$$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$$ is equal to:

If for a square matrix $$\mathrm{A}, A^2-A+I=\mathrm{O}$$, then $$\mathrm{A}^{-1}$$ equals:

$$\text { If } A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right], B=\left[\begin{array}{ll} x & 0 \\ 1 & 1 \end{array}\right] \text { and } A=B^2 \text {, then } x \text { equals: }$$

$$\text { If }\left|\begin{array}{lll} \alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1 \end{array}\right|=0 \text {, then the value of } \alpha \text { is: }$$