List of top Questions asked in GATE EC

Let \(z\) be a complex variable. If \(f(z) = \frac{\sin(\pi z)}{z^2 (z - 2)}\) and \(C\) is the circle in the complex plane with \(|z| = 3\), then: \[ \oint_C f(z) \, dz \] 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 \(\_\_\_\_\).

In a number system of base r, the equation x²-12x+37=0 has x=8 of its solutions. The value of r is____.

Consider a system \(S\) represented in state space as: \[ \frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix} x + \begin{bmatrix} 1 \\ 0 \end{bmatrix} r, \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix} x. \] Which of the state space representations given below has/have the same transfer function as that of \(S\)?

In the circuit given below, the switch S was kept open for a sufficiently long time and is closed at time t=0. The time constant (in seconds) of the circuit for t>0 is___.

The information bit sequence \(\{1 \, 1 \, 1 \, 0 \, 1 \, 0 \, 1 \, 0 \, 1\}\) is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is \(C(x) = x^4 + x + 1\). The encoded sequence of bits is \(\_\_\_\_\).

Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X≥Y is_____.

In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of \(R_1\) and the corresponding frequency of oscillation are \(\_\_\_\_\).

A full-scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is \(10 \, \mu {W}\). The effective number of bits (rounded off to the nearest integer) of the ADC is \(\_\_\_\_\).

The propagation delay of the \(2 \times 1\) MUX shown in the circuit is \(10 \, {ns}\). Consider the propagation delay of the inverter as \(0 \, {ns}\). If \(S\) is set to 1, then the output \(Y\) is \(\_\_\_\_\).

A causal and stable LTI system with impulse response \(h(t)\) produces an output \(y(t)\) for an input signal \(x(t)\). A signal \(x(0.5t)\) is applied to another causal and stable LTI system with impulse response \(h(0.5t)\). The resulting output is:

Let \( X(t) = A \cos(2\pi f_o t + \theta) \) 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, 2π], respectively. \( X(t) \) is fed to an 8-bit uniform mid-rise type quantizer.
Given that the autocorrelation of \( X(\tau) \) is \[ R_x(\tau) = \frac{2}{3} \cos(2\pi f_o \tau), \] the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is ___.

Consider two continuous-time signals \(x(t)\) and \(y(t)\) as shown below. If \(X(f)\) denotes the Fourier transform of \(x(t)\), then the Fourier transform of \(y(t)\) 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 context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:

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}

For a causal discrete-time LTI system with transfer function: \[ H(z) = \frac{2z^2 + 3}{(z + \frac{1}{3})(z - \frac{1}{3})}, \] which of the following statements is/are true?

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

In the circuit shown below, the transistors \(M_1\) and \(M_2\) are biased in saturation. Their small signal transconductances are \(g_{m1}\) and \(g_{m2}\), respectively. Neglect body effect, channel length modulation, and intrinsic device capacitances. Assuming that capacitor \(C_1\) is a short circuit for AC analysis, the exact magnitude of small signal voltage gain \(\left|\frac{v_{{out}}}{v_{{in}}}\right|\) is \(\_\_\_\_\).

The sequence of states (\(Q_1 Q_0\)) of the given synchronous sequential circuit is \(\_\_\_\_\).

A lossless transmission line with characteristic impedance Z_o = 50 Ω is terminated with an unknown load. The magnitude of the reflection co-efficient is |T| = 0.6. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in Ω) is____.

The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as
X[k] = F(x[n]}.
Another sequence y[n] is formed as below
y[n] = F F{F{F{F{x[n]}}}}.
For the sequence x[n] = {1, 2, 1, 3}, the value of Y[0] 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.

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____.

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}