In the expansion of left(sqrt[3]{2}+frac{1}{s | vedclass

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

Question

(C) The general term of the expansion is $T_{r+1} = {}^n C_r (2^{1/3})^{n-r} (3^{-1/3})^r$.The $15^{	ext{th}}$ term from the beginning is $T_{15} = {

Vedclass · Accepted Answer

$2300$

Vedclass · Answer

(C) The general term of the expansion is $T_{r+1} = {}^n C_r (2^{1/3})^{n-r} (3^{-1/3})^r$.The $15^{	ext{th}}$ term from the beginning is $T_{15} = {}^n C_{14} (2^{1/3})^{n-14} (3^{-1/3})^{14}$.The $15^{	ext{th}}$ term from the end is the $(n-15+1)^{	ext{th}} = (n-14)^{	ext{th}}$ term from the beginning,which is $T'_{15} = T_{n-14+1} = {}^n C_{n-14} (2^{1/3})^{14} (3^{-1/3})^{n-14}$.Given the ratio $\frac{T_{15}}{T'_{15}} = \frac{1}{6}$,and noting ${}^n C_{14} = {}^n C_{n-14}$:$\frac{(2^{1/3})^{n-14} (3^{-1/3})^{14}}{(2^{1/3})^{14} (3^{-1/3})^{n-14}} = \frac{1}{6}$$(2^{1/3})^{n-28} (3^{1/3})^{n-28} = 6^{-1}$$(6^{1/3})^{n-28} = 6^{-1}$$\frac{n-28}{3} = -1$ $\Rightarrow n-28 = -3$ $\Rightarrow n = 25$.Finally,${}^{25} C_3 = \frac{25 	imes 24 	imes 23}{3 	imes 2 	imes 1} = 25 	imes 4 	imes 23 = 2300$.

In the expansion of $\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^n, n \in N$,if the ratio of the $15^{\text{th}}$ term from the beginning to the $15^{\text{th}}$ term from the end is $\frac{1}{6}$,then the value of ${}^n C_3$ is:

Similar Questions

If the $6^{th}$ term in the expansion of the binomial $\left[ \frac{1}{x^{8/3}} + x^2 \log_{10} x \right]^8$ is $5600$,then $x$ equals to

The coefficient of $x^{70}$ in $x^2(1+x)^{98} + x^3(1+x)^{97} + x^4(1+x)^{96} + \ldots + x^{54}(1+x)^{46}$ is ${}^{99}C_p - {}^{46}C_q$. Then a possible value of $p+q$ is:

Find the term independent of $x$ $(x > 0, x \neq 1)$ in the expansion of $\left[\frac{(x+1)}{\left(x^{2/3}-x^{1/3}+1\right)}-\frac{(x-1)}{(x-\sqrt{x})}\right]^{10}$.

If ${x^m}$ occurs in the expansion of ${\left( {x + \frac{1}{{{x^2}}}} \right)^{2n}},$ then the coefficient of ${x^m}$ is

Find the mean of the values $0, 1, 2, \dots, n$ with respective weights $^nC_0, ^nC_1, ^nC_2, \dots, ^nC_n$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module