The input spectrum extends from −1000π to +1000π rad/s. Multiplication by cos(1000πt) shifts copies to ±1000π, so their combined support extends to ±2000π.
The filter $h(t)=\sin(1500\pi t)/(\pi t)$ passes only |ω|<1500π. Hence the output's highest frequency is 1500π/(2π)=750 Hz.
The Nyquist rate is twice that: **1500 samples/s, B**.
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