GATE EE 2017 Question Paper (11-Feb-2017) (Shift 2)

The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10 : 1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T₁ and T₂ are 90° and 270° respectively.



The rms value of the current through diode D₃ in amperes is ________

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ___________ .

Consider a function f(x, y, z) given by

f(x, y, z) = (x² + y² – 2z²)(y² + z²)

The partial derivative of this function with respect to x at the point x = 2, y = 1 and z = 3 is _______

Let x and y be integers satisfying the following equations

2x² + y² = 34

x + 2y = 11

The value of (x + y) is _______.

Let y² – 2y + 1 = x and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals ________. (Give the answer up to three decimal places)