The middle term in the expansion of ${\left( {x + \frac{1}{{2x}}} \right)^{2n}}$, is
The middle term in the expansion of ${\left( {x + \frac{1}{{2x}}} \right)^{2n}}$, is
- A
$\frac{{1.3.5....(2n - 3)}}{{n!}}$
- B
$\frac{{1.3.5....(2n - 1)}}{{n!}}$
- C
$\frac{{1.3.5....(2n + 1)}}{{n!}}$
- D
None of these
Similar Questions
Let the coefficients of three consecutive terms $T_r$, $T _{ r +1}$ and $T _{ r +2}$ in the binomial expansion of $( a + b )^{12}$ be in a $G.P.$ and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the binomial expansion of $(\sqrt[4]{3}+\sqrt[3]{4})^{12}$. Then $p + q$ is equal to :
- [JEE MAIN 2025]
The coefficient of ${t^{24}}$ in the expansion of ${(1 + {t^2})^{12}}(1 + {t^{12}})\,(1 + {t^{24}})$ is
The coefficient of ${t^{24}}$ in the expansion of ${(1 + {t^2})^{12}}(1 + {t^{12}})\,(1 + {t^{24}})$ is
- [IIT 2003]
The term independent of $x$ in the expansion of ${\left( {{x^2} - \frac{1}{x}} \right)^9}$ is
The term independent of $x$ in the expansion of ${\left( {{x^2} - \frac{1}{x}} \right)^9}$ is
If the co-efficient of $x^9$ in $\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}$ and the co-efficient of $x^{-9}$ in $\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}$ are equal, then $(\alpha \beta)^2$ is equal to $.............$.
If the co-efficient of $x^9$ in $\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}$ and the co-efficient of $x^{-9}$ in $\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}$ are equal, then $(\alpha \beta)^2$ is equal to $.............$.
- [JEE MAIN 2023]
Middle term in the expansion of ${(1 + 3x + 3{x^2} + {x^3})^6}$ is
Middle term in the expansion of ${(1 + 3x + 3{x^2} + {x^3})^6}$ is