$A$ particular straight line passes through the origin and a point whose abscissa is double the ordinate of the point. The equation of such a straight line is:

If $\angle P - \angle Q = 50^{\circ}$,then find the values of $\angle P$ and $\angle Q$.

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

The value of $\int\limits_0^{\frac{\pi }{{2\omega }}} {5\,\sin \omega t} \,dt$ is

The value of $\frac{d}{dx}(\log_e x)$ is:

$\frac{d}{dx}\left( \frac{1}{x^4 \sec x} \right) = $