GATE EC question library

The transfer function of a first-order controller is given as $$G_{C}(s) = \dfrac{K(s+a)}{s+b}$$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is

The modulation scheme commonly used for transmission from GSM mobile terminals is

A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t + m(t)).$ The bandwidth of $y(t)$

The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of the first iteration is __________.

A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.

Consider the differential equation $$\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0.$$ Given $x(0) = 20$ and $x(1) = 10/e,$ where $e = 2.718,$ the value of $x(2)$ is ________.

A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.

In the circuit shown, the current $I$ flowing through the $50\;\Omega$ resistor will be zero if the value of capacitor $C (\text{in}\: \mu F)$ is ______.

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 $M_{1}$ …