GATE EC question library

For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________.

A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \omega) / V_{\text{in}} (j \omega))$ of the circuuit is also provided (here, $\omega$ is the angular frequency in $\text{rad/s}.$) The values of $R$ and $C$ are ________________.

For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________.

Consider an even polynomial $p(s)$ given by $$p(s) = s^{4} + 5s^{2} + 4 + K,$$ where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is _____________.

Consider the following series: $$\sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$$ For which of the following combinations of $c, d$ values does this series converge?

The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure. Based on the given information, which of the four systems is/are definitely $\text{NOT LTI}$ (linear and time-invariant)?

Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices.

A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the probability of transition from state $A$ to $B$). For this state diagram, select the statement(s) which is/are universally true.

Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $’0’$ and $’1’$ are also available separately. Using instances of only $\text{D}$ gates and inputs $’0’$ and $’1’,$ _______________ (select the …

Two linear time-invariant systems with transfer functions $$G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$$ have unit step responses $y_{1}(t)$ and $y_{2}(t),$ respectively. Which of the following statements is/are true?

Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response $$H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$$ where $\omega_{0} = 10^{4} \; \text{rad/sec}.$ For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of $(R,C)$ values is/are _____________.

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can propagate in this waveguide is/are _________.

The value of the integral $$\iint_{D} 3(x^{2} + y^{2})dxdy,$$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).

A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance $R$ is connected across Port $2.$ As $R$ is varied, the measured voltage and current at Port $2$ is shown in $\text{Fig.(b)}$ as a $V_{2}$ versus $-I_{2}$ plot. Note …

For a vector $\overline{x} = \left[ x [0], x[1], \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right],$ where $$X[k] = \displaystyle \sum_{n=0}^{7} x[n] \; \text{exp} \left(-j \frac{2 \pi}{8} nk \right).$$ Here, …

A $p-$type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at $x = \pm 2l_{n},$ where $l_{n} = 10 ^{-4} \; \text{cm}$ is the diffusion length of electrons. Assume electronic charge, $q = – 1.6 \times 10^{-19} \; \text{C.}$ The profiles of …

A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).

Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).

Consider the circuit shown with an ideal long channel $n \text{MOSFET}$ (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier. $v_{i}$ is the small-signal ac input voltage. $v_{A}$ and $v_{B}$ represent the …

The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ respectively. Let the error signal be defined as $e(t) = r(t) – y(t).$ Assuming the reference input $r(t) = 0$ for all $t,$ the steady-state error $e (\infty),$ due …