Gate Exam

A smallest number exists that can be expressed as sum of cubes of two different sets of numbers of which one set is 10,9. The other set is.
option
a. 1,12
b. 4,11
c. 2,12
d. 4,13

Plz answer with explanation.

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Gate Other Question

In a gathering,there are an architect,a banker,an advocate,a contractor,a shopkeeper and a dentist. The dentist is the grand father of F,who is a contractor.The banker D is Married to A. C,the shopkeeper is married to the advocate. B is the mother of F,brother of E. There are two married couples in the group.A-C is a father-son pair and B-E is a mother-daughter pair. How many male members are there? given the sequence of terms, AD, CG, FK, JP, the next term is
option
A.OV
B.OW
C.PV
D.PW