GATE EC question library

A $230\: V$ rms source supplies power to two loads connected in parallel. The first load draws $10 \: kW$ at $0.8$ leading power factor and the second one draws $10\: kVA$ at $0.8$ lagging power factor. The complex power delivered by the source is

A periodic variable $x$ is shown in the figure as a function of time. The root-mean-square (rms) value of $x$ is _______.

In the circuit shown in the figure, the value of capacitor $C\:(\text{in}\: mF)$ needed to have critically damped response $i(t)$ is ____.

A BJT is biased in forward active mode. Assume $V_{EE} = 0.7\:V, \: kT/q = 25\:mV$ and reverse saturation current $I_{S} = 10^{-13}\:A.$ The transconductance of the BJT (in $mA/V$) is __________

The doping concentrations on the $p$-side and $n$-side of a silicon diode are $1\times 10^{16}\:cm^{-3}$ and $1\times 10^{17}\:cm^{-3},$ respectively. A forward bias of $0.3\:V$ is applied to the diode. At $T = 300\:K,$ the intrinsic carrier concentration of silicon $n_{i} = 1.5\times 10^{10}\:cm^{-3}$ and $\dfrac{kT}{q} = 26\:mV.$ The …

A depletion type $N$-channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume threshold voltage $V_{TH} = -0.5\:V,V_{GS} = 2.0\:V,V_{DS} = 5\:V,\:W/L = 100,C_{ox} = 10^{-8}\:F/cm^{2}$ and $\mu_{n} = 800\:cm^{2}/V$-$s.$ The value of the resistance of the voltage controlled resistor (in $\Omega)$ is _______.

In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has $V_{BE} = 0.7\:V$ and $\beta = 100,$ and the zener voltage is $4.7\:V.$ For a regulated output of $9\:V,$ the value of $R$ (in $\Omega)$ is ______.

In the circuit shown the op-amp has finite input impedance, infinite voltage gain, and zero input offset voltage. The output voltage $V_{out}$ is

For the amplifier shown in the figure, the BJT parameters are $V_{BE} = 0.7\:V, \beta = 200,$ and thermal voltage $V_{T} = 25\:mV.$ The voltage gain $(v_{0}/v_{i})$ of the amplifier is ______.

The output $F$ in the digital logic circuit shown in the figure is

Consider the Boolean function $F(w,x,y,z) = wy + xy + \overline{w}\:xyz + \overline{w}\:\overline{x}\:y + xz + \overline{x}\:\overline{y}\:\overline{z}.$ Which one of the following is the complete set of essential prime implicants?

The digital logic shown in the figure satisfies the given state diagram when $Q1$ is connected to input $A$ of the XOR gate. Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?

Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$

Consider a discrete time periodic signal $x[n] = \sin(\frac{\pi n}{s}).$ Let $a_{k}$ be the complex Fourier series coefficients of $x[n].$ The coefficients $\{a_{k}\}$ are non-zero when $k = Bm\: \pm 1,$ where $m$ is any integer. The value of $B$ is ______.

A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system. $$y(t) + 5y(t) = u(t)$$ When $y(0) = 1$ and $u(t)$ is a unit step function, $y(t)$ is

Consider the state space model of a system, as given below …

The phase margin in degrees of $G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}$ calculated using the asymptotic Bode plot is ______.

For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds. Which one of the following compensators $C(s)$ achieves this?

Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is

Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlation $E[X(t_{1})X(t_{2})]$ is