GATE EE 2024 Question Paper (11-Feb-2024) (Shift-2)

Consider the complex function $f(z)=\cos z+e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ________ (rounded off to 1 decimal place).

The sum of the eigenvalues of the matrix $A={\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]}^2$ is____________ (rounded off to the nearest integer).}

Let $X(\omega )$ be the Fourier transform of the signal
$x(t)=e^{-t^4}\cos t$, $-\infty <t<\infty$.
The value of the derivative of $X(\omega )$ at $\omega =0$ is ________ (rounded off to 1 decimal place).

The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is Rs. 7400 per MWh, then the common load in MW is ________ (rounded off to the nearest integer).

A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the ON-state drop across the power devices. Assume that the capacitor is initially charged to 50 V with the polarity shown in the figure. The load current ($I_L$) can be assumed to be constant at 10 A. Initially, $T{h}_M$ is ON and $T{h}_A$ is OFF. The turn-off time available to $T{h}_M$ in microseconds, when $T{h}_A$ is triggered, is ________ (rounded off to the nearest integer).