List of top Mathematics Questions asked in GATE Statistics

Let \( S = \{(x, y, z) \in \mathbb{R}^3 \setminus \{(0,0,0)\} : z = -(x + y)\} \). Denote:

\[ S^\perp = \{(p, q, r) \in \mathbb{R}^3 : px + qy + rz = 0 \text{ for all } (x, y, z) \in S\}. \]

Then which one of the following options is correct?
Among the following four statements about countability and uncountability of different sets, which is the correct statement?
Let \( f : [0, \infty) \to [0, \infty) \) be a differentiable function with \( f(x)>0 \) for all \( x>0 \), and \( f(0) = 0 \). Further, \( f \) satisfies} \[ (f(x))^2 = \int_{0}^{x} \left( (f(t))^2 + f(t) \right) \, dt, \, x>0. \] {Then which one of the following options is correct?