GATE IN 2021 Question Paper (06-Feb-2021) (Shift 1)

An air cored coil having a winding resistance of 10 Ω is connected in series with a variable capacitor Cx. The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is ________

A household fan consumes 60 W and draws a current of 0.3125 A (rms) when connected to a 230 V (rms) ac, 50 Hz single phase mains. The reactive power drawn by the fan in VAr is ____________ (rounded off to the nearest integer).

Given y(t) = e${}^{-3t}$ u(t) ∗ u(t + 3), where * denotes convolution operation. The value of y(t) as t → ∞ is ___________ (rounded off to two decimal places).

The input signal shown below



is passed through the filter with the following taps



The number of non-zero output samples is ____.

A sinusoid (√2 sin t) μ(t), where μ(t) is the step input, is applied to a system with transfer-function $G(s)=\frac{1}{s+1}$ The amplitude of the steady state output is ____.