Arrange $Ce^{+3}, La^{+3}, Pm^{+3}$ and $Yb^{+3}$ in increasing order of their ionic radii.

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at $40 \ cm$ from left end. A $30 \Omega$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20 \ cm$ to the right end. The value of smaller resistance in $\Omega$ is

The equivalent weight of $H_3PO_4$ in the following reaction is:
$H_3PO_4 + Ca(OH)_2 \to CaHPO_4 + 2H_2O$

If the position vectors of $A, B$ and $C$ are respectively $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then $\cos ^2 A$ is equal to

Which one of the following pairs of compounds illustrates the law of multiple proportions?

The figure shows the cross-sectional view of a hollow cylindrical conductor with inner radius $R$ and outer radius $2R$. The cylinder carries a uniformly distributed current $i$ along its axis. The magnetic induction at point $P$ at a distance $\frac{3R}{2}$ from the axis of the cylinder will be: