The length of the tangent drawn to the circle $x^2+y^2-2x+4y-11=0$ from the point $(1,3)$ is:

The value of $\cos ^{-1} \left[ \cot \left\{ \sin ^{-1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos ^{-1} \frac{\sqrt{12}}{4} + \sec ^{-1} \sqrt{2} \right\} \right]$ is

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$,then find the coefficient of linear expansion of vessel $B$.

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$,then show that $|3A| = 27|A|$.

If $|a|=4, |b|=5, |a-b|=3$ and $\theta$ is the angle between the vectors $a$ and $b$, then $\tan^2 \theta=$

Which statement is wrong for viruses?