1.

Thetermindependent ofxintheexpansions of(sqrtx -(2 ) /(sqrt x )) ^(18)is

Answer»

`- ""^(18)C_9 2 ^(9) `
`""^(18) C _ 9 2 ^(12)`
`""^(18) C_6 2 ^(6)`
`""^(18) C_6 2 ^(8)`

Solution : ` (sqrt x-(2 ) /(sqrt x ) ) ^( 18)`
LET` T_( r + 1 )=""^(18) c _ r (sqrt x) ^( 18 - r )(( - 2 ) /(sqrt x )) ^r `
`rArrx ^(9 -( r ) /(2) - (r )/(2)) =x ^(0)`
`9 - r =0 `
`thereforer=9 `
`thereforeT_(r+ 1 )=""^(18) c _9 (- 2 ) ^(9)`
`=""^(-18)c _ 9 2 ^(9) `


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