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

P = [1, 2, 3, 5, 4]
Two sorting algo Binary sort (BS), Insertion sort (IS) apply. Let N$_1$ be the total number of comparisons done by BS on the element of P and N$_2$ be the total number of comparisons done by IS on the elements of P. Which of the following option is/are correct?

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

Consider Quick sort algorithm used to sort an array of n distinct randomly ordered element. 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 current subarray. Which of the following option represents T(n) in this scenario.

Consider the 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 cycle but there is no self-loop, further G may not be strongly connected. Let G$^R$ be the graph obtained by reversing direction of all edges without changing set of vertices. Assume that BFS or DFS for any given vertex V of a graph will visit only the reachable vertices from V in that graph. Which of the following statement must always be true regardless of the structure of G?

A be a sorted array containing 1000 distinct integers. You perform 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 max number of comparisons that may have to be performed if y is not an element of A is __________ . (Answer in int)

A node size is 4096B. Node pointer size is 10B. Search key is 11B. Record pointer is 12B. What is the Max node pointers that can be stored in a non-leaf node of a B+ tree?

Which of the following NOT true? (The name of the predicate are intuitive)

A clinic specializes in testing for a Disease D. The result of the test can be either positive (+ve) or negative (-ve). A study reveals that if a person suffers from the Disease D, the test result in that clinic comes up +ve 80% of the time and negative 20% of the time. If a person is not suffering from the Disease D, the test comes out positive 10% of the time \& negative 90% of the time. It is also known among the general population the disease D occurs in 30% of the individuals. If the person tests positive for D in that clinic, the probability that he/she actually suffers from the Disease D is __________ (Round off to 2 decimal places).

Consider the visualization of a 3-dimensional data cube showing sales quantity for each combination of the attributes Product-type, Month \& Country. From this, if we want to further visualize the sale quantity for each combination of PT, M \& S, which of the following OLAP operator should be performed?

If \( xyz \) is a three-digit number and the product of its digits is \( 70 \), then find the sum of the digits.

Which of the following recurrence relations represents the average case time complexity of QuickSort?

Node size = 4096 B
Node pointer = 10 B
Search key = 11 B
Record pointer = 12 B
Find the maximum number of node pointers.

Consider the ER model:
E1 (A11, A12, A13)
E2 (A21, A22, A23)
Where:
- A21 is the key of E2
- A22 is a multivalued attribute
- R12 is a many-to-many relationship between E1 and E2
Find the minimum number of relations required to convert this ER model into tables.

Consider a binary tree whose preorder traversal is \[ P, Q, S, E, R, F, G \] and inorder traversal is \[ S, Q, E, P, F, R, G. \] Which of the following statements is correct?

In a data warehouse, a 3D cube initially has dimensions: Product type, Month, and Country. After visualization, the dimension Country is refined into State. Which OLAP operation is performed?

Which of the following logical statements is not valid?

Consider the relation \( R(A, B, C, D, E) \)
Functional Dependencies:
\[ A \rightarrow BC \] \[ CD \rightarrow E \] \[ E \rightarrow A \] Find the number of candidate keys.

Let \( p \) and \( q \) be any two propositions. Consider the following propositional statements.
S1: \( p \rightarrow q \), S2: \( \neg p \land q \), S3: \( \neg p \lor q \), S4: \( \neg p \lor \neg q \)
where \( \land \) denotes conjunction (AND operation), \( \lor \) denotes disjunction (OR operation), and \( \neg \) denotes negation (NOT operation).
(Note: \( \equiv \) denotes logical equivalence)
Which one of the following options is correct?

When does the worst case of binary search occur?

Suppose that insertion sort is applied to the array \([1,2,3,5,7,9,11,x,15,13]\) and it takes exactly 2 swaps to sort the array. Select all possible values of \( x \).

Given the lists: \[ A = [1,2,3], \quad B = [4,5,6] \] Which of the following statements will result in \[ A = [1,2,3,4,5,6]? \]

Given the relation: \[ R = \{A, B, C, D, E, F, G\} \] With the following functional dependencies (FDs): \[ A \rightarrow BCEF, \quad E \rightarrow DG, \quad BC \rightarrow A \] Which of the following statements is correct?