1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}$$ is
A
$$1$$
B
$$-1$$
C
zero
D
does not exist
2
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
$$3$$
3
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
$$1$$
4
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
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