IIM Bangalore (UGAT) Calculus > Differentiation PYQs

Let $f: (0, \frac{6}{5}) \to \mathbb{R}$ & $g: (0, \frac{6}{5}) \to \mathbb{R}$ be functions defined by $f(x) = [x^2]$ and $g(x) = (|x - 1| + |x - 2|)f(x)$ Here $[a] = $ the highest integer $\leq a$. Then

Let $h(x) = min[\sin x], [\cos x]]$, for all real numbers $x$. Let S be the set of points in $(0, \frac{\pi}{2})$ where $h(x)$ is not differentiable. Then the cardinality of S is:

The slope of the tangent to the curve $y = x^2 - 4\cos x$, $x \in [0, \pi]$ is maximum when $x$ is equal to

Let $f(x) = \tan^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right)$; $x \in (0,\pi)$. A normal to $y = f(x)$ at $x = \frac{\pi}{3}$ passes through the point: