GATE DA format:msq PYQs & Answers — Page 4

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Questions 31–40 of 44. Imported answers require independent review unless marked reviewed.

Topic practice 44 questionsPage 4 of 5

Consider a database relation R with attributes ABCDEFG, and having the following functional dependencies:

A → BCE E → DG BC → A

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

A is the only candidate key of R

A, BC are the candidate keys of R

A, BC, E are the candidate keys of R

Relation R is not in Boyce-Codd Normal Form (BCNF)

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Let

be a simple, unweighted, and undirected graph. A subset of the vertices and edges of

are shown below.

Diagram for Data Science and Artificial Intelligence question 58

It is given that

is a shortest path between

and

;

is a shortest path between

and

;

is a shortest path between

and

. Which of the following is/are NOT the edges of

Your answerSelect all correct options. You can choose more than one.

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Consider the following tree traversals on a full binary tree:

(i) Preorder (ii) Inorder (iii) Postorder

Which of the following traversal options is/are sufficient to uniquely reconstruct the full binary tree?

Your answerSelect all correct options. You can choose more than one.

(i) and (ii)

(ii) and (iii)

(i) and (iii)

(ii) only

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Let

and

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

Your answerSelect all correct options. You can choose more than one.

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Given the relational schema

and the set of functional dependencies:

Which of the following functional dependencies can be derived from the above set?

Your answerSelect all correct options. You can choose more than one.

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Select all choices that are subspaces of

Note:

denotes the set of real numbers.

Your answerSelect all correct options. You can choose more than one.

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Which of the following statements is/are TRUE?

Note:

denotes the set of real numbers.

Your answerSelect all correct options. You can choose more than one.

There exist

, and

such that

has a unique solution and

has infinite solutions.

There exist

, and

such that

has no solutions and

has infinite solutions.

There exist

, and

such that

has a unique solution and

has infinite solutions.

There exist

, and

such that

has a unique solution and

has no solutions.

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Let

be the set of real numbers,

be a subspace of

and

be the matrix corresponding to the projection onto the subspace

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a 1-dimensional subspace of

, then the null space of

is a 1-dimensional subspace.

is a 2-dimensional subspace of

, then the null space of

is a 1-dimensional subspace.

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Consider the function

where

is the set of all real numbers.

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a local maximum of

is a local minimum of

is a local maximum of

is a local minimum of

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Consider the directed acyclic graph (DAG) below:

Diagram for Data Science and Artificial Intelligence question 51

Which of the following are valid vertex orderings that can be obtained from a topological sort of the DAG?

Your answerSelect all correct options. You can choose more than one.

P Q R S T U V

P R Q V S U T

P Q R S V U T

P R Q S V T U

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GATE DA format:msq PYQs

Question 57

Question 58

Question 28

Question 29

Question 46

Question 47

Question 48

Question 49

Question 50

Question 51