Question

If 2nd, 3rd and 4th terms in the expansion of $(x+y{)}^n$ be 240, 720 and 1080, then n is:

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is B

5

${}^n{C}_1{x}^{n-1}.y=n{x}^{n-1}.y=240$.....(i)

${}^n{C}_2{x}^{n-2}.y^2=\frac{n(n-1)}{2}{x}^{n-2}.y^2=720$......(ii)

${}^n{C}_3{x}^{n-3}.y^3=\frac{n(n-1)(n-2)}{6}{x}^{n-3}.y^3=1080$......(iii)

$\frac{\left(ii\right)}{\left(i\right)}\Rightarrow \frac{n-1}{2}\frac{y}{x}=3$....(iv) and $\frac{\left(iii\right)}{\left(ii\right)}\Rightarrow \frac{n-2}{3}\frac{y}{x}=\frac{3}{2}$.....(v)

Solving (iv) and (v) we get n = 5