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

If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal
$x(t)=e^{t^2}[u(t-1)-u(t-10)]$ is

A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, $V_p$ is the applied primary voltage, $E_p$ is the induced primary voltage, $V_s$ is the open circuit secondary voltage, and $E_s$ is the induced secondary voltage.

The figure shows the single line diagram of a 4-bus power network. Branches $b_1$, $b_2$, $b_3$, and $b_4$ have impedances $4z$, $z$, $2z$, and $4z$ per-unit (pu), respectively, where $z=r+jx$, with $r>0$ and $x>0$. The current drawn from each load bus (marked as arrows) is equal to $I$ pu, where $I\ne 0$. If the network is to operate with minimum loss, the branch that should be opened is

For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is