1
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
$$\left( {2, + \infty } \right)$$
2
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
MCQ (Single Correct Answer)
+2
-0.5
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 1999
MCQ (Single Correct Answer)
+2
-0.5
The function $$f(x)=$$ $${\sin ^4}x + {\cos ^4}x$$ increases if
A
$$0 < x < \pi /8$$
B
$$\pi /4 < x < 3\pi /8$$
C
$$3\pi /8 < x < 5\pi /8$$
D
$$5\pi /8 < x < 3\pi /4$$
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