In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load $R_0$. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V . The value of $R_s$ is $6 \Omega$. The Zener diode has a maximum rated power dissipation of 2.5 W . Assuming the Zener diode to be ideal, the minimum value of $R_0$ is $\_\_\_\_$ $\Omega$.

In the BJT circuit shown, beta of the PNP transistor is 100 . Assume $V_{B E}=-0.7 \mathrm{~V}$. The voltage across $R_C$ will be 5 V when $R_2$ is $\_\_\_\_$ $\mathrm{k} \Omega$. (Round off to 2 decimal places)

In the circuit shown, the input $V_i$ is a sinusoidal AC voltage having an rms value of $230 \mathrm{~V} \pm 20 \%$. The worst case peak-inverse voltage seen across any diode is $\_\_\_\_$ V. (Round off to 2 decimal places)

A CMOS Schmitt-trigger inverter has a low output level of 0 V and a high output level of 5 V . It has input thresholds of 1.6 V and 2.4 V . The input capacitance and output resistance of the Schmitt trigger are negligible. The frequency of the oscillator shown in the figure is $\_\_\_\_$ Hz. (Round off to 2 decimal places)

The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the rms value of the full-wave rectified waveform to the rms value of the clipped waveform is $\_\_\_\_$ . (Round off to 2 decimal places,)

$$ \text { For the closed-loop system shown, the transfer function } \frac{E(s)}{R(s)} \text { is } $$

Consider a closed loop system as shown.

$$ G_p(s)=\frac{14.4}{s(1+0.1 s)} $$

is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}$. (Round off to 2 decimal places).

The Bode magnitude plot for the transfer function $\frac{V_0(s)}{V_i(s)}$ of the circuit is as shown. The value of $R$ is $\Omega$. (Round off to 2 decimal places)

In the given figure, plant $G_p(s)=\frac{2.2}{(1+0.1 s)(1+0.4 s)(1+1.2 s)}$ and compensator $G_c(s)=K\left[\frac{1+T_1 s}{1+T_2 s}\right]$.

The external disturbance input is $D(s)$. It is desired that when the disturbance is a unit step, the steady state error should not exceed 0.1 unit. The minimum value of $K$ is ____________. . (Round off to 2 decimal places)

$$ \text { The state space representation of a first-order system is given as } $$

$$ \begin{aligned} & \dot{x}=-x+u \\ & y=x \end{aligned} $$

Where, $x$ is the state variable, $u$ is the control input and $y$ is the controlled output. Let $u=-k x$ be the control law, where $K$ is the controller gain. To place a closed loop pole at -2 , the value of $k$ is $\_\_\_\_$

A 16 -bit synchronous binary up-counter is clocked with a frequency $f_{c l k}$. The two most significant bits are ORed together to form an output $Y$. Measurements shows that $Y$ is periodic and the duration for which $Y$ the remains high in each period is 24 ms . The clock frequency $f_{\text {clk }}$ is $\_\_\_\_$ MHz. (Round off to 2 decimal places)

A counter is constructed with three D flip-flops. The input-output pairs are named as $\left(D_0, Q_0\right)$, $\left(D_1, Q_1\right)$ and $\left(D_2, Q_2\right)$, where the subscript 0 denotes LSB. The output sequence is desired to be Graycode sequence $000,001,011,010,110,111,101$ and 100 , repeating periodically. Note that the bits are listed in the $Q_2 Q_1 Q_0$ format. The combination logic expression for $D_1$ is

In the given circuit, for voltage V_y to be zero, the value of β should be ______. (Round off to 2 decimal places).

In the given circuit, for maximum power to be delivered to R_L, its value should be ______ Ω. (Round off to 2 decimal places.)

In the circuit, switch 'S' is in the closed position for a very long time. If the switch is opened at time t = 0, then i_L (t) in amperes, for t ≥ 0 is

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals 'ab' is

A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is ______ μF.

(Round off to 2 decimal places)

$$ \text { The input impedance, } Z_{\text {in }}(s) \text {, for the network shown is } $$

Two single-core power cables have total conductor resistances of $0.7 \Omega$ and $0.5 \Omega$ respectively and their insulation resistances (between core and sheath) are $600 \mathrm{M} \Omega$ and $900 \mathrm{M} \Omega$ respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is $\_\_\_\_$ $\times 10^6$

In the given circuit, the value of capacitor $C$ that makes current $I=0$ is $\_\_\_\_$ $\mu \mathrm{F}$.

A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio $\left|\frac{I_B}{I_R}\right|$ is $\_\_\_\_$ .

A signal generator having a source resistance of $50 \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is $\_\_\_\_$ $\mu \mathrm{F}$. (Round off to 2 decimal places)

Inductance is measured by,

In a single phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz . The total iron loss is 850 W at 220 V and 25 Hz . Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are

$$ \text { Consider the table given : } $$

The correct combination that relates the constructional feature, machine type and mitigation is

An 8 pole, $50 \mathrm{~Hz}, 3$ phase, slip-ring induction motor has an effective rotor resistance of $0.08 \Omega$ per phase. Its speed at maximum torque is 650 rpm . The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is $\_\_\_\_$ $\Omega$. (Round off to 2 decimal places). Negleet magnetizing eurrent and stater leakage impedanee. Consider equivalent eireuit parameters referred to stator.

The power input to a $500 \mathrm{~V}, 50 \mathrm{~Hz}, 6$ pole, 3 phase induction motor running at 975 rpm is 40 kW . The stator losses are 1 kW . If the total friction and windage losses are 2.025 kW , then the efficiency is

$\_\_\_\_$ $\%$.

A belt-driven DC shunt generator running at 300 rpm delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is $0.025 \Omega$, field resistance is $50 \Omega$ and brush drop is 2 V . Ignoring armature reaction, the speed of the motor is _________ rpm. (Round off to 2 decimal places.)

An alternator with an internal voltage of $1 \delta_1$ pu and synchronous reactance of 0.4 pu is connected by a transmission line of reactance 0.1 pu to a synchronous motor having synchronous reactance 0.35 pu and internal voltage of $0.85 \delta_2 \mathrm{pu}$. If the real power supplied by the alternator is 0.866 pu , then ( $\delta_1-\delta_2$ ) is $\_\_\_\_$ degrees (Round off to 2 decimal places). (Machines are of non-salient type. Neglect resistances)

Which one of the following vector functions represents a magnetic field $\vec{B}$ ? ( $\hat{x}, \hat{y}$, and $\hat{z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis respectively)

A $1 \mu \mathrm{C}$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10 \mu \mathrm{C}$ is moved from $(0,10,0)$ to $(5,5,5)$ and subsequently to $(5,0,0)$, then the total work done is

$\_\_\_\_$ mJ . (Round off to 2 decimal places). Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ in SI units. All coordinates are in meters.

One Coulomb of point charge moving with a uniform velocity $10 \hat{x} \mathrm{~m} / \mathrm{s}$ enters the region $x \geq 0$ having a magnetic flux density $\vec{B}=(10 y \hat{x}+10 x \hat{y}+10 \hat{z}) \mathrm{T}$. The magnitude of force on the charge at $x=0^{+}$is

$\_\_\_\_$ N. ( $\hat{x}, \hat{y}$ and $\hat{z}$ are unit vectors along x -axis, y -axis and z -axis respectively)

Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity 5 . The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field $E_2$ in the gap to the original electric field $E_1$ is $\_\_\_\_$ .

Let $p$ and $q$ be real numbers such that $p^2+q^2=1$. The eigen values of the matrix $\left[\begin{array}{cc}p & q \\ q & -p\end{array}\right]$ are

Let $A$ be a $10 \times 10$ matrix such that $A^5$ is null matrix and let $I$ be the $10 \times 10$ identity matrix. The determinant of $A+I$ is $\_\_\_\_$ .

Let $f(x)$ be a real-valued function such that $f^{\prime}\left(x_0\right)=0$ for some $x_0 \in(0,1)$ and $f^{\prime \prime}\left(x_0\right)>0$ for all $x \in(0,1)$. Then $f(x)$ has

Let $(-1-j),(3-j),(3+j)$ and $(-1+j)$ be the vertices of rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of contour integral $\oint_C \frac{d z}{z^2(z-4)}$ is

Let $P(z)=z^3+(1+j) z^2+(2+j) z+3$, where $z$ is complex number. Which one of the following is true?

Suppose the probability that a coin toss shows "head" is $p$, where $0 < p < 1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is :

Suppose the circles $x^2+y^2=1$ and $(x-1)^2+(y-1)^2=r^2$ intersect each other orthogonally at the point $(u, v)$. Then $u+v=$ $\_\_\_\_$ .

In the open interval $(0,1)$, the polynomial $p(x)=x^4-4 x^3+2$ has

Consider the boost converter shown. Switch $Q$ is operating at 25 kHz with a duty cycle of 0.6 . Assume the diode and switch to be ideal. Under steady-state condition, the average resistance $R_{\text {in }}$ as seen by the source is $\_\_\_\_$ $\Omega$. (Round off to 2 decimal places)

A single-phase full bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across " $a b$ " as shown. To achieve a modulation index of 0.8 , the angle $\theta$ expressed in degrees should be $\_\_\_\_$ . (Round off to 2 decimal places)

(Modulation index is defined as the ratio of the peak of the fundamental component of $V_{d b}$ to the applied DC value)

Consider the buck-boost converter shown. Switch $Q$ is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady-state condition, the average current flowing through the inductor is $\_\_\_\_$ A.

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are

$$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$

They need to deliver a combined load of 260 MW . Ignoring the network losses, for economic operation, the generations $P_1$ and $P_2$ (in MW) are

A 3-bus network is shown. Consider generators as ideal voltage sources. If rows 1,2 and 3 of the $Y_{h s}$ matrix correspond to bus 1,2 and 3 respectively, then $Y_{h s}$ of the network is

In the figure shown, self-impedances of the two transmission lines are $1.5 j \mathrm{pu}$ each and $Z_m=0.5 j \mathrm{pu}$ is the mutual impedance. Bus voltages shown in the figure are in pu. Given that $\delta>0$, the maximum steady state real power that can be transferred in pu from bus- 1 to bus- 2 is

Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus. $P V$ buses and $P Q$ buses for load flow study. The number of $P Q$ buses is $N_L$. The balanced Newton-Raphson method is used to carry out load flow study in polar form $H, S, M$ and $R$ are sub-matrices of the Jacobian matrix $J$ as shown below:

$$ \left[\begin{array}{l} \Delta P \\ \Delta Q \end{array}\right]=J\left[\begin{array}{l} \Delta \delta \\ \Delta \gamma \end{array}\right] \text {, where } J=\left[\begin{array}{ll} H & S \\ M & R \end{array}\right] $$

The dimension of the sub matrix $M$ is

Suppose $I_A, I_B$ and $I_C$ are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current $I_{B 0}=0.1 \angle 0^0$ p.u. If phase-A current $I_A=1.1 \angle 0^0$ p.u and phase- $C$ current $I_C=\left(1 \angle 120^0+0.1\right)$ p.u., then $I_B$ in p.u is

The causal signal with $z$-transform $z^2(z-a)^{-2}$ is ( $u[n]$ is the unit step signal)

Let $f(t)$ be an even function, i.e., $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as

$F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-j \omega t} d t$. Suppose $\frac{d F(\omega)}{d \omega}=-\omega F(\omega)$ for all $\omega$ and $F(0)=1$. Then

If the input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\max [0, x(t)]$, then the system is

Two discrete-time linear time-invariant systems with impulse responses $h_1\lfloor n\rfloor=\delta\lfloor n-1\rfloor+\delta\lfloor n+1\rfloor$ and $h_2[n]=\delta[n]+\delta[n-1]$ are connected in cascade. Where $\delta[n]$ in the Kronecker delta. The impulse response of the cascade system

For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is

Seven Cars $P, Q, R, S, T, U$ and $V$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should be parked next to each other, whereas $P$ and $Q$ can't be parked next to each other. $Q$ and $S$ must be parked next to each other. $R$ is parked to the immediate right of $\mathrm{V} . \mathrm{T}$ is parked to the left of U .

Based on the above statements, the only incorrect option given below is

The people $\_\_\_\_$ were at the demonstration were from all sections of society.

Oasis is to sand as island is to $\_\_\_\_$ .

Which one of the following options maintains a similar logical relation in the above sentence?

The number of student passing or failing in an exam for a particular subject are presented in the bar chart below. Students who pass the exam cannot appear for the exam again. Students who fails the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt. The numbers of students who took the exam for the first time in the year $2^{\text {nd }}$ the year 3 respectively, are $\_\_\_\_$ .

Which one of the following numbers is exactly divisible by $\left(11^{13}+1\right) ?$

$$ \text { A transparent square sheet shown below is folded along the dotted line. The folded sheet will look like. } $$

In the figure shown above, each inside square is formed by joining the mid points of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $\mathrm{cm}^2$ is

Let $X$ is a continuous random variable denoting the temperature measured. The range of temperature is $[0,100]$ degree Celsius and let the probability density function of $X$ be $f(x)=0.01$ for $0 \leq X \leq 100$. The mean of $X$ is $\_\_\_\_$ .

The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?