The equations of the tangents to the circle $x^2+y^2=36$ which are perpendicular to the line $5 x+y=2$, are

If $\sin \mathrm{A}=\mathrm{n} \sin (\mathrm{A}+2 \mathrm{~B})$, then $\tan (\mathrm{A}+\mathrm{B})=$

The number of integral values of $p$ for which the vectors $(p+1) \hat{i}-3 \hat{j}+p \hat{k}, p \hat{i}+(p+1) \hat{j}-3 \hat{k}$ and $-3 \hat{\mathrm{i}}+\mathrm{p} \hat{\mathrm{j}}+(\mathrm{p}+1) \hat{\mathrm{k}}$ are linearly dependent vectors, are

$$ \int_0^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) d x= $$