Question

If $r$th term is middle term in ${(x^2-\frac{1}{2x})}^{20}$ then $(r+3)$th term is:

• A. $\frac{{{}^{20}C}_{7}x}{2^{13}}$
• B. $-\left(\frac{{{}^{20}C}_{5}x}{4^{13}}\right)$
• C. $-\left(\frac{{{}^{20}C}_{7}x}{2^{13}}\right)$
• D. $-\left(\frac{{{}^{20}C}_{14}x}{4^{13}}\right)$

Answer 1

Answer: (C)

$-\left(\frac{{{}^{20}C}_{7}x}{2^{13}}\right)$

$\therefore T_r=T_{11}$

Thus, $(r+3{)}^{th}$ terms is ${14}^{th}$ term of the given expansion

$T_{14}{=}^{20}{C}_{13}(x^2{)}^{20-13}{(-\frac{1}{2x})}^{13}$

$=\frac{{-}^{20}{C}_{13}x}{2^{13}}$

$=\frac{{-}^{20}{C}_{7}x}{2^{13}}$ $\left[A{s}^{20}{C}_{13}{=}^{20}{C}_7\right]$