A) 729
B) 64
C) 2187
D) 243
Correct Answer: A
Solution :
Number of terms in the expansion of \[{{\left( 1-\frac{2}{x}+\frac{4}{{{x}^{2}}} \right)}^{n}}\] is \[^{n+2}{{C}_{2}}\](considering \[\frac{1}{x}\]and \[\frac{1}{{{x}^{2}}}\]distinct) \[\therefore \]\[^{n+2}{{C}_{2}}=28\Rightarrow n=6\] \[\therefore \]Sum of coefficients = (1 ? 2 + 4)6 = 729 But number of dissimilar terms actually will be 2n + 1 (as\[\frac{1}{x}\]and\[\frac{1}{{{x}^{2}}}\]are functions as same variable) Hence it contains error, so a bonus can be expected.You need to login to perform this action.
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