Correct Option: B

Given, K K₁ = 99
s = j1 it means ω = 1 rad/sec.
We have to calculate sensitivity of closed loop system to variation in parameter K i.e.,

SMK =	∂M/M
	∂K/K

=	K	×	∂M
	M		∂K

or

SMK =	K	∂M
	G	∂K

Now,

M =	G(s)	=	K/(10s + 1)
	1 + G(s)H(s)		(1 + KKt)/(10s + 1)

or

M =	K
	(10s + 1+ KKt)

∂M	=	(10s + 1 + kkt)(∂/∂K).K - K (∂/∂K)(10s + 1 + kk1)
∂K		(10s + 1 + KKt)

or

∂M	=	10s + 1 + kkt - kkt
∂K		(10s + 1 + KKt)2

or

∂M	=	10s + 1
∂K		(10s + 1 + KKt)2

and SMK =	K	×	(10s + 1)
	K/(10s + 1 + kkt)		(10s + 1 + kkt)2

or

or SMK =	(10s + 1)
	(10s + 1 + kkt)

or SMK =	(10s + 1)
	10s + 1 + 99

SMK =	(10s + 1)
	10s (s + 10)

or

SMK =	√100ω2 + 1
	10√102ω2

or

SMK =	√100 + 1
	10√100 + 1

or S^M_K = 0·1
Hence alternative (B) is the correct choice.