GATE ME 2015 Set 3 | GATE ME Year Wise Previous Years Questions

GATE ME 2015 Set 3

Numerical

-0

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 & 2 \cr 1 & 3 \cr } } \right]$$ is ______.

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GATE ME 2015 Set 3

MCQ (Single Correct Answer)

-0.6

For a given matrix $$P = \left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right],$$ where $$i = \sqrt { - 1} ,$$ the inverse of matrix $$P$$ is

$${1 \over {24}}\left[ {\matrix{ {4 - 3i} & i \cr { - i} & {4 + 3i} \cr } } \right]$$

$${1 \over {25}}\left[ {\matrix{ i & {4 - 3i} \cr {4 + 3i} & i \cr } } \right]$$

$${1 \over {24}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$

$${1 \over {25}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$

GATE ME 2015 Set 3

Numerical

-0

The value of $$\mathop {Lim}\limits_{x \to 0} \left( {{{ - \sin x} \over {2\sin x + x\cos x}}} \right)\,\,\,$$ is __________.

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GATE ME 2015 Set 3

MCQ (Single Correct Answer)

-0.3

Let $$\phi $$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V $$ be an arbitrary smooth vector valued function in a three dimensional space. Which one of the following is an identity?

$$Curl\left( {\phi \overrightarrow V } \right) = \nabla \left( {\phi Div\overrightarrow V } \right)$$

$${Div\overrightarrow V = 0}$$

$${Div\,\,Curl\,\,\overrightarrow V = 0}$$

$$Div\,\,\left( {\phi \overrightarrow V } \right) = \phi Div\overrightarrow V $$

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2020