Evaluate the following `|(1, 1, 1),(a^2,b^2,c^2),(a^3,b^3,c^3)|`

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

If delta =|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| then the value of |(2a_1+3b_1+4c_1,b_1,c_1),(2a2+3b_2+4c_2,b_2,c_2),(2a_3+3b_3+4c_3,b_3,c_3)| is equal to

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|, then the value of Delta_1=|(a_1+2b_1+3c_1,2c_1+3c_1,c_1),(a_2+2b_2+3c_2,2b_2+3c_2,c_2),(a_3+2b_3+ 3c_3,2b_3+3c_3,c_3)| is equal to

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc^2,c^2+ra^2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)| then Delta_1=

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

Show that det[[1,1,1a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)

If in the determinant Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|,A_1,B_1,C_1 etc. be the co-factors of a_1,b_1,c_1 etc., then which of the following relations is incorrect-