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

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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 [2024]

1 6

2 8

3 10

4 4

Ans.
(3)

$Total number of subsets of set A = 2^{m}$

$Total number of subsets of set B = 2^{n}$

According to question, $2^{m} - 2^{n} = 56$

$\Rightarrow 2^{n} (2^{m - n} - 1) = 2^{3} \times 7$

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

$\Rightarrow n = 3 and m - n = 3 \Rightarrow m = 3 + n = 3 + 3 = 6$

$∴ m = 6 and n = 3$

$Now, distance between the points P (6, 3) and Q (- 2, - 3) is given by P Q = \sqrt{{(6 + 2)}^{2} + {(3 + 3)}^{2}} = \sqrt{64 + 36} = 10 units$

Want Us to Email you About Special Offers & Updates?