GATE IN 2011 Question Paper (13-Feb-2011) (Shift-2)

The transfer function of the system described by the state-space equations $\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}-4& -1\\ -3& -1\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}1\\ 1\end{array}\right]u$, $y=[10]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$ is

Consider the second-order system with the characteristic equation $s(s+3)+K(s+5)=0$. Based on the properties of the root loci, it can be shown that the complex portion of the root loci of the given system for $0<K<\infty$ is described by a circle, and the two breakaway points on the real axis are

In a flapper-nozzle displacement transducer, the values of the following parameters are given:

Diameter of the orifice = $0.2\text{ mm}$, Diameter of the nozzle = $0.8\text{ mm}$,

Supply pressure = $1.4\times 10^2\text{ kPa}$ (gauge), Ambient pressure = $0$ (gauge).

The maximum value of the sensitivity is

A differential push-pull type capacitive displacement sensor (nominal capacitance $C_0=0.01\mu F$) is connected in two adjacent arms of an ac bridge in such a way that the output voltage of the bridge is independent of the frequency of the supply voltage. Supply to the bridge is $1\text{V}$ at $1\text{ kHz}$, and two equal resistances ($R=3.9\text{ k}\Omega$) are placed in the other two arms of the bridge. The bridge sensitivity is

A turbine flowmeter is rotating at $72\text{ rpm}$. The flux linked to the nearby magnet and coil assembly is given by $\Psi (\theta )=3+\cos (4\theta )\text{ mWb}$, where $\theta$ is the angular position (in radian). The amplitude and frequency of the output voltage signal, respectively, are