If $a, b, c$ are digits,then the rational number represented by $0.cababab...$ is:

If for $x \in \left(0, \frac{\pi}{2}\right)$,$\log_{10} \sin x + \log_{10} \cos x = -1$ and $\log_{10}(\sin x + \cos x) = \frac{1}{2}(\log_{10} n - 1)$,$n > 0$,then the value of $n$ is equal to

The square root of $\frac{(0.75)^3}{1-0.75}+[0.75+(0.75)^2+1]$ is

$0.4\overline{23} = ?$

If $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b}$,then which of the following is true?

Evaluate: $\frac{{[4 + \sqrt{15}]}^{3/2} + {[4 - \sqrt{15}]}^{3/2}}{{[6 + \sqrt{35}]}^{3/2} - {[6 - \sqrt{35}]}^{3/2}}$