1
GATE ECE 2009
+2
-0.6
The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi$$ is given by
A
$$1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
B
$$- 1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
C
$$1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
D
$$- 1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
2
GATE ECE 2009
+2
-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 $$C.$$

A
$$\oint\limits_C {\overrightarrow V .\,\overrightarrow {dl} } = \int {\int_{{S_C}} {\overrightarrow A .\,\overrightarrow {ds} } }$$
B
$$\oint\limits_C {\overrightarrow A .\,\overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\overrightarrow \nabla .\,\overrightarrow {ds} } }$$
C
$$\oint\limits_C {\nabla \times \vec V.{\mkern 1mu} \overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {ds} } }$$
D
$$\oint\limits_C {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {dl} } = \int {\int_{{S_C}} {\vec V.{\mkern 1mu} \overrightarrow {ds} } }$$
3
GATE ECE 2009
+1
-0.3
A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?
A
$${\left( {{1 \over 2}} \right)^2}$$
B
$$10{c_2}\,{\left( {{1 \over 2}} \right)^2}$$
C
$${\left( {{1 \over 2}} \right)^{10}}$$
D
$$\,10{c_2}\,{\left( {{1 \over 2}} \right)^{10}}$$
4
GATE ECE 2009
+2
-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?
A
Both the student and the teacher are right
B
Both the student and the teacher are wrong
C
The student is wrong but the teacher is right
D
The student is right but the teacher is wrong
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