CSIR NET Maths previous year question papers

For $\alpha \ge 0$, consider the functional $J_\alpha[y] = \int_{1}^{2} (y')^{2}/x^\alpha$ dx defined for all continuously differentiable functions defined on the interval [1, 2] satisfying the conditions y(1) = 1, y(2) = 2. Then which of the following statements are true?

Let S denote the set of all 2 × 2 matrices A such that the iterative sequence generated by the Gauss-Seidel method applied to the system of linear equations $A(x_{1}, x_{2})^{T} = (2, 3)^{T}$ converges for every initial guess. Then which of the following statements are true?