In series LCR circuit, the capacitance is changed from C to 4C . To...

As resonance frequency remains unchanged, therefore $\omega ' = \omega$

$⇒ \dfrac{1}{\sqrt{L ' C '}} = \dfrac{1}{\sqrt{LC}}$

$⇒ L ' C ' = LC$

$⇒ L ' \left(4C\right) = LC$

$⇒ L ' = \dfrac{L}{4}$

$∵$ Inductance must be decreased by $\dfrac{3L}{4}$.