Find the correct stability order for the following carbocations:

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$,$\overrightarrow{b}=\hat{i}+\hat{j}$,$\overrightarrow{c}=\hat{i}$ and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}$,then $\lambda+\mu$ is equal to:

$A$ block of mass $2 \ kg$ slides down an inclined plane of inclination $30^{\circ}$. The coefficient of friction between the block and the plane is $0.5$. The contact force between the block and the plane is:

Let the function $g:(-\infty, \infty) \rightarrow \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}$. Then $g$ is

Leaching of $Ag_2S$ is carried out by heating it with a dilute solution of

$A$ bullet of mass $10 ~g$ is fired horizontally with a velocity $1000 ~ms^{-1}$ from a rifle situated at a height $50 ~m$ above the ground. If the bullet reaches the ground with a velocity $500 ~ms^{-1}$,the work done against air resistance in the trajectory of the bullet is : $(g=10 ~ms^{-2})$ (in $~J$)