Answer: B, C
A singlet carbene adds in a concerted step, so stereochemistry is retained. A triplet carbene must form two bonds in sequence: the first gives a triplet 1,3-diradical, which must undergo spin inversion before ring closure. During this time rotation about the single bond is possible, so cis and trans products form. The triplet is the ground state of CHX2, so the last statement is also false.