List of top Questions asked in GATE EC- 2024

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:

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:

Let \(\hat{i}\) and \(\hat{j}\) be the unit vectors along \(x\) and \(y\) axes, respectively, and let \(A\) be a positive constant. Which one of the following statements is true for the vector fields: \[ \vec{F_1} = A(\hat{i}y + \hat{j}x) \quad {and} \quad \vec{F_2} = A(\hat{i}y - \hat{j}x)? \]

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?

A continuous-time signal \(x(t) = 2 \cos(8\pi t + \pi/3)\) is sampled at a rate of 15 Hz. The sampled signal \(x_s(t)\) when passed through an LTI system with impulse response: \[ h(t) = \frac{\sin(2\pi t)}{\pi t} \cos(38\pi t - \pi/2), \] produces an output \(x_0(t)\). The expression for \(x_0(t)\) 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.

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (\(T\)) dependence of free electron concentration (\(n\))?

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?

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___.

Consider a unity negative feedback control system with forward path gain: \[ G(s) = \frac{K}{(s+1)(s+2)(s+3)}. \] The impulse response of the closed-loop system decays faster than \(e^{-t}\) if \(\_\_\_\_\).

In the given circuit, the current Ix (in mA) is

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

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?

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:

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:

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:

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:

Let \(\rho(x, y, z, t)\) and \(\mathbf{u}(x, y, z, t)\) represent density and velocity, respectively, at a point \((x, y, z)\) and time \(t\). Assume \(\frac{\partial \rho}{\partial t}\) is continuous. Let \(V\) be an arbitrary volume in space enclosed by the closed surface \(S\), and \(\mathbf{\hat{n}}\) be the outward unit normal of \(S\). Which of the following equations is/are equivalent to: \[ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0? \]

The free electron concentration profile \(n(x)\) in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three different positions. Which of the following statements is/are true?

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 \(\_\_\_\_\).

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:

As shown in the circuit, the initial voltage across the capacitor is 10 V, with the switch being open. The switch is then closed at t 0. The total energy dissipated = in the ideal Zener diode (V_z=5V) after the switch is____.

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?

A source transmits a symbol \(s\), taken from \(\{-4, 0, 4\}\) with equal probability, over an additive white Gaussian noise channel. The received noisy symbol \(r\) is given by \(r = s + w\), where the noise \(w\) is zero mean with variance 4 and is independent of \(s\). Using: \[ Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{t^2}{2}} dt, \] the optimum symbol error probability is \(\_\_\_\_\).