JEE Main 2026 Mathematics question

Consider the system of linear equations in x,y,z: x+2y+tz=0, 6x+y+5tz=0, 3x+t²y+f(t)z=0, where f : ℝ → ℝ is a differentiable function. If this system has infinitely many solutions for all t ∈ ℝ, then f

• (A)is a constant function
• (B)is strictly increasing on ℝCorrect
• (C)is strictly decreasing on ℝ
• (D)has two critical points