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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2023 · Mathematics · Permutation and Combination

m parallel lines cut n parallel lines giving rise to 60...

mm parallel lines cut nn parallel lines giving rise to 60 parallelograms. What is the value of (m+n)(m+n) ?

Options

  1. A66
  2. B77
  3. C88
  4. D99

Correct answer

D. 99

Step-by-step solution

Number of parallelogram =mC2×nC2mC2×nC2=60m(m−1)2×n(n−1)2=60m(m−1)×n(n−1)=240={ }^m C_2 \times{ }^n C_2{ }^m C_2 \times{ }^n C_2=60\frac{m(m-1)}{2} \times \frac{n(n-1)}{2}=60m(m-1) \times n(n-1)=240 By observation, m(m−1)=20=5×4n(n−1)=12=4×3m=5,n=4m+n=9m(m-1)=20=5 \times 4n(n-1)=12=4 \times 3m=5, n=4m+n=9
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