KCET · Maths · Sets and Relations
\(A\) and \(B\) are non-singleton sets and \(n(A \times B)=35\). If \(B \subset A\), then \({ }^{n(A)} C_{n(B)}\) is equal to
- A 28
- B 35
- C 42
- D 21
Answer & Solution
Correct Answer
(D) 21
Step-by-step Solution
Detailed explanation
Given, \(n(A \times B)=35, B \subset A\)
\(n(A \times B)=35\)
\(n(A \times B)=7 \times 5\)
\(n(A \times B)=n(A) \times n(B)\)
\(\therefore \quad n(A)=7\) and \(n(B)=5\)
\({ }^{n(A)} C_{n(B)}={ }^{7} C_{5}={ }^{7} C_{2}=21\)
\(n(A \times B)=35\)
\(n(A \times B)=7 \times 5\)
\(n(A \times B)=n(A) \times n(B)\)
\(\therefore \quad n(A)=7\) and \(n(B)=5\)
\({ }^{n(A)} C_{n(B)}={ }^{7} C_{5}={ }^{7} C_{2}=21\)
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