Which of the following plants is commonly used as green manure?

If $x > 0$ and $x^y = e^{x-y}$,then $\frac{dy}{dx}$ is equal to

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

Which of the following aquatic ferns is used as an excellent biofertilizer?

If $\frac{{}^{n+2} C_6}{{}^{n-2} C_2} = 11$,then $n$ satisfies the equation

For an ellipse with eccentricity $e = \frac{1}{2}$,the centre is at the origin. If one directrix is $x = 4$,then the equation of the ellipse is: