RRB NTPC Mains or Stage 2 Model Paper 4 with solutions

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Question : 14 of 120

Marks: +1, -0

The length of a line segment AB is 2 unit. It is divided into two parts at the point C such that

AC^2 = AB × CB.

What is the length of CB?

$3+ √2$ units
$3 – √5$ units
$2– √5$ units
$√3$ units

Solution:

(b) Given,

AC^2 = AB × CB

⇒x^2 = 2 × (2 – x)

⇒x^2 = 4 – 2x

⇒ x^2 + 2x – 4 = 0

⇒x ={–2 ±√{4+ 16}}/{2× 1}

⇒ x = –1± √5

Now,

BC = 2 – (–1=3±√ 5) = 3 ± √5

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