The block diagram of a feedback control system is shown in the figure.$$ \text { The transfer function } \frac{Y(s)}{X(s)} \text { of the system is } $$

The electrical system shown in the figure converts input source current $i_s(t)$ to output voltage $\theta_O(t)$.

Current $i_L(t)$ in the inductor and voltage $\vartheta_C(t)$ across the capacitor ate taken as the state variables, both assumed to be initially equal to Zero, i.e., $i_L(0)=0$ and $\vartheta_c(0)=0$. The system is

The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are $4 \mathrm{~ns}, 2 \mathrm{~ns}$ and 1 ns respectively.

If all the inputs $P, Q, R, S$ and $T$ are applied simultaneously and held constant, the maximum propagation delay of the circuit is

A digital transmission system uses a $(7,4)$ systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-code word pairs in this code ( $m_i ; c_i$ ). Where $c_i$ is the codeword corresponding to the $i^{\text {th }}$ message $m_i$, are known to be $(1100 ; 0101100),(1110 ; 001 1110)$ and $(0110 ; 1000110)$, then which of the following is a valid codeword in this code?