If fourth term in expansion of left(x+x^{log _{2} x}right)^{7} is 4480, then value of x where x ∈

English

Gujarati

Hindi

7.Binomial Theorem

hard

If the fourth term in the expansion of $\left(x+x^{\log _{2} x}\right)^{7}$ is $4480,$ then the value of $x$ where $x \in N$ is equal to

A

$2$

B

$4$

C

$3$

D

$1$

(JEE MAIN-2021)

Solution

${ }^{7} C _{3} x ^{4} x ^{\left(3 \log _{2}^{x}\right)}=4480$

$\Rightarrow x ^{\left(4+3 \log _{2}^{x}\right)}=2^{7}$

$\Rightarrow \quad(4+3 t ) t =7 ; t =\log _{2} x$

$\Rightarrow t =1, \frac{-7}{3} \Rightarrow x =2$

Standard 11

Mathematics

Share

Similar Questions

The term independent of $x$ in the expansion of ${\left( {2x + \frac{1}{{3x}}} \right)^6}$ is

easy

If the coefficient of $x ^{15}$ in the expansion of $\left(a x^3+\frac{1}{b x^{\frac{1}{3}}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{\frac{1}{3}}-\frac{1}{b x^3}\right)^{15}$, where $a$ and $b$ are positive real numbers, then for each such ordered pair $(a, b) :$

hard

(JEE MAIN-2023)

The number of positive integers $k$ such that the constant term in the binomial expansion of $\left(2 x^{3}+\frac{3}{x^{k}}\right)^{12}, x \neq 0$ is $2^{8} \cdot \ell$, where $\ell$ is an odd integer, is……

medium

(JEE MAIN-2022)

If coefficients of $2^{nd}$, $3^{rd}$ and $4^{th}$ terms in the binomial expansion of ${(1 + x)^n}$ are in $A.P.$, then ${n^2} – 9n$ is equal to

medium

Let $\alpha > 0$, be the smallest number such that the expansion of $\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}$ has a term $\beta x^{-\alpha}, \beta \in N$. Then $\alpha$ is equal to $………….$.

hard

(JEE MAIN-2023)