IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q17

If $\large ax^2+\frac{b}{x}≥c \text{ } \forall x \in R^+$ where a>0 and b>0, then

$mab^2≥nc^3$

with $m, n \in N$ and $GCD(m, n)=1$ . Which of the following is/are correct?

• (A) $LCM(m, n)=108$
• (B) $m$ is a perfect square
• (C) $n$ is a perfect cube
• (D) $m+n$ is the $10^{th}$ prime (if 2 is the $1^{st}$ prime)

Enter your answer as a 4-digit string of 1s and 9s – 1 for correct option, 9 for wrong. For example: if $A$ and $B$ are correct, and $C$ and $D$ are incorrect, enter 1199. None, one or all may also be correct.

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