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JEE Main 3-April-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 3-April-2025 Paper - Shift 24 Marks
MCQ
If the domain of the function
$f(x)=\log _{7}\left(1-\log _{4}\left(x^{2}-9 x+18\right)\right)$ is $(\alpha, \beta) \cup(\gamma, \delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to
  • A
    18
  • B
    16
  • C
    15
  • D
    17
✓

Answer

A. 18
Domain $1-\log _{4}\left(x^{2}-9 x+18\right)>0$
Also $x^{2}-9 x+18>0$
$(x-3)(x-6)>0$
$x \in(-\infty, 3) \cup(6, \infty) \quad ...(1)$
also $\mathrm{x}^{2}-9 \mathrm{x}+18<4$
$x^{2}-9 x+14<0$
$x \in(2,7) \quad ...(2)$
$(1) \cap(2) \quad(2,3) \cup(6,7)=(\alpha, \beta) \cup(\gamma, \delta)$
$\Rightarrow \alpha+\beta+\gamma+\delta=18$

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