How current can flow through open circuit output and 9v across diode?
C) 1k, 9.3mA


To get this answer we must assume that the 9V 1mA output and the diode forward current are occurring with opposite input polarities (ie. not at the same time). This is the only way the question makes sense because the circuit cannot put out 9V when the polarity is positive, while the diode can't draw current when it is negative.  

First calculation:- 

Vin = -10V, Vout = -9V and Iout =-1mA. 

R1 = (10V-9V)/1mA = 1k&ohm;.

Second calculation:- 

Vin = +10V. Diode Vf = ~0.7V. 

Diode current = (10-0.7)/1k&ohm; = 9.3mA.

This assumes that the load is not applied when positive voltage is applied, or that it draws insignificant current at 0.7V.