List of top Questions asked in GATE Electronics and Communication Engineering

Which of the following can be used as an n-type dopant for silicon?
Select the correct option(s).

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?

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): \[ f_{DSB}(t) = A_c m(t) \cos(2\pi f_c t) \] • Amplitude modulation (AM): \[ f_{AM}(t) = A_c \left( 1 + \mu m(t) \right) \cos(2\pi f_c t) \] Here, $ A_c $ and $ f_c $ are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, $ \mu $ 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?

Let $ x[n] $ be a discrete-time signal whose $ z $-transform is $ X(z) $. Which of the following statements is/are TRUE?

Consider the unity-negative-feedback system shown in Figure (i) below, where gain $ K \geq 0 $. The root locus of this system is shown in Figure (ii) below.
For what value(s) of $ K $ will the system in Figure (i) have a pole at $ -1 + j1 $?

Consider the function $ f: \mathbb{R} \to \mathbb{R} $, defined as \[ f(x) = 2x^3 - 3x^2 - 12x + 1. \] Which of the following statements is/are correct? (Here, $ \mathbb{R} $ is the set of real numbers.)

A full adder and an XOR gate are used to design a digital circuit with inputs $ X, Y, Z $, and output $ F $, as shown below. The input $ Z $ is connected to the carry-in input of the full adder.
If the input $ Z $ is set to logic ‘1’, then the circuit functions as _________ with $ X $ and $ Y $ as inputs.

A simplified small-signal equivalent circuit of a BJT-based amplifier is given below.
The small-signal voltage gain $ \frac{V_o}{V_S} $ (in V/V) is _________.

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?

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

Consider a continuous-time, real-valued signal $ f(t) $ whose Fourier transform \[ F(\omega) = \int_{-\infty}^{\infty} f(t) \exp(-j \omega t) \, dt { exists.} \] Which one of the following statements is always TRUE?

The Nyquist plot of a system is given in the figure below. Let $ \omega_P, \omega_Q, \omega_R, $ and $ \omega_S $ be the positive frequencies at the points $ P, Q, R, $ and $ S $, respectively. Which one of the following statements is TRUE?

Consider an additive white Gaussian noise (AWGN) channel with bandwidth $ W $ and noise power spectral density $ \frac{N_0}{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 $ N_0 $ fixed)?

Consider a frequency-modulated (FM) signal \[ f(t) = A_c \cos(2\pi f_c t + 3 \sin(2\pi f_1 t) + 4 \sin(6\pi f_1 t)), \] where $ A_c $ and $ f_c $ are, respectively, the amplitude and frequency (in Hz) of the carrier waveform. The frequency $ f_1 $ is in Hz, and assume that $ f_c>100 f_1 $. The peak frequency deviation of the FM signal in Hz is _________.

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?

Consider the following series:
(i) $ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} $
(ii) $ \sum_{n=1}^{\infty} \frac{1}{n(n+1)} $
(iii) $ \sum_{n=1}^{\infty} \frac{1}{n!} $
Choose the correct option.

Consider the matrix $ A $ below: \[ A = \begin{bmatrix} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{bmatrix} \] For which of the following combinations of $ \alpha, \beta, $ and $ \gamma $, is the rank of $ A $ at least three? (i) $ \alpha = 0 $ and $ \beta = \gamma \neq 0 $.
(ii) $ \alpha = \beta = \gamma = 0 $.
(iii) $ \beta = \gamma = 0 $ and $ \alpha \neq 0 $.
(iv) $ \alpha = \beta = \gamma \neq 0 $.

An ideal p-n junction germanium diode has a reverse saturation current of 10 $\mu A$ at 300 K. The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is _________. (Consider the Boltzmann constant $ k_B = 1.38 \times 10^{-23} { J/K} $ and the charge of an electron $ e = 1.6 \times 10^{-19} { C} $.

Let $ f(t) $ be a periodic signal with fundamental period $ T_0>0 $. Consider the signal \[ y(t) = f(\alpha t), \quad {where} \, \alpha>1. \] The Fourier series expansions of $ f(t) $ and $ y(t) $ are given by \[ f(t) = \sum_{k=-\infty}^{\infty} c_k e^{j \frac{2\pi}{T_0} k t}, \quad y(t) = \sum_{k=-\infty}^{\infty} d_k e^{j \frac{2\pi}{T_0 \alpha} k t}. \] Which of the following statements is/are TRUE?

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

Consider a non-negative function $ f(x) $ which is continuous and bounded over the interval [2, 8]. Let $ M $ and $ m $ denote, respectively, the maximum and the minimum values of $ f(x) $ over the interval. Among the combinations of $ \alpha $ and $ \beta $ given below, choose the one(s) for which the inequality \[ \beta \leq \int_2^8 f(x) \, dx \leq \alpha \] is guaranteed to hold.

A square metal sheet of 4 m $ \times $ 4 m is placed on the x-y plane as shown in the figure below. If the surface charge density (in $ \mu $C/m$^2$) on the sheet is $ \rho_s(x, y) = 4|y| $, then the total charge (in $ \mu $C, rounded off to the nearest integer) on the sheet is _________.

The electron mobility $ \mu_n $ in a non-degenerate germanium semiconductor at 300 K is 0.38 m$^2$/Vs. The electron diffusivity $ D_n $ at 300 K (in cm$^2$/s, rounded off to the nearest integer) is _________.

An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of $ 5.8 \times 10^7 \, {S/m} $. The current (in Amperes, rounded off to two decimal places) flowing through the wire is _________.

A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with frequency 500 kHz, the maximum SNR (in dB, rounded off to two decimal places) and the data rate (in Mbps) at the output of the ADC are _________, respectively.