NIMCET 2023 Question Paper with solutions

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Question : 14 of 120

Marks: +1, -0

If the numbers

a, b, c

and

d

are in harmonic progression and arithmetic mean of

a b, b c

and

c d

is 9 , then which of the following number is the value of

a d

?

3
9
12
4

Solution:

\;{a b+b c+c d}/{3}=9

⇒ \;\; a b+b c+c d=27

a, b, c

are in HP

⇒ b\;=\;{2 a c}/{a+c}

⇒ a+c\;=\;{2 a c}/{b}

....(i)

b, c, d

are in HP

⇒ c\;=\;{2 b d}/{b+d}

⇒ b+d\;=\;{2 b d}/{c}

...(ii)
Multiply (i) and (ii)

(a+c)(b+d)\;=\;{2 a c}/{b} \;{2 b d}/{c}=4 a d

(a b+a d+b c+d c)\;=4 a d

⇒ 3 a d\;=a b+b c+c d=27

⇒ a d\;=9 .

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