In an LCR circuit, the capacitance is made one-fourth, when in resonance. Then What should be change in inductance, so that the circuit remains in resonance?

4 times 

The resonant frequency is given by

$ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{LC}}$

For the circuit to be in resonance LC should be constant. When capacitance is made ¼ of its value, the value of L should be increased four times.