What topics are covered on Page 5 of GATE 2026 Electronics and Communication Engineering?

Page 5 contains the final Questions 53 to 65. Topics include resonant circuits, non-ideal inductors and capacitors, two-port ABCD parameters, random variables and correlation, Laplace transforms, sampling, discrete-time systems, impulse inputs, Fourier-series coefficients, signal energy, bandwidth, LTI systems and orthogonal signals.

Which Network Theory topics are asked on GATE 2026 ECE Page 5?

Network Theory questions cover average power at resonance, practical inductor-capacitor circuits with losses and determination of ABCD parameters for a two-port network.

Which Signals and Systems topics appear on GATE 2026 ECE Page 5?

Signals and Systems topics include convolution and Laplace transforms, sampling of analog sinusoids, stability and causality of discrete-time systems, impulse-driven state changes, Fourier-series symmetry, signal-energy scaling, energy bandwidth, interconnected LTI systems and signal orthogonality.

What happens to the even Fourier-series coefficients for a half-wave antisymmetric signal?

If a periodic signal satisfies x(t - T/2) = -x(t), it has half-wave symmetry. Consequently, the even-indexed Fourier-series coefficients are zero, so a2m = 0.

Are cos(2πnt) and 2sin(4πnt) orthogonal over one period?

Yes. The two sinusoids occur at different harmonic frequencies and are orthogonal over the interval from 0 to 1/n.

What mathematics topic accompanies Signals and Systems on Page 5?

Page 5 also includes a probability and random-process style question involving a uniformly distributed random variable, Gaussian noise and correlations between derived random variables.

Electronics and Communication Gate 2026 Questions with Answer

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Ques 53 GATE 2026

Consider the circuit shown in the Figure, where the input v_i(t) is in Volt.
The average power (in mW) dissipated in the load resistance of 1 kΩ at the resonant frequency is __.
(rounded off to two decimal places)

() is the correct answer.

Ques 54 GATE 2026

In the given circuit, L = 1 μH and C = 1 μF. The phasor diagram for I_C and I_L is also shown. Assume that the phase (θ₁ + θ₂) is 90° at a frequency of 159.15 kHz.
Among the following options, what is the nearest integer value of R_C × R_L?

() is the correct answer.

Ques 55 GATE 2026

Consider the two-port network as shown in the Figure.
Which of the following options provides the correct set of values of A, B, C and D parameters?

A = 1/2, B = 3×10³ Ω, C = 10^-3 Ω^-1, D = 1/2

A = 2, B = 3 Ω, C = 1 Ω^-1, D = 2

A = 2, B = 6×10³ Ω, C = 2×10^-3 Ω^-1, D = 2

A = 2, B = 3×10³ Ω, C = 10^-3 Ω^-1, D = 2

() is the correct answer.

Ques 56 GATE 2026

Let X, N, Y and Z be random variables. The variables X and N are independent of each other. X is uniformly distributed between -1 and 1; N follows Normal distribution with zero mean and unity variance.
Y and Z are defined as, Y = X + N and Z = X² + N.
Which of the following pairs represents the values of correlation between X and Y and that between X and Z?

1/3 and 0

1/3 and 1/9

1/3 and 1/3

1 and 0

() is the correct answer.

Ques 57 GATE 2026

The Laplace Transform of the signal x(t) = u(t - 2) * (tu(t)) is given by which of the following expressions?
[“*” represents convolution operator]

e^-2s/[s²(s - 2)]

e^-2(s-2)/s³

se^-2s/(s - 2)²

e^-2s/s³

() is the correct answer.

Ques 58 GATE 2026

Two analog signals x₁(t) and x₂(t) (t in second), are sampled at a rate F_s = 40 Hz, where
x₁(t) = cos(20πt), t ≥ 0, and x₂(t) = cos(100πt), t ≥ 0.
The first ten samples (starting from t = 0) are considered for the analysis.
Which of the following statements is TRUE?

All of the first three samples of x₁(t) are greater than the corresponding samples of x₂(t).

All of the last three samples of x₁(t) are greater than the corresponding samples of x₂(t).

All of the samples of x₂(t) are greater than the corresponding samples of x₁(t).

All of the fourth to seventh samples of x₁(t) are equal to the corresponding samples of x₂(t).

() is the correct answer.

Ques 59 GATE 2026

The response of a discrete time system y[n] obeys the following relation:
y[n] = (5/6)y[n - 1] - (1/6)y[n - 2] + x[n].
The input to the system is x[n] = δ[n] - (1/3)δ[n - 1].
Which of the following options is TRUE for y[n]?

Stable and causal response

Stable and non-causal response

Unstable and causal response

Unstable and non-causal response

() is the correct answer.

Ques 60 GATE 2026

The relation between the input current (I) and the output voltage (V) of a circuit is governed by the equation: C dV/dt = I(t) − m(t). The circuit is excited by I(t) = qδ(t), where q is a real valued constant. V at t = 0⁻ is V₀.
Which of the following is an equivalent representation of the above case?

C dV/dt = −m(t), with V(t = 0⁻) = V₀ + q/C

C dV/dt = −m(t), with V(t = 0⁻) = V₀ + q/C + m(t = 0⁻)

C dV/dt = −m(t), with V(t = 0⁻) = V₀ - q/C + m(t = 0⁻)

C dV/dt = −m(t), with V(t = 0⁻) = q/C

() is the correct answer.

Ques 61 GATE 2026

The continuous time signal x(t) is real, periodic with period T and satisfies the Dirichlet conditions.
The Fourier series representation of x(t) = Σ_-∞^∞ a_ne^j(2πnt/T) and x(t) satisfies the following: x(t − T/2) = −x(t).
For any integer m, which of the following options is correct?

a_2m = 0

a_2m = 1

a_2m = a_2m+1

a_2m = -1

() is the correct answer.

Ques 62 GATE 2026

Consider a real signal x(t), -∞ < t < ∞, such that
x(t) = 0 for t <0, x(t) = 2 for 0 ≤ t < 1 and x(t) = 0 for t ≥ 1.
Let E[x(t)] = ∫_-∞^∞[x(t)]²dt.
Which of the following options correctly represents the ratio, E[x(t)]/E[3 x(−3t + 5)]?

1/3

1/9

() is the correct answer.

Ques 63 GATE 2026

Consider a real baseband signal x(t) = e^−2t, for t (in seconds) ≥ 0.
If 99% of energy of x(t) lies within B Hz, then which of the following options is TRUE for the value of B?

B > 1 kHz

63/π Hz < B < 64/π Hz

126/π Hz < B < 128/π Hz

B < 1 Hz

() is the correct answer.

Ques 64 GATE 2026

Consider the discrete time system (S) with input x[n] and output y[n] as shown in the Figure. The two sub-systems represented by their impulse responses h₁[n] and h₂[n] are linear and time invariant.
Which of the following statements is necessarily TRUE?

S is causal.

S is linear and time invariant.

S is linear and time varying.

S is non-linear.

() is the correct answer.

Ques 65 GATE 2026

Let x₁(t) = cos(2πnt) and x₂(t) = 2sin(4πnt) represent two sinusoids for a positive integer n and −∞ < t < ∞.
Which of the following statements about x₁(t) and x₂(t) is/are valid?

x₁(t) and x₂(t) are orthogonal to each other over 0 ≤ t < 1/n.

x₁(t) and x₂(t) are orthonormal to each other over 0 ≤ t < 1/n.

x₂(t) is a harmonic of x₁(t).

x₁(t) and x₂(t) are non-orthogonal to each other over 0 ≤ t < 1/(2n).

() is the correct answer.

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