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If sum of the coefficients of the first, second and third terms of the expansion of ${(x^{2} + \frac{1}{x})}^{m}$ is 46,
then the coefficient of the term that does not contain x is

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Correct option is A

Given, mC0+mC1+mC2=46⇒ 2m+m(m−1)=90⇒ m2+m−90=0⇒m=9 as m>0 Now, (r+1) thtermof x2+1xm is mCrx2m−r1xr=mCrx2m−3rFor this to be independent of x put 2m-3r=0⇒r=6.'. Coefficient of the term independent of x is 9C6=84.

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If sum of the coefficients of the first, second and third terms of the expansion of x2+1xm is 46, then the coefficient of the term that does not contain x is

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If sum of the coefficients of the first, second and third terms of the expansion of ${(x^{2} + \frac{1}{x})}^{m}$ is 46,
then the coefficient of the term that does not contain x is