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.

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.