(i) Find the value of r, if the coefficients of (2r + 2)th and (r-2)th terms in the expansion of (1+x)^{18} are equal.

(ii) Find the coefficient of $x^{-} 17$ in the expansion of ${(x^{4} - \frac{1}{x^{3}})}^{15}$

(iii) Find the term independent of x in the expansion of ${(2 x - \frac{1}{x})}^{10}$

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Solution

(i) r = 6

(ii) -1365

(iii) x = - 8064

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