Question

If the fourth term in the expansion of $(px+1/x{)}^n$ is 5/2 then the value of p is

• A. 1
• B. 1/2
• C. 6
• D. 2

Answer 1

Answer: (B)

1/2

${(px+\frac{1}{x})}^n$

General term ${}^n{C}_r{\left(px\right)}^r{\left(\frac{1}{x}\right)}^{n-r}$

$4^{th}$ term $r=3^n{C}_3{\left(px\right)}^3{\left(\frac{1}{x}\right)}^{n-3}=\frac{5}{2}$

$n=6$

${}^6{C}_3.p^3.x^3\frac{1}{x^3}=\frac{5}{2}$

$\frac{p^3}{6}=\frac{5}{2}$

$p^3=\frac{1}{8}\Rightarrow \therefore p=\frac{1}{2}$