Over the $(1,n)$-dimensional real superspace, $n>1$, we classify

$\mathcal{K}(n)$-invariant binary differential operators acting on the
superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie
superalgebra of contact vector fields. This result allows us to compute the
first differential cohomology of %the Lie superalgebra $\mathcal{K}(n)$ with
coefficients in the superspace of linear differential operators acting on the
superspaces of weighted densities--a superisation of a result by Feigin and
Fuchs. We explicitly give 1-cocycles spanning these cohomology spaces.