GATE MA format:mcq PYQs & Answers — Page 14

Questions 131–140 of 366. Imported answers require independent review unless marked reviewed.

Consider the Cauchy problem

on the initial curve

. Consider the following statements:

: If

, then there exists a unique solution to the Cauchy problem in a neighborhood of

: If

, then there exist infinitely many solutions to the Cauchy problem in a neighborhood of

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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Consider the linear system

, where

and

. Suppose

, where

and

are lower triangular and upper triangular square matrices, respectively. Consider the following statements:

: If each element of the main diagonal of

is 1, then

: For any choice of the initial vector

, the Jacobi iterates

converge to the unique solution of the linear system

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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Let

and

be two linearly independent solutions of the ordinary differential equation

Let

be such that

and

for all

. Consider the following statements:

for all

Then

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

both

and

are FALSE

both

and

are TRUE

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As you grow older, an injury to your ________ may take longer to ________.

Your answerChoose one option.

heel / heel

heal / heel

heal / heal

heel / heal

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In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m.

What is the distance between P and Q (in m) when P wins the race?

Your answerChoose one option.

140

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Three bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.

If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

Your answerChoose one option.

5:00 PM

5:30 PM

6:00 PM

6:30 PM

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

Statement 1: Some bottles are cups.

Statement 2: All cups are knives.

Conclusion I: Some bottles are knives.

Conclusion II: Some knives are cups.

Conclusion III: All cups are bottles.

Conclusion IV: All knives are cups.

Which one of the following options can be logically inferred?

Your answerChoose one option.

Only conclusion I and conclusion II are correct

Only conclusion II and conclusion III are correct

Only conclusion II and conclusion IV are correct

Only conclusion III and conclusion IV are correct

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The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.

What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

Your answerChoose one option.

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Altruism is the human concern for the wellbeing of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a group. The notion that altruism may be attributed to empathy or guilt has now been rejected.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

Your answerChoose one option.

Humans engage in altruism due to guilt but not empathy

Humans engage in altruism due to empathy but not guilt

Humans engage in altruism due to group identification but not empathy

Humans engage in altruism due to empathy but not familiarity

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There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V?

Your answerChoose one option.

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GATE MA format:mcq PYQs

Question 39

Question 40

Question 41

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7