$n$ moles of an ideal gas undergo a process $A \rightarrow B$ as shown in the figure. The maximum temperature of the gas during the process will be

$A$ bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega \ rad/s$ about the vertical axis. About the point of suspension:

The number of solutions of the system of equations $2x + y - z = 7$, $x - 3y + 2z = 1$, and $x + 4y - 3z = 5$ is

The monomers used in the production of nylon-$6,6$ are

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\pi/2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is (in $I$)

If $\left|\begin{array}{cc}1-i & i \\ 1+2 i & -i\end{array}\right|=x+i y$,then $x$ is equal to