JEE Mains · Maths · STD 11 - 6. permutation and combination
The lines \(\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}\) are distinct. For \(\mathrm{n}=1,2,3, \ldots, 10\) all the lines \(\mathrm{L}_{2 \mathrm{n}-1}\) are parallel to each other and all the lines \(L_{2 n}\) pass through a given point \(P\). The maximum number of points of intersection of pairs of lines from the set \(\left\{\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}\right\}\) is equal to :
- A \(425\)
- B \(101\)
- C \(357\)
- D \(110\)
Answer & Solution
Correct Answer
(B) \(101\)
Step-by-step Solution
Detailed explanation
\(\mathrm{L}_1, \mathrm{~L}_3, \mathrm{~L}_5,--\mathrm{L}_{19}\) are Parallel \(\mathrm{L}_2, \mathrm{~L}_4, \mathrm{~L}_6,--\mathrm{L}_{20}\) are Concurrent Total points of intersection \(={ }^{20} \mathrm{C}_2-{ }^{10} \mathrm{C}_2-{ }^{10} \mathrm{C}_2+1\) \(=101\)
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