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):
If \[ a+b+c=6, \quad ab+bc+ca=11, \] then \[ a^2+b^2+c^2=14 \]
Statement-2 (Reason):
\[ (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca) \]
Solution:
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca) \]
Substituting the given values:
\[ 6^2 = a^2+b^2+c^2+2(11) \]
\[ 36 = a^2+b^2+c^2+22 \]
\[ a^2+b^2+c^2 = 14 \]
Therefore, Statement-1 is true.
Statement-2 is also true and correctly explains Statement-1.
Hence, the correct answer is
\[ \boxed{(a)} \]