Sankalp JEE Full Test-1 Question-11 Solution

Question 11. Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B . Then the distance of the point P(m, n) from the point Q(-2,-3) is

(1) 10

(2) 6

(3) 4

(4) 8

Answer (1)

Explanation:

\quad 2^{m}-2^{n}=56 2^{n}\left(2^{m-n}-1\right)=2^{3} \times 7

2^{n}=2^{3} and 2^{m-n}-1=7

\Rightarrow n=3 and 2^{m-n}=8

\Rightarrow n=3 and m-n=3

\Rightarrow n=3 and m=6

P(6,3) and Q(-2,-3)

PQ=\sqrt{8^{2}+6^{2}}=\sqrt{100}=10

Hence option (1) is correct