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

For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where $\alpha ,\beta ,\gamma$, and $x$ are strictly positive. The bus injections $P_1$ and $P_2$ are in pu. If $P_1=m{P}_2$, where $m>0$, and the real power flow from bus 1 to bus 2 is 0 pu, then which one of the following options is correct?

A BJT biasing circuit is shown in the figure, where $V_{BE}=0.7$ V and $\beta =100$. The Quiescent Point values of $V_{CE}$ and $I_C$ are respectively

Let $f(t)$ be a real-valued function whose second derivative is positive for $-\infty <t<\infty$. Which of the following statements is/are always true?

Consider the function $f(t)=(max(0,t){)}^2$ for $-\infty <t<\infty$, where $max(a,b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true?

Which of the following differential equations is/are nonlinear?