The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object,the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

In the given $(V-T)$ diagram,what is the relation between pressure $P_1$ and $P_2$?

The bond energy of $Cl_2$,$Br_2$,and $I_2$ follows the order:

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is:

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to produce caustic soda. When $CO_2$ is passed through a solution of $A$,it turns milky. What is the chemical formula of $A$?

If the point $P(1,3)$ undergoes the following transformations successively:
$(i)$ Reflection with respect to the line $y=x$.
(ii) Translation through $3$ units along the positive direction of the $X$-axis.
(iii) Rotation through an angle of $\frac{\pi}{6}$ about the origin in the clockwise direction.
Then,the final position of the point $P$ is