c
(c)  \(Z = \sqrt {{R^2} + {{\left( {2\pi fL - \frac{1}{{2\pi fC}}} \right)}^2}} \)

From above equation at \(f\) = \(0\) \( \Rightarrow z = \infty \)

When \(f = \frac{1}{{2\pi \sqrt {LC} }}\) (resonant frequency) \( \Rightarrow Z = R\)

For \(f > \frac{1}{{2\pi \sqrt {LC} }} \Rightarrow \) \( Z\) starts increasing.

i.e., for frequency \(0 -\) \(fr\), \(Z\) decreases and for fr to \(\infty\), \(Z\) increases. This is justified by graph \(c\).