For the reaction HX <---> H+ + X- the equilibrium concentrations are as follows:
[HX] = 1 x 10-1 ; [H+],[X-] = 1 x 10-3. Ka would be:
a. 1 x 10-5
b. 1 x 10-10
c. 1 x 10-7
d. 1 x 10-5

Hello,

The equilibrium constant, k, is used to quantitate the equilibrium
state of a chemical reaction.  In general form:

           k
  mA + nB --->  xC + yD


             [C]^x * [D]^y       where '[' ']' indicate concentration
of
where k  =  -----------------    such as [C] indications concentration
of C
             [A]^m * [B]^n       and 'n,m,x,y' are the # of molecules

now, applying this to the equation in this question gives:

HX <---> H+  +  X-

    [H+]^1 * [X-]^1                 [H+]*[X-]
k = ---------------- or more simply ---------
      [HX]^1                         [HX]

the question asks specifically for Ka - Ka is the equilibrium constant
for an acid base equation, so, Ka:

     (1*10^-3)*(1*10^-3)
Ka = -----------------   =  1 * 10^-5
      (1*10^-1)   


A nice reference on equilibrium equations:
http://dbhs.wvusd.k12.ca.us/Equilibrium/Equilibrium-Constant.html

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equilibrium constant