GATE EC question library

In the circuit shown below, the transistors $M_{1}$ and $M_{2}$ are biased in saturation. Their small signal transconductances are $g_{m 1}$ and $g_{m 2}$ respectively. Neglect body effect, channel length modulation and intrinsic device capacitances. Assuming that capacitor $C_{1}$ is a short circuit for $\mathrm{AC}$ analysis, the exact …

Which of the following statements is/are true for a $\text{BJT}$ with respect to its DC current gain $\beta$ ?

Consider a system $S$ represented in state space as $$\frac{d x}{d t}=\left[\begin{array}{ll} 0 & -2 \\ 1 & -3 \end{array}\right] x+\left[\begin{array}{l} 1 \\ 0 \end{array}\right] r, y=\left[\begin{array}{ll} 2 & -5 \end{array}\right] x .$$ Which of the state space representations given below has/have the same transfer function as that of …

Let $F_{1}, F_{2}$, and $F_{3}$ be functions of $(x, y, z)$. Suppose that for every given pair of points $A$ and $B$ in space, the line integral $\int_{C}\left(F_{1} \mathrm{~d} x+F_{2} \mathrm{~d} y+F_{3} \mathrm{~d} z\right)$ evaluates to the same value along any path $C$ that starts at $A$ and ends at $B$. Then which of the following …

​​​​​Consider the matrix $\left[\begin{array}{ll}1 & k \\ 2 & 1\end{array}\right]$, where $k$ is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

​​​​​The radian frequency value(s) for which the discrete time sinusoidal signal $x[n]=A \cos (\Omega n+\pi / 3)$ has a period of $40$ is/are $\_\_\_\_\_\_$.

Let $X(t)=A \cos \left(2 \pi f_{0} t+\theta\right)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0,2 \pi]$, respectively. $X(t)$ is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of $X(t)$ is …

A lossless transmission line with characteristic impedance $\mathrm{Z}_{0}=50 \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma|=0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$ ) is $\_\_\_\_\_\_.$

The relationship between any N-length sequence $x[n]$ and its corresponding $\mathrm{N}$-point discrete Fourier transform $X[k]$ is defined as $$X[k]=\mathcal{F}\{x[n]\} .$$ Another sequence $y[n]$ is formed as below $$y[n]=\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\} .$$ For the sequence $x[n]=\{1,2,1,3\}$, the value of …

For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.

Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of $100 \mathrm{~nm}$, a fixed positive oxide charge of $10^{-8} \mathrm{C} / \mathrm{cm}^{2}$ at the oxide-silicon interface, and a metal work function of $4.6 \mathrm{eV}$. Assume that the relative permittivity of the oxide is 4 and the absolute permittivity of free space is …

In the network shown below, maximum power is to be transferred to the load $R_{L}$. The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.

A non-degenerate n-type semiconductor has $5 \%$ neutral dopant atoms. Its Fermi level is located at $0.25 \mathrm{eV}$ below the conduction band $\left(E_{C}\right)$ and the donor energy level $\left(E_{D}\right)$ has a degeneracy of $2$. Assuming the thermal voltage to be $20 \mathrm{mV}$, the difference between $E_{C}$ and $E_{D}$ (in …

An $\text{NMOS}$ transistor operating in the linear region has $I_{D S}$ of $5 \mu \mathrm{A}$ at $V_{D S}$ of $0.1 \mathrm{~V}$. Keeping $V_{G S}$ constant, the $V_{D S}$ is increased to $1.5 \mathrm{~V}$. Given that $\mu_{n} C_{o x} \frac{W}{L}=50 \mu \mathrm{A} / \mathrm{V}^{2}$, the transconductance at the new operating point (in …

The photocurrent of a $\text{PN}$ junction diode solar cell is $1 \mathrm{~mA}$. The voltage corresponding to its maximum power point is $0.3 \mathrm{~V}$. If the thermal voltage is $30 \mathrm{mV}$, the reverse saturation current of the diode (in $\mathrm{nA}$, rounded off to two decimal places) is $\_\_\_\_\_\_$.

“I cannot support this proposal. My _________ will not permit it.”

Courts : _________: : Parliament : Legislature (By word meaning)

What is the smallest number with distinct digits whose digits add up to $45?$

In a class of $100$ students, there are $30$ students who neither like romantic movies nor comedy movies, the number of students who like romantic movies is twice the number of students who like comedy movies, and the number of students who like both romantic movies and comedy movies is $20$. How many students in the class like romantic movies?

How many rectangles are present in the given figure?