GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

In the circuit given, the Thevenin equivalent resistance $R_{th}$ across the terminals ‘a’ and 'b' is ______ $\Omega$ (rounded off to one decimal place).

X is a discrete random variable which takes values 0, 1 and 2. The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[.]$ denoting the expectation operator, the value of $E[X]-E[X^2]$ is ______ (rounded off to one decimal place).

The diode in the circuit is ideal. The current source $i_s(t)=\pi \sin (3000\pi t)$ mA. The magnitude of the average current flowing through the resistor R is ______ mA (rounded off to two decimal places).

The full-scale range of the wattmeter shown in the circuit is 100 W. The turns ratio of the individual transformers are indicated in the figure. The RMS value of the ac source voltage $V_s$ is 200 V. The wattmeter reading will be ______ W (rounded off to the nearest integer).

The no-load steady-state output voltage of a DC shunt generator is 200 V when it is driven in the clockwise direction at its rated speed. If the same machine is driven at the rated speed but in the opposite direction, the steady-state output voltage will be ______ V (rounded off to the nearest integer).