GATE EE 2024
Paper was held on Sun, Feb 11, 2024 9:00 AM
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GATE EE

A BJT biasing circuit is shown in the figure, where $V_{BE} = 0.7\,V$ and $\beta = 100$. The Quiescent Point values of $
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In the given circuit, the diodes are ideal. The current I through the diode D1 in milliamperes is _____ (rounded off to
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A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifi
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For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is
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Consider the standard second-order system of the form $\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$ with the
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Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which on
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Consider the closed-loop system shown in the figure with $$G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}.$$ The root
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Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant
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Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of
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Simplified form of the Boolean function $$ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q
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In the circuit, the present value of $Z$ is $1$. Neglecting the delay in the combinatorial circuit, the values of $S$ an
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To obtain the Boolean function $F(X, Y) = X\overline{Y} + \overline{X}$, the inputs $PQRS$ in the figure should be
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The number of junctions in the circuit is
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All the elements in the circuit are ideal. The power delivered by the 10 V source in watts is
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The circuit shown in the figure with the switch S open, is in steady state. After the switch S is closed, the time const
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For a two-phase network, the phase voltages $V_p$ and $V_q$ are to be expressed in terms of sequence voltages $V_\alpha$
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Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is $Z_P =
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For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magneticall
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In the circuit shown, $Z_1 = 50\angle -90^{\circ} \Omega$ and $Z_2 = 200\angle -30^{\circ} \Omega$. It is supplied by a
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The table lists two instrument transformers and their features:table { width: 100%; border-collapse: collapse; margin: 2
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A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss
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Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Her
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A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor $(\sqrt{3}/2)$ via a lo
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Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator
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A 3-phase star connected slip ring induction motor has the following parameters referred to the stator:$R_s = 3\, \Omega
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A 5 kW, 220 V DC shunt motor has 0.5 $\Omega$ armature resistance including brushes. The motor draws a no-load current o
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In the $(x, y, z)$ coordinate system, three point-charges $Q$, $Q$, and $\alpha Q$ are located in free space at $(-1, 0,
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The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, i
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Which one of the following matrices has an inverse?
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Let $X$ be a discrete random variable that is uniformly distributed over the set {$-10, -9, \cdots, 0, \cdots, 9, 10$}.
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Which of the following complex functions is/are analytic on the complex plane?
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Consider the complex function $f(z) = \cos z + e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z
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The sum of the eigenvalues of the matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ______ (rounded off to
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Consider a vector $\vec{u} = 2\hat{x} + \hat{y} + 2\hat{z}$, where $\hat{x}$, $\hat{y}$, $\hat{z}$ represent unit vector
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Let $f(t)$ be a real-valued function whose second derivative is positive for $- \infty
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Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty
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Which of the following differential equations is/are nonlinear?
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If the following switching devices have similar power ratings, which one of them is the fastest?
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A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values
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A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the ON-state drop across the power d
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A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering
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A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a
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In the DC-DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is 5
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A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC mo
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The figure shows the single line diagram of a 4-bus power network. Branches $b_1$, $b_2$, $b_3$, and $b_4$ have impedanc
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The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figu
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For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per
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The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable
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Suppose signal $y(t)$ is obtained by the time-reversal of signal $x(t)$, i.e., $y(t) = x(-t)$, $-\infty
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If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal $x(t) =
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Let $X(\omega)$ be the Fourier transform of the signal$x(t) = e^{-t^4} \cos t, \quad -\infty The value of the derivative
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The input $x(t)$ and the output $y(t)$ of a system are related as $$ y(t) = e^{-t} \int\limits_{-\infty}^{t} e^{\tau
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Consider the discrete-time systems $T_1$ and $T_2$ defined as follows:{ $T_1 x[ n ] = x[ 0 ] + x[ 1 ] + \cdots + x[ n ]
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If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n]
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If the energy of a continuous-time signal $x(t)$ is $E$ and the energy of the signal $2x(2t - 1)$ is $cE$, then $c$ is _
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General Aptitude

If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [ple
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P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wan
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The decimal number system uses the characters 0, 1, 2, ... , 8, 9, and the octal number system uses the characters 0, 1,
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A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% tax
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If, for non-zero real variables $x$, $y$, and real parameter $a > 1$,$x : y = (a + 1) : (a - 1)$,then, the ratio $(x^2 -
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In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.Following a row ____(i) __
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In the following figure, CD = 5 cm, BE = 10 cm, AE = 12 cm,∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90° Points AFCD create a rhomb
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The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2
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The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are pe
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A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position a
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