Question

One term of (x+y)^m is 31,824x^18y^11 What is the value of m ?

Answer 1

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of $(x+y)^m$ is $31,824x^{18}y^{11}$  ...(i)

We know that that (r+1)th term in $(a+b)^n$ is given by :-

$T_{r+1}=^nC_ra^{n-r}b^r$  ...(ii)

On comparing (i) with (ii) , we get

$a= x \text{ and } b= y \\n-r =18 \text{ and } r=11\\n=m$

i.e.

$m-r=18\Rightarow\ m-11=18\\\\\Rightarrow\ m=18+11=29$

Hence, the value of m is 29.