While keeping the area of cross-section of a solenoid the same, the number of turns and length of the solenoid are both doubled. The self-inductance of the coil will be?

Correct option is B. Doubled

We know that
Self inductance of the coil, L = μN²A/l
where
μ = Permittivity of the space
N = No. of turns in solenoid
l = length of the solenoid
A = Cross-section area of solenoid

When N will become 2N and l becomes 2l
Then Self inductance of coil, L' = μ(2N)²A/(2l) = 2μN²A/l = 2L

Hence, Self inductance of the coil will be doubled