List of top Data Science and Artificial Intelligence Questions on Algorithm design techniques

Let x and y be two propositions. Which of the following statements is a tautology /are tautologies ?

Consider sorting the following array of integers in ascending order using an in-place Quicksort algorithm that uses the last element as the pivot.

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The minimum number of swaps performed during this Quicksort is ________.

Euclidean distance based k-means clustering algorithm was run on a dataset of 100 points with k = 3. If the points \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} -1 \\ 1 \end{bmatrix}\) are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3 ?