Correct Option: C

(A) x(t) = sin 15πt
The fundamental period is

T0 =	2π	=	2π	=	2
	ω		15π		15

(B) x₂(t) = sin 20πt,

T0 =	2π
	ω

The fundamental period,

T0 =	2π	=	1
	20π		10

(C) x(t) = sin 15πt + sin 20πt
where, sin 15πt → x₁(t)
sin 20πt → x₂(t)
The fundamental period of

x1(t)= T1 =	2π	=	2
	15π		15

The fundamental period of

x2(t)= T2 =	2π	=	2
	20π		10

For the function x(t) to be period the ratio of T₁/T₂ should be rational i.e.,

	=	2
T1		15
T2		2
		10

=	3	= 1.5
	2

which is not rational i.e., x(t) is a periodic.
(D) x(t) = sin 20πt + sin 5πt
where, sin 15πt → x₁(t)
sin 20πt → x₂(t)
The fundamental period of

x1(t)= T1 =	2π	=	1
	2π		10

The fundamental period of

x2(t)= T2 =	2π	=	2
	5π		5

Ratio		=	1
	T1		10
	T2		2
			5

=	1
	4

which can be expressed as ratio of integers. Hence, x(t) is periodic.
Hence, alternative (C) is the correct choice.