1
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
$$\left( { - \infty ,\infty } \right)$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots on the line Re z = 1, then it is necessary that :
A
$$\beta \, \in ( - 1,0)$$
B
$$\left| {\beta \,} \right| = 1$$
C
$$\beta \, \in (1,\infty )$$
D
$$\beta \, \in (0,1)$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $$ Then $$f$$ has
A
local minimum at $$\pi $$ and $$2\pi $$
B
local minimum at $$\pi $$ and local maximum at $$2\pi $$
C
local maximum at $$\pi $$ and local minimum at $$2\pi $$
D
local maximum at $$\pi $$ and $$2\pi $$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\overrightarrow d $$ are two vectors satisfying $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d $$ and $$\overrightarrow a .\overrightarrow d = 0\,\,.$$ Then the vector $$\overrightarrow d $$ is equal to :
A
$$\overrightarrow c + \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
B
$$\overrightarrow b + \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
C
$$\overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
D
$$\overrightarrow b - \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
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