GATE ECE area:engineering-mathematics PYQs & Answers — Page 8

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Questions 71–80 of 100. Imported answers require independent review unless marked reviewed.

Topic practice 100 questionsPage 8 of 10

Consider the homogeneous ordinary differential equation

, with

as a general solution. Given that

and

, the value of

, rounded off to two decimal places, is ______.

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A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. (i) 85% of cabs in the city are green and the remaining cabs are blue. (ii) A witness identified the cab involved in the accident as blue. (iii) It is known that a witness can correctly identify the cab colour only 80% of the time.

Which of the following options is closest to the probability that the accident was caused by a blue cab?

Your answerChoose one option.

12%

15%

41%

80%

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Consider p(s) = s³ + a₂s² + a₁s + a₀ with all real coefficients. It is known that its derivative p′(s) has no real roots. The number of real roots of p(s) is

Your answerChoose one option.

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Let M be a real

matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?

Your answerChoose one option.

S1 implies S2

S1 implies S3

S2 implies S1

S3 implies S2

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Let

, where a and b are constants. If

and

, then the relation between a and b is

Your answerChoose one option.

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Consider matrix

and vector

. The number of distinct real values of

for which the equation

has infinite many solutions is ______.

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Let

and

be independent normal random variables with zero mean and unit variance. The probability that

is the smallest among the four is ______.

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Taylor series expansion of

around

has the form

The coefficient

(correct to two decimal places) is equal to ______.

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A curve passes through the point (x = 1, y = 0) and satisfies the differential equation

The equation that describes the curve is

Your answerChoose one option.

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The position of a particle

is described by the differential equation:

The initial conditions are

and

. The position (accurate to two decimal places) of the particle at

is ______.

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GATE ECE area:engineering-mathematics PYQs

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