GATE EC 2015 Question Paper (01-Feb-2015) (Shift 1)

The position control of a DC servo-motor is given in the figure. The values of the parameters are K${}_T$ = 1 N-m/A, Rₐ = 1 Ω, Lₐ = 0.1 H, J = 5 kg-m², B = 1 N-m/(rad/sec) and K${}_b$ = 1 V/(rad/sec).



The steady-state position response (in radians) due to unit impulse disturbance torque T${}_d$ is _______.

For the system shown in the figure, s = -2.75 lies on the root locus if K is ________.

The characteristic equation of an LTI system is given by F(s) = s⁵ + 2s⁴ + 3s³ + 6s² – 4s – 8 = 0. The number of roots that lie strictly in the left half s-plane is _________.

Two sequences x₁[n] and x₂[n] have the same energy. Suppose x₁[n] = α.0.5ⁿ u[n], where α is a positive real number and u[n] is the unit step sequence. Assume

x_2≤ft[ n ] = ≤ft\{ {*20c 1.5 for&n = 0, 1 \\ 0&otherwise } .

Then the value of α is _________.

The variance of the random variable X with probability density function $f\left(x\right)=\frac{1}{2}\left|x\right|e^{-|x|}$ is __________.