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Ifthecoefficient ofxinthe expansionof(x ^ 2+(k )/(x) ) ^5is 270 , then k isequalto

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Solution : ` (x ^ 2+(k)/(x)) ^5 `
Theco-efficient of` x ^m`intheexpansionof` (ax ^p +(B)/(x^Q))^N `is` ""^nC_r a ^( n - r) b ^ r `,where
` r = (np - m ) /( p + q )`, for all ` n in N `.
Here, ` p = 2 , q = 1 ,n = 5, m = 1, a= 1 , b =k `
`thereforer = (np- m ) /(p +q ) `
`= ((5)/(2) - 1 )/( 2 + 1 ) `
`thereforer = 3`
`therefore`co - efficientofxis ` ""^5C_3 ( 1 ) ^(5-3) (k) ^3 `
`therefore""5C_3 k^ 3=270`
` k^ 3=(270 )/(""5C _ 3 )`
`k ^ 3=(270 xx 1xx 2 ) /(5 xx 4 ) `
`k^ 3=27`
` rArrk =3 `


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