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The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be 𝐸� � and the binding energy of a neutron be 𝐸� � in the nucleus. Which of the following statement(s) is(are) correct? (A) 𝐸� � − 𝐸� � is proportional to 𝑍(𝑍 − 1) where Z is the atomic number of the nucleus. (B) 𝐸� � − 𝐸� � is proportional to 𝐴� � � where A is the mass number of the nucleus. (C) 𝐸� � − 𝐸� � is positive. (D) 𝐸� � increases if the nucleus undergoes a beta decay emitting a positron.

Six charges are placed around a regular hexagon of side length 𝑎 as shown in the figure. Five of them have charge 𝑞, and the remaining one has charge 𝑥. The perpendicular from each charge to the nearest hexagon side passes through the center O of the hexagon and is bisected by the side. Which of the following statement(s) is(are) correct in SI units? (A) When 𝑥 = 𝑞, the magnitude of the electric field at O is zero. (B) When 𝑥 = −𝑞, the magnitude of the electric field at O is � �� �� ��. (C) When 𝑥 = 2𝑞, the potential at O is �� �√����� . (D) When 𝑥 = −3𝑞, the potential at O is − �� �√����� .