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Q.

If a, b, c are respectively the p^th, q^th, r^th terms of an HP then (q-r)bc+(r-p)ca+(p-q)ab=

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a

pbc + qca + rab

b

0

c

(p + q + r)abc

d

abc

answer is D.

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Detailed Solution

$\begin{array}{l} A + (p - 1) D = \frac{1}{a} \\ \Rightarrow A + (q - 1) D = \frac{1}{b} \\ A + (r - 1) D = \frac{1}{c} \\ gives (p - q) D = \frac{b - a}{ab} \\ \Rightarrow (p - q) ab = \frac{b - a}{D} \end{array}$
gives $\Rightarrow \sum (p - q) ab = 0$

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