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

Three currents i₁, i₂ and i₃ meet at a node as shown in the figure. If i₁ = 3 cos (ωt) ampere, i₂ = 4 sin (ωt) ampere and i₃ = I₃ cos (ωt + θ) ampere, the value of I₃ in ampere is

An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting skin effect) will be ________.

A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial charge. The voltage across the capacitor for t > 2s in volt is ____

The signal x[n] shown in the figure below is convolved with itself to get y[n]. The value of y[-1] is______

In the circuit shown below:

(V₁ + V₂) = [1 sin(2π 10000t) + 1 sin(2π 30000t]V

The RMS value of the current through the resistor R will be minimum if the value of the capacitor C in microfarad is ______.