$A$ particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$,then its velocity at $x=12 \,m$ is .............. $m/s$.

The plane faces of two identical plano-convex lenses,each having a focal length of $40 \, cm$,are placed against each other to form a biconvex lens. The distance from this lens at which an object must be placed to obtain a real,inverted image with magnification $-1$ is ...... $cm$.

How many atoms of calcium will be deposited from a solution of $CaCl_2$ by a current of $25 \ mA$ flowing for $60 \ s$?

Wires $P$ and $Q$ have the same resistance at ordinary (room) temperature. When heated,the resistance of $P$ increases and that of $Q$ decreases. We conclude that

In the given figure,a ring of mass $m$ is kept on a horizontal surface,while a body of equal mass $m$ is attached through a string wound on the ring. When the system is released,the ring rolls without slipping. Consider the following statements and choose the correct option.
$(i)$ Acceleration of the centre of mass of the ring is $g/3$.
$(ii)$ Acceleration of the hanging particle is $2g/3$.
$(iii)$ Frictional force (on the ring) acts along the forward direction.
$(iv)$ Frictional force (on the ring) acts along the backward direction.

Which of the following represents a correct group of Embryophyta?