The value of $\frac{\cot 54^\circ}{\tan 36^\circ} + \frac{\tan 20^\circ}{\cot 70^\circ}$ is

Identify the order in which the spin-only magnetic moment (in $BM$) increases for the following four ions:
$I. Fe^{2+}$
$II. Ti^{2+}$
$III. Cu^{2+}$
$IV. V^{2+}$

On which of the following lines does the point of intersection of the line $\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1}$ and the plane $x + y + z = 2$ lie?

Select the incorrect statement.

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

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is