NIMCET 2021 Question Paper with solutions

© examsiri.com

Question : 43 of 120

Marks: +1, -0

{H}_{1}, {H}_{2},......{H}_{{n}}

be a Harmonic mean between

{a}\ \& \ { b}

then

{{H}_{1}+{a}}/{{H}_{1}-{a}}+{{H}_{{n}}+{b}}/{{H}_{{n}}-{b}}=

$2 n$
$n+1$
$n-1$
$2 n+1$

Solution:

⇒{1}/{H_{1}}={1}/{a}+({1}/{b}-{1}/{a}) {1}/{n+1}

{1}/{H_{n}}={1}/{b}-({1}/{b}-{1}/{a}) {1}/{n+1}

\⇒{a}/{H_{1}}={a+b_{n}}/{b+b_{n}}, {b}/{H_{n}}={a_{n}+b}/{a_{n}+a}

{H_{1}+a}/{H_{1}+a}={a+b+2 n b}/{b-a}

.......(1)

{H_{n}+b}/{H_{n}-b}={a+b-2 n a}/{a-b}

.......(2)
On adding

(1) \ \&\ (2)

{{H}_{1}+{a}}/{{H}_{1}-{a}}+{{H}_{{n}}+{b}}/{{H}_{{n}}-{b}}=2n

© examsiri.com

Go to Question:

Prev Question

Next Question