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):
The square root of \[ \frac{1}{abc}(a^2+b^2+c^2)+2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right) \] is \[ \sqrt{\frac{a}{bc}} + \sqrt{\frac{b}{ca}} + \sqrt{\frac{c}{ab}} \]
Statement-2 (Reason):
\[ a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca) \]
Solution:
\[ \frac{1}{abc}(a^2+b^2+c^2) = \frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab} \]
So,
\[ \frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab} + 2\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right) \]
\[ = \frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab} + 2\left( \sqrt{\frac{a}{bc}\cdot\frac{b}{ca}} + \sqrt{\frac{b}{ca}\cdot\frac{c}{ab}} + \sqrt{\frac{c}{ab}\cdot\frac{a}{bc}} \right) \]
\[ = \left( \sqrt{\frac{a}{bc}} + \sqrt{\frac{b}{ca}} + \sqrt{\frac{c}{ab}} \right)^2 \]
Hence, Statement-1 is true.
Statement-2 is also true, but it does not explain Statement-1.
Hence, the correct answer is
\[ \boxed{(b)} \]