1

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
2

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$${\log _e}x > x$$
3

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$$1$$
4

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
Let $$f\left( x \right) = \int {{e^x}\left( {x - 1} \right)\left( {x - 2} \right)dx.} $$ Then $$f$$ decreases in the interval
A
$$\left( { - \infty ,2} \right)$$
B
$$\left( { - 2, - 1} \right)$$
C
$$\left( {1,2} \right)$$
D
$$\left( {2, + \infty } \right)$$

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