If $A+2 B=\begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2 A-B=\begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$,then $\operatorname{Tr}(A)-\operatorname{Tr}(B) = $

$\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x=$

The equilibrium constant for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_C$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)}$ at the same temperature is:

Which of the following oxides of nitrogen is a blue solid?

Every planet revolves around the sun in an elliptical orbit. Consider the following statements:
$A.$ The gravitational force acting on a planet is inversely proportional to the square of the distance from the sun.
$B.$ The gravitational force acting on a planet is inversely proportional to the product of the masses of the planet and the sun.
$C.$ The centripetal force acting on the planet is directed away from the sun.
$D.$ The square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
Choose the correct statements from the options given above:

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamic process,which of the following is true?