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:

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The initial temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of the air at $0^{\circ} C$ is (in $cm$ of $Hg$):

$A$ $10 \mu F$ capacitor is charged by a $100 \text{ V}$ battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu F$. During this process,the electrostatic energy lost by the first capacitor is

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that:

The number of common tangents to the two circles $x^2+y^2-8x+2y=0$ and $x^2+y^2-2x-16y+25=0$ is:

The orthocentre of the triangle formed by the lines $x+3y=10$ and $6x^2+xy-y^2=0$ is