In which plant group is the structure shown below found?

If $y=y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y = x^2$ satisfying $y(1)=1$,then $y\left(\frac{1}{2}\right)$ is equal to

Product $(A)$ is

The cubic equation whose roots are thrice to each of the roots of $x^3+2 x^2-4 x+1=0$ is

$(\tan ^{-1} x)^2+(\cot ^{-1} x)^2=\frac{5 \pi^2}{8} \Rightarrow x=$

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$, then $g(x)$ is equal to