InterviewSolution
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InterviewSolution
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Find the coefficient of (i) `x^(5)" in the expansion of "(x+3)^(8)` (ii) `x^(6) " in the expansion of "(3x^(2) - a/(3x))^(9)` (iii) `x^(-15) " in the expansion of " (3x^(2) - a/(3x^(3)))^(10).` (iv) `a^(7)b^(5)" in the expansion of "(a-2b)^(12)`. |
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Answer» Correct Answer - (i) 1512 (ii) 378 (iii) `(-40)/27a^(7)` (iv)-25344 (iii) `T_(r+1)= ( - 1)^(r) xx .^(10)C_(r) ( 3x^(2))^((10-r)) xx (a/(3x^(3)))^(r)` `rArr T_(r+1) = ( -1)^(r) xx . ^(10)C_(r) xx 3 ^((10-r)) xx x^((20 xx 5r)) xx a^(r).` Now, `20 - 5r = -15 rArr 5r = -15 rArr 5r = 35 rArr r = 7.` (iv) `T_(r+1) =(-1)^(r) xx .^(12) C _(r) xxa^((12-r)) xx ( 2b)^(r)` ` rArr T_(r+1) = (-1)^(r) xx .^(12)C_(r) xx 2^(r) xx a^((12-r)) b^(r).` Put`r=5 and " get " T_(6).` |
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