1
AIEEE 2005
+4
-1
$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]$$
equals
A
$${1 \over 2}\sec 1$$
B
$${1 \over 2}$$cosec 1
C
tan 1
D
$${1 \over 2}$$tan 1
2
AIEEE 2005
+4
-1
Suppose $$f(x)$$ is differentiable at x = 1 and

$$\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) = 5$$, then $$f'\left( 1 \right)$$ equals
A
3
B
4
C
5
D
6
3
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
$${{{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
4
AIEEE 2005
+4
-1
Let f be differentiable for all x. If f(1) = -2 and f'(x) $$\ge$$ 2 for
x $$\in \left[ {1,6} \right]$$, then
A
f(6) $$\ge$$ 8
B
f(6) < 8
C
f(6) < 5
D
f(6) = 5
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