If $x = \sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$,then $x^2(x-4)^2$ is equal to:

If the combined equation of the lines joining the origin to the points of intersection of the curve $x^2+y^2-2x-4y+2=0$ and the line $x+y-2=0$ is $(l_1x+m_1y)(l_2x+m_2y)=0$,then $l_1+l_2+m_1+m_2=$

Efficiency of a heat engine whose sink is at a temperature of $300 ~K$ is $40 \%$. To increase the efficiency to $60 \%$,keeping the sink temperature constant,the source temperature must be increased by (in $~K$)

The equation of a curve in polar coordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$. This equation represents:

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

Which logic gate is represented by the following combination of logic gates?