MHT CET · Maths · Permutation Combination
If \(T_n\) denotes the number of triangles which can be formed using the vertices of regular polygon of \(\mathrm{n}\) sides and \(\mathrm{T}_{\mathrm{n}+1}-\mathrm{T}_{\mathrm{n}}=21\), then \(\mathrm{n}=\)
- A 5
- B 7
- C 6
- D 4
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
According to the given condition, \(\mathrm{T}_{\mathrm{n}}={ }^{\mathrm{n}} \mathrm{C}_3\)
\(\therefore \mathrm{T}_{\mathrm{n}+1}-\mathrm{T}_{\mathrm{n}}=21 \Rightarrow{ }^{\mathrm{n}+1} \mathrm{C}_3-{ }^{\mathrm{n}} \mathrm{C}_3=21\)
Note that \(\mathrm{n}=7\) satisfies the above condition.
\(\therefore\) Option (B) is correct.
\(\therefore \mathrm{T}_{\mathrm{n}+1}-\mathrm{T}_{\mathrm{n}}=21 \Rightarrow{ }^{\mathrm{n}+1} \mathrm{C}_3-{ }^{\mathrm{n}} \mathrm{C}_3=21\)
Note that \(\mathrm{n}=7\) satisfies the above condition.
\(\therefore\) Option (B) is correct.
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