GATE EE 2015 Set 2 | GATE EE Year Wise Previous Years Questions

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements is TRUE?

If $$f(z)$$ is differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$

If $$g(z)$$ & $$h(z)$$ are differentiable at $${z_0},$$ then $$f(z)$$ is also differentiable at $${z_0}.$$

If $$f(z)$$ is continuous at $${z_0},$$ then it is differentiable at $${z_0}.$$

If $$f(z)$$ is differentiable at $${z_0},$$ then so are its real and imaginary parts.

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi } $$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The Laplace transform of $$g\left( t \right) = \sqrt {1/\pi t} $$ is

$$3{s^{ - 5/2}}/2$$

$${s^{ - 1/2}}$$

$${s^{1/2}}$$

$${s^{3/2}}$$

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

We have a set of $$3$$ linear equations in $$3$$ unknown. $$'X \equiv Y'$$ means $$X$$ and $$Y$$ are equivalent statements and $$'X \ne Y'$$ means $$X$$ and $$y$$ are not equivalent statements.

$$P:$$ There is a unique solution.
$$Q:$$ The equations are linearly independent .
$$R:$$ All eigen values of the coefficient matrix are non zero .
$$S:$$ The determinant of the coefficient matrix is non-zero .

Which one of the following is TRUE?

$$P \equiv Q \equiv R \equiv S$$

$$P \equiv R \ne Q \equiv S$$

$$P \equiv Q \ne R \equiv S$$

$$P \ne Q \ne R \ne S$$

GATE EE 2015 Set 2

Numerical

-0

The volume enclosed by the surface $$f\left( {x,y} \right) = {e^x}$$ over the triangle bounded by the lines $$x=y;$$ $$x=0;$$ $$y=1$$ in the $$xy$$ plane is ________.

Your input ____

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