If $m_1$ and $m_2$ are the roots of the equation $x^2+(\sqrt{3}+2) x+(\sqrt{3}-1)=0$,then the area of the triangle formed by the lines $y=m_1 x, y=m_2 x$ and $y=c$ is:

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 $(\gamma = 5/3)$. (in $~K$)

The output $(X)$ of the logic circuit shown in the figure will be:

$A$ particle is tied to a $20\,cm$ long string. It performs circular motion in a vertical plane. What is the angular velocity of the string when the tension in the string at the top is zero? (Take $g = 9.8\,m/s^2$)

In the circuit shown in the figure,the potential difference between points $A$ and $B$ is $16 \, V$. The current passing through the $2 \, \Omega$ resistance will be ................. $A$.

$C_2H_6 \stackrel{450^{\circ}C}{\longrightarrow} C_2H_4 + H_2$. The above reaction is called: