1

### 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
$$3$$
2

### 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.
3

### 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 $$x=2$$
4

### IIT-JEE 1986

MCQ (More than One Correct Answer)
If the line $$ax+by+c=0$$ is a normal to the curve $$xy=1$$, then
A
$$a > 0,b > 0$$
B
$$a > 0,b < 0$$
C
$$a < 0,b > 0$$
D
$$a < 0,b < 0$$

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