$A$ complex current wave is given by $i = 5 + 5\, \sin(100\, \omega t)\, A$. Its average value over one complete time period is given as.....$A$.

Observe the following statements:
$I$. If $dy + 2xy dx = 2e^{-x^2} dx$, then $ye^{x^2} = 2x + c$.
$II$. If $ye^{-x^2} - 2x = c$, then $dx = (2e^{-x^2} - 2xy) dy$.
Which of the following is a correct statement?

When a capacitor is connected in series to an $LR$ circuit,the alternating current flowing in the circuit

In the process of transcription in eukaryotes, the $\text{RNA}$ polymerase $\text{II}$ transcribes

Two springs have spring constants $K_A$ and $K_B$ such that $K_A > K_B$. If both springs are stretched by the same extension $x$,the work required will be:

Let $f(x)$ be a continuous and differentiable function for all real numbers such that $f(x + y) = f(x) - 3xy + f(y)$. If $\lim_{h \to 0} \frac{f(h)}{h} = 7$,then the value of $f'(x)$ is: