A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm, is:

The interval in which $f(x)=\frac{x}{\log x}$ is increasing, is:

For the function $f(x)=x^4-2x^2+5, x\in R$, then which of the following statements are True?

A. $f(x)$ is increasing on $(-\infty,-1)$

B. $f(x)$ is decreasing on $(-\infty,-1)$

C. $f(x)$ is increasing on $(-1,0)\cup(1,\infty)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

An open box is made from a cardboard measuring 12cm x 12cm by cutting off equal squares from the corner and turning up the side. Then maximum possible volume of the box would be:

For the function $f(x) = \frac{1}{x^2+2x+2}$

which of the following statements are TRUE?

A. $f(x)$ is increasing on $(-\infty, -1)$

B. $f(x)$ is decreasing on $(-\infty, -1)$

C. $f(x)$ is decreasing on $(-1, \infty)$

D. maximum value of $f(x)$ is 1

Choose the correct answer from the options given below:

For the function $f(x) = e^{-2x}(2-x)^2$, the point of local maxima is:

The height of a closed cylinder of given surface area and maximum volume is equal to the