Let the coefficients of third, fourth and fif | vedclass

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Question

$T _{ r +1} ={ }^{ n } C _{ r }( x )^{ n - r }\left(\frac{ a }{ x ^{2}}\right)^{ r }$

$={ }^{n} C _{ r } a ^{ r } x ^{ n -3 r }$

${ }^{ n } C _{

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$T _{ r +1} ={ }^{ n } C _{ r }( x )^{ n - r }\left(\frac{ a }{ x ^{2}}ight)^{ r }$

$={ }^{n} C _{ r } a ^{ r } x ^{ n -3 r }$

${ }^{ n } C _{2} a ^{2}:{ }^{ n } C _{3} a ^{3}:{ }^{ n } C _{4} a ^{4}=12: 8: 3$

After solving

$n =6, a =\frac{1}{2}$

For term independent of $x ^{\prime} \Rightarrow n =3 r$

$r =2$

$	herefore$ Coefficient is ${ }^{6} C _{2}\left(\frac{1}{2}ight)^{2}=\frac{15}{4}$

Nearest integer is $4 .$

Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^{2}}\right)^{n}, x \neq 0,$ be in the ratio $12: 8: 3 .$ Then the term independent of $x$ in the expansion, is equal to ...... .

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