JEE MAIN - Mathematics (2021 - 25th July Morning Shift - No. 18)
The ratio of the coefficient of the middle term in the expansion of (1 + x)20 and the sum of the coefficients of two middle terms in expansion of (1 + x)19 is _____________.
Answer
1
Explanation
Coeff. of middle term in (1 + x)20 = $${}^{20}{C_{10}}$$ & Sum of coeff. of two middle terms in (1 + x)19 = $${}^{19}{C_{9}}$$ + $${}^{19}{C_{10}}$$
So required ratio = $${{{}^{20}{C_{10}}} \over {^{19}{C_9}{ + ^{19}}{C_{10}}}} = {{^{20}{C_{10}}} \over {^{20}{C_{10}}}} = 1$$
So required ratio = $${{{}^{20}{C_{10}}} \over {^{19}{C_9}{ + ^{19}}{C_{10}}}} = {{^{20}{C_{10}}} \over {^{20}{C_{10}}}} = 1$$
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