If $r$ is real number such that $| r | < 1$ and if $a = 5 (1 - r)$ , then

$- 5 < a < 5$

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$0 < a < 10$

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$0 < a < 5$

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$- 10 < a < 10$

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Solution

The correct option is B
$0 < a < 10$

Explanation for the correct option:
Finding the range of $a$ .
It is given that, $| r | < 1$ ,
$\Rightarrow - 1 < r < 1 [∵ |a| < 1 \Rightarrow - 1 < a < 1] \Rightarrow 1 > - r > - 1 \Rightarrow - 1 < - r < 1$
By adding $1$ , we get
$\Rightarrow 0 < 1 - r < 2$
By multiplying by 5, we get
$\Rightarrow 0 < 5 (1 - r) < 10 \Rightarrow 0 < a < 10$
Therefore, the correct answer is option B.

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If $r$ is real number such that $| r | < 1$ and if $a = 5 (1 - r)$ , then