If $\operatorname{sech}^{-1} x=\log 2$ and $\operatorname{cosech}^{-1} y=-\log 3$, then $(x+y)=$

If the sides $a, b, c$ of the $\triangle A B C$ are in harmonic progression, then $\operatorname{cosec}^2 A / 2, \operatorname{cosec}^2 B / 2, \operatorname{cosec}^2 C / 2$ are in

In $\triangle A B C$, if $r=3$ and $R=5$, then $\frac{1}{a b}+\frac{1}{b c}+\frac{1}{c a}=$

An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms . A person on the ground observed that the angle of elevation of the plane is changed from $15^{\circ}$ to $30^{\circ}$ in the duration of 50 seconds, then the speed of the plane (in kmph ) is