Assertion : $a, b, c$ are three unequal positive numbers.
STATEMENT-1 : The product of their sum and the sum of their reciprocals exceeds 9. Reason: STATEMENT-2 : AM of $n$ positive numbers exceeds their HM.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

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Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for Statement-1

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Statement-1 is True, Statement-2 is False

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Statement-1 is False, Statement-2 is True

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Solution

The correct option is A Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
For n positive unequal numbers $A M > H M ∴$ Reason is correct.

$\Rightarrow \frac{a + b + c}{3} > \frac{3}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}$

$\Rightarrow (a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) > 9$
$∴ A$ is correct.

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Similar questions

- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

a > 1

- 2 :

a > 1, {log}_{a} x

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

\sum_{k = 1}^{n} (k^{3} - (k - 1)^{3}) = n^{3},

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