The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in G.P., is

$1$

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$2$

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$3$

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$4$

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Solution

The correct option is B
$2$

Explanation for the correct option
Let $x$ be the number added to $2, 14, 62$ , so that the resulting number may be G.P
So $(2 + x), (14 + x), (62 + x)$ will be in G.P
Therefore, according to $b^{2} = a c$ ,
${(14 + x)}^{2} = (2 + x) (62 + x) \Rightarrow 196 + 28 x + x^{2} = 124 + 62 x + 2 x + x^{2} \Rightarrow 36 x = 72 \Rightarrow x = 2$
Hence, the correct option is $(B)$

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