GATE PI area:engineering-mathematics PYQs & Answers — Page 5

Questions 41–50 of 87. Imported answers require independent review unless marked reviewed.

Topic practice 87 questionsPage 5 of 9

An operator manufactures 10 identical spur gears in a lot. One spur gear is defective in the lot. Three spur gears are drawn at random without replacement. The probability of getting all three gears as non-defective is____________. [round off to two decimal places]

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If a matrix is squared, then

Your answerChoose one option.

both eigenvalues and eigenvectors must change

both eigenvalues and eigenvectors are retained

eigenvalues get squared but eigenvectors are retained

eigenvalues are retained but eigenvectors change

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Consider the following ordinary differential equation:

Given that

and

are constants, the general solution of the differential equation is

Your answerChoose one option.

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A market survey with a sample size of 1000 was conducted for a parameter that follows normal distribution. The confidence interval was estimated as [500, 700] with a mean of 600. It is now desired to reduce the confidence interval to [550, 650]. The sample size for achieving the desired interval at the same confidence level is

Your answerChoose one option.

1000

4000

9000

16000

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The value of

is ____________. [round off to one decimal place]

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with

being real and

, then

____________. [correct up to one decimal place]

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The minimum value of function

defined by

is ____________. [in integer]

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The eigenvalues of matrix

are 5 and 10. For matrix

, where

is a constant and

is a 2×2 identity matrix, its eigenvalues are

Your answerChoose one option.

5, 10

5 + α, 10 + α

5 - α, 10 - α

5α, 10α

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The probability mass function

of a discrete random variable X is given by

, where x = 1, 2, ···, ∞. The expected value of X is _________. [in integer]

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The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _________. [round off to 3 decimal places]

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GATE PI area:engineering-mathematics PYQs

Question 25

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Question 37

Question 38

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Question 24

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Question 37

Question 38