A quantity Q is formulated as $$X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}$$. X, Y and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is

The quantity is $$Q = X^{-2}\,Y^{-\,\frac{3}{2}}\,Z^{\frac{2}{5}}$$.

For a physical quantity of the form $$Q = X^{a}\,Y^{b}\,Z^{c}$$, the maximum fractional (relative) error is obtained by adding the absolute contributions of each factor:
$$\frac{\Delta Q}{Q}\Big|_{\max}=|a|\;\frac{\Delta X}{X}+|b|\;\frac{\Delta Y}{Y}+|c|\;\frac{\Delta Z}{Z}$$.

Here $$a=-2,\;b=-\frac{3}{2},\;c=\frac{2}{5}$$.
Their absolute values are $$|a|=2,\;|b|=\frac{3}{2}=1.5,\;|c|=\frac{2}{5}=0.4$$.

The given fractional errors are
$$\frac{\Delta X}{X}=0.1,\qquad \frac{\Delta Y}{Y}=0.2,\qquad \frac{\Delta Z}{Z}=0.5$$.

Substituting these values:
$$\frac{\Delta Q}{Q}\Big|_{\max}=2(0.1)+1.5(0.2)+0.4(0.5)$$

Calculate each term:
$$2(0.1)=0.2,\qquad 1.5(0.2)=0.3,\qquad 0.4(0.5)=0.2$$

Add them:
$$0.2+0.3+0.2 = 0.7$$

Therefore, the maximum fractional error in $$Q$$ is $$0.7$$.

Option C is correct.