$$ \lim _{n \rightarrow \infty}\left[\frac{n+3}{n^2+1^2}+\frac{n+6}{n^2+2^2}+\frac{n+9}{n^2+3^2}+\ldots+\frac{2}{n}\right]= $$

If the area lying in the first quadrant and bounded by the circle $x^2+y^2-4 x=0$, the parabola $y^2=x$ and the $X$-axis is $A$, then $6 A-9 \sqrt{3}=$

If the order and degree of the differential equation corresponding to the family of curves $(x-2)^2+(y-a)^2=b^2$, (where $a$ and $b$ are parameters) are $m$ and $n$ respectively, then $m^2+n=$

Consider the differential equation $\frac{d y}{d x}=\frac{1}{a x+4 y+7}$ and the following statements

A. The given differential equation is linear in $x$.

B. The given differential equation is not linear in $y$.

C. The given differential equation is linear in $y$.

D. $e^{a x}$ is the integrating factor of the given differential equation.

Which one of the following options is true?