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Question

If a, b, c, d are in H.P., then ab + bc + cd is equal to


A

3ad

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B

(a + b)(c + d)

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C

3ac

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D

None of these

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Solution

The correct option is A

3ad


Since a, b, c, d are in H.P., therefore b is the H.M. of a and c

i.e., b = 2acb+d, (a+c)(b+d) = 2acb.2bdc

ab+ad+bc+cd = 4ad ab+bc+cd = 3ad

Trick : Check for a =1, b = 12, c = 13, d = 14


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