Correct Answer  Option 1 :
\(\sqrt{L_1\times L_2}\)
Concept:
 The inductor is an electrical component that is capable of storing electrical energy in the form of magnetic energy.
 The property of an electrical component that causes an emf to be generated by changing the current flow is known as inductance. Inductance is of two types

Selfinductance: This is the phenomena in which change in electric current produce an electromotive force in the same circuit, and is given by
ϕ = L I
Where ϕ = Magnetic flux, L = Self inductance, I = Current
Mutual inductance: This is the phenomena in which change in flux linked with one circuit produce an emf in another coil and is given by
ϕ = MI
Where M = mutual inductance, ϕ = magnetic flux, I = Current
The coupling coefficient is the ratio of mutual inductance to the maximum possible value of mutual inductance and is given by
\(K = \dfrac{M}{\sqrt{L_{1}L_{2}}}\)
Where M = Mutual inductance, L1, L2 = Selfinductance of coil 1 and coil 2 respectively
Explanation:
The maximum possible value of mutual inductance is at K = 1
M = \(\sqrt{L_1\times L_2}\)