GATE MA branch:ma PYQs & Answers — Page 34

Questions 331–340 of 650. Imported answers require independent review unless marked reviewed.

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bring the short edges of the sheet together. Sheet N is cut into equal square pieces and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is ______.

Your answerChoose one option.

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Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost (Profit % =

). The discount on item Q, as a percentage of its marked price, is ______.

Items	Cost (₹)	Profit %	Marked Price (₹)
P	5,400	---	5,860
Q	---	25	10,000

Your answerChoose one option.

12.5

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There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is ______.

Your answerChoose one option.

0.3024

0.4235

0.6976

0.8125

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Given below are two statements 1 and 2, and two conclusions I and II. Statement 1: All bacteria are microorganisms. Statement 2: All pathogens are microorganisms. Conclusion I: Some pathogens are bacteria. Conclusion II: All pathogens are not bacteria. Based on the above statements and conclusions, which one of the following options is logically CORRECT?

Your answerChoose one option.

Only conclusion I is correct

Only conclusion II is correct

Either conclusion I or II is correct.

Neither conclusion I nor II is correct.

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Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the passage?

Your answerChoose one option.

The proposed AOM addresses the core problems that cause obesity.

If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

AOM are addressing the core problems and are likely to succeed.

AOM are addressing the problem superficially.

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Let

be a

matrix and

be a

matrix with real entries such that

is non-singular. Consider the following statements:

P: Nullity of

is 0.

is a non-singular matrix.

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

for

, where

and

are real numbers, be a non-constant analytic function on the complex plane

. Let

and

denote the first order partial derivatives of

and

with respect to real variables

and

, respectively. Consider the following two functions defined on

Then

Your answerChoose one option.

both

and

are analytic in

is analytic in

and

is NOT analytic in

and

is analytic in

neither

nor

is analytic in

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Let

, be the Möbius transformation which maps the points

in the

-plane onto the points

in the

-plane, respectively. Then the image of the set

under the map

Your answerChoose one option.

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Let

be the row reduced echelon form of a

real matrix

and let the third column of

. Consider the following statements:

P: If

is a solution of

, then

Q: For all

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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The eigenvalues of the boundary value problem

are given by

Your answerChoose one option.

, where

are the roots of

, where

are the roots of

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GATE MA branch:ma PYQs

Question 6

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Question 9

Question 10

Question 1

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Question 5