$A$ thin wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular loop (as shown in the figure) with center $O$. The moment of inertia of the loop about the axis $XX'$ is:

$A$ particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$. If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$,then

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction,the magnetic field at the centre of the double loop will be

An aqueous solution of sodium carbonate is alkaline. This is because sodium carbonate is a salt of which of the following?

If $p$ and $q$ are the perpendicular distances from the origin to the straight lines $x \sec \theta - y \operatorname{cosec} \theta = a$ and $x \cos \theta + y \sin \theta = a \cos 2 \theta$,then

Which one of the following molecules contains both ionic and covalent bonds?