(b) Voltage across zener diode is constant
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$i_{1k\Omega} = \frac{15\ volt}{1k\Omega} = 15mA$
$i_{250\Omega} = \frac{(20 - 15)V}{250\Omega} = \frac{5V}{250\Omega} = \frac{20}{1000}A = 20mA$
$\therefore i_{zener\ diode} = (20 - 15) = 5\ mA$