GATE EE 2020 Question Paper (08-Feb-2020) (Shift 1)

For real numbers, x and y with y = 3x² + 3x + 1, the maximum and minimum value of y for x ∈ [-2, 0] are respectively, ______

The vector function expressed by

$F=a_x\left(5y-k_{1}z\right)+a_y\left(3z+k_{2}x\right)+a_z\left(k_{3}y-4x\right)$

Represents a conservative field, where aₓ, a${}_y$, a${}_z$ are unit vectors along x, y and z directions, respectively. The values of constant k₁, k₂, k₃ are given by:

A 250 V dc shunt motor has an armature resistance of 0.2 Ω and a field resistance of 100 Ω. When the motor is operated on no-load at rated voltage, it draws an armature current of 5 A and runs at 1200 rpm. When a load is coupled to the motor, it draws total line current of 50 A at rated voltage, with a 5 % reduction in the air-gap flux due to armature reaction. Voltage drop across the brushes can be taken as 1 V per brush under all operating conditions. The speed of the motor, in rpm, under this loaded condition, is closest to:

Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:

Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_D=I_S\left(\exp \left(\frac{V_D}{n{V}_T}\right)-1\right)$, where n > 1, V${}_T$ > 0, V${}_D$ is the voltage across the diode and I${}_D$ is the current through it. The circuit is biased so that voltage, V > 0 and current, I < 0. If you had to design this circuit to transfer maximum power from the current source (I₁) to a resistive load (not shown) at the output, what values of R₁ and R₂ would you choose?