If the numerical coefficient of the $p{}^{th}$  terms in the expansion of ${\left(2x+3\right)}^6$  is 4860, then the following is (are) true

Given expansion ${\left(2x+3\right)}^6$  is,

We have general term in the expansion ${\left(x+a\right)}^n$

$(\therefore T_{r+1}={}^n{\text{C}}_r{x}^{n-r}{\left(a\right)}^r$ be the expansion of ${(x+a)}^n)$

$p{}^{th}$  terms:

$T_p={}^6{C}_{p-1}{2}^{7-p}{3}^{p-1}$  

The $p{}^{th}$  terms in the expansion of ${\left(2x+3\right)}^6$  is 4860, then

$T_p{=}^6{C}_{p-1}{2}^{7-p}{3}^{p-1}=4860=2^2\times 3^5\times \mathrm{5......................}\left(1\right)$

               

For $p=2$ , L.H.S. of (1) $={6.2}^5.3=2^6{.3}^2$

For $p=3$ , L.H.S. of (1) $={15.2}^5{.3}^2=2^5{.3}^3.5$

For $p=4$ , L.H.S. of (1) $={20.2}^3{.3}^3=2^5{.3}^3.5$

For  $p=5$ , L.H.S. of (1) $={15.2}^2{.3}^4=2^2{.3}^5.5=$ R.H.S.

$\therefore p=5$