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MathsJEE Main 23 Jan 2026, Shift 1·Q1·MCQ·Moderate

Sets, Relations & Functions · Domain of logarithmic function

Let the domain of the function f(x)=log⁡3log⁡5log⁡7(9x−x2−13)f(x) = \log_3\log_5\log_7(9x - x^2 - 13) be the interval (m,n)(m, n). Let the hyperbola x2a2−y2b2=1\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 have eccentricity n3\dfrac{n}{3} and the length of the latus rectum 8m3\dfrac{8m}{3}. Then b2−a2b^2 - a^2 is equal to:
  1. (1)5
  2. (2)11
  3. (3)9
  4. (4)7

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