A satellite attitude control system, as shown below, has a plant with transfer function: $ G(s) = \frac{1}{s^2}, $ cascaded with a compensator: $ C(s) = \frac{K(s + \alpha)}{s + 4}, $ where $ K $ and $ \alpha $ are positive real constants. In order for the closed-loop system to have poles at $ -1 \pm j\sqrt{3} $, the value of $ \alpha $ must be $\_\_\_\_\_$.
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
Two resistors are connected in a circuit loop of area 5 m\(^2\), as shown in the figure below. The circuit loop is placed on the \( x-y \) plane. When a time-varying magnetic flux, with flux-density \( B(t) = 0.5t \) (in Tesla), is applied along the positive \( z \)-axis, the magnitude of current \( I \) (in Amperes, rounded off to two decimal places) in the loop is (answer in Amperes).
A 50 \(\Omega\) lossless transmission line is terminated with a load \( Z_L = (50 - j75) \, \Omega.\) { If the average incident power on the line is 10 mW, then the average power delivered to the load
(in mW, rounded off to one decimal place) is} _________.
In the circuit shown below, the AND gate has a propagation delay of 1 ns. The edge-triggered flip-flops have a set-up time of 2 ns, a hold-time of 0 ns, and a clock-to-Q delay of 2 ns. The maximum clock frequency (in MHz, rounded off to the nearest integer) such that there are no setup violations is (answer in MHz).