GATE IN 2018 Question Paper (04-Feb-2018) (Shift 2)

Consider the standard negative feedback configuration with $G\left(s\right)=\frac{s^2+0.2s+100}{s^2-0.2s+100}$ and $H\left(s\right)=\frac{1}{2}$. The number of clockwise encirclements of (−1, 0) in the Nyquist plot of the Loop transfer-function G(s)H(s) is _____.

Consider the linear system x = ≤ft[ {*20c - 1&0\\ 0& - 2 } ]x, with initial condition x≤ft( 0 ) = ≤ft[ {*20c 1\\ 1 } ]. The solution x(t) for this system is

Consider a standard negative feedback configuration with $G\left(s\right)=\frac{1}{\left(s+1\right)\left(s+2\right)}$ and $H\left(s\right)=\frac{s+\alpha }{s}$. For the closed loop system to have poles on the imaginary axis, the value of α should be equal to (up to one decimal place) _____.

Unit step response of a linear time invariant (LTI) system is given by y(t) = (1 − e${}^{-2t}$) u(t). Assuming zero initial condition, the transfer function of the system is

An op-amp that is powered from a ± 5 V supply is used to build a non-inverting amplifier having a gain of 15. The slew rate of the op-amp is 0.5 × 10⁶ V/s. For a sinusoidal input with amplitude of 0.3 V, the maximum frequency (in kHz) up to which it can be operated without any distortion is (up to one decimal place) ___.