The self-inductance (L) of a long solenoid on doubling its number of turns and length, keeping other factors constant, will become

$2L$

The correct answer is Option (3) → $2L$

The self-inductance of a solenoid is

$L = \mu_0 \frac{N^2 A}{l}$

where $N$ = number of turns, $A$ = cross-sectional area, $l$ = length.

If $N \to 2N$ and $l \to 2l$ :

$L' = \mu_0 \frac{(2N)^2 A}{2l}$

$L' = \mu_0 \frac{4N^2 A}{2l}$

$L' = 2 \mu_0 \frac{N^2 A}{l}$

$L' = 2L$

Final Answer: $2L$