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Statement 1 : In a $∆ A B C$ , if $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in HP; then $r_{1}, r_{2}, r_{3}$ are in AP.
and
Statement 2 : If $x, y, z$ are in HP, $y = \frac{2 x z}{x + z}$

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Statement-1 is True, Statement-2 is False

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

Statement-1 is False, Statement-2 is True

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

answer is D.

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Detailed Solution

Statement 2 is true

Consider Statement 1

$\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in HP

$\Rightarrow$ a, b, c are in AP.

$\Rightarrow$ $- a, - b, - c$ are in AP

$\Rightarrow$ $s - a, s - b, s - c$ are in AP

$\Rightarrow \frac{s - a}{Δ}, \frac{s - b}{Δ}, \frac{s - c}{Δ}$ are in AP

$\Rightarrow \frac{1}{r_{1}}, \frac{1}{r_{2}}, \frac{1}{r_{3}}$ are in A.P

$\Rightarrow r_{1}, r_{2}, r_{3}$ areinH.P

Statement 1 is false

Choice (d)

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