If $\left|\begin{array}{ccc}-bc& b^2+bc& c^2+bc\\ a^2+ac& -ac& c^2+ac\\ a^2+ab& b^2+ab& -ab\end{array}\right|=64$ then the value of ab + bc + ca is equal to 

The value of $4f\left(2\right),$ where $f\left(x\right)$ satisfies $f\left(x\right)+f(1-\frac{1}{x})=1+x\forall x\in R-\{0,1\}$

Number of values of $\theta$ in $[0,2\pi )$ satisfying $\left|\begin{array}{ccc}\sin 3\theta & -1& 1\\ \cos 2\theta & 4& 3\\ 2& 7& 7\end{array}\right|=0$

Number of real solutions of the equation $x{\log }_{10}5+{\log }_{10}2=x+{\log }_{10}(2^x-1)$

The value of $\left|\begin{array}{ccc}{\sin }^{2}A& \cot A& 1\\ {\sin }^{2}B& \cot B& 1\\ {\sin }^{2}C& \cot C& 1\end{array}\right|$ (given A + B + C = $\pi$ )