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JEE Main 202622 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2026 · 22 January · Evening Shift · Mathematics · Functions

Let the domain of the function f(x)= _ 3 _ 5 (7- _ 2 (x^ 2 -10...

Let the domain of the function f(x)=log⁡3log⁡5f(x)=\log _{3} \log _{5}\left(7-\log _{2}\left(x^{2}-10 x+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 x-7}{17-x}\right|\right) be (α,β](\alpha, \beta]. Then α+β\alpha+\beta is equal to :

Options

  1. A9
  2. B10
  3. C12
  4. D8

Correct answer

A. 9

Step-by-step solution

For log⁡3log⁡5(⋅)\log_3\log_5(\cdot) we need log⁡5(⋅)>0\log_5(\cdot)>0
So 7−log⁡2(x2−10x+85)>17-\log_2(x^2-10x+85)>1, giving x2−10x+85<64x^2-10x+85<64
(x−3)(x−7)<0(x-3)(x-7) < 0
⇒3<x<7\Rightarrow 3 < x < 7.
For sin⁡−1\sin^{-1}\left(\left|\frac{3x-7}{17-x}\right|\right)weneedwe need|3x-7|\leq|17-x|<br>i.e,<br>i.e,(x-6)(x+5)\leq 0 \Rightarrow -5\leq x\leq 6.<br>Intersection:.<br>Intersection:(3,6],so, so\alpha=3,\beta=6.<br>.<br>\alpha+\beta=9
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