List of practice Questions

Let continuous-time signals \( x_1(t) \) and \( x_2(t) \) be defined as:

\[ x_1(t) = \begin{cases} 1, & t \in [0, 1] \\ 2 - t, & t \in [1, 2] \\ 0, & \text{otherwise} \end{cases} \quad \text{and} \quad x_2(t) = \begin{cases} t, & t \in [0, 1] \\ 2 - t, & t \in [1, 2] \\ 0, & \text{otherwise} \end{cases} \]

Consider the convolution \( y(t) = x_1(t) * x_2(t) \). Then

\[ \int_{-\infty}^{\infty} y(t)\,dt =\ ? \]

In the circuit shown below, if the values of \( R \) and \( C \) are very large, the form of the output voltage for a very high frequency square wave input is best represented by: 

In the circuit, \( I_{DC} \) is an ideal current source. The transistors \( M_1 \) and \( M_2 \) are assumed to be biased in saturation, wherein \( V_{in} \) is the input signal and \( V_{DC} \) is fixed DC voltage. Both transistors have a small signal resistance of \( r_{ds} \) and transconductance of \( g_m \). The small signal output impedance of this circuit is: 

A Boolean function is given as \[ f = (\bar{u} + \bar{v} + \bar{w} + \bar{x}) \cdot (\bar{u} + \bar{v} + \bar{w} + x) \cdot (\bar{u} + v + \bar{w} + \bar{x}) \cdot (\bar{u} + v + \bar{w} + x) \] The simplified form of this function is represented by:
Let \( X \) and \( Y \) be continuous random variables with probability density functions \( P_X(x) \) and \( P_Y(y) \), respectively. Further, let \( Y = X^2 \) and \[ P_X(x) = \begin{cases} 1, & x \in (0,1] \\ 0, & \text{otherwise} \end{cases} \] Which one of the following options is correct?
Which of the following reactions is an example of the Finkelstein reaction?
What is the antonym of eradicate?

The freezing point depression constant (\( K_f \)) for water is \( 1.86 \, {°C·kg/mol} \). If 0.5 moles of a non-volatile solute is dissolved in 1 kg of water, calculate the freezing point depression.

The induced emf in a 3.3 kV, 4-pole, 3-phase star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no-load condition.

On application of a mechanical load, the induced emf phasor is deflected by an angle of \( 2^\circ \) mechanical with respect to the terminal voltage phasor.
If the synchronous reactance is \( 2 \, \Omega \), and stator resistance is negligible, then the motor armature current magnitude, in amperes, during loaded condition is closest to: \[ \text{(round off to two decimal places).} \]

In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with \( I = 10 \, \text{A} \) and \( V = 15 \, \text{V} \). The power delivered by the current source, in W, is:

\[ \text{(round off to the nearest integer).} \]

Consider a distribution feeder, with \( R/X \) ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is: \[ \text{(round off to three decimal places).} \]
The maximum percentage error in the equivalent resistance of two parallel connected resistors of 100 \( \Omega \) and 900 \( \Omega \), with each having a maximum 5% error, is: \[ \text{(round off to nearest integer value).} \]
A continuous time periodic signal \( x(t) \) is given by: \[ x(t) = 1 + 2\cos(2\pi t) + 2\cos(4\pi t) + 2\cos(6\pi t) \] If \( T \) is the period of \( x(t) \), then evaluate: \[ \frac{1}{T} \int_0^T |x(t)|^2 \, dt \quad \text{(round off to the nearest integer).} \]

The open-loop transfer function of the system shown in the figure is: \[ G(s) = \frac{K s (s + 2)}{(s + 5)(s + 7)} \] For \( K \geq 0 \), which of the following real axis point(s) is/are on the root locus? 

Instrument(s) required to synchronize an alternator to the grid is/are:

The operating region of the developed torque \( T_{em} \) and speed \( \omega \) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque \( T_L \) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time? 

Which one of the following figures represents the radial electric field distribution ER caused by a spherical cloud of electrons with a volume charge density,

ρ = -3ρ0 for 0 ≤ R ≤ a (both ρ0, a are positive and R is the radial distance),

and ρ = 0 for R > a?

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a:

The Nyquist plot of a strictly stable \( G(s) \), having the numerator polynomial as \( (s - 3) \), encircles the critical point \(-1\) once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in the figure is correct?

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is:

Time (sec)0.61.62.610∞
Output0.781.652.182.983
Consider a continuous-time signal \[ x(t) = -t^2 \left\{ u(t+4) - u(t-4) \right\} \] where \( u(t) \) is the continuous-time unit step function. Let \( \delta(t) \) be the continuous-time unit impulse function. The value of \[ \int_{-\infty}^{\infty} x(t)\delta(t+3) \, dt \] is:

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, \( R \), will behave as a

The I-V characteristics of the element between the nodes X and Y is best depicted by 

Consider discrete random variables \( X \) and \( Y \) with probabilities as follows:

\( P(X=0 \text{ and } Y=0) = \frac{1}{4}, \)
\( P(X=1 \text{ and } Y=0) = \frac{1}{8}, \)
\( P(X=0 \text{ and } Y=1) = \frac{1}{2}, \)
\( P(X=1 \text{ and } Y=1) = \frac{1}{8}. \)

Given \( X = 1 \), the expected value of \( Y \) is