TS EAMCET · Maths · Functions
If \({ }^n C_r\) denotes the number of combinations of \(n\) distinct things taken \(r\) at a time, then the domain of the function \(g(x)={ }^{(16-x)} C_{(2 x-1)}\) is
- A \(\{1,2,3,4,5\}\)
- B \(\{0,1,2,3,4\}\)
- C \(\phi\)
- D \(\{0\}\)
Answer & Solution
Correct Answer
(A) \(\{1,2,3,4,5\}\)
Step-by-step Solution
Detailed explanation
\(g(x)={ }^{16-x} \mathrm{C}_{2 x-1}\) \(16-x>0\) and \(2 x-1 \geq 0\) and \(16-x \geq 2 x-1\) \(x < 16\) and \(x \geq \frac{1}{2}\) and \(x \leq \frac{17}{3}\) Also \(x\) must be integer \[ \therefore x \in\{1,2,3,4,5\} \]
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