1
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
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)
+4
-1
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 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
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)
+5
-1.25
$$f(x)$$ 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 $$f(0)=15$$
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