Question

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 

• A. \(6\)
• B. \(3\)
• C. \(5\)3
• D. \(2\)
• E. \(4\)

Answer 1

Answer: (E)

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)