The correct option is (a) 1 dyne/esu
To elaborate: We know that electric field intensity at r distance from a point charge q is defined as \(\frac {q}{r^2}\) in the CGS system. Here q=100 esu, r=10cm. Substituting the value we get E=1dyne/esu. We must remember that factor \(\frac {1}{4\pi\varepsilon}\) is considered only in the SI system and its value is 9*10^9, but in the CGS system, we simply take the value of this constant as unity.