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 (1) is false. Also, if circuit has inductive nature, the current will lag behind voltage. Hence (4) is also false

If $\omega =\frac{1}{\sqrt{LC}}\left(\omega L=\frac{1}{\omega C}\right)$, the circuit will have resistance nature. Hence, (2) is false.

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

If $\omega L=\frac{1}{\omega C}$.

Hence, (3) is true.