GATE XE branch:xe PYQs & Answers — Page 74

Questions 731–740 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 74 of 178

Given below are two statements and four conclusions drawn based on the statements.

Statement 1: Some soaps are clean.

Statement 2: All clean objects are wet.

Conclusion I: Some clean objects are soaps.

Conclusion II: No clean object is a soap.

Conclusion III: Some wet objects are soaps.

Conclusion IV: All wet objects are soaps.

Which one of the following options can be logically inferred?

Your answerChoose one option.

Only conclusion I is correct

Either conclusion I or conclusion II is correct

Either conclusion III or conclusion IV is correct

Only conclusion I and conclusion III are correct

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An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.

The ant first turns

anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.

moves forward for 10 cm.

turns

clockwise.

The pattern made by the trace left behind by the ant is

Your answerChoose one option.

Diagram for Engineering Sciences question 10

Diagram for Engineering Sciences question 10 (figure 2)

Diagram for Engineering Sciences question 10 (figure 3)

Diagram for Engineering Sciences question 10 (figure 4)

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The value of

Your answerChoose one option.

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Let

be the set of complex numbers. Let the function

for

be analytic in

, where

denotes the derivative of

, then

Your answerChoose one option.

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If the partial differential equation

is parabolic on the circle

, then the values of

and

are given by

Your answerChoose one option.

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Let

be the positively oriented circle

in the

-plane. If

where

is a real constant, then

is equal to ______.

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Let

and

be two linearly independent solutions of

Let

denote the Wronskian of

and

. If

then

is equal to ______.

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Let

. Then the sum of the geometric multiplicities of the distinct eigenvalues of

is equal to ______.

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In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of female and 30% of male in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).

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Let

be the continuous function such that

for all

, where

for all

. Then

is equal to

Your answerChoose one option.

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GATE XE branch:xe PYQs

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18