IIM Bangalore (UGAT)Calculus > Mediumfff is discontinuous at exactly two points in (0,65)(0, \frac{6}{5})(0,56)ggg is not differentiable at exactly one point in (0,65)(0, \frac{6}{5})(0,56)fff is discontinuous at exactly three points in (0,65)(0, \frac{6}{5})(0,56)ggg is not differentiable at exactly two points in (0,65)(0, \frac{6}{5})(0,56)✅ Correct Option: 2Related questions:Sample PaperThe slope of the tangent to the curve y=x2−4cosxy = x^2 - 4\cos xy=x2−4cosx, x∈[0,π]x \in [0, \pi]x∈[0,π] is maximum when xxx is equal toSample PaperLet f(x)=tan−1(1−cosx1+cosx)f(x) = \tan^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right)f(x)=tan−1(1+cosx1−cosx); x∈(0,π)x \in (0,\pi)x∈(0,π). A normal to y=f(x)y = f(x)y=f(x) at x=π3x = \frac{\pi}{3}x=3π passes through the point:PYP 2025Let h(x)=min[sinx],[cosx]]h(x) = min[\sin x], [\cos x]]h(x)=min[sinx],[cosx]], for all real numbers xxx. Let S be the set of points in (0,π2)(0, \frac{\pi}{2})(0,2π) where h(x)h(x)h(x) is not differentiable. Then the cardinality of S is: