List of top Questions asked in GATE Electronics and Communication Engineering

A digital communication system transmits through a noiseless bandlimited channel \([-W, W]\). The received signal \(z(t)\) at the output of the receiving filter is given by: \[ z(t) = \sum_n b[n] x(t - nT), \] where \(b[n]\) are the symbols and \(x(t)\) is the overall system response to a single symbol. The received signal is sampled at \(t = mT\). The Fourier transform of \(x(t)\) is \(X(f)\). The Nyquist condition that \(X(f)\) must satisfy for zero intersymbol interference at the receiver is:

Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances \(z_{inA}\), \(z_{inB}\), \(z_{inC}\), and \(z_{inD}\) (indicated in the figure) are: \begin{center} \includegraphics[width=8cm]{15.png} \end{center}

In the context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:

In the feedback control system shown in the figure below, \[ G(s) = \frac{6}{s(s+1)(s+2)}. \] \vspace{0.5cm} \begin{center} \includegraphics[width=10cm]{13.png} \end{center} \(R(s)\), \(Y(s)\), and \(E(s)\) are the Laplace transforms of \(r(t)\), \(y(t)\), and \(e(t)\), respectively. If the input \(r(t)\) is a unit step function, then:

Let \(\hat{i}\) and \(\hat{j}\) be the unit vectors along \(x\) and \(y\) axes, respectively, and let \(A\) be a positive constant. Which one of the following statements is true for the vector fields: \[ \vec{F_1} = A(\hat{i}y + \hat{j}x) \quad {and} \quad \vec{F_2} = A(\hat{i}y - \hat{j}x)? \]

The general form of the complementary function of a differential equation is given by: \[ y(t) = (At + B)e^{-2t}, \] where \(A\) and \(B\) are real constants determined by the initial condition. The corresponding differential equation is:

Examples of mirror and water reflections are shown in the figures below: \begin{center} \includegraphics[width=10cm]{9.png} \end{center} An object appears as the following image after first reflecting in a mirror and then reflecting on water: \vspace{0.5cm} \includegraphics[width=4cm]{9i.png} The original object is:

Four identical cylindrical chalk-sticks, each of radius \( r = 0.5 \, {cm} \) and length \( l = 10 \, {cm} \), are bound tightly together using a duct tape as shown in the following figure. \begin{center} \includegraphics[width=6cm]{7.png} \end{center} The width of the duct tape is equal to the length of the chalk-stick. The area (in cm\(^2\)) of the duct tape required to wrap the bundle of chalk-sticks once, is:

Sequence the following sentences (P, Q, R, S) in a coherent passage: P: Shifu’s student exclaimed, “Why do you run since the bull is an illusion?”
Q: Shifu said, “Surely my running away from the bull is also an illusion.”
R: Shifu once proclaimed that all life is illusion.
S: One day, when a bull gave him chase, Shifu began running for his life.

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023. Based on the data provided, which one of the following options is INCORRECT? \begin{center} \includegraphics[width=8cm]{8.png} \end{center}

The greatest prime factor of \((3^{199} - 3^{196})\) is:

Two identical sheets A and B, of dimensions \( 24 \, {cm} \times 16 \, {cm} \), can be folded into half using two distinct operations, FO1 or FO2. In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge. If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is:

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5. What was his father's age when Aman was born?

For a real number \(x>1\), solve the equation: \[ \frac{1}{\log_2x} +\frac{1}{\log_3x} + \frac{1}{\log_4x} = 1 \] The value of x is:

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. If S and Q are single children, and the room allocations shown below are acceptable to all: \[ \begin{array}{|c|c|c|} P, R & T, S & Q
P, Q & R, T & S
\end{array} \] Then, which one of the given options is the siblings?