If $f : R \to R$ and $g : R \to R$ are defined as $f(x) = 2x - |x|$ and $g(x) = 2x + |x|$, then

Which of the following function is discontinuous at $x = 0$ ?

If $y = x \cdot 7^x$, then the value of $\dfrac{dx}{dy}$ when $x = 1$ is

If $y = [(x+1)(2x+1)(3x+1)\ldots\ldots(nx+1)]^4$, where $n \in N$ and $\dfrac{dy}{dx}$ at $x = 0$ is $2k$, then the value of $k$ is