If {x^4} occurs in the {r^{th}} term in the e | vedclass

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(C) The general term ${T_k}$ in the expansion of ${(a + b)^n}$ is given by ${T_{k+1} = {^nC_k} a^{n-k} b^k}$.Here,$n = 15$,$a = x^4$,and $b = x^{-3}$.

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) The general term ${T_k}$ in the expansion of ${(a + b)^n}$ is given by ${T_{k+1} = {^nC_k} a^{n-k} b^k}$.Here,$n = 15$,$a = x^4$,and $b = x^{-3}$.The ${r^{th}}$ term is ${T_r = T_{(r-1)+1} = {^{15}C_{r-1}} (x^4)^{15-(r-1)} (x^{-3})^{r-1}}$.${T_r = {^{15}C_{r-1}} (x^4)^{16-r} (x^{-3})^{r-1} = {^{15}C_{r-1}} x^{64-4r} x^{-3r+3} = {^{15}C_{r-1}} x^{67-7r}}$.Given that the term contains ${x^4}$,we set the exponent of $x$ equal to $4$:$67 - 7r = 4$.$7r = 63$.$r = 9$.

If ${x^4}$ occurs in the ${r^{th}}$ term in the expansion of ${\left( {{x^4} + \frac{1}{{{x^3}}}} \right)^{15}}$,then $r = $

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