1.

Ifthecoefficientsofr^(th)and( r +1 ) ^(th)termsintheexpansionof(3 + 7x ) ^(29)areequal , then r isequalto

Answer»

14
15
18
21

Solution : ` (3 +7x ) ^(29) `
Theco- efficientof`r^(th ) `term=Co - efficient` (r + 1 ) ^(th) `term
`rArr29 _(c_(r-1)) ( 3) ^(29-r + 1 )( 7) ^( r - 1 )= 29_(c _r ) (3) ^(29 - r )= (7) ^(r ) `
` rArr(29 _(c_r )) /(29 _ (c _ (r - 1 )) )= (3 ^( 29 - r + 1 ) )/(3 ^(29 - r ))XX ( 7 ^(r - 1 )) /( 7 ^ (r )) `
` rArr(29 -r+ 1 ) /(r ) = (3 ) /(7)""[ because(n _ c _ r ) /(n _(c_(r - 1 ))) = ( n - r+ 1 ) /( r ) ] `
`= (30- r)/( r )=(3 ) /(7) `
` 210-7r=3r `
`210=10 r`
`thereforer= 21 `


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