GATE IN 2016 Question Paper (31-Jan-2016) (Shift 2)

If X(s), the Laplace transform of signal x(t) is given by $X\left(s\right)=\frac{\left(s+2\right)}{\left(s+1\right){\left(s+3\right)}^2},$ then the value of x(t) as t → ∞ is _______.

The number of times the Nyquist plot of $G\left(s\right)=\frac{s-1}{s+1}$ will encircle the origin clockwise is ______.

The value of a₀ which will ensure that the polynomial s³ + 3s² + 2s + a₀ has roots on the left half of the s-plane is

The input i(t) = 2 sin (3t + π) is applied to a system whose transfer function $G\left(s\right)=\frac{8}{{\left(s+10\right)}^2}$. The amplitude of the output of the system is ________

The diode D used in circuit below is ideal. The voltage drop V${}_{ab}$ across the 1 kΩ Resistor in volt is ____