Two solenoids of the same length and the same cross-sectional area have 400 turns and 250 turns, respectively. The ratio of self-inductance of the two solenoids, respectively, is

64 : 25

The correct answer is Option (1) → 64 : 25

The self-inductance of a solenoid is

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

For the same length $l$ and area $A$,

$\frac{L_1}{L_2} = \left(\frac{N_1}{N_2}\right)^2$

$\frac{L_1}{L_2} = \left(\frac{400}{250}\right)^2 = \left(\frac{8}{5}\right)^2 = \frac{64}{25}$

Ratio = $64 : 25$