NIMCET 2018 Question Paper with solutions

Question : 27 of 120

Marks: +1, -0

a_1,a_2,a_3

, ..... ,

a_n

are positive real numbers whoseproduct is a fixed number C, then the minimum value of

a_1+a_2+...+2a_n

Solution:

Here,

a _{1} × a _{2} × .... a _{ n }= C

AM ≥ GM

⇒(\;{a_{1}+a_{2}+....+a_{n}}/{n}) ≥((a_{1} × a_{2} × ..... a_{n})^{\;{1}/{n}})

⇒( a _{1}+ a _{2}+.......+ a _{ n }) ≥(( C )^{\;{1}/{n}}) × n

So, the minimum value of

a_{1}+a_{2}+. . .+2 a_{n}

n ( C )^{1 \/ n }

Hence, option (3) is correct.

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