GATE EC question library

The $ABCD$ parameters of the following $2$-port network are

A network is described by the state model as $$\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2}$$ The transfer function $H(s)\left(=\dfrac{Y(s)}{U(s)}\right)$ is

The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the figure. Which one of the following statements is NOT TRUE?

The current in an enhancement mode NMOS transistor biased in saturation mode was measured to be $1\: mA$ at a drain-source voltage of $5\: V.$ When the drain-source voltage was increased to $6\: V$ while keeping gate-source voltage same, the drain current increased to $1.02\: mA.$ Assume that drain to source saturation voltage is much smaller than …

An npn BJT having reverse saturation current $I_{S} = 10^{-15}\:A$ is biased in the forward active region with $V_{BE} = 700\: mV.$ The thermal voltage $(V_{T})$ is $25\: mV$ and the current gain $(β)$ may vary from $50$ to $150$ due to manufacturing variations. The maximum emitter current $(\text{in}\: \mu A)$ is ________.

A three bit pseudo random number generator is shown. Initially the value of output $Y\equiv Y_{2} Y_{1} Y_{0}$ is set to $111.$ The value of output $Y$ after three clock cycles is

A universal logic gate can implement any Boolean function by connecting sufficient number of them appropriately. Three gates are shown. Which one of the following statements is TRUE?

An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs are provided using the push-button switches. It is observed that the circuit fails to work as desired. The SR latch can be made functional by changing

In the circuit shown, assume that the opamp is ideal. If the gain $(v_{0} / v_{in})$ is $–12,$ the value of $R\: (\text{in}\: k\Omega)$ is _____.

In the circuit shown, both the enhancement mode NMOS transistors have the following characteristics:$k_{n} ݇ = \mu _{n}C_{ox}(W/L) = 1\:mA/V^{2};V_{TN} = 1V.$ Assume that the channel length modulation parameter $\lambda$ is zero and body is shorted to source. The minimum supply voltage ܸ$V_{DD}$ (in volts) needed to ensure that transistor $M_{1}$ …

In the circuit shown, assume that the diodes $D1$ and $D2$ are ideal. The average value of voltage $V_{ab}\: (\text{in Volts}),$ across terminals $‘a’$ and $‘b’$ is _________.

Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Which one of the following statements is TRUE for the signal $x[n]$?

A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is

Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(-j\dfrac{\pi}{8} kn\big)$ for all $k .$ The value of the coefficient ܽ$a_{31}$ is _______.

Consider a continuous-time signal defined as $$x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$$ where $’\ast’$ denotes the convolution operation and $t$ is in seconds. The Nyquist sampling rate $\text{(in samples/sec)}$ for $x(t)$ is _______.

The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steady-state position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.

For the system shown in the figure, $s=-2.75$ lies on the root locus if $K$ is _______.

The characteristic equation of an LTI system is given by $F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0.$ The number of roots that lie strictly in the left half $s$-plane is _________.

Two sequences $x_{1}[n]$ and $x_{2}[n]$ have the same energy. Suppose $x_{1}[n]=\alpha\: 0.5 ^{n}\:u[n],$ where $\alpha$ is a positive real number and $u[n]$is the unit step sequence. Assume ݊$$x_{2}[n]= \begin{cases} \sqrt{1.5}& \text{for } n = 0,1 \\ 0 &\text{otherwise.} \end{cases}$$ Then the value of $\alpha$ is _________.

The variance of the random variable $X$ with probability density function $f(x)=\dfrac{1}{2}\mid x \mid e^{- \mid x \mid}$ is __________.