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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. `(1)/(2^(5))(10!)/(5!)^(2)`D. None of these |
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Answer» Correct Answer - 3 `Cr(x sin alpha)^(10-r),x^(-1 cos alpha^(r))` `Cr(sin alpha)^(10-r) (cos alpha)^(r ).(x)^(10-2r)` "for independent of x" `10-2r=0 rArr r= 5 ` `rArr T_(5+1)=C_(5)(sin alpha )^(5).(cos alpha)^(5) = C_(5)(sin 2 alpha)^(5)/(2)^(5)` `rArr "greatest value" = (C_(5))/(2)^(5)` |
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