GATE DA topic:data-science PYQs & Answers — Page 3

Questions 21–30 of 195. Imported answers require independent review unless marked reviewed.

Let

be a

matrix, where

, and

. Which of the following options is equal to

Your answerChoose one option.

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Consider a set

. Let

be another set which is a subspace of

with dimension two. Which of the following gives the area of

Your answerChoose one option.

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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.

Task	Algorithm
T1 – Clustering	A1 – Markov Chain Monte Carlo
T2 – Classification	A2 – K-Medoid
T3 – Sampling	A3 – Linear Discriminant Analysis
T4 – Feature Extraction	A4 – Naive Bayes

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

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

T1:A4, T2:A3, T3:A1, T4:A2

T1:A2, T2:A4, T3:A1, T4:A3

T1:A3, T2:A4, T3:A1, T4:A2

T1:A4, T2:A2, T3:A1, T4:A3

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Sentence

is said to entail Sentence

if whenever

is TRUE,

also must hold TRUE.

Which of the following statements is/are correct if

entails

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

is FALSE

then

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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?

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

Node P is the root of T

The Post-order traversal of T is: S E Q F G R P

Node Q has only one child

The left subtree of node R contains the node G

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Consider two relations r and s defined on the relational schemas R(A, B) and S(E, C), respectively. A is the primary key of R and E is a foreign key of S referencing A in R.

Which of the following operations will NEVER violate the foreign key constraint?

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

Inserting records into relation r

Deleting records from relation s

Deleting records from relation r

Inserting records into relation s

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Let

be a function defined on

Which of the following statements is/are correct?

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

has exactly two roots in

has a minimum at 2 only.

has maximum at 0 only.

has a root at 1.

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Suppose a random variable

follows Normal

distribution with probability density function

and cumulative distribution function

. Another random variable

follows

distribution with probability density function

and cumulative distribution function

. Let

be the positive real number for which

Which of the following statements is/are correct?

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

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Consider that for a supervised learning task, the objective function being minimized is

, where

is the input and

is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates. Suppose that at the end of iteration

, the value of

becomes 10.00. Let

be the input for iteration

. The value of

at the end of iteration

is __________ . (Rounded off to two decimal places)

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Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value of a terminal node represents the utility of the game state if the game ends there. The numbers written next to the edges denote the strategies. There are two players MAX and MIN. At any particular state of the game, MAX prefers to move to a state of maximum value. On the other hand, MIN prefers to move to a state of minimum value. Suppose MAX starts the game at the root and has three strategies: 1, 2 and 3. Next, MIN plays and also has three strategies: 1, 2 and 3. The game ends there. Both players always take optimal strategies throughout the game. At the root, the best strategy for MAX is __________ . (Answer in integer)

Diagram for Data Science and Artificial Intelligence question 30

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GATE DA topic:data-science PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30