Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is $112$ more than of the second set. The values of $m$ and $n$ respectively are

4, 7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7, 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4, 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7, 7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $7, 4$
Given that $m$ and $n$ are elements of two finite sets
Also given $2^{m} - 2^{n} = 112$
$\Rightarrow 2^{n} (2^{m - n} - 1) = 2^{4} (2^{3} - 1)$
On comparing, we get
$n = 4$ and $m - n = 3$
$\Rightarrow n = 4$ and $m = 7$ .

Suggest Corrections

Similar questions

Q. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively

(a) 4, 7 (b) 7, 4 (c) 4, 4 (d) 7, 7

Q. Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are.

Q. Two finite sets have

m, n

elements respectively. The total number of subsets of the first set is

224

more than the total number of subsets of the second. The values of

m

and

n

are

Two finite ets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of ma and n are respectively.

Q. Two finite sets have

m

and

n

elements. The total number of subsets of the first set is

64

more than the total number of subsets of the second set. The values of

m

and

n

are

Join BYJU'S Learning Program

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than of the second set. The values of m and n respectively are

The correct option is D 7,4Given that m and n are elements of two finite setsAlso given 2m−2n=112⇒2n(2m−n−1)=24(23−1)On comparing, we get n=4 and m−n=3⇒n=4 and m=7.

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is $112$ more than of the second set. The values of $m$ and $n$ respectively are

The correct option is D $7, 4$
Given that $m$ and $n$ are elements of two finite sets
Also given $2^{m} - 2^{n} = 112$
$\Rightarrow 2^{n} (2^{m - n} - 1) = 2^{4} (2^{3} - 1)$
On comparing, we get
$n = 4$ and $m - n = 3$
$\Rightarrow n = 4$ and $m = 7$ .