List of top Data Science and Artificial Intelligence Questions asked in GATE DA

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.

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

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 __________.

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 _______.

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?

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?

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 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)

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_________.

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?

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

Consider the game tree for a 2-player turn-taking minimax game shown in the figure. The value of the terminal node represent the utility of the game state if the game end there. There are two player Max \& Min. At any particular point state of the game Max prefers to move to a state of maximum value, on the other hand Min prefers to move to a state of min value. Suppose Max starts the game at the root and has three strategies 1, 2, 3. Next, Min plays and also has three strategies 1, 2, 3. The game end there. Both player always take optimal strategies throughout the game. At the root, the best strategy for max is ________ (int).

For a classification problem PCA has been used to reduce the dimensionality of a feature space from 100 to 10. Which of the following option is true about the angle b/w first 2 and 10th principal components?

A$_{5\times5$ each element following Bernoulli (P = 0.50) Dist. independently. The prob. that row sum of the second row and column sum of the third column are both equal to 3 is-}

Let P(x) be a predicate. Which of the following is NOT valid in first-order logic?

Let y1, y2, y3 eigen value of M = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & \sin t & \cos t \end{bmatrix}$ Where t $\in$ [-$\pi$,$\pi$] \& y$_1$ + y$_2$ + y$_3$ = 1 + $\sqrt{2}$ then t = ?

Let X be an exp. distributed random variable with mean $\lambda$($>$ 0) if P (X$>$ 5) = 0.35 then the conditional probability P(x$>$ 10$|$ x$>$ 5) is _______.

Let X be a discrete valued random variable with cumulative dist. F(x) is/are correct:

Let 4 points in 3D: P1 = [2,3,4,], P2 = [3,1,1], P3 = [5, -2, 3] ,P4 = [3,3,3]. Hierarchical Agglomerative clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which two points will be merged first?