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MathsJEE Main 5 Apr 2026, Shift 1·Q4·MCQ·Moderate

Matrices & Determinants · Homogeneous system infinitely many solutions

Consider the system of linear equations in x,y,zx, y, z: x+2y+tz=0,6x+y+5tz=0,3x+t2y+f(t)z=0,\begin{aligned} &x + 2y + tz = 0,\\ &6x + y + 5tz = 0,\\ &3x + t^2y + f(t)z = 0, \end{aligned} Where f:R→Rf : \mathbb{R} \to \mathbb{R} is a differentiable function. If this system has infinitely many solutions for all t∈Rt \in \mathbb{R}, then ff
  1. (1)is a constant function
  2. (2)is strictly increasing on R\mathbb{R}
  3. (3)is strictly decreasing on R\mathbb{R}
  4. (4)has two critical points

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See the full 5 Apr 2026, Shift 1 paper