JEE Advanced2026MathematicsTrigonometric EquationsActual
Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The number of elements in the set x [- , ] : ^6 x + ^4 x = 1 (1) is 1 (Q) The number of elements in the set x [- 2 , 2 ] : ^2 x + ^6 x = 1 (2) is 2 (R) The number of elements in the set x [- , ] : ^2 ( x 2 ) - ^2 x = 1 2 (3) is 3 (S) The number of elements in the set x [-2 , 2 ] : 6 ^2 ( x 2 ) - 3x = 3 (4) is
Options
- A(P) (2), (Q) (5), (R) (3), (S) (4)
- B(P) (5), (Q) (3), (R) (2), (S) (4)
- C(P) (5), (Q) (4), (R) (1), (S) (3)
- D(P) (4), (Q) (3), (R) (2), (S) (5)
Correct answer
B. (P) (5), (Q) (3), (R) (2), (S) (4)
Step-by-step solution
For (P): ^6 x + ^4 x = 1 ^6 x + (1 - ^2 x)^2 = 1 ^6 x + 1 - 2 ^2 x + ^4 x = 1 ^2 x ( ^4 x + ^2 x - 2) = 0 ^2 x ( ^2 x - 1)( ^2 x + 2) = 0 This gives ^2 x = 0 or ^2 x = 1 . In the interval [- , ] , the solutions are x - , - 2 , 0, 2 , . Number of solutions = 5 . For (Q): ^2 x + ^6 x = 1 1 - ^2 x + ^6 x = 1 ^2 x ( ^4 x - 1) = 0 This gives ^2 x = 0 or ^2 x = 1 . In the interval [- 2 , 2 ] , the solutions are x - 2 , 0, 2 . Number of solutions = 3 . For (R): ^2 ( x 2 ) - ^2 x = 1 2 1 + x 2 - (1 - ^2 x) = 1 2 1 + x - 2