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If the positive integers $a, b, c, d$ are in $A P$, then the numbers $a b c, a b d, a c d, b c d$ are in
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The correct answer is:
$H P$
Given, $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ are in A.P.
$\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}, \frac{1}{d}$ are in H.P.
$\Rightarrow \frac{1}{d}, \frac{1}{c}, \frac{1}{b}, \frac{1}{a}$ are also in H.P.
Now, multiply each term by abcd.
$\frac{\text { abcd }}{\mathrm{d}}, \frac{\text { abcd }}{\mathrm{c}}, \frac{\text { abcd }}{\mathrm{b}}, \frac{\text { abcd }}{\mathrm{a}}$
abc, abd, acd, bed, are in H.P.
$\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}, \frac{1}{d}$ are in H.P.
$\Rightarrow \frac{1}{d}, \frac{1}{c}, \frac{1}{b}, \frac{1}{a}$ are also in H.P.
Now, multiply each term by abcd.
$\frac{\text { abcd }}{\mathrm{d}}, \frac{\text { abcd }}{\mathrm{c}}, \frac{\text { abcd }}{\mathrm{b}}, \frac{\text { abcd }}{\mathrm{a}}$
abc, abd, acd, bed, are in H.P.
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