GATE IN 2012 Question Paper (12-Feb-2012) (Shift-2)

If $V_A-V_B=6$ V, then $V_C-V_D$ is

Assuming both the voltage sources are in phase, the value of $R$ for which maximum power is transferred from circuit A to circuit B is

The voltage gain $A_v$ of the circuit shown below is

The state variable description of an LTI system is given by

$\left(\begin{array}{c}\dot{x_1}\\ \dot{x_2}\\ \dot{x_3}\end{array}\right)=\left(\begin{array}{ccc}0& a_1& 0\\ 0& 0& a_2\\ a_3& 0& 0\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)u$

$y=\left(\begin{array}{ccc}1& 0& 0\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right)$

where $y$ is the output and $u$ is the input. The system is controllable for

The state transition diagram for the logic circuit shown is