GATE ME area:engineering-mathematics PYQs & Answers — Page 3

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Questions 21–30 of 148. Imported answers require independent review unless marked reviewed.

Topic practice 148 questionsPage 3 of 15

Take two long dice (rectangular parallelepiped), each having four rectangular faces labeled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the die is the score of the throw.

If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?

Your answerChoose one option.

3/8

1/8

1/16

3/16

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In order to numerically solve the ordinary differential equation

for

, with an initial condition

, the following scheme is employed

Here,

is the time step and

for

This numerical scheme will yield a solution with non-physical oscillations for

. The value of

Your answerChoose one option.

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The value of the surface integral

where

is the external surface of the sphere

Your answerChoose one option.

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Let

be an analytic function, where

. If the real part of

, and the imaginary part of

is zero for

, then

Your answerChoose one option.

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Consider the system of linear equations

The values of

and

such that there exists a non-trivial null space and the system admits infinite solutions are

Your answerChoose one option.

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Let

be a twice differentiable function from

. If

where

is sufficiently small (here

is the Euclidean norm or distance function), then

where

is a point on the line segment joining

and

. If

is a strict local minimum of

, then which one of the following statements is TRUE?

Your answerChoose one option.

and

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The matrix

(where

) has a negative eigenvalue if

is greater than

Your answerChoose one option.

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If the value of the double integral

, then

is ______ (answer in integer).

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satisfies the differential equation

subject to the condition

, then the value of

is ______ (rounded off to 2 decimal places).

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Let

be a continuous random variable defined on

such that its probability density function

for

and 0 otherwise. Let

. Then the expected value of

is _____. (rounded off to 2 decimal places)

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GATE ME area:engineering-mathematics PYQs

Question 5

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Question 43

Question 44