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1

### IIT-JEE 2001 Screening

If $$f\left( x \right) = x{e^{x\left( {1 - x} \right)}},$$ then $$f(x)$$ is
A
increasing on $$\left[ { - 1/2,1} \right]$$
B
decreasing on $$R$$
C
increasing on $$R$$
D
decreasing on $$\left[ { - 1/2,1} \right]$$
2

### IIT-JEE 2000 Screening

Let $$f\left( x \right) = \left\{ {\matrix{ {\left| x \right|,} & {for} & {0 < \left| x \right| \le 2} \cr {1,} & {for} & {x = 0} \cr } } \right.$$ then at $$x=0$$, $$f$$ has
A
a local maximum
B
no local maximum
C
a local minimum
D
no extremum
3

### IIT-JEE 2000 Screening

For all $$x \in \left( {0,1} \right)$$
A
$${e^x} < 1 + x$$
B
$${\log _e}\left( {1 + x} \right) < x$$
C
$$\sin x > x$$
D
$${\log _e}x > x$$
4

### IIT-JEE 2000 Screening

If the normal to the curve $$y = f\left( x \right)$$ and the point $$(3, 4)$$ makes an angle $${{{3\pi } \over 4}}$$ with the positive $$x$$-axis, then $$f'\left( 3 \right) =$$
A
$$-1$$
B
$$- {3 \over 4}$$
C
$${4 \over 3}$$
D
$$1$$

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Class 12