Let \(f\left(x\right)=\text{ }\lim _{\theta \text{ }\to \text{ }0}\text{ }\left(\frac{\cos \text{ }\pi \text{ }x−\text{ …

Let \(f\left(x\right)=\text{ }\lim _{\theta \text{ }\to \text{ }0}\text{ }\left(\frac{\cos \text{ }\pi \text{ }x−\text{ }{x}^{\left(\frac{2}{\theta }\right)}\text{ }\sin \left(x−1\right)}{1+{x}^{\left(\frac{2}{\theta }\right)}\text{ }\left(x−1\right)}\right),\text{ }x\text{ }\in \text{ }R.\)

Consider the following two statements:

(I) \(f\left(x\right)\) is discontinuous at \(x = 1\).

(II) \(f\left(x\right)\) is continuous at \(x = – 1\).

Then,

[JEE Main 2026, 28 Jan (Shift 2)]