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

A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student calculates the mean of $$X$$ as $$3.5$$ and her teacher calculates the variance to $$X$$ as $$1.5.$$ Which of the following statements is true? GATE ECE 2009 Engineering Mathematics - Probability and Statistics Question 32 English

GATE ECE 2009 Engineering Mathematics - Probability and Statistics Question 32 English

Both the student and the teacher are right

Both the student and the teacher are wrong

The student is wrong but the teacher is right

The student is right but the teacher is wrong

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