Vitamins and Deficiency Diseases

The fat-soluble vitamins are A, D, E and K.
Retinol is vitamin A, a fat-soluble vitamin. Its deficiency causes night blindness and xerophthalmia (dryness of the conjunctiva and cornea). So this pair is correct on both counts.
Cobalamine is vitamin $B_{12}$, which is water soluble; its deficiency causes pernicious anaemia. Beri-beri is caused by the deficiency of thiamine (vitamin $B_1$).
Calciferol is vitamin D, which is fat soluble, but its deficiency causes rickets in children and osteomalacia in adults. Pellagra is caused by the deficiency of niacin (vitamin $B_3$).
Ascorbic acid is vitamin C; it is correctly matched with scurvy, but it is a water-soluble vitamin.
So the fat-soluble vitamin correctly matched with its deficiency disease is Retinol - Xerophthalmia.

(b) is correct: beri-beri is a deficiency disease caused by the lack of thiamine (vitamin $B_1$), which is needed as a coenzyme in carbohydrate metabolism.
(d) is correct: it occurs mainly where the staple diet is polished rice, because thiamine is present in the husk and outer layers of the grain, which are removed in polishing.
(e) is correct: the symptoms include pain due to neuritis, paralysis, muscle wasting, progressive oedema, mental deterioration and finally heart failure.
(a) is not correct: beri-beri is not a disease specific to sub-Saharan Africa.
(c) is not correct: a disorder in infants and children due to protein deficiency describes kwashiorkor, not beri-beri.
So the group containing all three correct statements is b, d and e.