List of top Questions asked in GATE Electrical Engineering

Consider the discrete-time systems \( T_1 \) and \( T_2 \) defined as follows: \[ [T_1x][n] = x[0] + x[1] + \dots + x[n], \] \[ [T_2x][n] = x[0] + \frac{1}{2}x[1] + \dots + \frac{1}{2^n}x[n]. \] Which of the following statements is true?

The input \( x(t) \) and the output \( y(t) \) of a system are related as \[ y(t) = e^{-t} \int_{-\infty}^t e^t x(\tau) d\tau, \quad -\inftyLt;tLt;\infty. \] The system is:

A forced commutated thyristorized step-down chopper is shown. Neglect the ON-state drop across power devices. Assume that the capacitor is initially charged to 50 V with the polarity shown in the figure. The load current \(I_l\) can be assumed to be constant at 10 A. Initially, \(Th_M\) is ON and \(ThA\) is OFFThe turn-off time available to \( T_{H4} \) in microseconds, when \( T_{H4} \) is triggered, is \_\_\_\_\_ (rounded off to the nearest integer).
\includegraphics[width=0.5\linewidth]{35.png}

Let \( X(\omega) \) be the Fourier transform of the signal \( x(t) = e^{-4t \cos(t), -\inftyLt;tLt;\infty \). The value of the derivative of \( X(\omega) \) at \( \omega = 0 \) is \_\_\_\_\_ (rounded off to 1 decimal place).}

The incremental cost curves of two generators (\( \text{Gen A} \) and \( \text{Gen B} \)) in a plant supplying a common load are shown. If the incremental cost of supplying the common load is \( \lambda = 7400 \, \text{Rs/MWh} \), the common load in MW is \_\_\_\_\_ (rounded to the nearest integer).
\includegraphics[width=0.5\linewidth]{34.png}

Consider the complex function \( f(z) = \cos z + e^{z^2 \). The coefficient of \( z^5 \) in the Taylor series expansion of \( f(z) \) about the origin is \_\_\_\_\_ (rounded off to 1 decimal place).}

In the circuit, the present value of \( Z \) is 1. Neglecting the delay in the combinational circuit, the values of \( S \) and \( Z \), respectively, after the application of the clock will be:
\includegraphics[width=0.5\linewidth]{25.png}

To obtain the Boolean function \( F(X, Y) = XY + \overline{X \), the inputs \( P, Q, R, S \) in the figure should be:}
\includegraphics[width=0.5\linewidth]{26.png}

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step response of the original and the approximated systems are the same?
\includegraphics[width=0.5\linewidth]{22.2.png}

The table lists two instrument transformers and their features:
\begin{tabular}{|l|l|} \hline Instrument Transformers & Features
\hline X) Current Transformer (CT) & P) Primary is connected in parallel to the grid
& Q) Open circuited secondary is not desirable
& R) Primary current is the line current
\hline Y) Potential Transformer (PT) & S) Secondary burden affects the primary current
\hline \end{tabular}
Which matches are correct?

Simplified form of the Boolean function: \[ F(P, Q, R, S) = \overline{P}\overline{Q}R + \overline{P}QS + PQ\overline{R}S \] is:

For the block diagram shown in the figure, the transfer function \( \frac{C(s){R(s)} \) is:}
\includegraphics[width=0.5\linewidth]{20.png}

The figure shows the single-line diagram of a 4-bus power network. Branches \( b_1, b_2, b_3 \), and \( b_4 \) have impedances \( 4z, z, 2z \), and \( 4z \) per-unit (pu), respectively, where \( z = r + jx \) with \( r>0 \) and \( x>0 \). The current drawn from each load bus (marked as arrows) is equal to \( 1 \, \text{pu} \), where \( I \neq 0 \). If the network is to operate with minimum loss, the branch that should be opened is:
\includegraphics[width=0.5\linewidth]{19.png}

Consider the standard second-order system of the form: \[ \frac{\omega_n^2}{s^2 + 2\xi\omega_n s + \omega_n^2}, \] with the poles \(p\) and \(p^*\) having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below: System 1: \( \omega_n = 3 \, \text{rad/sec} \) and \( \theta = 60^\circ \). System 2: \( \omega_n = 1 \, \text{rad/sec} \) and \( \theta = 70^\circ \). Which one of the following statements is correct?
\includegraphics[width=0.5\linewidth]{22.png}

If \( u(t) \) is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal \( x(t) = {e^t^2 [ u(t-1) - u(t-10) ] \) is:}

Suppose signal \( y(t) \) is obtained by the time-reversal of signal \( x(t) \), i.e., \( y(t) = x(-t) \),\(-\inftyLt;tLt;\infty\) Which of the following options is always true for the convolution of \( x(t) \) and \( y(t) \)?

The circuit shown in the figure with the switch \( S \) open is in steady state. After the switch \( S \) is closed, the time constant of the circuit in seconds is:
\includegraphics[width=0.5\linewidth]{14.png}