1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then the value of $$a$$ and $$b$$, are
A
$$a$$ = 1 and $$b$$ = 2
B
$$a$$ = 1 and $$b$$ $$\in R$$
C
$$a$$ $$\in R$$ and $$b$$ = 2
D
$$a$$ $$\in R$$ and $$b$$ $$\in R$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}$$ = k, the value of k is
A
$$- {2 \over 3}$$
B
0
C
$$- {1 \over 3}$$
D
$${2 \over 3}$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Let $$f(a) = g(a) = k$$ and their nth derivatives
$${f^n}(a)$$, $${g^n}(a)$$ exist and are not equal for some n. Further if

$$\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4$$

then the value of k is
A
0
B
4
C
2
D
1
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}$$ is
A
$$\infty$$
B
$${1 \over 8}$$
C
0
D
$${1 \over 32}$$
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