In a hypothetical system,a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle having charge $q$. Assuming Bohr's model to be true for this system,the orbital velocity of mass $m$ when it is in its ground state is:

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index $1.5$. When the telescope is adjusted to infinity,the separation between the two lenses is $16 ~cm$. If the space between the lenses is now filled with water (refractive index $4/3$) and the telescope is again adjusted for infinity,then the present separation between the lenses is: (in $~cm$)

In the circuit shown in the following figure,the value of $Y$ is:

At $298 \ K$,the solubility product of $PbCl_2$ is $1.0 \times 10^{-6}$. What will be the solubility of $PbCl_2$ in moles/litre?

If $f(x) = \sin^2 \left( \frac{\pi}{8} + \frac{x}{2} \right) - \sin^2 \left( \frac{\pi}{8} - \frac{x}{2} \right)$,then the period of $f$ is

If $A$ and $B$ are two sets,then $(A - B) \cup (B - A) \cup (A \cap B)$ is equal to