An engine is supposed to operate between two reservoirs at temperatures $727^{\circ}C$ and $227^{\circ}C$. The maximum possible efficiency of such an engine is:

The smallest unit of life is...

$A$ cubical block of side '$a$' and density '$\rho$' slides over a fixed inclined plane with constant velocity '$v$'. There is a thin film of viscous fluid of thickness '$t$' between the plane and the block. If the angle of inclination is $37^{\circ}$,then the coefficient of viscosity of the thin film will be:

If the lines $2x + y + 12 = 0$ and $kx - 3y - 10 = 0$ are conjugate with respect to the circle $x^2 + y^2 - 4x + 3y - 1 = 0$,then $k =$

The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

Two blocks of masses $1 ~kg$ and $2 ~kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 ~N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 ~m/s^2$.