JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q67

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If the number of terms in the expansion of $\left(1-\dfrac2x+\dfrac4{x^2}\right)^n$ , $x\ne0$ , is 28, then the sum of the coefficients of all the terms in this expansion, is :

2187

243

729

Answer and worked solution

Official answer: D

Treated as a trinomial, the expansion has $\binom{n+2}2=28$ terms, so $n=6$ . The sum of the coefficients is the value at $x=1$ : $(1-2+4)^6=729$ .

Topics:Binomial expansion Combinations

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 67