If the coefficients of second, third and fourth term in the expansion of ${(1 + x)^{2n}}$ are in $A.P.$, then $2{n^2} - 9n + 7$ is equal to

  • A

    $-1$

  • B

    $0$

  • C

    $1$

  • D

    $3\over2$

Similar Questions

The coefficient of $x^{1012}$ in the expansion of ${\left( {1 + {x^n} + {x^{253}}} \right)^{10}}$ , (where $n \leq 22$ is any positive integer), is

  • [JEE MAIN 2014]

If the coefficients of $x^7$ in $\left( ax ^2+\frac{1}{2 bx }\right)^{11}$ and $x ^{-7}$ in $\left(a x-\frac{1}{3 b x^2}\right)^{11}$ are equal, then

  • [JEE MAIN 2023]

Prove that $\sum\limits_{r = 0}^n {{3^r}{\,^n}{C_r} = {4^n}} $

If for some positive integer $n,$ the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in the ratio $5: 10: 14,$ then the largest coefficient in this expansion is

  • [JEE MAIN 2020]

The term independent of $x$ in ${\left( {\sqrt x - \frac{2}{x}} \right)^{18}}$ is