The coefficients of linear expansion of P and Q are $α_{1} and α_{2}$ respectively. If the coefficient of cubical expansion of ' Q ' is three times the coefficient of superficial expansion of P, then which of the following is true ?

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$α_{1} = 2 α_{2}$

$α_{2} = 3 α_{1}$

$α_{1} = 3 α_{2}$

$α_{2} = 2 α_{1}$

answer is A.

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Detailed Solution

First we note that coefficient of cubical expansion = 3 x coefficient of linear expansion
Coefficient of superficial expansion = 2 x coefficient of linear expansion
Now it is given that coefficient of cubical expansion of Q is three times the coefficient of superficial expansion of P.
So, 3 x coefficient of linear expansion of Q = 3 x 2 x coefficient of linear expansion of P
So $α_{2} = 2 α_{1}$

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