GATE EC 2017 Set 1 Q50 — Digital Communications

In binary frequency shift keying (FSK), the given signal waveforms are 

$$u_{0}(t)=5\, \cos(20000\pi t)\, ;0\leq t\leq T \text{, and } \\ u_{1}(t)=5\, \cos(22000\pi t)\, ;0 \leq t \leq T,$$

where $T$ is the bit-duration interval and $t$ is in seconds.Both $u_{0}(t)$ and $u_{1}(t)$ are zero outside the interval  $0\leq t\leq T$. With a matched filter (correlator) based receiver, the smallest positive value of $T$ (in milliseconds) required to have  $u_{0}(t)$ and $u_{1}(t)$ uncorrelated is