GATE ECE 2009 | GATE ECE Year Wise Previous Years Questions

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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?

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

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

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

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

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4$$ and $$1/4$$ respectively. What is the conditional probability $$P(X+Y=2/X-Y=0)?$$

$$0$$

$$1/16$$

$$1/6$$

$$1$$

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