List of top Questions asked in GATE CS

TCP client \( P \) successfully establishes a connection to TCP server \( Q \). Let \( N_P \) denote the sequence number in the SYN sent from \( P \) to \( Q \). Let \( N_Q \) denote the acknowledgement number in the SYN ACK from \( Q \) to \( P \). Which of the following statements is/are CORRECT?
Which of the following process state transitions is/are NOT possible?
Which of the following statements about a relation \( R \) in first normal form (1NF) is/are TRUE?
Which of the following is/are Bottom-Up Parser(s)?
In a B+ tree, the requirement of at least half-full (50\%) node occupancy is relaxed for which one of the following cases?
Let \( L_1, L_2 \) be two regular languages and \( L_3 \) a language which is not regular. Which of the following statements is/are always TRUE?
Which of the following statements about threads is/are TRUE?
Which one of the following statements is FALSE?
Consider a permutation sampled uniformly at random from the set of all permutations of \( \{1, 2, 3, \dots, n\} \) for some \( n \geq 4 \). Let \( X \) be the event that 1 occurs before 2 in the permutation, and \( Y \) the event that 3 occurs before 4. Which one of the following statements is TRUE?
A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are all initially empty. The following packets leave the user’s computer in some order: HTTP GET request for the index page DNS request to resolve the web server’s name to its IP address HTTP GET request for an image object TCP SYN to open a connection to the web server Which one of the following is the CORRECT chronological order (earliest in time to latest) of the packets leaving the computer?
Given an integer array of size \( N \), we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is:
Consider the following C program: \begin{verbatim} #include stdio.h int main(){ int a = 6; int b = 0; while(a<10) { a = a / 12 + 1; a += b; } printf("%d", a); return 0; } \end{verbatim} Which one of the following statements is CORRECT?
Consider the following C program: \begin{verbatim} #include stdio.h void fX(); int main(){ fX(); return 0; } ____________________________ void fX(){ char a; if((a = getchar()) != '\n') fX(); if(a != '\n') putchar(a); } \end{verbatim} Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?
Let \( S \) be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one of the following ER diagrams CORRECTLY represents \( S \)? \includegraphics[width=6.5cm]{21a.png}
\includegraphics[width=6.5cm]{21b.png}
\includegraphics[width=6.5cm]{21c.png}
\includegraphics[width=6.5cm]{21d.png}
The least number of squares to be added in the figure to make AB a line of symmetry is: \begin{center} \includegraphics[width=6cm]{10.png} \end{center}
The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. The typical energy density (kcal/g) of these macronutrients is given in the table. \begin{center} \includegraphics[width=10cm]{8.png} \{0.5cm} \begin{tabular}{|c|c|} \hline Macronutrient & Energy density (kcal/g)
\hline Carbohydrates & 4
Proteins & 4
Unsaturated fat & 9
Saturated fat & 9
Trans fat & 9
\hline \end{tabular} \end{center} The total fat (all three types), in grams, this person consumes is:
The product of all eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2 & 3
4 & 5 & 6
7 & 8 & 9 \end{bmatrix} is: \]
Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers \( A \) and \( B \) are represented as \( A = 01010 \) and \( B = 11010 \). Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?
Let \( f: \mathbb{R} \to \mathbb{R} \) be a function such that \( f(x) = \max\{x, x^3\ \), \( x \in \mathbb{R} \), where \( \mathbb{R} \) is the set of all real numbers. The set of all points where \( f(x) \) is NOT differentiable is:}
A rectangular paper of 20 cm \( \times \) 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is:
A rectangular paper sheet of dimensions \( 54 \, \text{cm} \times 4 \, \text{cm} \) is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is:
The number of coins of Rs.1, Rs.5, and Rs.10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in Rs.5 coins is:
If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.
Steve was advised to keep his head \_\_\_ (i) \_\_\_ before heading \_\_\_ (ii) \_\_\_ to bat; for, while he had a head \_\_\_ (iii) \_\_\_ batting, he could only do so with a cool head \_\_\_ (iv) \_\_\_ his shoulders.
Consider the following sample of numbers: \[ 9, \, 18, \, 11, \, 14, \, 15, \, 17, \, 10, \, 69, \, 11, \, 13 \] The median of the sample is: