Find the greatest integer $c$ which satisfies the inequality:
$1 < {(c - 1)}^{2} < 36$

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Solution

The correct option is A 6
Given, $1 < (c - 1)^{2} < 36$
Squire root both the sides, we get
$1 < (c - 1) < 6$
Add $1$ for all sides, we get
$c - 1 < 6$
$\Rightarrow c - 1 + 1 < 6 + 1$
$\Rightarrow c < 7$
Then $c$ is less then integer $7$
The value of integer less then $7$ is $6$ .

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