JEE Mains · Maths · STD 11- 2. Relation and Function
If the domain of the function \(\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _e\left(\frac{3 x^2-8 x+5}{x^2-3 x-10}\right)\) is \((\alpha, \beta]\), then \(3 \alpha+10 \beta\) is equal to :
- A \(97\)
- B \(100\)
- C \(95\)
- D \(98\)
Answer & Solution
Correct Answer
(A) \(97\)
Step-by-step Solution
Detailed explanation
\(-1 \leq \frac{3 x-22}{2 x-19} \leq 1 \) \( \frac{3 x^2-8 x+5}{x^2-3 x-10}>0 \) \(x \in\left(5, \frac{41}{5}\right] \) \(3 \alpha+10 \beta=97 \) Option (\(1\))
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