For an LCR series circuit with an ac source of angular frequency $\omega$  

The circuit will have inductive nature if

$\omega =\frac{1}{\sqrt{LC}}\left(\omega L>\frac{1}{\sqrt{LC}}\right)$

Hence (a) is false. Also, circuit has inductive nature the current will lag behind voltage. Hence (d) is also false.

If $\omega =\frac{1}{\sqrt{LC}}\left(\omega L=\frac{1}{\omega C}\right)$ the circuit will have résistance nature.

Hence (b) is false.

Power factor $\cos \varphi =\frac{R}{\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)}}=1$