Practice tests · GATE

GATE communications: 5 practice questions with answers

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Communications is a section of the GATE EC paper that blends formula recall with short derivations: modulation power and bandwidth, sampling and quantisation, channel capacity, digital modulation and error control. The 2027 description of the section includes information theory, Hamming codes and CRC. The five original questions below take one problem from each of those areas.

What GATE tests in communications

The GATE 2027 EC syllabus lists Communications as a section that includes information theory, Hamming codes and CRC. Confirm the full, revised list on the official syllabus page. The standard content is random processes and noise, analog modulation (AM, FM and PM), sampling and PCM, digital modulation (ASK, FSK, PSK and QAM) with error probability, matched filtering, and channel coding.

Questions are usually one formula plus careful arithmetic: total power in an AM wave, bandwidth of a modulated signal, bit rate of a PCM system, the error probability for a given Eb/N0, or the syndrome of a received codeword. The real paper has MCQ, MSQ and NAT questions. All five below are MCQ.

Practice questions

Question 1

A carrier of power 400 W is amplitude modulated by a single tone with modulation index 0.5. The total power in the AM wave is:

• A. 450 W
• B. 500 W
• C. 550 W
• D. 600 W

Question 2

A noisy channel has a bandwidth of 3 kHz and a signal-to-noise ratio of 1023 (a plain ratio, not dB). The Shannon capacity of the channel is:

• A. 3 kbps
• B. 15 kbps
• C. 30 kbps
• D. 3069 kbps

Question 3

A message signal limited to 5 kHz is sampled at its Nyquist rate. Each sample is quantised to one of 256 levels and sent as a binary code. The resulting bit rate is:

• A. 20 kbps
• B. 40 kbps
• C. 60 kbps
• D. 80 kbps

Question 4

A 16-QAM system transmits at a bit rate of 2 Mbps using rectangular pulses. Taking the null-to-null bandwidth as twice the symbol rate, the bandwidth is:

• A. 4 MHz
• B. 2 MHz
• C. 1 MHz
• D. 0.5 MHz

Question 5

A (7,4) Hamming code uses even parity. Parity bits sit at positions 1, 2 and 4, and data bits at positions 3, 5, 6 and 7. Parity bit 1 checks positions 1, 3, 5 and 7, parity bit 2 checks positions 2, 3, 6 and 7, and parity bit 4 checks positions 4, 5, 6 and 7. The received word, with position 1 first, is 0110111, and it contains a single error. The position in error is:

• A. 5
• B. 3
• C. 6
• D. 7

Answers and explanations

1. A. For single-tone AM, the total power is Pt = Pc (1 + m²/2) = 400 × (1 + 0.25/2) = 400 × 1.125 = 450 W. The sidebands carry 50 W in total. Only the sidebands carry the message, which is why AM is power-inefficient.
2. C. Capacity C = B log₂(1 + SNR) = 3000 × log₂(1024) = 3000 × 10 = 30 000 bps = 30 kbps. Option D multiplies by the SNR instead of taking the logarithm.
3. D. The Nyquist rate is 2 × 5 kHz = 10 kHz, so there are 10 000 samples per second. 256 levels need log₂ 256 = 8 bits per sample. The bit rate is 10 000 × 8 = 80 000 bps = 80 kbps.
4. C. Each 16-QAM symbol carries log₂ 16 = 4 bits, so the symbol rate is 2 Mbps / 4 = 0.5 Msymbols/s. The null-to-null bandwidth for rectangular pulses is 2 × 0.5 = 1 MHz. Raising the modulation order reduces the bandwidth required for the same bit rate.
5. A. Compute the three checks on 0110111 (positions 1 to 7 are 0, 1, 1, 0, 1, 1, 1). Check 1: positions 1, 3, 5, 7 give 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1. Check 2: positions 2, 3, 6, 7 give 1 ⊕ 1 ⊕ 1 ⊕ 1 = 0. Check 4: positions 4, 5, 6, 7 give 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1. The syndrome (check 4, check 2, check 1) is 101 in binary, which is 5. Flipping position 5 gives 0110011, which passes all three checks.

How to prepare communications

• Memorise the AM and FM formulas with their bandwidths: AM power and efficiency, DSB-SC and SSB, Carson's rule for FM, and the SNR advantage of FM over AM.
• Learn the PCM chain in order: sampling, quantisation, encoding. For quantisation, know the step size, the error range and the SNR (about 6 dB per bit for a full-scale sine).
• Make a table of digital modulation schemes with bits per symbol, bandwidth and error probability in terms of the Q function. Practise comparing BPSK, QPSK and 16-QAM.
• Understand entropy and capacity with small examples: entropy of a source with given probabilities, mutual information of a simple channel, and Shannon's formula.
• Do syndrome decoding and CRC division by hand, at least five of each. They are mechanical, short and appear regularly.
• Review random processes lightly, with autocorrelation, power spectral density and noise through an LTI system, since these underpin the error-probability results.

This section builds on signals and systems and sits beside digital circuits in the EC paper. The GATE ECE preparation guide lays out all eight EC sections, and analog circuits covers the hardware side.

Take the full topic test on PrepMatic

PrepMatic's topic tests run about 15 questions in 30 minutes, which makes a useful check that you can complete formula-driven communications questions on the clock. The free assessment shows your weakest subjects first.

← All practice tests