A determinant is called cyclic if it follows the arrangement symmetrical with a, b and c e.g.`|(1,1,1),(a,b,c),(a^2,b^2,c^2)|`. Now if we increase the degree of any row in this determinant its value is increased by an expression which is also cyclic and increase the degee of the value of determinant then use this statement to solve the following questions.
(1) The value of `|(1,1,1),(a^2,b^2,c^2),(bc,ca,ab)|` is equal to
(a) `(a-b)(b-c)(c-a)`
(b) `(a-b)(b-c)(c-a)(a+b+c)`
(c) `(a-b)(b-c)(c-a)(ab+bc+ca)`
(d) `(a-b)(b-c)(c-a)abc`



(2) The value of `|(a,b,c),(a^2,b^2,c^2),(bc,ca,ab)|` is equal to
(a) `(a-b)(b-c)(c-a)`
(b) `(a-b)(b-c)(c-a)(a+b+c)`
(c) `(a-b)(b-c)(c-a)(ab+bc+ca)`
(d) `(a-b)(b-c)(c-a)abc`

Answer

(1) B, (2) C