GATE DA branch:da PYQs & Answers — Page 11

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Questions 101–110 of 195. Imported answers require independent review unless marked reviewed.

Topic practice 195 questionsPage 11 of 20

Let

, where

is a normal random variable with mean

and variance

. The variance of

Your answerChoose one option.

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Let

be such that

. Which one of the following statements is ALWAYS correct?

Your answerChoose one option.

is invertible

Determinant of

is 0

The sum of the diagonal elements of

is 1

and

have the same rank

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Let

be a set of linearly independent vectors in

. Let the

-th element of matrix

be given by

. Which one of the following statements is correct?

Your answerChoose one option.

is invertible

0 is a singular value of

Determinant of

is 0

for some non-zero

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Consider the cumulative distribution function (CDF) of a random variable

The value of

Your answerChoose one option.

0.625

0.25

0.5

0.5625

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A random variable

is said to be distributed as

, denoted by

, if

for

. Let

, where

be independent and identically distributed random variables with

. The value of

, after approximation through Central Limit Theorem, is given by (Recall that

)

Your answerChoose one option.

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For

, the floor function is denoted by

and defined as follows

where

is an integer. Let

, where

is an exponentially distributed random variable with mean

, where

denotes natural logarithm. For any positive integer

, one can write the probability of the event

as follows

The value of

Your answerChoose one option.

0.1

0.01

0.5

0.434

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Consider the neural network shown in the figure with inputs:

weights:

output:

denotes the ReLU function,

Diagram for Data Science and Artificial Intelligence question 42

Given

which one of the following is correct?

Your answerChoose one option.

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Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is the output of the utility function.

Diagram for Data Science and Artificial Intelligence question 43

For what ranges of

and

, the right child of node

and the right child of node

will be pruned by alpha-beta pruning algorithm?

Your answerChoose one option.

and

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The state graph shows the action cost along the edges and the heuristic function h associated with each state.

Diagram for Data Science and Artificial Intelligence question 44

Suppose

algorithm is applied on this state graph using priority queue to store the frontier. In what sequence are the nodes expanded?

Your answerChoose one option.

S,A,E,C,B,D,G

S,E,A,C,B,D,G

S,A,E,B,C,D,G

S,A,B,E,C,D,G

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A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6. An event

represents the set of all outcomes where at least one of the dice shows a 1. Then,

Your answerChoose one option.

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