1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If $$\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)$$ and $$\overrightarrow b = {1 \over 7}\left( {2\widehat i + 3\widehat j - 6\widehat k} \right),$$ then the value

of $$\left( {2\overrightarrow a - \overrightarrow b } \right)\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a + 2\overrightarrow b } \right)} \right]$$ is :
A
$$-3$$
B
$$5$$
C
$$3$$
D
$$-5$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The domain of the function f(x) = $${1 \over {\sqrt {\left| x \right| - x} }}$$ is
A
$$\left( {0,\infty } \right)$$
B
$$\left( { - \infty ,0} \right)$$
C
$$\left( { - \infty ,\infty } \right) - \left\{ 0 \right\}$$
D
$$\left( { - \infty ,\infty } \right)$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to 2} \left( {{{\sqrt {1 - \cos \left\{ {2(x - 2)} \right\}} } \over {x - 2}}} \right)$$
A
Equals $$\sqrt 2 $$
B
Equals $$-\sqrt 2 $$
C
Equals $${1 \over {\sqrt 2 }}$$
D
does not exist
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The value of $$p$$ and $$q$$ for which the function

$$f\left( x \right) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{3/2}}}}} & {,x > 0} \cr } } \right.$$

is continuous for all $$x$$ in R, are
A
$$p =$$ $${5 \over 2}$$, $$q = $$ $${1 \over 2}$$
B
$$p =$$ $$-{3 \over 2}$$, $$q = $$ $${1 \over 2}$$
C
$$p =$$ $${1 \over 2}$$, $$q = $$ $${3 \over 2}$$
D
$$p =$$ $${1 \over 2}$$, $$q = $$ $$-{3 \over 2}$$
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