Analyze Statement I: "Hyperconjugation is not a permanent effect."

Hyperconjugation is a delocalization effect involving overlap of a $\sigma$-bond (usually $\text{C–H}$ or $\text{C–C}$) with an adjacent empty $p$-orbital or $\pi$-system.

In standard organic chemistry classification, hyperconjugation is treated as a permanent electronic effect because it exists in the ground state of the molecule whenever the required structural arrangement is present.

Therefore, the statement "Hyperconjugation is not a permanent effect" is false.

Analyze Statement II: "In general, greater the number of alkyl groups attached to a positively charged C atom, greater is the hyperconjugation interaction and stabilization of the cation."

For carbocations, alkyl groups provide adjacent $\text{C–H}$ bonds that can participate in hyperconjugation with the empty $p$-orbital on the positively charged carbon.

Hence, more alkyl groups generally mean more hyperconjugative structures and greater stabilization:

$3^\circ > 2^\circ > 1^\circ > \text{methyl cation}$

So Statement II is true.

Conclusion:

• Statement I = False
• Statement II = True

Therefore, the correct option is:

A: Statement I is false but Statement II is true.