If $log_{10} (xy) = 2$,then the value of $xy$ is

If $\tan \theta = \frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant,the value of $\cos \theta$ is

If $y = \frac{1}{a - z}$,then $\frac{dz}{dy} = $

What is the value of $\alpha$ if $\alpha = \frac{25}{50}$?

$\int \frac{dx}{{(2ax - x^2)}^{1/2}} = a^n \sin^{-1} \left( \frac{x}{a} - 1 \right)$. In this formula,$n =$ . . . . . . .

At point $P$ on the given curve,the value of $\frac{dy}{dx}$ is: