List of top Engineering Mathematics Questions on Lagrange and Newton's interpolations asked in GATE XE

Suppose the polynomial \(p(x)=a+bx+cx^{2}+dx^{3}\) interpolates the data \((-1,1),\ (0,3),\ (1,2),\ (2,4)\). Then which one of the following statements is correct?

The second smallest eigenvalue of the eigenvalue problem \[ \frac{d^2 y}{dx^2} + (\lambda - 3)\,y = 0,\qquad y(0)=y(\pi)=0, \] is