GATE EE 2017 Set 1 | GATE EE Year Wise Previous Years Questions

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

A function $$f(x)$$ is defined as
$$f\left( x \right) = \left\{ {\matrix{ {{e^x},x < 1} \cr {\ln x + a{x^2} + bx,x \ge 1} \cr } \,\,,\,\,} \right.$$ where $$x \in R.$$

Which one of the following statements is TRUE?

$$f(x)$$ is NOT differentiable at $$x=1$$ for any values of $$a$$ and $$b.$$

$$f(x)$$ is differentiable at $$x=1$$ for the unique values of $$a$$ and $$b.$$

$$f(x)$$ is differentiable at $$x=1$$ for all values of $$a$$ and $$b$$ such that $$a+b=c.$$

$$f(x)$$ is differentiable at $$x=1$$ for all values of $$a$$ and $$b.$$

GATE EE 2017 Set 1

Numerical

-0

Let $${\rm I} = c\int {\int {_Rx{y^2}dxdy,\,\,} } $$ where $$R$$ is the region shown in the figure and $$c = 6 \times {10^{ - 4}}.\,\,$$ The value of $${\rm I}$$ equals ___________. GATE EE 2017 Set 1 Engineering Mathematics - Calculus Question 7 English

Your input ____

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ with $$y\left( 1 \right) = 2\pi .$$ There exists a unique solution for this differential equation when $$t$$ belongs to the interval

$$(-2, 2)$$

$$(-10, 10)$$

$$(-10, 2)$$

$$(0, 10)$$

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-0.3

For the power semiconductor devices $$IGBT, MOSFET,$$ Diode and Thyristor, which one of the following statements is TRUE?

All of the four are majority carrier devices.

All the four are minority carrier devices

$$IGBT$$ and $$MOSFET$$ are majority carrier devices, whereas Diode and Thyristor are minority carrier devices.

$$MOSFET$$ is majority carrier device, whereas $$IGBT,$$ Diode, Thyristor are minority carrier devices.

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