SATHEE: Permutations and Combinations 2 Question 2

Permutations and Combinations 2 Question 2

2. Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is

(2019 Main, 10 April II)

(a) 180

(b) 210

(d) 190

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Answer:

Correct Answer: 2. (c)

Solution:

It is given that, there are 20 pillars of the same height have been erected along the boundary of a circular stadium.

Now, the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then total number of beams $=$ number of diagonals of 20 -sided polygon.

$∵^{20} C_{2}$ is selection of any two vertices of 20 -sided polygon which included the sides as well.

So, required number of total beams $=^{20} C_{2} - 20$

$[∵$ the number of diagonals in a $n$ -sided closed

$\begin{aligned} = \frac{20 \times 19}{2} - 20 \\ = 190 - 20 = 170 \end{aligned}$

polygon $=^{n} C_{2} - n]$

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Permutations and Combinations 2 Question 2

2. Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Permutations and Combinations 2 Question 2

2. Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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