In an ideal gas at temperature $T$,the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is:

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

$A$ line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\alpha$ keeping the origin fixed,the same line $L$ has intercepts $p$ and $q$ on the new axes. Then

During the electrolysis of cryolite,aluminium and fluorine are formed in ........ molar ratio :

In the $CGS$ system,the magnitude of the force is $100 \text{ dynes}$. In another system where the fundamental physical quantities are kilogram,meter,and minute,the magnitude of the force is: