Answer
a) $\frac{1}{2}$
b) $1$
c) $4$
Work Step by Step
We know that the electric field outside a sphere (since in the given 3 cases $r\gt R$) is given by
$$E=\dfrac{Q}{4\pi\epsilon_0 r^2}$$
$$\color{blue}{\bf [a]}$$
when $Q_f=\frac{1}{2}Q$, but all other variables remain constant,
$$\dfrac{E_f}{E_i}=\dfrac{\dfrac{Q_f}{4\pi\epsilon_0 r^2}}{\dfrac{Q}{4\pi\epsilon_0 r^2}}=\dfrac{Q_f}{Q}=\dfrac{\frac{1}{2}Q}{Q}$$
$$\dfrac{E_f}{E_i}=\color{red}{\bf \dfrac{1}{2}}$$
$$\color{blue}{\bf [b]}$$
when $R_f=\frac{1}{2}R$, but all other variables remain constant, nothing happens to the electric field outside the sphere at a distance of $r$ since the charge remains constant and $r$ is still constant.
$$\dfrac{E_f}{E_i}=\color{red}{\bf 1}$$
$$\color{blue}{\bf [c]}$$
when $r_f=\frac{1}{2}r$, but all other variables remain constant,
$$\dfrac{E_f}{E_i}=\dfrac{\dfrac{Q}{4\pi\epsilon_0 r_f^2}}{\dfrac{Q}{4\pi\epsilon_0 r^2}}=\dfrac{r^2}{r_f^2}=\dfrac{r^2}{(\frac{1}{2}r)^2} $$
$$\dfrac{E_f}{E_i}=\color{red}{\bf 4}$$
