An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is:

$A$ parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, V$ battery. What is the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ while remaining connected to the battery?

$A$ uniform magnetic field $B$ that is perpendicular to the plane of the page passes through the loops,as shown. The field is confined to a region of radius $a$,where $a < b$,and is changing at a constant rate. The induced emf in the wire loop of radius $b$ is $\varepsilon$. What is the induced emf in the wire loop of radius $2b$?

The potential difference between $A$ and $B$ in the figure is .............. $V$.

$A$ long straight wire along the $z$-axis carries a current $I$ in the negative $z$-direction. The magnetic vector field $\vec B$ at a point having coordinates $(x, y)$ in the $z = 0$ plane is

Insects belong to which phylum?