Refer to the equation given below. If x is very small compared to a then y  will be approximately equal to
 $y=\frac{1}{\left(8a^3-x^3\right)^{\frac{2}{3}}}-\frac{1}{\left(8a^3+x^3\right)^{\frac{2}{3}}}$  

Simplify the following using Binomial approximation
 $\lfloor\sqrt{70}\rfloor^{\frac{1}{3}}$  

The value of  $\frac{1}{\sqrt{200}}$  is same as

The rate of flow of liquid (I) in a tube of radius r and length l due to a pressure difference P is given by  $I=\frac{\pi}{8\eta}\ \frac{P}{l}r^4$  Here  $\eta$  is called coefficient of viscosity.  If Pressure increases by 4%, length decreases by 2%,  radius increases by 1.5%  and coefficient of viscosity increases by 0.5%, find the percentage change in rate of flow

The mass and radius of a spherical object are 40 g and 4 cm respectively. if mass reduces by 2 g and radius increases by 4 mm then the percentage change in density is given by

The value of $\left(5+\sqrt{10}\right)^{\frac{1}{3}}$  

Refer to the equation given below. If x is very small compared to a then y  will be approximately equal to
 $y=\frac{1}{\left(a-x\right)^4}-\frac{1}{\left(a+x\right)^4}$  

The power dissipated in a bulb is given by $P=\frac{V^2}{R}$ . If the voltage is decreased by  3% and resistance increases by 2% then the percentage change in power is

A physical quantity is given by $y=\frac{a^3b^4}{c^{\frac{3}{2}}}$ . The value of a, b and c are 2, 3 and 4. If the variation of the same are given by 0.04, 0.06 and -0.08, the relative variation in y  is