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Question
If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then ris equal to
Options
7
8
9
10
Solution
9
\[\text{ Coefficients of the rth and } (r + 4)\text{ th terms in the given expansion are }^{20}{}{C}_{r - 1} \text{ and } {}^{20} C_{r + 3} . \]
\[\text{ Here } , \]
\[^{20}{}{C}_{r - 1} = {}^{20} C_{r + 3} \]
\[ \Rightarrow r - 1 + r + 3 = 20 \left[ \because \text{ if } {}^n C_x =^n C_y \Rightarrow x = y \text{ or } x + y = n \right]\]
\[ \Rightarrow r = 2\text{ or } 2r = 18\]
\[ \Rightarrow r = 9 \]
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