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)

$4$

Answer 2

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)