List of top Questions asked in GATE EE

In the given figure, plant \(G_p(s)=\dfrac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)}\) and compensator \(G_c(s)=K \left\{ \dfrac{1+T_1 s}{1+T_2 s} \right\}\). The disturbance input is \(D(s)\). The disturbance is a unit step, and the steady-state error must not exceed 0.1 unit. Find the minimum value of \(K\). (Round off to 2 decimal places.)

For the closed-loop system with \(G_p(s) = \frac{14.4}{s(1 + 0.1s)}\) and \(G_c(s) = 1\), the unit-step response shows damped oscillations. The damped natural frequency is \(\underline{\hspace{2cm}}\) rad/s. (Round off to 2 decimal places.)

A continuous-time signal \(x(t)\) is defined as \(x(t)=0\) for \(|t|>1\), and \(x(t)=1-|t|\) for \(|t|\le 1\). Let its Fourier transform be \(X(\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t}\,dt\). The maximum magnitude of \(X(\omega)\) is \(\underline{\hspace{2cm}}\).
 

A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the \(Y_{\text{Bus}}\) matrix correspond to Bus 1, 2 and 3 respectively, then \(Y_{\text{Bus}}\) of the network is 

In the given circuit, for maximum power to be delivered to \(R_L\), its value should be \(\underline{\hspace{1cm}}\) \(\Omega\). (Round off to 2 decimal places.) 

A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio \(\left|\frac{I_B}{I_R}\right|\) is \(\underline{\hspace{1cm}}\). 

In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and $Z_m = 0.5j$ p.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that $\delta > 0$, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is 

Let $f(t)$ be an even function. The Fourier transform is $F(\omega)=\int_{-\infty}^\infty f(t)e^{-j\omega t}dt$. Suppose $\frac{dF(\omega)}{d\omega} = -\omega F(\omega)$ for all $\omega$, and $F(0)=1$. Then
 

The causal signal with z-transform $z^{2}(z-a)^{-2}$ is ($u[n]$ is the unit step signal)
 

Find the input impedance \(Z_{in}(s)\) of the coupled-inductor network shown. 

In the circuit, switch S is closed for a long time and opened at \(t=0\). Find \(i_L(t)\) for \(t \ge 0\). 

In the circuit shown, a 5 V Zener diode regulates the voltage across load \(R_0\). The input DC varies from 6 V to 8 V. The series resistor is \(R_S = 6\,\Omega\). The Zener diode has a maximum power rating of 2.5 W. Assuming an ideal Zener diode, the minimum value of \(R_0\) is \(\underline{\hspace{2cm}}\) \(\Omega\). 

In the circuit shown, the input \(V_i\) is a sinusoidal AC voltage having an RMS value of \(230\,V \pm 20%\). The worst-case peak-inverse voltage seen across any diode is \(\underline{\hspace{2cm}}\) V. (Round off to 2 decimal places.) 

In the BJT circuit shown, beta of the PNP transistor is 100. Assume \(V_{BE} = -0.7\text{ V}\). The voltage across \(R_C\) will be 5 V when \(R_2\) is \(\underline{\hspace{1cm}}\) k\(\Omega\). (Round off to 2 decimal places.) 

Evaluate $\displaystyle \oint_C \frac{dz}{z^2(z-4)}$ where $C$ is the rectangle with vertices $(-1-j), (3-j), (3+j), (-1+j)$ traversed counter-clockwise.

For the given Bode magnitude plot of the transfer function, the value of R is \(\underline{\hspace{2cm}}\) Ω. (Round to 2 decimals). 
 

In the given circuit, for voltage \(V_y\) to be zero, the value of \(\beta\) should be \(\underline{\hspace{1cm}}\). (Round off to 2 decimal places). 

In the given circuit, the value of capacitor \(C\) that makes current \(I = 0\) is \(\underline{\hspace{1cm}}\) \(\mu\text{F}\). 

Suppose the circles \(x^{2}+y^{2}=1\) and \((x-1)^{2}+(y-1)^{2}=r^{2}\) intersect each other orthogonally at the point \((u,v)\). Then \(u+v=\) \(\underline{\hspace{1cm}}\).
 

Two generators have cost functions with incremental-cost characteristics: 
\[ \frac{dF_1}{dP_1} = 40 + 0.2 P_1, \frac{dF_2}{dP_2} = 32 + 0.4 P_2 \] They must supply a total load of 260 MW. Find the optimal generation (economic dispatch) ignoring losses. 
 

For the feedback system shown, the transfer function \(\dfrac{E(s)}{R(s)}\) is:

The correct combination that relates the constructional feature, machine type and mitigation is \(\underline{\hspace{2cm}}\). 

Let $p$ and $q$ be real numbers such that $p^2 + q^2 = 1$. The eigenvalues of the matrix $\begin{bmatrix} p & q \\ q & -p \end{bmatrix}$ are