The coefficients of linear expansion of P and Q are ${\alpha }_1\text{ and }{\alpha }_2$ 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 ?

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 ${\mathrm{\alpha }}_2=2{\mathrm{\alpha }}_1$
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