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GATE EC Networks, Signals and Systems questions

Practise Networks, Signals and Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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20 on this page
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
The Laplace Transform of the signal x(t)=u(t−2)∗(tu(t))x(t)=u(t-2) *(t u(t)) is given by which of the following expressions? ["*" represents convolution operator]
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Two analog signals x1(t)x_{1}(t) and x2(t)(tx_{2}(t)(t in second )), are sampled at a rate Fs=40 HzF_{s}=40 \mathrm{~Hz}, where x1(t)=cos⁡(20πt),t≥0, and x2(t)=cos⁡(100πt),t≥0x_{1}(t)=\cos (20 \pi t), t \geq 0, \text{ and } x_{2}(t)=\cos (100 \pi t), t \geq 0 The first ten samples (starting from t=0t=0 ) are considered for the analysis. Which of the following statements is TRUE?
Official PYQ2026Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The response of a discrete time system y[n]y[n] obeys the following relation: y[n]=56y[n−1]−16y[n−2]+x[n].y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] . The input to the system is x[n]=δ[n]−13δ[n−1]x[n]=\delta[n]-\frac{1}{3} \delta[n-1]. Which of the following options is TRUE for y[n]y[n]?
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
The relation between the input current ( II ) and the output voltage ( VV ) of a circuit is governed by the equation: CdVdt=I(t)−m(t)C \dfrac{d V}{d t}=I(t)-m(t). The circuit is excited by I(t)=qδ(t)I(t)=q \delta(t), where qq is a real valued constant. VV at t=0−t=0^{-}is V0V_{0}. Which of the following is an equivalent representation of the above case?
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
The output voltage VoV_{o} (in Volt) for the network given in the Figure is ____\_\_\_\_ . (rounded off to two decimal places)
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
Consider the circuit shown in the Figure, where the input vi(t)v_{i}(t) is in Volt. The average power (in mW\text{mW} ) dissipated in the load resistance of 1 kΩ1 ~\mathrm{k} \Omega at the resonant frequency is ____\_\_\_\_ . (rounded off to two decimal places)
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
For a lossless passive two-port network, ∣S11∣\left|S_{11}\right| and ∣S21∣\left|S_{21}\right| intersect at −3-3 dB . For a lossy passive two-port network, ∣S11∣\left|S_{11}\right| and ∣S21∣\left|S_{21}\right| intersect at −4-4 dB . The percentage of power dissipated in the lossy network at the intersection frequency is ____\_\_\_\_. (rounded off to two …
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
The continuous time signal x(t)x(t) is real, periodic with period TT and satisfies the Dirichlet conditions. The Fourier series representation of x(t)=∑−∞∞anej(2πntT)x(t)=\sum_{-\infty}^{\infty} a_{n} e^{j\left(\frac{2 \pi n t}{T}\right)} and x(t)x(t) satisfies the following: x(t−T2)=−x(t)x\left(t-\frac{T}{2}\right)=-x(t). For any integer mm, which of the following options is …
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
In the given circuit, L=1μHL=1 \mu \mathrm{H} and C=1μ FC=1 \mu \mathrm{~F}. The phasor diagram for ICI_{C} and ILI_{L} is also shown. Assume that the phase (θ1+θ2)\left(\theta_{1}+\theta_{2}\right) is 90∘90^{\circ} at a frequency of 159.15 kHz.159.15 ~\text{kHz}. Among the following options, what is the nearest integer value of RC×RL?R_{C} \times R_{L}?
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider a real signal x(t),−∞<t<∞x(t),-\infty < t < \infty, such that x(t)=0fort<0,x(t)=2for0≤t<1andx(t)=0fort≥1x(t) = 0\quad\text{for}\quad t <0, x(t) =2 \quad\text{for} \quad0 \leq t < 1\quad \text{and}\quad x(t) = 0\quad \text{for} \quad t \geq 1. Let E[x(t)]=∫−∞∞[x(t)]2dtE[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2} d t. Which of the following options correctly represents the ratio, …
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider a real baseband signal x(t)=e−2tx(t)=e^{-2 t}, for tt (in seconds) ≥0\geq 0. If 99%99 \% of energy of x(t)x(t) lies within B HzB \mathrm{~Hz}, then which of the following options is TRUE for the value of B?{B}?
Official PYQ2026Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Consider the discrete time system (S) with input x[n]x[n] and output y[n]y[n] as shown in the Figure. The two sub-systems represented by their impulse responses h1[n]h_{1}[n] and h2[n]h_{2}[n] are linear and time invariant. Which of the following statements is necessarily TRUE?
Official PYQ2026Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
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\mathrm{A}, \mathrm{B}, \mathrm{C} and D\text{D} parameters?
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMSQ · 2 marks
Let x1(t)=cos⁡(2πnt)x_{1}(t)=\cos (2 \pi n t) and x2(t)=2sin⁡(4πnt)x_{2}(t)=2 \sin (4 \pi n t) represent two sinusoids for a positive integer nn and −∞<t<∞-\infty < t < \infty. Which of the following statements about x1(t)x_{1}(t) and x2(t)x_{2}(t) is/are valid?
Official PYQ2025Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
Consider the discrete-time system below with input x[n]x[n] and output y[n]y[n]. In the figure, h1[n]h_{1}[n] and h2[n]h_{2}[n] denote the impulse responses of LTI Subsystems 11 and 22, respectively. Also, δ[n]\delta[n] is the unit impulse, and b>0b>0. Assuming h2[n]≠δ[n]h_{2}[n] \neq \delta[n], the overall system (denoted by the dashed box) is …
Official PYQ2025Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Consider a continuous-time, real-valued signal f(t)f(t) whose Fourier transform F(ω)=∫−∞∞f(t)exp⁡(−j ωt)dtF(\omega)=\int_{-\infty}^{\infty} f(t) \exp (-j \: \omega t) d t exists. Which one of the following statements is always TRUE?
Official PYQ2025Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the 3Ω3 \Omega resistor are as indicated. The voltage (in Volts) at node XX is ______\_\_\_\_\_\_
Official PYQ2025Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
Let iC,iLi_{C}, i_{L}, and iRi_{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?
Official PYQ2025Networks, Signals and SystemsDiscrete-time SignalsMSQ · 1 mark
Let x[n]x[n] be a discrete-time signal whose zz-transform is X(z)X(z). Which of the following statements is/are TRUE?
Official PYQ2025Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
All the components in the bandpass filter given below are ideal. The lower −3-3 dB frequency of the filter is 11 MHz. The upper −3-3 dB frequency (in MHz , rounded off to the nearest integer) is _______\_\_\_\_\_\_\_