$\int_{\frac{1}{2}}^2 \frac{1}{x} \operatorname{cosec}^{101}\left(x-\frac{1}{x}\right) \mathrm{d} x=$

Matrix A is non-singular matrix and $(A-3 I)(A-5 I)=0$, then $\frac{15}{8} A^{-1}=\ldots \ldots$

If the plane $\frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1$ cuts the co-ordinate axes at points $A, B, C$ respectively, then area of the triangle ABC is

The number of positive integral solutions of $\tan ^{-1} x+\cos ^{-1}\left(\frac{y}{\sqrt{1+y^2}}\right)=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)$ are