1

### JEE Advanced 2013 Paper 1 Offline

MCQ (More than One Correct Answer)
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $$8:15$$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $$100$$, the resulting box has maximum volume. Then the lengths of the vsides of the rectangular sheet are
A
$$24$$
B
$$32$$
C
$$45$$
D
$$60$$
2

### IIT-JEE 2012 Paper 2 Offline

MCQ (More than One Correct Answer)
If $$f\left( x \right) = \int_0^x {{e^{{t^2}}}} \left( {t - 2} \right)\left( {t - 3} \right)dt$$ for all $$x \in \left( {0,\infty } \right),$$ then
A
$$f$$ has a local maximum at $$x=2$$
B
$$f$$ is decreasing on $$(2, 3)$$
C
there exists some $$c \in \left( {0,\infty } \right),$$ such that $$f'(c)=0$$
D
$$f$$ has a local minimum at $$x=3$$
3

### IIT-JEE 2009

MCQ (More than One Correct Answer)
For the function $$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$\$
A
for at least one $$x$$ in the interval $$\left[ {1,\infty } \right)$$, $$f\left( {x + 2} \right) - f\left( x \right) < 2$$
B
$$\mathop {\lim }\limits_{x \to \infty } f'\left( x \right) = 1$$
C
for all $$x$$ in the interval $$\left[ {1,\infty } \right)f\left( {x + 2} \right) - f\left( x \right) > 2$$
D
$$f'(x)$$ is strictly decreasing in the interval $$\left[ {1,\infty } \right)$$
4

### IIT-JEE 2006

MCQ (More than One Correct Answer)
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

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