Question
The number of solutions of ^ -1 4x + ^ -1 6x = 6 , where - 1 2 6 < x < 1 2 6 , is equal to
JEE Main
Mathematics
Inverse Trigonometric Functions
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 3
- B. 0
- C. 2
- D. 1
Answer
D. 1
Step-by-step solution
For x (- 1 2 6 , 1 2 6 ), 24x^2 So ^ -1 (4x) + ^ -1 (6x) = ^ -1 ( 10x 1-24x^2 ) = 6 . 10x 1-24x^2 = 1 3 24x^2 + 10 3 x - 1 = 0. x = -10 3 300+96 48 = -5 3 3 11 24 . x_1 = -5 3 +3 11 24 0.054 (valid, lies in range). x_2 = -5 3 -3 11 24 -0.776 (rejected, outside range). Number of solutions = 1.
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks