Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $a^{2}+b^{2}+c^{2}=1$, what is the maximum value of $a b c$ ?
(a)$\frac{1}{3}$
(b)$\frac{1}{3 \sqrt{3}}$
(c)$\frac{2}{\sqrt{3}}$
(d)1
Answer
Answer (as printed): B
Explanation
$a^{2}+b^{2}+c^{2}=1$. So, the maximum value of $a^{2} b^{2} c^{2}=\left(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\right)=\frac{1}{27}$. ( ∵ when sum of three positive quantities is fixed, the product will be maximum when the quantities are equal) Hence, maximum value of $a b c=\frac{1}{\sqrt{27}}=\frac{1}{3 \sqrt{3}}$.
Explanation as extracted from the printed page; notation may be imperfect.