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Arrange the expansion of `(x^(1//2) + (1)/(2x^(1//4)))^n` in decreasing powers of x. Suppose the coefficient of the first three terms form an arithemetic progression. Then the number of terms in the expression having integer powers of x is -(A) 1 (B) 2 (C) 3 (D) more than 3A. 1B. 2C. 3D. more than 3 |
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Answer» Correct Answer - C `T_(r+1)=.^(n)C_(n)(x^(1//2))^(n-r)(1)/((2x^(1//4))^(r)) = (.^(n)C_(r))/(2^(r))x^((2n-3r)/(4))` `T_(1), T_(2), T_(3) rarr AP` ` (2.^(n)C_(1))/(2) = .^(n)C_(0) + (.^(n)C_(2))/(2^(2))` `n-1 = (n(n-1))/(8) rArr n = 8` `(16-3r)/(4) = "Integers" , r= 0,4,8` |
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