Q. The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d (t) is given by d(t) = 0.1sin(wt) where w = 5 rad s , the steady-state amplitude of the output y(t) is Sol: as r = 0 […]

Q. A complex function 𝑓(𝑧) = 𝑢(𝑥, 𝑦) + 𝑖 𝑣(𝑥, 𝑦) and its complex conjugate 𝑓∗(𝑧) = 𝑢(𝑥, 𝑦) − 𝑖 𝑣(𝑥, 𝑦) are both analytic in the entire complex plane, where 𝑧 = 𝑥 + 𝑖 𝑦 and 𝑖 = √−1 . The function 𝑓 is then given by Sol: f(z) = u(x,

Q. The function 𝑝(𝑥) is given by 𝑝(𝑥) = 𝐴/𝑥𝜇 where 𝐴 and 𝜇 are constants with 𝜇 > 1 and 1 ≤ 𝑥 < ∞ and 𝑝(𝑥) = 0 for −∞ < 𝑥 < 1. For 𝑝(𝑥) to be a probability density function, the value of 𝐴 should be equal to Sol:

Q. The curve y = f (x) is such that the tangent to the curve at every point (𝑥, 𝑦) has a 𝑌-axis intercept 𝑐, given by 𝑐 = −𝑦. Then, f (x) is proportional to (A) x–1 (B) x2 (C) x3 (D) x4 Ans: x2 Sol: Let the equation of tangent is, y =

Q. A signal cos(2p fmt) modulates a carrier cos(2p fct) using the double-sideband-with-carrier (DSBWC) scheme to yield a modulated signal cos(2p fct) + 0.3cos(2p fmt) cos(2p fct) . The modulation index is___________.(Answer should be rounded off to one decimal place)     . Sol: The standard equation of AM is

Q. A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m3. If the pressure difference measured by the tube is 200 N/m2, the velocity of the fluid, assuming the pitot-tube coefficient to be 1.0, is                   m/s. Sol: Given that, density = 1 kg/m3 Pressure difference (ΔP) = 200