If $0.5 \ mol$ of $CaBr_2$ is mixed with $0.2 \ mol$ of $K_3PO_4$,then the maximum number of moles of $Ca_3(PO_4)_2$ obtained will be:

If $\omega$ is a complex cube root of unity,then $225 + (3\omega + 8\omega^2)^2 + (3\omega^2 + 8\omega)^2 = $

What is the correct order of spin only magnetic moment (in $BM$) of $Mn^{2+}, Cr^{2+}$ and $V^{2+}$?

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of ${C^{14}}$ (half-life $= 5700 \, years$) to ${C^{12}}$ is only one-fourth of that found in the cells of living plants. The age of the wood is about ........ $years$.

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of $800$ $Gauss$, experiences a torque of $0.016 ext{ N.m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} ext{ J}$. The value of $\alpha$ is . . . . . . . . . .

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is