The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be ........ $\%$
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In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
The density of a material in $SI$ units is $128\, kg\, m^{-3}.$ In certain units in which the unit of length is $25\, cm$ and the unit of mass $50\, g$, the numerical value of density of the material is