If the numerical coefficient of the $p^{t h}$ term in the expansion of $(2 x + 3)^{6}$ is 4860, then the value(s) of p is /are

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Solution

The correct option is D 5
$T_{p} = T_{(p - 1) + 1} =^{6} C_{p - 1} (2 x)^{6 - (p - 1) 3^{p - 1}} =^{6} C_{p - 1} 2^{7 - p} 3^{p - 1} x^{7 - p} ∴ C o e f f i c i e n t o f T_{p} =^{6} C_{p - 1} 2^{7 - p} 3^{p - 1} x^{7 - p} = 4860 (g i v e n) c l e a r l y, p = 5 i s t h e s o l u t i o n$

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If the numerical coefficient of the pth term in the expansion of (2x+3)6 is 4860, then the value(s) of p is /are

The correct option is D 5Tp=T(p−1)+1=6Cp−1(2x)6−(p−1)3p−1=6Cp−127−p3p−1x7−p∴CoefficientofTp=6Cp−127−p3p−1x7−p=4860 (given)clearly, p=5 is the solution

If the numerical coefficient of the $p^{t h}$ term in the expansion of $(2 x + 3)^{6}$ is 4860, then the value(s) of p is /are

The correct option is D 5
$T_{p} = T_{(p - 1) + 1} =^{6} C_{p - 1} (2 x)^{6 - (p - 1) 3^{p - 1}} =^{6} C_{p - 1} 2^{7 - p} 3^{p - 1} x^{7 - p} ∴ C o e f f i c i e n t o f T_{p} =^{6} C_{p - 1} 2^{7 - p} 3^{p - 1} x^{7 - p} = 4860 (g i v e n) c l e a r l y, p = 5 i s t h e s o l u t i o n$