1
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
$$p =$$ $${1 \over 2}$$, $$q = $$ $$-{3 \over 2}$$
2
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
3
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
$$\left( { - \infty ,\infty } \right)$$
4
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
$$\beta \, \in (0,1)$$
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