1
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.$$

Then which one of the following is true?
A
$$f$$ is neither differentiable at x = 0 nor at x = 1
B
$$f$$ is differentiable at x = 0 and at x = 1
C
$$f$$ is differentiable at x = 0 but not at x = 1
D
$$f$$ is differentiable at x = 1 but not at x = 0
2
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where
Y = { y $$ \in $$ N, y = 4x + 3 for some x $$ \in $$ N }.
Show that f is invertible and its inverse is
A
$$g\left( y \right) = {{3y + 4} \over 4}$$
B
$$g\left( y \right) = 4 + {{y + 3} \over 4}$$
C
$$g\left( y \right) = {{y + 3} \over 4}$$
D
$$g\left( y \right) = {{y - 3} \over 4}$$
3
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
It is given that the events $$A$$ and $$B$$ are such that
$$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$$ and $$P\left( {B|A} \right) = {2 \over 3}.$$ Then $$P(B)$$ is :
A
$${1 \over 6}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${1 \over 2}$$
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the number obtained is less than $$5.$$ Then $$P\left( {A \cup B} \right)$$ is :
A
$${3 \over 5}$$
B
$$0$$
C
$$1$$
D
$${2 \over 5}$$
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