Two finite sets have m and `n ( m gt n)` elements .The number of subes of the first set is 112 more than that of the second set. The value of mn is

Options

A. 18
B. 28
C. 32
D. 36

Answer

B

Explanation

According to the question
`2^m-2^m= 112 `
`rArr 2^n (2^(m-n)-1)= 2^4 xx 7`
Comparing exponets on both sides ,we get
`2^n-2^4 and 2^(m-n)-1= 7 `
Now ,`2^n= 2^4`
`rArr n=4`
And `2^(m-n)=8`
`rArr 2^(m-n)=2^3`
`rArr m-n =3`
`therefore m=7`