If $A=\left[\begin{array}{cc}1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1\end{array}\right]$ then $A^{-1}=$

If $\bar{a}, \bar{b}, \bar{c}$ are three unit vectors such that $|\overline{\mathrm{a}}+\overline{\mathrm{b}}|^2+|\overline{\mathrm{a}}+\overline{\mathrm{c}}|^2=8$, then $|\overline{\mathrm{a}}+3 \overline{\mathrm{~b}}|^2+|\overline{\mathrm{a}}+3 \overline{\mathrm{c}}|^2=$

The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at most 2 components out of 4 tested, will survive is

From the following options, the nearest line to the origin is ….