InterviewSolution
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InterviewSolution
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If the term free form x in the expansion of `(sqrt(x)-m/(x^(2)))^(10)` is 405, find the value of m. |
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Answer» The general term in the given expansion is given by `T_(r+1) = (-1)^(r) xx .^(10) C_(r) xx (sqrt(x))^((10-r)) xx (m/(x^(2)))^(r)` `=(-1)^(r) xx .^(10) C _(r) xx x^((5-r/2)) xx (m^(r))/(x^(2r))` `= (-1)^(r) xx . ^ (10) C _(r) xx x ^((5-r/2-2r)) xx m ^(r)` `= (-1)^(r) xx.^(10)C_(r) xx x^((5-(5r)/2)) xx m^(r)." "`...(i) Let `T_(r+1)` be free from x. Then, the power of x in `T_(r+1)` must be 0. `:. 5 - (5r)/2 = 0 rArr (5r)/2 = 5 rArr r=2 rArr r+1 = 3 .` So, `T_(3)` will be free from x. Now, `T_(3) = T_(2+1)` `=(-1)^(20 )xx .^(10) C _(2) xx x^(0) xx m ^(2) " "` [putting r=2 in (i) ] `= ( (10 xx 9)/2 xx m^(2)) = 45m^(2).` But, it is given that the term free from x is 405. `:. 45m^(2) = 405 rArr m^(2) = 9 rArrm = pm3.` Hence, `m=pm 3.` |
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