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The maximum data rate of binary signals on a noiseless $3\:KHz$ channel is :

  1. $3000$ bps.
  2. $6000$ bps.
  3. $9000$ bps.
  4. $12,000$ bps.
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Option B

Maximum data rate to transmit binary signal is 2H.Nyquist's Theorem - If the signal has V discrete levels over a transmission medium of bandwidth H, the maximum data rate = 2H log2 V bits/sec.

where H is the bandwidth, V is the discrete levels. Here H is 3 kHz and V is 2.

So, data rate = 2*3000 log22 bps = 6000 bps.