A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of the two pieces so that the combined area of the square and the circle is minimum, are respectively

If a spherical balloon has a variable diameter $3x + \dfrac{9}{2}$ units, then the rate of change of its volume with respect to $x$ is

$\displaystyle\int \dfrac{30x^{14} + 15^x \log 225}{x^{15} + 15^x} \, dx =$

If $\displaystyle\int \dfrac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx = f(x) + c$ where c is constant of integration, then the value of $\tan(f(x))$ is