Which one of the following ions exhibits the highest magnetic moment?

If $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to

If $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to

The following compounds have been arranged in order of their increasing thermal stabilities. Identify the correct order.
$I.$ $K_2CO_3$ $II.$ $MgCO_3$
$III.$ $CaCO_3$ $IV.$ $BeCO_3$

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on the earth at a distance $r$ from the sun. (Where $r_0$ is the radius of the earth and $\sigma$ is Stefan's constant.)

The image formed by a convex mirror of focal length $30 \ cm$ is a quarter of the size of the object. The distance of the object from the mirror is $... \ cm$.