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If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is
If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is
Updated On: Aug 28, 2024
\(6\)
\(3\)
\(5\)3
\(2\)
\(4\)
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The Correct Option is
Solution and Explanation
Given that
\((5r + 4)\text{th term} = 25C_{5r+3}x^{5r+4}\)
\( (r − 1)^{1/4}\text{ term } = 25C_{r−2}x^ {r−1}\)
\(25C_{5r+3} x^{5r+4} = 25C_{r−2}\)
\((5r + 3) + (r − 2) = 25\)
\(6r+1=25\)
\(r=4\) (_Ans)
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