1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}$$ is
A
$$\infty $$
B
$${1 \over 8}$$
C
0
D
$${1 \over 32}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
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 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
In an experiment with 15 observations on $$x$$, then following results were available:
$$\sum {{x^2}} = 2830$$, $$\sum x = 170$$
One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is :
A
188.66
B
177.33
C
8.33
D
78.00
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set :
A
is increased by 2
B
is decreased by 2
C
is two times the original median
D
remains the same as that of the original set
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