List of practice Questions

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}

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}

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}

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 \( y(t) \)?

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:}

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 number of junctions in the circuit is:
\includegraphics[width=0.5\linewidth]{13.png}

The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the country (in Million liters). Considering the data presented in the chart, which one of the following options is true?
\includegraphics[width=0.5\linewidth]{8.png}

The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left (\(\leftarrow\)) or the right (\(\rightarrow\)) direction. If the object \(A\) (Rack) is translating towards the right (\(\rightarrow\)) direction, the correct statement among the following is:
\includegraphics[width=0.5\linewidth]{9.png}