1
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
Let $$f\left( x \right) = \left\{ {\matrix{ {{e^x},} & {0 \le x \le 1} \cr {2 - {e^{x - 1}},} & {1 < x \le 2} \cr {x - e,} & {2 < x \le 3} \cr } } \right.$$ and $$g\left( x \right) = \int\limits_0^x {f\left( t \right)dt,x \in \left[ {1,3} \right]}$$
then $$g(x)$$ has
A
local maxima at $$x=1+In$$ $$2$$ and local minima at $$x=e$$
B
local maxima at $$x=1$$ and local minima at $$x=2$$
C
no local maxima
D
no local minima
2
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
The function $$f\left( x \right) = \int\limits_{ - 1}^x {t\left( {{e^t} - 1} \right)\left( {t - 1} \right){{\left( {t - 2} \right)}^3}\,\,\,{{\left( {t - 3} \right)}^5}}$$ $$dt$$ has a local minimum at $$x=$$
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
3
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
Let $$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right)^2} + {\left( {f\left( x \right)} \right)^3}$$ for every real number $$x$$. Then
A
$$h$$ is increasing whenever $$f$$ is increasing
B
$$h$$ is increasing whenever $$f$$ is decreasing
C
$$h$$ is decreasing whenever $$f$$ is decreasing
D
nothing can be said in general.
4
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
If $$f\left( x \right) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr {37 - x} & {2 < x \le 3} \cr } } \right.$$ then:
A
$$f(x)$$ is increasing on $$\left[ { - 1,2} \right]$$
B
$$f(x)$$ is continues on $$\left[ { - 1,3} \right]$$
C
$$f'(2)$$ does not exist
D
$$f(x)$$ has the maximum value at $$x=2$$
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