Two finite sets have m and n elements. The to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The number of subsets of a set with $k$ elements is $2^k$. Given that the first set has $m$ elements and the second set has $n$ elements,the numbe

Vedclass · Accepted Answer

$6, 3$

Vedclass · Answer

(B) The number of subsets of a set with $k$ elements is $2^k$. Given that the first set has $m$ elements and the second set has $n$ elements,the number of subsets are $2^m$ and $2^n$ respectively. According to the problem,$2^m - 2^n = 56$. $2^n(2^{m-n} - 1) = 56$. We can write $56$ as $8 	imes 7 = 2^3 	imes (8 - 1) = 2^3 	imes (2^3 - 1)$. Comparing $2^n(2^{m-n} - 1) = 2^3(2^3 - 1)$,we get $n = 3$ and $m - n = 3$. Substituting $n = 3$ into $m - n = 3$,we get $m - 3 = 3$,so $m = 6$. Thus,the values are $m = 6$ and $n = 3$.

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

Similar Questions

Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero is

If $\log _{0.3}(x - 1) < \log _{0.09}(x - 1),$ then $x$ lies in the interval

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled,then the maximum speed of the car:

What is the correct order of occurrence ($\%$ by weight) in air of $Ne, Ar$ and $Kr$?

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module