GATE ES area:engineering-mathematics PYQs & Answers — Page 2

Questions 11–20 of 57. Imported answers require independent review unless marked reviewed.

Assuming

; Laplace transform of

Your answerChoose one option.

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For the ordinary differential equation

, the general solution is

Your answerChoose one option.

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Consider the following two series

Choose the correct option from the following

Your answerChoose one option.

P is convergent series; Q is divergent series

P is divergent series; Q is convergent series

Both P and Q are convergent series

Both P and Q are divergent series

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Consider the following statements

(i) Environmental pollutant concentration is generally modeled using lognormal distribution. (ii) Environmental pollutant concentration is generally modeled using Poisson distribution. (iii) The weekly rate of exceedance of environmental pollutant concentration with regard to a given standard is generally modeled using lognormal distribution. (iv) The weekly rate of exceedance of environmental pollutant concentration with regards to a given standard is generally modeled using Poisson distribution.

Choose the correct option(s) from the following

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

(i) and (iv) are correct

(i) is correct and (iii) is incorrect

(ii) and (iv) are correct

(ii) and (iv) are incorrect

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is ____________ (rounded off to two decimal places).

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A residential family is considering two cities for relocation. The data related to pollutant exposure and associated health cost per year are given in the following figure.

Diagram for Environmental Science and Engineering question 47

The pollutant exposure is characterized in high, mild and low exposure categories with respective probability values. The difference in expected value of health cost of City 1 with respect to that of City 2 is ____________ lakhs/year. (rounded off to two decimal places).

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The following is a system of linear equations

The value of

is __________. (rounded off to two decimal places)

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The value of

is ________. (rounded off to two decimal places)

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A tank has inflow, outflow and stirring mechanism. Initially, the tank holds 500 L of a brine solution of concentration 200 g/L. At

, an inflow of another brine solution of concentration 100 g/L starts entering the tank at the rate of 15 L/minute. At the same time the outflow of thoroughly stirred mixture also takes place at the same rate so that the volume of brine in the tank remains constant. The brine concentration

(g/L) in the tank at any time

(minute) can be expressed by the following differential equation

The brine concentration in the tank at

hour is ________ g/L. (rounded off to two decimal places)

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The sum of the following infinite series is

Your answerChoose one option.

1/3

7/2

13/4

9/2

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GATE ES area:engineering-mathematics PYQs

Question 11

Question 12

Question 13

Question 24

Question 34

Question 47

Question 48

Question 49

Question 50

Question 4