List of top Questions asked in GATE IE

The signal \( x(t) = (t - 1)^2 u(t - 1) \), where \( u(t) \) is the unit-step function, has the Laplace transform \( X(s) \). The value of \( X(1) \) is_________
A proportional-integral-derivative (PID) controller is employed to stably control a plant with transfer function \[ P(s) = \frac{1}{(s + 1)(s + 2)}. \] Now, the proportional gain is increased by a factor of 2, the integral gain is increased by a factor of 3, and the derivative gain is left unchanged. Given that the closed-loop system continues to remain stable with the new gains, the steady-state error in tracking a ramp reference signal_________
A resistor ladder digital-to-analog converter (DAC) receives a digital input that results in the circuit having the state as shown in the figure. For this digital input, the Thevenin voltage, \( V_{th} \), and Thevenin resistance, \( R_{th} \), as seen at the output node are _________
The Nyquist plot of a stable open-loop system \( G(j\omega) \) is plotted in the frequency range \( 0 \leq \omega>\infty \) as shown. It is found to intersect a unit circle with center at the origin at the point \( P = -0.77 - 0.64j \). The points \( Q \) and \( R \) lie on \( G(j\omega) \) and assume values \( Q = 14.40 + 0.00j \) and \( R = -0.21 + 0.00j \). The phase margin (PM) and the gain margin (GM) of the system are _________
The global minimum of \(x^3 e^{-|x|}\) for \(x \in (-\infty, \infty)\) occurs at \(x =\) _________ (round off to one decimal place).
A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _________.
The transfer function of a system is: \[ \frac{(s + 1)(s + 3)}{(s + 5)(s + 7)(s + 9)}. \] In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________.
A Zener diode is used as a 4 V voltage regulator in the circuit shown. Given that the diode requires a minimum current of 4 mA for voltage regulation, the maximum current (in milliamperes) permitted to flow through the load \( R_L \) is _________ (round off to one decimal place)
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is _________ (round off to two decimal places)
In the bandpass filter circuit shown, \( R_0 = 50 \, \Omega \), \( L_0 = 1 \, \text{mH} \), \( C_0 = 10 \, \text{nF} \). The Q factor of the filter is _________ (round off to two decimal places).
The Newton-Raphson method is applied to determine the solution of \( f(x) = 0 \) where \( f(x) = x - \cos(x) \). If the initial guess of the solution is \( x_0 = 0 \), the value of the next approximation \( x_1 \) is _________ (round off to two decimal places).
An OPAMP has a gain of \( 10^4 \), an input impedance of 10 MΩ and an output impedance of 100Ω. The OPAMP is used in unity-gain feedback configuration in a voltage buffer circuit. The closed-loop output impedance of the OPAMP (in milliohms) in the circuit is _________.
A signal \( V_{\text{in}}(t) \) shown is applied from \( t = 0 \) ms to \( t = 6 \) ms to the circuit shown. Given the initial voltage across the capacitor is 0.3 V, and that the diode is ideal, the open circuit voltage \( V_{\text{out}}(t) \) at \( t = 5 \) ms is _________
The logic block shown has an output \( F \) given by _________
In which of the following bridge(s) is the balancing condition frequency-independent?
The output F of the digital circuit shown can be written in the form _________
Given \( M = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix} \), which of the following statement(s) is/are correct?
An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of bits (in integer) in the output is _________
Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is _________ (round off to two decimal places)
A photodiode is made of a semiconductor with a bandgap of 1.42 eV. Given that Planck’s constant is \(6.626 \times 10^{-34}\) J·s, the speed of light in vacuum is \(3 \times 10^8\) m/s, and \(1 \, \text{eV} = 1.6 \times 10^{-19}\) J, the cut-off wavelength (in nanometers) of the photodiode is _________ (round off to one decimal place).
The output of a system \( y(t) \) is related to its input \( x(t) \) according to the relation \( y(t) = x(t) \sin(2\pi t) \). This system is _________
A unity-gain negative-feedback control system has a loop-gain \( L(s) \) given by \[ L(s) = \frac{6}{s(s-5)} \] The closed-loop system is _________

A sinusoidal carrier wave with amplitude \( A_c \) and frequency \( f_c \) is amplitude modulated with a message signal \( m(t) \) having frequency \( 0<f_m \ll f_c \) to generate the modulated wave \( s(t) \) given by \[ s(t) = A_c[1 + m(t)]\cos(2\pi f_c t) \] The message signal that can be retrieved completely using envelope detection is _________

A Hall sensor is based on the principle of _________
A signal \( x(t) \) is band-limited between 100 Hz and 200 Hz. A signal \( y(t) \) is related to \( x(t) \) as follows:
y(t) = x(2t - 5)
The statement that is always true is_________