z$ by a transaction $T_i$. Consider the following two schedules.

Which one of the following options is correct?

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is

where the data bits and the check bits are given in the following tables:

Which one of the following choices gives the correct values of $x$ and $y$?

Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by $PQR$ as 000, what are the next three states?

An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let $T$ be a DFS tree obtained by doing DFS in a connected undirected graph $G$.

Which of the following options is/are correct?

Consider the following Boolean expression.

Which of the following Boolean expressions is/are equivalent to $\overline{F}$, the complement of $F$?

A TCP server application is programmed to listen on port number $P$ on host $S$. A TCP client is connected to the TCP server over the network.

Consider that while the TCP connection was active, the server machine $S$ crashed and rebooted. Assume that the client does not use the TCP keepalive timer.

Which of the following behaviors is/are possible?

Consider two hosts $P$ and $Q$ connected through a router $R$. The maximum transfer unit (MTU) value of the link between $P$ and $R$ is 1500 bytes, and between $R$ and $Q$ is 820 bytes.

A TCP segment of size 1400 bytes was transferred from $P$ to $Q$ through $R$, with IP identification value as 0x1234. Assume that the IP header size is 20 bytes. Further, the packet is allowed to be fragmented, i.e., Don't Fragment (DF) flag in the IP header is not set by $P$.

Which of the following statements is/are correct?

Consider a dynamic hashing approach for 4-bit integer keys:

1. There is a main hash table of size 4.
2. The 2 least significant bits of a key are used to index into the main hash table.
3. Initially, the main hash table entries are empty.
4. Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to a main hash table entry is organized as a binary tree that grows on demand.
5. First, the 3rd least significant bit is used to divide the keys into left and right subtrees.
6. To resolve more collisions, each node of the binary tree is further sub-divided into left and right subtrees based on the 4th least significant bit.
7. A split is done only if it is needed, i.e., only when there is a collision.

Consider the following state of the hash table.

Which of the following sequences of key insertions can cause the above state of the hash table? Assume the keys are in decimal notation.

A relation $R$ is said to be circular if $aRb$ and $bRc$ together imply $cRa$.

Which of the following options is/are correct?

Consider the following pseudocode, where $S$ is a semaphore initialized to 5 in line #2 and counter is a shared variable initialized to 0 in line #1. Assume that the increment operation in line #7 is not atomic.

1. int counter = 0;
2. Semaphore S = init(5);
3. void parop(void)
4. {
5.     wait(S);
6.     wait(S);
7.     counter++;
8.     signal(S);
9.     signal(S);
10.}

If five threads execute the function parop concurrently, which of the following program behavior(s) is/are possible?

Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. Consider the array of prices:

Which of the following statements is/are correct about $R_7$?

Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following:

• The time taken for processing the data frame by the receiver is negligible.
• The time taken for processing the acknowledgement frame by the sender is negligible.
• The sender has infinite number of frames available for transmission.
• The size of the data frame is 2,000 bits and the size of the acknowledgement frame is 10 bits.
• The link data rate in each direction is 1 Mbps $(=10^6 \text{ bits per second})$.
• One way propagation delay of the link is 100 milliseconds.

The minimum value of the sender's window size in terms of the number of frames, rounded to the nearest integer, needed to achieve a link utilization of 50% is __________.

A five-stage pipeline has stage delays of 150, 120, 150, 160 and 140 nanoseconds. The registers that are used between the pipeline stages have a delay of 5 nanoseconds each.

The total time to execute 100 independent instructions on this pipeline, assuming there are no pipeline stalls, is __________ nanoseconds.

A sender $(S)$ transmits a signal, which can be one of the two kinds, $H$ and $L$, with probabilities 0.1 and 0.9 respectively, to a receiver $(R)$.

In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u,v \in \{H,L\}$.

If the received signal is $H$, the probability that the transmitted signal was $H$, rounded to 2 decimal places, is __________.

Consider the following matrix:

The largest eigenvalue of the above matrix is __________.

Consider the following ANSI C function:

int SimpleFunction(int Y[], int n, int x)
{
    int total = Y[0], loopIndex;
    for (loopIndex = 1; loopIndex <= n - 1; loopIndex++)
        total = x * total + Y[loopIndex];

    return total;
}

Let Z be an array of 10 elements with Z[i] = 1, for all i such that $0 \le i \le 9$.

The value returned by SimpleFunction(Z, 10, 2) is __________.

Consider the following C code segment:

a = b + c;
e = a + 1;
d = b + c;
f = d + 1;
g = e + f;

In a compiler, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is __________.

In a pushdown automaton $P = (Q, \Sigma, \Gamma, \delta, q_0, F)$, a transition of the form shown below represents

where $p,q \in Q$, $a \in \Sigma \cup \{\epsilon\}$, and $X,Y \in \Gamma \cup \{\epsilon\}$.

Consider the following pushdown automaton over the input alphabet $\Sigma=\{a,b\}$ and stack alphabet $\Gamma=\{\#, A\}$.

The number of strings of length 100 accepted by the above pushdown automaton is __________.

Consider the following instruction sequence where registers R1, R2 and R3 are general purpose and MEMORY[X] denotes the content at the memory location X.

Assume that the content of memory location 5000 is 10, and the content of register R3 is 3000. The content of each of the memory locations from 3000 to 3010 is 50. The instruction sequence starts from memory location 1000. All numbers are in decimal format. Assume that the memory is byte addressable.

After the execution of the program, the content of memory location 3010 is __________.