Recent questions tagged gate2015-ee-2

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at $50$ Hz. The “air-gap” voltage, $V_{g}$ across the magnetizing in...

The current $i$ (in Ampere) in the $2 \Omega$ resistor of the given network is ________.

The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.

A series $RL$ circuit is excited at $t = 0$ by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\dfrac{d^{2}i}{dt^{2}}$ at $t=0^{+...

A $3$-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is$\begin{bmatrix}-j6 &j3 &j4 \\ j3&-j7 &j5 \\ ...

An open loop control system results in a response of $e^{-2t}(\sin 5t+\cos 5t)$ for a unit impulse input. The $DC$ gain of the control system is ________.

A shunt-connected $DC$ motor operates at its rated terminal voltage. Its no-load speed is $200$ radian/second. At its rated torque of $500$ Nm, its speed is $180$ radian/...

When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base $(CB)$ and the...

The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. T...

Find the transformer ratios $a$ and $b$ such that the impedance ($Z_{in}$) is resistive and equals $2.5 \Omega$ when the network is excited with a sine wave voltage of an...

A $4$-pole, separately excited, wave wound $DC$ machine with negligible armature resistance is rated for $230$ V and $5$ kW at a speed of $1200$ rpm. If the same armature...

Consider the following Sum of Products expression, $F$.$F= ABC + \overline{A} \: \: \overline{B}C + A\overline{B}C + \overline{A}BC + \overline{A} \: \overline{B} \: \ove...

In the following circuit, the transistor is in active mode and $V_{C} = 2 V$. To get $V_{C} = 4 V$, we replace $R_{C}$ with $R′_{C}$. Then the ratio $R'_{C}$/ $R_{C}$ is ...

The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is.$3s^{-5/2} /2$$s^{-1/2}$$s^{1/2}$$s^{3/2}$

Match the following.$\begin{array}{|l|l|l|l|} \hline P. & \text{Stokes’s Theorem} & 1. & ∯ D.ds = Q \\ \hline Q. & \text{Gauss’s Theorem} & 2. & \oint f(z) dz =0 \\ \hlin...

The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is $V_{i} = 2 \sin(2\pi \times 2000t)$. The amplitude of the output voltage $V_{o}$ (i...

Two semi-infinite dielectric regions are separated by a plane boundary at $y = 0$. The dielectric constants of region $1 (y < 0)$ and region $2 (y 0)$ are $2$ and $5$, r...

A circular turn of radius $1$ m revolves at $60$ rpm about its diameter aligned with the $x$-axis as shown in the figure. The value of $\mu_{0}$ is $4\pi \times 10^{-7}$ ...

A capacitive voltage divider is used to measure the bus voltage $V_{\text{bus}}$ in a high-voltage $50$ Hz AC system as shown in the figure. The measurement capacitors $C...

Match the following:$\begin{array}{|l|l|l|l|} \hline & \textbf{Instrument Type} & & \textbf{Used for} \\ \hline P. & \text{Permanent magnet moving coil} & 1. & \text{DC...

A $3$-phase balanced load which has a power factor of $0.707$ is connected to a balanced supply. The power consumed by the load is $5$ kW. The power is measured by the tw...

In the following circuit, the input voltage $V_{in}$ is $100 \sin(100 \pi t)$. For $100 \pi RC = 50$, the average voltage across $R$ (in Volts) under steady-state is near...

The filters $F1$ and $F2$ having characteristics as shown in Figures $(a)$ and $(b)$ are connected as shown in Figure $(c)$.The cut-off frequencies of $F1$ and $F2$ are $...

We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equiva...

Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE?If $f(z)$ is differentia...

If the list of letters, $P, R, S, T, U$ is an arithmetic sequence, which of the following are also in arithmetic sequence?$2P, 2R, 2S, 2T, 2U$$P-3, R-3, S-3, T-3, U-3$$P^...

In a triangle $PQR$, $PS$ is the angle bisector of $\angle QPR$ and $\angle QPS =60^\circ$. What is the length of $PS$ ?$\dfrac{(q+r)}{qr} \\$$\dfrac{qr}{(q+r)} \\$$\sqrt...

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage:Since the report lacked needed information, it was of no use to t...

Consider a function $f(x) = 1 - |x|$ on $-1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the minimum value of the function are:$0, -1$$-1...