Electronics and Communication GATE 2025 Questions with Answer

Ques 1 Circuit Theory

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the 3Ω resistor are as indicated.
The voltage (in Volts) at node X is

Ques 2 Circuit Theory

Let i_C, i_L, and i_R be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S).
Which one of the following is TRUE?

Ques 3 Circuit Theory

In the circuit below, M₁ is an ideal AC voltmeter and M₂ is an ideal AC ammeter.
The source voltage (in Volts) is v_s(t)=100 cos(200t)
What should be the value of the variable capacitor C such that the RMS readings on M₁ and M₂ are 25 V and 5 A, respectively?

Ques 4 Circuit Theory

The Z-parameter matrix of a two port network relates the port voltages and port currents as follows: [(V₁); (V₂)] = Z [(I₁); (I₂)]
The Z-parameter matrix (with each entry in Ohms) of the network shown below is

A

B

C

D

Ques 5 Circuit Theory

Two resistors are connected in a circuit loop of area 5 m², as shown in the figure below. The circuit loop is placed on the x-y plane.
When a time-varying magnetic flux, with flux-density B(t)=0.5t (in Tesla), is applied along the positive z-axis, the magnitude of current I (in Amperes, rounded off to two decimal places) in the loop is

Ques 6 Communication Systems

Consider a frequency-modulated (FM) signal
f(t)=A_ccos(2πf_ct+3 sin(2πf₁t)+4 sin(6πf₁t)).
where A_c and f_c are, respectively, the amplitude and frequency (in Hz) of the carrier waveform. The frequency f₁ is in Hz, and assume that f_c>100f₁.
The peak frequency deviation of the FM signal in Hz is

Ques 7 Communication Systems

Consider an additive white Gaussian noise (AWGN) channel with bandwidth W and noise power spectral density N₀/2. Let P_av denote the average transmit power constraint.
Which one of the following plots illustrates the dependence of the channel capacity C on the bandwidth W (keeping P_av and N₀ fixed)?

A

B

C

D

Ques 8 Communication Systems

Consider a message signal m(t) which is bandlimited to [-W, W], where W is in Hz. Consider the following two modulation schemes for the message signal:
Double sideband-suppressed carrier (DSB-SC): f_DSB(t)=A_cm(t)cos(2πf_ct)
Amplitude modulation (AM): f_AM(t)=A_c(1+μm(t))cos(2πf_ct)
Here, A_c and f_c are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, μ denotes the modulation index.
Consider the following statements:
(i) An envelope detector can be used for demodulation in the DSB-SC scheme if m(t)>0 for all t.
(ii) An envelope detector can be used for demodulation in the AM scheme only if m(t)>0 for all t.
Which of the following options is/are correct?

Ques 9 Communication Systems

The generator matrix of a (6,3) binary linear block code is given by

Ques 10 Communication Systems

A source transmits symbol S that takes values uniformly at random from the set {-2,0,2}. The receiver obtains Y=S+N, where N is a zero-mean Gaussian random variable independent of S. The receiver uses the maximum likelihood decoder to estimate the transmitted symbol S.
Suppose the probability of symbol estimation error P_e is expressed as follows:
P_e=α P(N>1),
where P(N>1) denotes the probability that N exceeds 1.
What is the value of α ?

Ques 11 Communication Systems

The random variable X takes values in {-1,0,1} with probabilities P(X=-1)=P(X=1)=α and P(X=0)=1-2α, where 0<α<1/2.
Let g(α) denote the entropy of X (in bits), parameterized by α.
Which of the following statements is/are TRUE?

Ques 12 Communication Systems

X and Y are Bernoulli random variables taking values in {0,1}. The joint probability mass function of the random variables is given by:
P(X=1,Y=1)=0.56
P(X=0,Y=0)=0.06
P(X=0,Y=1)=0.14
P(X=1,Y=0)=0.24
The mutual information I(X;Y) is ______ (rounded off to two decimal places).

Ques 13 Control Systems

The Nyquist plot of a system is given in the figure below. Let ω_P, ω_Q, ω_R, and ω_S be the positive frequencies at the points P, Q, R, and S, respectively.
Which one of the following statements is TRUE?