List of top Questions asked in GATE DA- 2026

Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. These four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
1. The first game was the only game where two students of the same class played against each other.
2. The students of Class 5 won more games than the students of Class 4.
3. The boys won 2 games and the girl won 1 game.
The student who did not lose any game is:

Consider two distinct positive numbers $ m, n $ with $ m > n $. Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between $ x $ and $ y $ is -

Consider the supervised learning task. The objective function being minimized is $ f(w) = w \cdot x $, where $ w \in \mathbb{R} $ is the parameter. Stochastic Gradient Descent with learning rate of 0.10. Let $ w = 10.00 $ be the $ i^{\text{th}} $ iteration ($ w_i $). The value of $ w $ at the end of iteration $ (i+1) $ is if $ x = 10 $ ________. Round off 2 decimal.

The value of \[ \sum_{j=0}^{\infty} \sum_{i=1}^{\infty} 2^{-j} 3^{-i} \] is ________.

Consider the Ridge LRR is being used to learn prediction function $ y_{\text{pred}} = w^T x $ where $ w, x \in \mathbb{R}^2 $ & mean absolute error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer. At an intermediate step of training process assume that the parameter $ w = [-3.00, 4.00]^T $. In the next step for the I/P $ x = [1.00, 2.00]^T $, the predicted value of $ y $ is noted. Let the relation b/w $ x = [x_1, x_2]^T $ & the true value of $ y $ be $ y_{\text{true}} = x_1 + x_2 $. The value of the overall regularized loss for instance is __________ (upto 2 decimal).

S$_1$ = \{x = (x$_1$, x$_2$, x$_3$)$^T$ $\in$ R$^3$ $|$ x$^T$x $\le$ 16\}. Let S$_2$ be subspace of R$^3$ with dimension 2 then Area of S$_1$ $\cap$ S$_2$ ?

Let $ M = \left(I_n - \frac{1}{n} 11^T \right) $ be a matrix where $ 1 = (1,1,\dots,1)^T \in \mathbb{R}^n $ and $ I_n $ is the identity matrix of order $ n $. The value of \[ \max_{x \in S} x^T M x \] where \[ S = \{ x \in \mathbb{R}^n \mid x^T x = 1 \} \] is ________.

Let L = lim$_{n \to \infty \sum_{k=0}^{n} \frac{e^{-n} }n^k}{k!}$ value of L

R(A B C D E)
F = A$\rightarrow$ BC, CD$\rightarrow$ E, E$\rightarrow$A
Which of the following is correct?

For a given data set ${X$_1$, X$_2$, ..., X$_n$}$ where n = 100
$\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$
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 __________.

You are given the following preorder and In-order traversal of binary Tree T with nodes E, F, G, P, Q, R, S-
Preorder : P, Q, S, E, R, F, G
Inorder: S, Q, E, P, F, R, G
Which of the following statements is/are true about the binary True T?

Let X be a random variable that follows uniform (-1, 1) dist. The conditional dist. of the random variable Y given X = x is the Uniform (x$^2$ - 0.1, x$^2$ + 0.1) dist. The value of correlation (X, Y) is _______.

A recursive function is given:
def mystery(n):
if n $<=$ 0:
return 1
else:
return mystery(n-1) + mystery(n-2)
Find the value of mystery(4).

Assume a typical runtime stack is used for the recursive function mystery(n) as defined earlier. How many total function calls (stack activations), including the initial call, are made to compute mystery(4)?

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)

def append_to_lst(val, lst=[]):
lst.append(val)
return lst
print(append_to_lst(1))
print(append_to_lst(2))
print(append_to_lst(3, []))

X is said to entail sentence Y. If whenever X is true, Y is also TRUE. Which of the following is/are correct if X entails Y?

def outer():
x = []
def inner(val):
x.append(val)
return x
return inner
f1 = outer()
f2 = outer()
print(f1(10)) \# line P
print(f1(20)) \# line Q
print(f2(30)) \# line R
print(f1(40)) \# line S
Which of the following is/are correct?

Consider that 20 stories of author X and 10 stories of author Y were kept together without mentioning the names of the authors. A classifier was then asked to predict the author (X or Y) of each of the stories. Later out of X's stories 6 were classified as that of Y. On the other hand, out of Y's stories 2 were classified as that of X. Considering X and Y as two classes, then which of the following is/are true?

Which one of the following is true for Ridge Regression (RR)

Assume that creative (C) person will succeed (S) if the person is also disciplined (D) but will not succeed otherwise.
Statement:
(i) C $\land$ S $\leftrightarrow$ D
(ii) C $\rightarrow$ (S $\rightarrow$ D)
(iii) C $\leftrightarrow$ ((D $\rightarrow$ S) $\lor$ $\neg$S)

M = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ , $\theta$ = $\frac{2\pi}{5}$ then M$^{2026}$ = ?

M = (I$_n$-$\frac{1}{n}$11$^T$) be a matrix where 1 = (1,1,...,1)$^T$ $\in$ R$^n$ and I$_n$ is the identity matrix of order n. then which of the following is/are true.

Consider that you are training a classifier for a 10-class classification problem. Each I/P is represented as a 512 dimensional vector. There are 1000 samples out of which first 100 will be used for testing. Let Leave-one-out-Cross-Validation (LOOCV) be used for selection of the classifier model before testing. Which of the following option is the correct option for no. of validation split that will be generated?

Consider a fully connected forward multi-layer perceptron. It has 30 neurons in the i/p layer foll. by two hidden layers and an o/p layer. The first hidden layer has 4 neurons and the second 3 neurons. The o/p layer has only 1 neuron. Assume that no biased parameter parameter in the mul_________.