If $x$ and $y$ are two positive integers such that $x+2 y=10$ and $x^2 y^3$ is maximum, then $x^2+2 y^3=$

The equation of the normal to the curve $\sin y=\sqrt{3} x \sin \left(\frac{\pi}{6}+y\right)$ at $x=0$, is

Assertion (A) The curves $y^2=4 x$ and $x^2=-2 y$ intersect at $(1,2)$ orthogonally.

Reason (R) If the product of the slopes of the tangents drawn to two curves at their point of intersection is -1 , then the curves are said to cut each other orthogonally.

Let $f(x)=\left\{\begin{array}{cc}1+6 x-3 x^2 & x \leq 1 \\ x+\log _2\left(b^2+7\right) & x>1\end{array}\right.$. Then, the set of all possible values of $b$ such that $f(1)$ is the maximum value of $f(x)$ is