GATE DA topic:computing PYQs & Answers — Page 12

Questions 111–120 of 195. Imported answers require independent review unless marked reviewed.

Consider a fact table in an OLAP application: Facts (D1, D2, val), where D1 and D2 are its dimension attributes and val is a dependent attribute. Suppose attribute D1 takes 3 values and D2 takes 2 values, and all combinations of these values are present in the table Facts. How many tuples are there in the result of the following query?

SELECT D1, D2, sum(val)

FROM Facts

GROUP BY CUBE (D1, D2);

Your answerChoose one option.

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Consider the following Python code snippet.

A={"this","that"}

B={"that","other"}

C={"other","this"}

while "other" in C:

if "this" in A:

A,B,C=A-B,B-C,C-A

if "that" in B:

A,B,C=C|A,A|B,B|C

When the above program is executed, at the end, which of the following sets contains "this"?

Your answerChoose one option.

Only A

Only B

Only C

A, C

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Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as

, where

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

ReLU is continuous everywhere

ReLU is differentiable everywhere

ReLU is not differentiable at

, for all

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Consider the function

. Which of the following statements is/are correct?

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

The maximum value of

is attained at

The minimum value of

is attained at

The maximum value of

The minimum value of the derivative of

is attained at

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Let

be a system of orthonormal vectors in

. Consider the matrix

. Which of the following statements is/are correct?

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

Singular values of

are also its eigenvalues

Singular values of

are either 0 or 1

Determinant of

is 1

is invertible

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Let

be a twice-differentiable function and suppose its second derivative satisfies

for all

. Which of the following statements is/are ALWAYS correct?

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

has a local minima

There does not exist

and

, such that

has at most one global minimum

has at most one local minimum

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matrix

with real entries satisfies the property:

, for all

, where

denotes the Euclidean norm. Which of the following statements is/are ALWAYS correct?

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

must be orthogonal

, where

denotes the identity matrix, is the only solution

The eigenvalues of

are either

has full rank

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Consider designing a linear binary classifier

on the following training data:

Class-1:

, Class-2:

Hard-margin support vector machine (SVM) formulation is solved to obtain

and

. Which of the following options is/are correct?

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

and

The number of support vectors is 3

The margin is

Training accuracy is 98%

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Consider a coin-toss experiment where the probability of head showing up is

. In the

coin toss, let

if head appears, and

if tail appears. Consider

where

is the total number of independent coin tosses. Which of the following statements is/are correct?

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

increases, variance of

decreases

Variance of

does not depend on

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Consider a two-class problem in

with class labels

and

. Let

and

be the means of the two classes. Given test sample

, a classifier calculates the squared Euclidean distance (denoted by

) between

and the means of the two classes and assigns the class label that the sample

is closest to. That is, the classifier computes

and assigns the label

, and

otherwise. Which of the following statements is/are correct?

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

The sample

is assigned the label

is a linear function of

, where

and

are functions of

and

is a quadratic polynomial in

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GATE DA topic:computing PYQs

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