List of top Questions asked in GATE DA- 2026

The number of bijections \(f(\cdot)\) from the set \(S = \{1, 2, 3, 4\}\) to itself such that \(f(f(n)) = n\), for all \(n \in S\), is ________. (Answer in integer)

Let \(M = \left(I_n - \frac{1}{n}\mathbf{1}\mathbf{1}^T\right)\) be a matrix, where \(\mathbf{1} = (1,1,1,\ldots,1)^T \in \mathbb{R}^n\) and \(I_n\) is the identity matrix of order \(n\).

Which of the following options is/are correct?

Let \(X\) be an exponentially distributed random variable with mean \(\lambda (> 0)\). If \(P(X > 5) = 0.35\), then the conditional probability \(P(X > 10 \mid X > 5)\) is ________. (Rounded off to two decimal places)

A recursive function in Python is given.

def mystery(n):
    if n <= 0:
        return 1
    else:
        return mystery(n-1) + mystery(n-2)

Now, consider the following function call:
mystery(4)
Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.
Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.

Ignoring permutations, the number of ways to pick these five integers is _____

Consider the given Python program.

def fun(L, i=0):
    if i >= len(L)-1:
        return 0
    if L[i] > L[i+1]:
        L[i+1], L[i] = L[i], L[i+1]
        return 1+fun(L, i+1)
    else:
        return fun(L, i+1)

data = [5, 3, 4, 1, 2]
count = 0
for _ in range(len(data)):
    count += fun(data)
print(count)

The output of the program is _______. (Answer in integer)

Let
\[ L = \lim_{n \to \infty} \sum_{k=0}^{n} \frac{e^{-n} n^{k}}{k!} \]
Which of the following is the value of \(L\)?

Consider two relations \(r\) and \(s\) defined on the relational schemas \(R(A,B)\) and \(S(E,C)\), respectively. \(A\) is the primary key of \(R\) and \(E\) is a foreign key of \(S\) referencing \(A\) in \(R\).

Which of the following operations will NEVER violate the foreign key constraint?

'If his latest movie had been a commercial success, the actor would have made enough money to sponsor his next movie.'

Based only on the above sentence, which one of the following statements is true?

Consider a B+ Tree where the maximum number of key values in each leaf node is 2 and the maximum number of pointers in each non-leaf node is 3. Let the content of the B+ Tree be as shown in the figure.

Which of the following options denotes the key value(s) stored in the root node after inserting a key value 3 in the given B+ Tree?

Let \(X\) be a discrete valued random variable with cumulative distribution function \(F(x)\).

Which of the following statements is/are correct?

Consider a table Employee(EmpID, TeamID), where the column EmpID (ID of an employee) is the primary key. The column TeamID denotes the team ID of the team of which the employee is a member. TeamID is a NOT NULL column.

We want to display the size of the team (denoted as TeamSize) in which each employee is a member by using SQL. As an example, the desired output for the given Employee table is also shown in tabular form.

Which of the following is/are correct?

Employee table:

EmpID	TeamID
1	8
2	8
3	8
4	7
5	7
6	9

Output table:

EmpID	TeamSize
1	3
2	3
3	3
4	2
5	2
6	1

In the given figure, \(P\), \(Q\), and \(R\) are three points on a circle of radius 10 cm with \(O\) as its center, \(\overline{PQ} = \overline{RQ}\), and \(\angle PQR = 45^{\circ}\). The figure is representative.
The area of the shaded region \(PQRO\) is ______________ \(\text{cm}^2\).

Let Account be a relation as shown.

Table: Account

AccNo	Balance
A1	5000
A2	5000
A3	10000
A4	15000
A5	18000

Consider the given SQL query.

SELECT AccNo FROM Account AS A
WHERE (SELECT COUNT(*) FROM Account AS B
WHERE A.Balance < B.Balance) >= (SELECT COUNT(*)
FROM Account AS C WHERE A.Balance > C.Balance)

The number of rows returned by the SQL query is _______. (Answer in integer)

For a given data set \(\{x_1, x_2, \ldots, x_n\}\), where \(n = 100\), it is known that
\[ \frac{1}{2000}\sum_{i=1}^{n}\sum_{j=1}^{n}(x_i - x_j)^2 = 99 \]
Let us denote \(\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i\)

The value of \(\frac{1}{99}\sum_{i=1}^{n}(x_i - \bar{x})^2\) is _______. (Answer in integer)

Which of the following algorithms is NOT an example of uninformed search?

'My friend and I parted __ the door __ the cabin that I had rented __ the night.'

Choose the option with the correct sequence of words to fill the blanks.

Sentence \(X\) is said to entail Sentence \(Y\) if whenever \(X\) is \(TRUE\), \(Y\) also must hold \(TRUE\).
Which of the following statements is/are correct if \(X\) entails \(Y\)?

Let \(A_{5\times5}\) be a matrix such that each of its elements follows \(Bernoulli(p=0.50)\) distribution independently.

The probability that the row-sum of the second row and the column-sum of the third column are both equal to 3 is __________. (Rounded off to two decimal places)

Assume that a Creative (\(C\)) person will Succeed (\(S\)) if the person is also Disciplined (\(D\)), but will not succeed otherwise. Now, consider the following statements:
(i) \(C \wedge S \Leftrightarrow D\)
(ii) \(C \Rightarrow (S \Leftrightarrow D)\)
(iii) \(C \Leftrightarrow ((D \Rightarrow S) \vee \neg S)\)
Which of the following options is correct?

Consider the concept hierarchies as shown in the figure.