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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Functions

If the domain of the function ^ -1 ((3 x-22)/(2 x-19))+ _ e ((3...

If the domain of the function sin⁡−1\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _{\mathrm{e}}(3x2−8x+5x2−3x−10)\left(\frac{3 x^2-8 x+5}{x^2-3 x-10}\right) is (α,β](\alpha, \beta], then 3α+10β3 \alpha+10 \beta is equal to:

Options

  1. A100
  2. B95
  3. C97
  4. D98

Correct answer

C. 97

Step-by-step solution

−1≤3x−222x−19≤13x2−8x+5x2−3x−10>0x∈(5,415]3α+10β=97\begin{array}{ll} -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 & \end{array}
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