A) \[50\le d\le 100\]
B) \[101\le d\le 150\]
C) \[151\le d\le 200\]
D) \[201\le d\]
Correct Answer: C
Solution :
[c]We have, \[n(X)=5\] |
A and B are subset of X |
Such that \[A\ne \phi ,\]\[B\ne \phi A\cap B=\phi \] |
Total number of order pair (A, B) is \[{}^{5}{{C}_{2}}\times 2!+{}^{5}{{C}_{3}}\left( \frac{3!}{2!}\times 2! \right)+{}^{5}{{C}_{4}}\left( \frac{4!}{3!}2!+\frac{4!}{2!2!} \right)\]\[+{}^{5}{{C}_{5}}\left( \frac{5!}{4!}2!+\frac{5!}{2!3!}\times 2! \right)\] |
\[=10\,(2)+10\,(6)+5\,(8+6)+(10+20)\] |
\[=20+60+70+30=180\] |
\[\therefore \]\[d\in [151,200]\] \[\Rightarrow \]\[151\le d\le 200\] |
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