1
IIT-JEE 2002 Screening
+2
-0.5
The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is
A
$${\pi \over 3}$$
B
$${\pi \over 2}$$
C
$${3\pi \over 2}$$
D
$$\pi$$
2
IIT-JEE 2002 Screening
+2
-0.5
The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)
A
$$\left( { \pm {4 \over {\sqrt 3 }}, - 2} \right)$$
B
$$\left( { \pm \sqrt {{{11} \over 3}} ,1} \right)$$
C
$$(0,0)$$
D
$$\left( { \pm {4 \over {\sqrt 3 }}, 2} \right)$$
3
IIT-JEE 2001 Screening
+2
-0.5
If $$f\left( x \right) = x{e^{x\left( {1 - x} \right)}},$$ then $$f(x)$$ is
A
increasing on $$\left[ { - 1/2,1} \right]$$
B
decreasing on $$R$$
C
increasing on $$R$$
D
decreasing on $$\left[ { - 1/2,1} \right]$$
4
IIT-JEE 2001 Screening
+2
-0.5
The triangle formed by the tangent to the curve $$f\left( x \right) = {x^2} + bx - b$$ at the point $$(1, 1)$$ and the coordinate axex, lies in the first quadrant. If its area is $$2$$, then the value of $$b$$ is
A
$$-1$$
B
$$3$$
C
$$-3$$
D
$$1$$
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