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Question

If a,b,c are in H.P., then ab+c,bc+a,ca+b are in

A
A.P.
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B
G.P.
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C
H.P.
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D
None
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Solution

The correct option is C H.P.
a,b,c are in H.P.
1a,1b,1c are in A.P.
a+b+ca,a+b+cb,a+b+cc are in A.P.
Multiplying an A.P. with a constant (a+b+c), resulting sequence will also be in A.P.
1+b+ca,1+a+cb,1+a+bc are in A.P.
b+ca,a+cb,a+bc are in A.P.
ab+c,ba+c,ca+b are in H.P.

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