GATE exam stream

GATE DA — Data Science & AI

35 questions and papers

GATE DA (Data Science and Artificial Intelligence) began in 2024. Alongside its own papers, this stream lists the CS questions on the probability, statistics, linear algebra, machine learning, databases and programming topics in the DA syllabus.

GATE DA 2025 — Question 60

Numerical answer 2 marks Data Science Ml 2025

Let \(D = \{x^{(1)}, \dots, x^{(n)}\}\) be a dataset of \(n\) observations where each \(x^{(i)} \in \mathbb{R}^{100}\). It is given that \(\sum_{i=1}^{n} x^{(i)} = 0\). The covariance matrix computed from \(D\) has eigenvalues \(\lambda_i = 100^{\,2-i}\), \(1 \le i \le 100\). Let \(u \in \mathbb{R}^{100}\) be the direction of maximum variance with…

GATE DA 2025 — Question 53

Multiple select 2 marks Data Science Ml 2025

Consider designing a linear binary classifier \(f(x) = \mathrm{sign}(w^{T} x + b)\), \(x \in \mathbb{R}^{2}\), on the following training data:Class-1: \((2,\, 0)^{T}, (0,\, 2)^{T}, (2,\, 2)^{T}\)Class-2: \((0,\, 0)^{T}\)Hard-margin support vector machine (SVM) formulation is solved to obtain \(w\) and \(b\). Which of the following options is/are correct?

GATE DA 2025 — Question 30

Multiple select 1 mark Data Science Ml 2025

Let \(C_1\) and \(C_2\) be two sets of objects. Let \(D(x, y)\) be a measure of dissimilarity between two objects \(x\) and \(y\). Consider the following definitions of dissimilarity…

GATE DA 2025 — Question 34

Numerical answer 1 mark Data Science Ml 2025

Given data \(\{(-1, 1), (2, -5), (3, 5)\}\) of the form \((x, y)\), we fit a model \(y = wx\) using linear least-squares regression. The optimal value of \(w\) is ______…

GATE DA 2025 — Question 22

Multiple choice 1 mark Data Science Ml 2025

Consider designing a linear classifier\(y = \mathrm{sign}\big(f(x, w, b)\big), \qquad f(x, w, b) = w^{T} x + b\)on a dataset \(D = \{(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)\}\), with \(x_i \in \mathbb{R}^{d}\), \(y_i \in \{+1, -1\}\), \(i = 1, 2, \dots, N\). Recall that the sign function outputs \(+1\) if the argument is positive, and \(-1\) if the argument is non-positive. The parameters \(w\) and \(b\) are updated as per the following training algorithm:\(w_{\mathrm{new}} = w_{\mathrm{old}} + y_n x_n, \qquad b_{\mathrm{new}} = b_{\mathrm{old}} + y_n\)whenever \(\mathrm{sign}\big(f(x_n, w_{\mathrm{old}}, b_{\mathrm{old}})\big) \neq y_n\). In…