If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A x B and B x A are

If two sets $A$ and $B$ are having 99 elements in common, then the number of elements common to each of the sets $A x B$ and $B x A$ are

A
$2^{99}$
B
$99^{2}$
C
100
D
18

Solution:

$n [(A x B) \cap (B x A)] = n [(A \cap B) x (B \cap A)] = n (A \cap B) x n (B \cap A) = 99 x 99 = 99^{2}$

Related content

JEE Main 2023 Question Papers with Solutions

JEE Main 2024 Syllabus

Best Books for JEE Main 2024

JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria

JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria

JEE 2024: Exam Date, Syllabus, Eligibility Criteria

NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3

JEE Crash Course – JEE Crash Course 2023

NEET Crash Course – NEET Crash Course 2023

JEE Advanced Crash Course – JEE Advanced Crash Course 2023