If $y = \tan^{-1}(\sec x - \tan x)$,then $\frac{dy}{dx} = $

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases $T_f$ in terms of $T_0$ is:

$A$ small metal ball is suspended in a uniform electric field with the help of an insulated thread. If a high-energy $X$-ray beam falls on the ball,then the ball

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semicircle. What is its moment of inertia about an axis passing through the ends of the wire?

The angle between the lines whose direction cosines are given by the equations $l^2+m^2-n^2=0$ and $l+m+n=0$ is