1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}$$ is
A
$$\infty $$
B
$${1 \over 8}$$
C
0
D
$${1 \over 32}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$f(x) = \left\{ {\matrix{ {x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0} \cr 0 & {,x = 0} \cr } } \right.$$

then $$f(x)$$ is
A
discontinuous everywhere
B
continuous as well as differentiable for all x
C
continuous for all x but not differentiable at x = 0
D
neither differentiable nor continuous at x = 0
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}$$ is
A
$$1$$
B
$$-1$$
C
zero
D
does not exist
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$
A
$${e^4}$$
B
$${e^2}$$
C
$${e^3}$$
D
$$1$$
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