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***In each paragraph 3 multiple choice questions have to be answered. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.*

Paragraph:

*When a particle of mass m moves on the x-axis in a potential of the form V(x) = Kx^{2} it performs simple harmonic motion. The corresponding time period is proportional to as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from Kx^{2} and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx^{4}(α>0) for ∣X∣ near the origin and becomes a constant equal to V_{0} for ∣X∣≥X_{0} (see figure). *

The acceleration of this particle for ∣

*X*∣>

*X*

_{0}is