The value of $\tan ^2\left(\sec ^{-1} 4\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)$ is

In a triangle ABC , with usual notations, if $\mathrm{a}=5, \mathrm{~b}=4, \cos (\mathrm{~A}-\mathrm{B})=\frac{31}{32}$, then $\mathrm{c}=$

Which of the following is the negation of the statement " For all M>0, there exist $x \in \mathrm{~s}$ such that $x \geqslant \mathrm{M}^{\prime \prime}$

The equation of the line passing through the point of intersection of $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ and also through the point ( $2,1,-2$ ) is