A d.c. series motor has linear magnetization characteristics and negligible armature resistance. The motor speed is

where T = load torque

Concept:

In a DC series machine, both field and armature winding is connected in series. 

Therefore, field current will be equal to armature current.

Torque produced ∝ I_f × I_a

i.e., T ∝ ϕ . I_a

∵ ϕ ∝ I_a (in DC series motor)

∴ T ∝ I²_a

or, √T ∝ I_a

we also know that,

\(N \propto \frac{1}{\phi} \propto \frac{1}{I_a} \propto \frac{1}{\sqrt T}\)

∴ \(N\propto \frac{1}{\sqrt T}\)

Therefore, curve will be rectangular hyperpolar.

Therefore, correct option will be (2)