List of top Questions asked in GATE DA- 2026

Let \(P(x)\) be a predicate.

Which of the following statements is/are NOT valid in first-order logic?

For a classification problem, Principal Component Analysis (PCA) has been used to reduce the dimensionality of a feature space from 100 to 10.
Which of the following options is true about the angle \(\theta\) between the first and the tenth principal components?

Consider that you are training a classifier for a 10-class classification problem. Each input is represented as a 512-dimensional vector. There are 1000 samples, out of which the 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 options is the correct number of validation splits that will be generated?

In the following table, the Task column lists a few tasks related to machine learning. The Algorithm column lists a few algorithms.
Each entry "t" from the Task column is to be matched with an appropriate entry "a" from the Algorithm column such that the task "t" can be solved using the algorithm "a". Denote such a match as t:a.

Which of the following options is/are the correct matching(s)?

Consider that for a supervised learning task, the objective function being minimized is \(f_w(x) = wx\), where \(x \in \mathbb{R}\) is the input and \(w \in \mathbb{R}\) is the parameter. Stochastic Gradient Descent with a learning rate of 0.10 is used for parameter updates.

Suppose that at the end of iteration \(i\), the value of \(w\) becomes 10.00.

Let \(x = 10.00\) be the input for iteration \((i+1)\).

The value of \(w\) at the end of iteration \((i+1)\) is __________. (Rounded off to two decimal places)

Let four points in three-dimensional space be:
\(P1: [2, 3, -1]\), \(P2: [3, 1, 1]\), \(P3: [5, -2, 3]\) and \(P4: [3, 3, 3]\).
Hierarchical Agglomerative Clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which of the following options indicates the two points that will be merged first?

Which of the following statements is true for Ridge Regression?

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 these stories. Let, 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, which of the following statements is/are true?

Consider that Linear Ridge Regression is being used to learn a prediction function \(y_{pred} = w^T x\), where \(w, x \in \mathbb{R}^2\) and 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 the training process, assume that the parameter \(w = [-3.00,\ 4.00]^T\). In the next step, for the input \(x = [1.00,\ 2.00]^T\), the predicted value of \(y\) is noted. Let the relation between \(x = [x_1,\ x_2]^T\) and the true value of \(y\) be \(y_{true} = x_1 + x_2\).

The value of the overall regularized loss function for this instance is _______ . (Rounded off to two decimal places)

Consider a fully-connected feed-forward multi-layer perceptron. It has 30 neurons in the input layer, followed by two hidden layers and an output layer. The first hidden layer has 4 neurons and the second hidden layer has 3 neurons. The output layer has only one neuron. Assume that no bias parameters are used.

The number of learnable parameters in the multi-layer perceptron is _______ . (Answer in integer)

Consider that the quick sort algorithm is used to sort an array of \(n\) distinct randomly ordered elements. In every call, the pivot is chosen as the first element of the current subarray.
Let \(T(n)\) denote the expected time to sort the array. Assume that the time to partition is linear in the size of the current subarray.
Which of the following recurrence relations correctly represents \(T(n)\) in this scenario?

You are given the following Pre-order and In-order traversals of a Binary Tree \(T\) with nodes E, F, G, P, Q, R, S.

Pre-order: P Q S E R F G
In-order: S Q E P F R G

Which of the following statements is/are true about the Binary Tree \(T\)?

Let \(A\) be a sorted array containing 1000 distinct integers. You perform a recursive binary search on \(A\) to find an element \(y\). Suppose each comparison checks whether the middle element computed during the current recursive step is equal to, less than, or greater than \(y\).

The maximum number of comparisons that may have to be performed if \(y\) is not an element of \(A\) is __________. (Answer in integer)

Consider a directed graph \(G = (V, E)\), where \(V\) is the finite set of vertices and \(E\) is the set of directed edges between the vertices. \(G\) may contain cycles but there is no self-loop. Further, \(G\) may not be strongly connected.
Let \(G^R\) be the graph obtained by reversing the directions of all the edges in \(G\) without changing the set of vertices.
Assume that Breadth First Search (BFS) or Depth First Search (DFS) from any given vertex \(v\) of a graph visits only the reachable vertices from \(v\) in that graph.
Which of the following statements must always be true, regardless of the structure of \(G\)?

Consider the problem of sorting the given array in ascending order:

\(P = [1, 2, 3, 5, 4]\)

Consider two sorting algorithms Bubble Sort (BS) and Insertion Sort (IS).

Let \(N_1\) be the total number of comparisons done by BS on the elements of \(P\) and \(N_2\) be the total number of comparisons done by IS on the elements of \(P\).

Which of the following options is/are correct?