JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of elements in the set \(S = \left\{(r, k) : k \in \mathbb{Z} \text{ and } {}^{36}C_{r+1} = \dfrac{6\left({}^{35}C_r\right)}{(k^2 - 3)}\right\}\), is :
- A \(2\)
- B \(4\)
- C \(8\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
Given equation: \(^{36}C_{r+1} = \dfrac{6 \left(^{35}C_r\right)}{k^2 - 3}\) Using the property \(^{n}C_r = \dfrac{n}{r} {}^{n-1}C_{r-1}\), we can write: \(^{36}C_{r+1} = \dfrac{36}{r+1} {}^{35}C_r\) Substituting this into the given equation:…
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