1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Let $$f(2) = 4$$ and $$f'(x) = 4.$$

Then $$\mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \over {x - 2}}$$ is given by
A
$$2$$
B
$$- 2$$
C
$$- 4$$
D
$$3$$
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$
A
$${e^4}$$
B
$${e^2}$$
C
$${e^3}$$
D
$$1$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+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
4
AIEEE 2002
MCQ (Single Correct Answer)
+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
$${1 \over 2}$$
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