1
JEE Main 2015 (Offline)
+4
-1
Let $$f(x)$$ be a polynomial of degree four having extreme values
at $$x=1$$ and $$x=2$$. If $$\mathop {\lim }\limits_{x \to 0} \left[ {1 + {{f\left( x \right)} \over {{x^2}}}} \right] = 3$$, then f$$(2)$$ is equal to :
A
$$0$$
B
$$4$$
C
$$-8$$
D
$$-4$$
2
JEE Main 2014 (Offline)
+4
-1
If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying
$$f\left( 0 \right) = 2 = g\left( 1 \right),g\left( 0 \right) = 0$$ and $$f\left( 1 \right) = 6,$$ then for some $$c \in \left] {0,1} \right[$$
A
$$f'\left( c \right) = g'\left( c \right)$$
B
$$f'\left( c \right) = 2g'\left( c \right)$$
C
$$2f'\left( c \right) = g'\left( c \right)$$
D
$$2f'\left( c \right) = 3g'\left( c \right)$$
3
JEE Main 2013 (Offline)
+4
-1
The intercepts on $$x$$-axis made by tangents to the curve,
$$y = \int\limits_0^x {\left| t \right|dt,x \in R,}$$ which are parallel to the line $$y=2x$$, are equal to :
A
$$\pm 1$$
B
$$\pm 2$$
C
$$\pm 3$$
D
$$\pm 4$$
4
AIEEE 2012
+4
-1
A spherical balloon is filled with $$4500\pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $$72\pi$$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases $$49$$ minutes after the leakage began is :
A
$${{9 \over 7}}$$
B
$${{7 \over 9}}$$
C
$${{2 \over 9}}$$
D
$${{9 \over 2}}$$
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