$A$ stone tied to a string of length $L$ is whirled in a vertical circle,with the other end of the string at the center. At a certain instant of time,the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

The differential equation of the family of parabolas with the focus at the origin and the axis along the $X$-axis is:

What causes a decrease in soil fertility?

The electronic configurations of $Eu$ (Atomic No $63$),$Gd$ (Atomic No $64$) and $Tb$ (Atomic No $65$) are

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

The cell reaction $Mn + 2Ag_{(C_1)}^{+} (aq) \to Mn_{(C_2)}^{+2} (aq) + 2Ag$ is represented by