In the expansion of (a-1√ a)^7 the coefficient of a^-(1)/(2) is:

1963 AMC 12 Problem 9

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In the expansion of

\left(a-\dfrac1{\sqrt a}\right)^7

the coefficient of

a^{-\frac{1}{2}}

is:

-7

7

-21

21

35

The term choosing the second summand

r

times has exponent

7-\frac{3r}{2}

Set that exponent equal to

-\frac{1}{2}

before finding the binomial coefficient and sign

The term using

-a^{-\frac{1}{2}}

exactly

r

times has exponent

7-r-\frac{r}{2}=7-\frac{3r}{2}.

Setting this to

-\frac{1}{2}

gives

r=5.

Its coefficient is

\binom75(-1)^5=-21.

Therefore, the correct answer is C.