GATE ECE 2009 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are

$$3, 3 + 5j, 6 - j$$

$$-6 + 5j, 3 + j, 3 - j$$

$$3+j, 3-j, 5+j$$

$$3, -1+3j, -1-3j$$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

$$1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - - $$

$$ - 1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - - $$

$$1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - - $$

$$ - 1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - - $$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

If a vector field$$\overrightarrow V $$ is related to another field $$\overrightarrow A $$ through $$\,\overrightarrow V = \nabla \times \overrightarrow A ,$$ which of the following is true?

Note: $$C$$ and $${S_C}$$ refer to any closed contour and any surface whose boundary is $$C.$$

$$\oint\limits_C {\overrightarrow V .\,\overrightarrow {dl} } = \int {\int_{{S_C}} {\overrightarrow A .\,\overrightarrow {ds} } } $$

$$\oint\limits_C {\overrightarrow A .\,\overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\overrightarrow \nabla .\,\overrightarrow {ds} } } $$

$$\oint\limits_C {\nabla \times \vec V.{\mkern 1mu} \overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {ds} } } $$

$$\oint\limits_C {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {dl} } = \int {\int_{{S_C}} {\vec V.{\mkern 1mu} \overrightarrow {ds} } } $$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?

$${\left( {{1 \over 2}} \right)^2}$$

$$10{c_2}\,{\left( {{1 \over 2}} \right)^2}$$

$${\left( {{1 \over 2}} \right)^{10}}$$

$$\,10{c_2}\,{\left( {{1 \over 2}} \right)^{10}}$$

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