List of top Questions asked in GATE EE

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

An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 \(\Omega\) per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is \(\underline{\hspace{3cm}}\) \(\Omega\). (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.
A counter uses three D flip-flops generating the Gray code sequence 000, 001, 011, 010, 110, 111, 101, 100 repeatedly. The bits are in $Q_2 Q_1 Q_0$ format. The combinational logic expression for $D_1$ is \(\underline{\hspace{1cm}}\).
Let \(A\) be a \(10 \times 10\) matrix such that \(A^{5}\) is a null matrix, and let \(I\) be the \(10 \times 10\) identity matrix. The determinant of \(A + I\) is \(\underline{\hspace{1cm}}\).
One coulomb of point charge moving with a uniform velocity \(10\hat{x}\) m/s enters the region \(x \ge 0\) having magnetic flux density \(\vec{B} = (10y\hat{x} + 10x\hat{y} + 10\hat{z})\) T. The magnitude of force on the charge at \(x = 0^+\) is \(\underline{\hspace{2cm}}\) N.
A parallel-plate capacitor with dielectric of relative permittivity 5 is charged to \(V\) and disconnected. The slab is pulled out completely. The ratio of new electric field \(E_2\) to original field \(E_1\) is \(\underline{\hspace{2cm}}\).
A DC shunt generator running at 300 RPM delivers 100 kW at 200 V. When belt breaks, it becomes a motor taking 10 kW from 200 V supply. Armature resistance = 0.025 \(\Omega\), field resistance = 50 \(\Omega\), brush drop = 2 V. Neglect armature reaction. Speed of motor is \(\underline{\hspace{2cm}}\) RPM. (Round off to 2 decimals.)
In a single-phase transformer, total iron loss is 2500 W at 440 V, 50 Hz. At 220 V, 25 Hz, the iron loss is 850 W. Find hysteresis and eddy current losses at nominal voltage and frequency.
Suppose \(I_A, I_B\) and \(I_C\) are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current is \(I_{B0} = 0.1\angle 0^\circ\) p.u. If the phase-A current \(I_A = 1.1\angle 0^\circ\) p.u and phase-C current \(I_C = (1\angle 120^\circ + 0.1)\) p.u, then \(I_B\) in p.u is
In the open interval (0, 1), the polynomial $P(x) = x^4 - 4x^3 + 2$ has \(\underline{\hspace{1cm}}\).
The expected number of tosses until the first head appears, given that head occurs with probability $p$, is \(\underline{\hspace{1cm}}\).
A 1 µC point charge is held at the origin. A second point charge of 10 µC is moved from (0,10,0) to (5,5,5) and then to (5,0,0). The total work done is \(\underline{\hspace{2cm}}\) mJ. (Round off to 2 decimal places).
Take \[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9} \]