KVPY 2020-21 SA Exam Previous Papers

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Question : 5 of 80

Marks: +1, -0

Let

x

and

y

be two positive real numbers such that

x+y=1

. Then the minimum value of

{1}/{x}+{1}/{y}

is

2
${5}/{2}$
3
4

Solution:

AM ≥ HM

{x+y}/{2} \≥{2}/{{1}/{x}+{1}/{y}}

(x+y)({1}/{x}+{1}/{y}) \≥4

{1}/{x}+{1}/{y} \≥4 [\∵(x+y=1)]

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