InterviewSolution
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InterviewSolution
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Find the greatest value of the term independent of `x`in the expansion of `(xsinalpha+(cosalpha)/x)^(10)`, where `alpha in Rdot`A. `2^(5)`B. `(10!)/((5!)^(2))`C. `(10!)/(2^(5) xx(5 !))^(2)`D. none of these |
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Answer» Correct Answer - c Let `(r + 1)^(th)` term be indepandent of x. We have, `T_(r + 1) = ""^(10)C_(r) (x sin alpha)^(10 - r) ((cos alpha)/(x))^(r)` `rArr T_(r +1) = ""^(10)C_(r) x ^(10 - 2r) (sin alpha)^(10 - r) (cos alpha )^(r)` If it is independent of x, then r = 5 `therefore ` Term independent of x, `= T_(6)= ""^(10)C_(5)(sin alpha cos alpha)^(5) = ""^(10)C_(5) xx2 ^(-5) (sin 2 alpha)^(5)` Clearly , it is greatest when 2 `alpha = pi 2` and its greatest value is `""^(10)C_(5) xx2^(-5) = (10!)/(2^(5) (5!)^(2))` |
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