For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation

$\left(x^2-5\right) \frac{d y}{d x}-2 x y=-2 x\left(x^2-5\right)^2$ such that $y(2)=7$.

Then the maximum value of the function $y(x)$ is :

Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of 20 given that it is a multiple of 5 . Then the value of $38 p$ is equal to :

Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a point on the circle and let $P A_i$ denote the distance between the points $P$ and $A_i$ for $i=1,2, \ldots, 8$. If $P$ varies over the circle, then the maximum value of the product $P A_1 \times P A_2 \times \cdots \cdots \times P A_8$, is :

Let $R=\left\{\left(\begin{array}{lll}a & 3 & b \\ c & 2 & d \\ 0 & 5 & 0\end{array}\right): a, b, c, d \in\{0,3,5,7,11,13,17,19\}\right\}$.

Then the number of invertible matrices in $R$ is :