The greatest coefficient in the expansion of ${(1 + x)^{2n + 2}}$ is

  • A

    $\frac{{(2n)!}}{{{{(n!)}^2}}}$

  • B

    $\frac{{(2n + 2)!}}{{{{\{ (n + 1)!\} }^2}}}$

  • C

    $\frac{{(2n + 2)!}}{{n!(n + 1)!}}$

  • D

    $\frac{{(2n)!}}{{n!(n + 1)!}}$

Similar Questions

Find an approximation of $(0.99)^{5}$ using the first three terms of its expansion.

Coefficient of $x$ in the expansion of ${\left( {{x^2} + \frac{a}{x}} \right)^5}$ is

Let ${\left( {x + 10} \right)^{50}} + {\left( {x - 10} \right)^{50}} = {a_0} + {a_1}x + {a_2}{x^2} + .... + {a_{50}}{x^{50}}$ , for $x \in R$; then $\frac{{{a_2}}}{{{a_0}}}$ is equal to

  • [JEE MAIN 2019]

The smallest natural number $n,$ such that the coefficient of $x$ in the expansion of ${\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}$ is $^n{C_{23}}$ is

  • [JEE MAIN 2019]

If the coefficients of ${5^{th}}$, ${6^{th}}$and ${7^{th}}$ terms in the expansion of ${(1 + x)^n}$be in $A.P.$, then $n =$