(A) ∣x∣ is continuous everywhere - True.
(B) ∣x∣ continuous everywhere, not differentiable at x=0 - True.
(C) x1 is continuous on its domain R−{0} - True.
(D) ∣x−1∣+∣x−2∣ is continuous everywhere, not differentiable at exactly x=1,2 - True.
(E) cotx is discontinuous at multiples of π - False.
Hence (A), (B), (C), (D) only.