Question:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): \[ (a+b+c)^2=a^2+b^2+c^2-2(ab+bc+ca) \]
Statement-2 (Reason): \[ a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca) \]
Solution:
\[ (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca) \]
So, \[ (a+b+c)^2 \ne a^2+b^2+c^2-2(ab+bc+ca) \]
Therefore, Statement-1 is false.
Statement-2 is a correct algebraic identity, hence it is true.
Hence, the correct answer is
\[ \boxed{(d)} \]