AktiraAktira JEE
Subscribe
MathsJEE Main 22 Jan 2026, Shift 1·Q14·MCQ·Moderate

Inverse Trigonometry · Domain of inverse trigonometric functions

If the domain of the function f(x)=sin⁡−1(5−x3+2x)+1log⁡e(10−x)f(x) = \sin^{-1}\left(\frac{5-x}{3+2x}\right) + \frac{1}{\log_e(10-x)} is (−∞,α]∪[β,γ)−{δ}(-\infty, \alpha] \cup [\beta, \gamma) - \{\delta\}, then 6(α+β+γ+δ)6(\alpha + \beta + \gamma + \delta) is equal to
  1. (1)70
  2. (2)66
  3. (3)67
  4. (4)68
We corrected a printing error in the original paper

Source printed the second term garbled as “1log⁡e(1-0\dfrac{1}{\log_e(1\text{-}0}” (a stroke through the 1, the closing “x)x)” missing); corrected to the intended “1log⁡e(10−x)\dfrac{1}{\log_e(10-x)}” (the source solution uses 10−x>010 - x > 0, 10−x≠110 - x \neq 1, and the printed key needs γ=10\gamma = 10, δ=9\delta = 9).

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.

Subscribe

See the full 22 Jan 2026, Shift 1 paper

More on Domain of inverse trigonometric functions