A fair $n$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$, then $\mathrm{n}=($ where $\mathrm{n} \in \mathbb{N})$

A fair coin is tossed a fixed number of times. If the probability of getting 5 tails is same as the probability of getting 7 tails, then the probability of getting 3 tails is

In the above figure, P divides AC in the ratio $3: 4$ and Q divides BC in the ratio $4: 3$. Then M divides AQ in the ratio

The tangent to the ellipse $9 x^2+16 y^2=288$ making equal intercepts on the co-ordinate axes intersects the X -axis and the Y -axis in the points $A$ and $B$ respectively. Then $A(\triangle O A B)=$ (where O is origin)