Two concentric shells of masses M₁ and M₂, are . having radii r₁, andr₂. Which of the following is correct expression for the gravitational field on a mass m? 

We know that the gravitational field in aside a shell is zero but for points outside it, the shell behaves as if whole of its mass is concentrated at its centre. When a point lies in between the shells $\left({\mathrm{r}}_1<\mathrm{r}<{\mathrm{r}}_2\right)$, there will be field due to inner shell only. The gravitational field is given by
$\mathrm{F}=\left({\mathrm{GM}}_1/{\mathrm{r}}^2\right)$
The gravitational field due to outer shell will be zero because the point lies within the shell