1
AIEEE 2005
+4
-1
Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then

$$\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}$$ is equal to
A
$${{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
B
0
C
$$- {{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
D
$${{{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
2
AIEEE 2005
+4
-1
If $$f$$ is a real valued differentiable function satisfying

$$\left| {f\left( x \right) - f\left( y \right)} \right|$$ $$\le {\left( {x - y} \right)^2}$$, $$x, y$$ $$\in R$$
and $$f(0)$$ = 0, then $$f(1)$$ equals
A
-1
B
0
C
2
D
1
3
AIEEE 2004
+4
-1
Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

If $$f(x)$$ is continuous in $$\left[ {0,{\pi \over 2}} \right]$$, then $$f\left( {{\pi \over 4}} \right)$$ is
A
$$-1$$
B
$${1 \over 2}$$
C
$$-{1 \over 2}$$
D
$$1$$
4
AIEEE 2004
+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 $$b$$ $$\in R$$
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