List of top Questions asked in GATE EE

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 = \(\underline{\hspace{2cm}}\) %.
An alternator with internal voltage and reactances is delivering 0.866 p.u real power. Find (δ₁ − δ₂). (Round to 2 decimals).
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 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.)
Inductance is measured by
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 \(\underline{\hspace{1cm}}\) \(\times 10^{6}\).
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
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
The dimension of the sub-matrix $M$ in the Newton-Raphson Jacobian is \(\underline{\hspace{2cm}}\).
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?