List of top Questions asked in GATE EE- 2024

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:}

A three-phase, 50 Hz, 6-pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is:

Which one of the following options represents possible voltage polarities in a single-phase two winding transformer? Here, \( V_p \) is the applied primary voltage, \( E_p \) is the induced primary voltage, \( V_s \) is the open circuit secondary voltage, and \( E_s \) is the induced secondary voltage.

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}

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

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:

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}

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:

For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where $\alpha$, $\beta$, $\gamma$, and $x$ are strictly positive. The bus injections $P_1$ and $P_2$ are in pu. If $P_1 = mP_2$, where $m>0$ and the real power flow from bus 1 to bus 2 is 0 pu, then which one of the following options is correct?
\includegraphics[width=0.5\linewidth]{41.png}

A BJT biasing circuit is shown in the figure, where $V_{BE = 0.7V$ and $\beta = 100$. The Quiescent Point values of $V_{CE}$ and $I_{C}$ are respectively:} \includegraphics[width=0.4\linewidth]{42.png}