The interval in which $x$ must lie so that the greatest term in the expansion of ${(1 + x)^{2n}}$ has the greatest coefficient, is

  • A

    $\left( {\frac{{n - 1}}{n},\frac{n}{{n - 1}}} \right)$

  • B

    $\left( {\frac{n}{{n + 1}},\frac{{n + 1}}{n}} \right)$

  • C

    $\left( {\frac{n}{{n + 2}},\frac{{n + 2}}{n}} \right)$

  • D

    None of these

Similar Questions

The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2 x^2+\frac{1}{2 x}\right)^{11}$ is equal to

  • [JEE MAIN 2023]

The coefficient of ${x^{100}}$ in the expansion of $\sum\limits_{j = 0}^{200} {{{(1 + x)}^j}} $ is

The Coefficient of $x ^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is $........$.

  • [JEE MAIN 2023]

Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$

If $\frac{{{T_2}}}{{{T_3}}}$ in the expansion of ${(a + b)^n}$ and $\frac{{{T_3}}}{{{T_4}}}$ in the expansion of ${(a + b)^{n + 3}}$ are equal, then $n=$