1

### IIT-JEE 2006

MCQ (More than One Correct Answer)
$$f(x)$$ is cubic polynomial with $$f(2)=18$$ and $$f(1)=-1$$. Also $$f(x)$$ has local maxima at $$x=-1$$ and $$f'(x)$$ has local minima at $$x=0$$, then
A
the distance between $$(-1,2)$$ and (a$$f(a)$$) where $$x=a$$ is the point of local minima is $$2\sqrt 5$$
B
$$f(x)$$ is increasing for $$x \in \left[ {1,2\sqrt 5 } \right]$$
C
$$f(x)$$ has local minima at $$x=1$$
D
the value of $$f(0)=15$$
2

### IIT-JEE 1999

MCQ (More than One Correct Answer)
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)
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)
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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