List of top Questions asked in GATE CS- 2026

An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is ______.

The antonym of the word protagonist is ______.

Consider a relational database schema with two relations \(R(P, Q)\) and \(S(X, Y)\).
Let \(E = \{\langle u \rangle \mid \exists v\, \exists w\; \langle u, v \rangle \in R \wedge \langle v, w \rangle \in S\}\) be a tuple relational calculus expression.
Which one of the following relational algebraic expressions is equivalent to \(E\)?

Consider a relational database schema with a relation \(R(A, B, C, D)\). If \(\{A, B\}\) and \(\{A, C\}\) are the only two candidate keys of the relation \(R\), then the number of superkeys of relation \(R\) is ______.

Consider the following recurrence relations. For all \(n > 1\),
\[ T_1(n) = 4T_1\left(\frac{n}{2}\right) + T_2(n) \]
\[ T_2(n) = 5T_2\left(\frac{n}{4}\right) + \Theta(\log_2 n) \]
Assume that for all \(n \leq 1\), \(T_1(n) = 1\) and \(T_2(n) = 1\).
Which one of the following options is correct?

Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are 64 players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly 15 credits of core courses and exactly 20 credits of project. In addition, a student has to enroll for a minimum of 10 credits of specialization courses. The maximum credits of elective courses that a student can enroll for is ______

Let \(P, Q, R\) and \(S\) be the attributes of a relation in a relational schema. Let \(X \rightarrow Y\) indicate functional dependency in the context of a relational database, where \(X, Y \subseteq \{P, Q, R, S\}\).
Which of the following options is/are always true?

In the 2020 summer Olympics' Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:
(i) The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.
(ii) The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.
(iii) After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.
(iv) In the fourth round, the throw by Jakub Vadlejch was the best in that round.
In which round did Vitezlav Vesely have his best throw?

The figure shows two 4-tile patterns.

Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?

'When the teacher is in the room, all students stand silently.'
If the above statement is true, which one of the following statements is not necessarily true?

In the context of relational database normalization, which of the following statements is/are true?

Let \(G\) be an undirected graph, which is a path on 8 vertices. The number of matchings in \(G\) is ______. (answer in integer)

For positive real numbers \(S\) and \(K\), the function \(H_K(S)\) is defined as:
\[ H_K(S) = \max(S-K, 0) \]
The max function is defined as:
\[ \max(a,b) = \begin{cases} a, & \text{when } a > b \\ b, & \text{when } a \leq b \end{cases} \]
The graph below shows the plot of a function \(N(S)\) versus \(S\).

\(N(S)\) can be expressed as ______.

In Panel I of the figure below, the front view and top view of a structure are shown. Which one of the 3D structures shown in Panel II possesses the views shown in Panel I?

A TCP sender successfully establishes a connection with a TCP receiver and starts the transmission of segments. The TCP congestion control mechanism's slow-start threshold is set to 10000 segments. Assume that the round-trip time is fixed at 1 millisecond. Assume that the sender always has data to send, the segments are numbered from 1, and no segment is lost. Let \(t\) denote the time (in milliseconds) at which the transmission of segment number 2000 starts.
Which one of the following options is correct?

Which one of the following protocols may need to broadcast some of its messages?

Which one of the following CPU scheduling algorithms cannot be preemptive?

Consider the following two statements about interrupt handling mechanisms in a
CPU.
S1: In non-vectored interrupt mechanism, it usually takes more time to start the
Interrupt Service Routine (ISR) when compared to that in a vectored interrupt
mechanism.
S2: In daisy-chain interrupt mechanism, the CPU polls all the input devices
individually to determine the source of the interrupt.
Which one of the following options is correct with respect to S1 and S2 ?

In the context of DBMS, consider the two sets T and S given below.
T
S
I: Logical schema
L: Views
II: Physical schema
M: File organization and indexes
III: External schema N: Relations
Which one of the following is the correct match from T to S ?

The figure in Panel I below is a grid of cells with four rows and four columns.
The numbers on the top and on the left represent the number of cells that are to
be shaded in that column and row, respectively. Which one of the options shown
in Panel II below represents the grid shaded correctly?

Figures (i) and (ii) represent intercity highway systems. The black dots represent
cities and the line segments between them represent intercity highways.
A salesperson needs to make a trip. She needs to start from a city, visit each of the
remaining cities exactly once, and finally return to the same city from which she
started.
Which one of the following options is then true?

The set T represents various traversals over binary tree. The set S represents the
order of visiting nodes during a traversal.
T
S
I: Inorder
L: left subtree, node, right subtree
II: Preorder
M: node, left subtree, right subtree
III: Postorder N: left subtree, right subtree, node
Which one of the following is the correct match from T to S ?

The values of Stock A and Stock B on a particular day are Rs. 50 and Rs. 80,
respectively. An investor invests Rs. 100 in Stock A and Rs. 80 in Stock B. He
sells all the stocks the next day when the value of Stock A is Rs. 55 and Stock B
is Rs. 70. The profit made by the investor is Rs. ________

Two tiles are missing in Panel I. Which one of the options in Panel II is the
appropriate choice for the missing tiles?