1
AIEEE 2007
+4
-1
Let $$f:R \to R$$ be a function defined by

$$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$, then which of the following is true?
A
$$f(x)$$ is differentiale everywhere
B
$$f(x)$$ is not differentiable at x = 0
C
$$f(x) > 1$$ for all $$x \in R$$
D
$$f(x)$$ is not differentiable at x = 1
2
AIEEE 2007
+4
-1
The function $$f:R/\left\{ 0 \right\} \to R$$ given by

$$f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}}$$

can be made continuous at $$x$$ = 0 by defining $$f$$(0) as
A
0
B
1
C
2
D
$$-1$$
3
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
4
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
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