1
AIEEE 2002
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}$$, $$n \in N$$, ( [x] denotes the greatest integer less than or equal to x )
A
has value $$-1$$
B
has value $$0$$
C
has value $$1$$
D
does not exist
2
AIEEE 2002
+4
-1
If $$f\left( 1 \right) = 1,{f^1}\left( 1 \right) = 2,$$ then
$$\mathop {\lim }\limits_{x \to 1} {{\sqrt {f\left( x \right)} - 1} \over {\sqrt x - 1}}$$ is
A
$$2$$
B
$$4$$
C
$$1$$
D
$${1 \over 2}$$
3
AIEEE 2002
+4
-1
$$f$$ is defined in $$\left[ { - 5,5} \right]$$ as

$$f\left( x \right) = x$$ if $$x$$ is rational

$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$= - x$$ if $$x$$ is irrational. Then
A
$$f(x)$$ is continuous at every x, except $$x = 0$$
B
$$f(x)$$ is discontinuous at every $$x,$$ except $$x = 0$$
C
$$f(x)$$ is continuous everywhere
D
$$f(x)$$ is discontinuous everywhere
4
AIEEE 2002
+4
-1
f(x) and g(x) are two differentiable functions on [0, 2] such that

f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3, g(2) = 9

then f(x) - g(x) at x = $${3 \over 2}$$ is
A
0
B
2
C
10
D
5
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