List of top Questions asked in GATE EC

An NMOS transistor operating in the linear region has \(I_{DS} = 5 \, \mu{A}\) at \(V_{DS} = 0.1 \, {V}\). Keeping \(V_{GS}\) constant, the \(V_{DS}\) is increased to \(1.5 \, {V}\). Given that: \[ \mu_n C_{ox} \frac{W}{L} = 50 \, \mu{A}/{V}^2, \] the transconductance at the new operating point (in \(\mu{A}/{V}\), rounded off to two decimal places) is \(\_\_\_\_\).

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is \(\_\_\_\_\).

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

A non-degenerate n-type semiconductor has \(5\%\) neutral dopant atoms. Its Fermi level is located at \(0.25 \, {eV}\) below the conduction band (\(E_C\)) and the donor energy level (\(E_D\)) has a degeneracy of \(2\). Assuming the thermal voltage to be \(20 \, {mV}\), the difference between \(E_C\) and \(E_D\) (in \({eV}\), rounded off to two decimal places) 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 \(\_\_\_\_\).

Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of \(100 \, {nm}\), a fixed positive oxide charge of \(10^{-8} \, {C/cm}^2\) at the oxide-silicon interface, and a metal work function of \(4.6 \, {eV}\). Assume that the relative permittivity of the oxide is \(4\), and the absolute permittivity of free space is \(8.85 \times 10^{-14} \, {F/cm}\). If the flatband voltage is \(0 \, {V}\), the work function of the p-type silicon (in eV, rounded off to two decimal places) is \(\_\_\_\_\).

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

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. If S and Q are single children, and the room allocations shown below are acceptable to all: P, R & T, S & Q
P, Q & R, T & S
Then, which one of the given options is the siblings?

If ‘\(\rightarrow\)’ denotes increasing order of intensity, then the meaning of the words {charm} ---- {enamor} ------ {bewitch} is analogous to {bored} ----- _________ ---- {weary} . Which one of the given options is appropriate to fill the blank?

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5. What was his father's age when Aman was born?

For a real number \(x>1\), solve the equation: \[ \frac{1}{\log_2x} +\frac{1}{\log_3x} + \frac{1}{\log_4x} = 1 \] The value of x is:

The greatest prime factor of \((3^{199} - 3^{196})\) is:

Sequence the following sentences (P, Q, R, S) in a coherent passage: P: Shifu’s student exclaimed, “Why do you run since the bull is an illusion?”
Q: Shifu said, “Surely my running away from the bull is also an illusion.”
R: Shifu once proclaimed that all life is illusion.
S: One day, when a bull gave him chase, Shifu began running for his life.

Four identical cylindrical chalk-sticks, each of radius \( r = 0.5 \, {cm} \) and length \( l = 10 \, {cm} \), are bound tightly together using a duct tape as shown in the following figure.

The width of the duct tape is equal to the length of the chalk-stick. The area (in cm\(^2\)) of the duct tape required to wrap the bundle of chalk-sticks once, is:

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023. Based on the data provided, which one of the following options is INCORRECT?

Examples of mirror and water reflections are shown in the figures below:

An object appears as the following image after first reflecting in a mirror and then reflecting on water:

The original object is:

Two identical sheets A and B, of dimensions \( 24 \, {cm} \times 16 \, {cm} \), can be folded into half using two distinct operations, FO1 or FO2. In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge. If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is:

The general form of the complementary function of a differential equation is given by: \[ y(t) = (At + B)e^{-2t}, \] where \(A\) and \(B\) are real constants determined by the initial condition. The corresponding differential equation is:

In the context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:

In the feedback control system shown in the figure below, \[ G(s) = \frac{6}{s(s+1)(s+2)}. \]\(R(s)\), \(Y(s)\), and \(E(s)\) are the Laplace transforms of \(r(t)\), \(y(t)\), and \(e(t)\), respectively. If the input \(r(t)\) is a unit step function, then:

A digital communication system transmits through a noiseless bandlimited channel \([-W, W]\). The received signal \(z(t)\) at the output of the receiving filter is given by: \[ z(t) = \sum_n b[n] x(t - nT), \] where \(b[n]\) are the symbols and \(x(t)\) is the overall system response to a single symbol. The received signal is sampled at \(t = mT\). The Fourier transform of \(x(t)\) is \(X(f)\). The Nyquist condition that \(X(f)\) must satisfy for zero intersymbol interference at the receiver is:

Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances \(z_{inA}\), \(z_{inB}\), \(z_{inC}\), and \(z_{inD}\) (indicated in the figure) are: \begin{center} \includegraphics[width=8cm]{15.png} \end{center}

For the Boolean function: \[ F(A, B, C, D) = \Sigma m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15), \] the essential prime implicants are:

A white Gaussian noise \(w(t)\) with zero mean and power spectral density \(\frac{N_0}{2}\), when applied to a first-order RC low-pass filter produces an output \(n(t)\). At a particular time \(t = t_k\), the variance of the random variable \(n(t_k)\) is:

For the closed-loop amplifier circuit shown below, the magnitude of open-loop low-frequency small signal voltage gain is 40. All the transistors are biased in saturation. The current source \(I_{SS}\) is ideal. Neglect body effect, channel length modulation, and intrinsic device capacitances. The closed-loop low-frequency small signal voltage gain \(\frac{v_{out}}{v_{in}}\) (rounded off to three decimal places) is: \begin{center} \includegraphics[width=6cm]{18.png} \end{center}