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

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Questions 31–40 of 174. Imported answers require independent review unless marked reviewed.

Topic practice 174 questionsPage 4 of 18

Pick the CORRECT solution for the following differential equation

Your answerChoose one option.

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Consider the function given below and pick one or more CORRECT state(s) from the following choices.

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

f(x) has a local minimum at x = 3.

f(x) has a local maximum at x = 3.

f(x) has a local minimum at x = 2.

f(x) has a local maximum at x = 2.

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Pick the CORRECT eigen value(s) of the matrix [A] from the following choices.

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

-2

-10

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Let

be the solution of the initial value problem

, where

and

. Then,

is equal to ____________________ (rounded off to 1 decimal place).

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The maximum value of the function

in the interval [-1,5] is equal to ____________________ (rounded off to 1 decimal place).

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Consider the differential equation given below. Using the Euler method with the step size (

) of 0.5, the value of

is equal to __________ (rounded off to 1 decimal place).

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Consider a discrete random variable

whose probabilities are given below. The standard deviation of the random variable is _____ (round off to one decimal place).

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A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80). The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the speed limit is __________ (rounded off to 1 decimal place).

Note: X is a uniform random variable on the interval (α, β), if its probability density function is given by

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The smallest positive root of the equation

lies in the range

Your answerChoose one option.

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The second-order differential equation in an unknown function

is defined as

Assuming

, and

, the general solution of the above differential equation is

Your answerChoose one option.

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GATE CE area:engineering-mathematics PYQs

Question 36

Question 44

Question 45

Question 47

Question 48

Question 49

Question 51

Question 63

Question 11

Question 12