GATE EE area:engineering-mathematics PYQs & Answers — Page 4

Questions 31–40 of 97. Imported answers require independent review unless marked reviewed.

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation

. The

is estimated by randomly drawing out 10,000 numbers of samples (

). The estimates

are computed in the following two ways.

Which of the following statements is true?

Your answerChoose one option.

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In the following differential equation, the numerically obtained value of y(t), at t = 1, is __________ (Round off to 2 decimal places).

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Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is __________ (Round off to 2 decimal places).

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Consider the following equation in a 2-D real-space.

for

Which of the following statement(s) is/are true.

Your answerSelect all correct options. You can choose more than one.

When p = 2, the area enclosed by the curve is

When p tends to

, the area enclosed by the curve tends to 4.

When p tends to 0, the area enclosed by the curve is 1.

When p = 1, the area enclosed by the curve is 2.

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The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is __________ (Round off to 3 decimal places).

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The closed curve shown in the figure is described by

The magnitude of the line integral of the vector field

around the closed curve is ________ (Round off to 2 decimal places).

Diagram for Electrical Engineering question 62

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A quadratic function of two variables is given as

The magnitude of the maximum rate of change of the function at the point (1,1) is ________ (Round off to the nearest integer).

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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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Consider a 3 x 3 matrix

whose

-th element,

. Then the matrix

will be

Your answerChoose one option.

symmetric.

skew-symmetric.

unitary.

null.

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denotes the exponential of a square matrix

. Suppose

is an eigenvalue and

is the corresponding eigen-vector of matrix

. Consider the following two statements: Statement 1:

is an eigenvalue of

. Statement 2:

is an eigen-vector of

. Which one of the following options is correct?

Your answerChoose one option.

Statement 1 is true and statement 2 is false.

Statement 1 is false and statement 2 is true.

Both the statements are correct.

Both the statements are false.

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GATE EE area:engineering-mathematics PYQs

Question 25

Question 34

Question 35

Question 42

Question 45

Question 62

Question 65

Question 7

Question 20

Question 40