List of top Questions asked in GATE EE

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.
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 \(\underline{\hspace{1cm}}\).
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 \(\underline{\hspace{1cm}}\).
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.)
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 \(\underline{\hspace{2cm}}\).
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.
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 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.
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 16-bit synchronous binary up-counter is clocked with frequency \(f_{CLK}\). The two most significant bits are OR-ed to form output Y. Y remains high for 24 ms. The clock frequency \(f_{CLK}\) is \(\underline{\hspace{1cm}}\) MHz. (Round off to 2 decimal places.)
An alternator with internal voltage and reactances is delivering 0.866 p.u real power. Find (δ₁ − δ₂). (Round to 2 decimals).
A 500 V, 50 Hz, 3-phase induction motor receives 40 kW input. Stator losses = 1 kW, friction and windage losses = 2.025 kW. Efficiency = \(\underline{\hspace{2cm}}\) %.
A signal generator having a source resistance of 50\(\Omega\) is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is \(\underline{\hspace{1cm}}\) \(\mu\text{F}\). (Round off to 2 decimal places.)
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 \[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9} \]
Two single-core power cables have conductor resistances 0.7\(\Omega\) and 0.5\(\Omega\), and insulation resistances 600 M\(\Omega\) and 900 M\(\Omega\). When joined in series, the ratio of insulation resistance to conductor resistance is \(\underline{\hspace{1cm}}\) \(\times 10^{6}\).
Inductance is measured by
Let $f(x)$ be a real-valued function such that $f'(x_0)=0$ for some $x_0 \in (0,1)$, and $f''(x) > 0$ for all $x \in (0,1)$. Then $f(x)$ has
The dimension of the sub-matrix $M$ in the Newton-Raphson Jacobian is \(\underline{\hspace{2cm}}\).
Two discrete-time linear time-invariant systems with impulse responses \(h_1[n] = \delta[n-1] + \delta[n+1]\) and \(h_2[n] = \delta[n] + \delta[n-1]\) are connected in cascade. The impulse response of the cascaded system is
Let $p(z) = z^3 + (1 + j)z^2 + (2 + j)z + 3$, where $z$ is a complex number. Which one of the following is true?