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

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

If $x^3+3xy+y^3=1$,then the correct option$(s)$ is/are:-
$(A) \left(\frac{dy}{dx}\right)_{(1,1)}=-1$
$(B) \left(\frac{dy}{dx}\right)_{(1,1)}=-2$
$(C) \left(\frac{dy}{dx}\right)_{(1,0)}=-1$
$(D) \left(\frac{dy}{dx}\right)_{(1,0)}=-3$

$\int \frac{3}{(2-x)^2} \, dx$ is equal to $:-$

The value of $\frac{d^2}{dx^2} (4x^3 - 3x^2 + 2x + 1)$ is ..... (in $x - 6$)

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