The number of possible straight lines passing through $(2, 3)$ and forming a triangle with the coordinate axes,whose area is $12 \, sq. \, units$,is

$A$ block of mass $2 ~kg$ is initially at rest on a horizontal frictionless surface. $A$ horizontal force $\overrightarrow{F} = (9 - x^2) \hat{i} ~N$ acts on it,starting from $x = 0$. The maximum kinetic energy of the block between $x = 0$ and $x = 3 ~m$ in joules is:

Which of the following is not correctly matched?

The ratio of $C_p$ and $C_v$ of a gas $X$ is $1.4$. The number of atoms of the gas $X$ present in $11.2 \ L$ of it at $NTP$ will be:

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

Example of a biodegradable polymer pair is