JEE Advanced 2024 Physics question on Oscillations and Waves

Two uniform strings of mass per unit length $\mu$ and $4\mu$, and length $L$ and $2L$, respectively, are joined at point O, and tied to two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension $T$. If we define the frequency $\nu_0 = \dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$, which of the following statement(s) is(are) correct?

1. A.
   With a node at O, the minimum frequency of vibration of the composite string is $\nu_0$.
2. B.
   With an antinode at O, the minimum frequency of vibration of the composite string is $2\nu_0$.
3. C.
   When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes.
4. D.
   No vibrational mode with an antinode at O is possible for the composite string.

[JEE Advanced 2024 · Paper 1]