Consider the tangent lines to the circle $x^2+y^2=1$ at points $P=(1,0)$ and $Q=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$. If $R$ is the point of intersection of these two tangent lines, then $\angle P R Q$ is:

The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is

The value of the integral

$$ \int_1^{100} \frac{[x]}{x} d x $$

where $[x]$ is the greatest integer less than or equal to $x$ for any real number $x$, is

For arbitrary constants $\alpha, \beta$, the differential equation representing the family of curves $y=$ $(\alpha x+\beta) e^x$ is