The term independent of y in the expansion of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The general term $T_{r+1}$ in the expansion of $(y^{-1/6} - y^{1/3})^9$ is given by:$T_{r+1} = ^9C_r (y^{-1/6})^{9-r} (-y^{1/3})^r$$T_{r+1} = ^9C_

Vedclass · Accepted Answer

$-84$

Vedclass · Answer

(D) The general term $T_{r+1}$ in the expansion of $(y^{-1/6} - y^{1/3})^9$ is given by:$T_{r+1} = ^9C_r (y^{-1/6})^{9-r} (-y^{1/3})^r$$T_{r+1} = ^9C_r (-1)^r y^{-(9-r)/6} y^{r/3}$$T_{r+1} = ^9C_r (-1)^r y^{(-9+r+2r)/6} = ^9C_r (-1)^r y^{(3r-9)/6}$For the term to be independent of $y$,the exponent of $y$ must be $0$:$(3r-9)/6 = 0$ $\Rightarrow 3r = 9$ $\Rightarrow r = 3$Substituting $r = 3$ into the general term expression:$T_{3+1} = ^9C_3 (-1)^3 y^0$$T_4 = - ^9C_3 = - \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = - 84$.

The term independent of $y$ in the expansion of $(y^{-1/6} - y^{1/3})^9$ is

Similar Questions

Which of the following pairs of ions are colourless?

In a resonance pipe,the first and second resonances are obtained at lengths $22.7 \ cm$ and $70.2 \ cm$ respectively. What will be the end correction in $cm$?

$Fe$ is made passive by

With respect to chlorobenzene,which of the following statements is not correct?

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$,then the ordered pair $(m, M)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module