If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is

If $$A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$$ and $$A^{-1}=\left[\begin{array}{rrr}3 & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2\end{array}\right]$$, then the values of $$\alpha$$ and $$\beta$$ are, respectively.

The differential equation obtained from the function $$y=a(x-a)^2$$ is

In a quadrilateral $$ABCD, M$$ and $$N$$ are the mid-points of the sides $$A B$$ and $$C D$$ respectively. If $$\mathbf{A D}+\mathbf{B C}=t \mathbf{M N}$$, then $$t=$$