If voltage across zener diode is 6V, then find out the value of maximum resistance in this condition.

Correct option is D. 4kΩ
Current through the circuit, i = (30/R) + 1 mA
Voltage across 1 kΩ = (30/R) + 1 = 30/R + 1 = Vz (Since zener diode is a voltage regulator and regulates Vz across resistance R = 1 kΩ)
Also i = 6mA (Given)
30/R + 1 = 6
30/R = 6 - 1
30 = 5R
R = 30/5 = 4 kΩ